diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 7 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 61 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 61 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/syntax.spad.pamphlet | 183 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 1628 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1612 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1315 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 9063 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 28375 |
10 files changed, 21265 insertions, 21042 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 9c24e981..40b2b1ce 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,12 @@ 2008-09-21 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/syntax.spad.pamphlet (SpadAstExports): New. + * algebra/Makefile.pamphlet (axiom_algebra_layer_user): Add + SPADXPT. Update dependency rules. + * share/algebra: Update algebra databases. + +2008-09-21 Gabriel Dos Reis <gdr@cs.tamu.edu> + * algebra/boolean.spad.pamphlet (Boolean): Now belong to OrderedFinite. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 4dab8997..db67d2ad 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -825,7 +825,7 @@ axiom_algebra_layer_user = \ LSTAST EXITAST RETAST SEGAST PRTDAST CRCAST \ LETAST SUCHAST RDUCEAST COLONAST ADDAST CAPSLAST \ CASEAST HASAST ISAST CATAST WHEREAST COMMAAST \ - QQUTAST DEFAST MACROAST + QQUTAST DEFAST MACROAST SPADXPT axiom_algebra_layer_user_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user)) @@ -838,40 +838,41 @@ SASTCAT.NRLIB/code.$(FASLEXT): $(OUT)/ASTCAT.$(FASLEXT) LITERAL.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) IDENT.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) HEADAST.NRLIB/code.$(FASLEXT): $(OUT)/IDENT.$(FASLEXT) -ATTRAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -TYPEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) +SPADXPT.NRLIB/code.$(FASLEXT): $(OUT)/ASTCAT.$(FASLEXT) +ATTRAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +TYPEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) IMPTAST.NRLIB/code.$(FASLEXT): $(OUT)/TYPEAST.$(FASLEXT) MAPPAST.NRLIB/code.$(FASLEXT): $(OUT)/TYPEAST.$(FASLEXT) SIGAST.NRLIB/code.$(FASLEXT): $(OUT)/SIG.$(FASLEXT) JOINAST.NRLIB/code.$(FASLEXT): $(OUT)/TYPEAST.$(FASLEXT) -IFAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RPTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -WHILEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -INAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CLLCTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -LSTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -EXITAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RETAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -SEGAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -SEQAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -PRTDAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CRCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RSTRCAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -LETAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RDUCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -SUCHTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -COLONAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -ADDAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CAPSLAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -HASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -ISAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CATAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -WHEREAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -COMMAAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) +IFAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RPTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +WHILEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +INAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CLLCTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +LSTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +EXITAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RETAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +SEGAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +SEQAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +PRTDAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CRCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RSTRCAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +LETAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RDUCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +SUCHTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +COLONAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +ADDAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CAPSLAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +HASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +ISAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CATAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +WHEREAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +COMMAAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) QQUTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -DEFAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -MACROAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) +DEFAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +MACROAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) .PHONY: all all-algebra mkdir-output-directory all: all-ax diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index d34998bd..c4a89300 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -1252,7 +1252,7 @@ axiom_algebra_layer_user = \ LSTAST EXITAST RETAST SEGAST PRTDAST CRCAST \ LETAST SUCHAST RDUCEAST COLONAST ADDAST CAPSLAST \ CASEAST HASAST ISAST CATAST WHEREAST COMMAAST \ - QQUTAST DEFAST MACROAST + QQUTAST DEFAST MACROAST SPADXPT axiom_algebra_layer_user_nrlibs = \ $(addsuffix .NRLIB/code.$(FASLEXT),$(axiom_algebra_layer_user)) @@ -1265,40 +1265,41 @@ SASTCAT.NRLIB/code.$(FASLEXT): $(OUT)/ASTCAT.$(FASLEXT) LITERAL.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) IDENT.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) HEADAST.NRLIB/code.$(FASLEXT): $(OUT)/IDENT.$(FASLEXT) -ATTRAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -TYPEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) +SPADXPT.NRLIB/code.$(FASLEXT): $(OUT)/ASTCAT.$(FASLEXT) +ATTRAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +TYPEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) IMPTAST.NRLIB/code.$(FASLEXT): $(OUT)/TYPEAST.$(FASLEXT) MAPPAST.NRLIB/code.$(FASLEXT): $(OUT)/TYPEAST.$(FASLEXT) SIGAST.NRLIB/code.$(FASLEXT): $(OUT)/SIG.$(FASLEXT) JOINAST.NRLIB/code.$(FASLEXT): $(OUT)/TYPEAST.$(FASLEXT) -IFAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RPTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -WHILEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -INAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CLLCTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -LSTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -EXITAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RETAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -SEGAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -SEQAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -PRTDAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CRCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RSTRCAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -LETAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -RDUCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -SUCHTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -COLONAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -ADDAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CAPSLAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -HASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -ISAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -CATAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -WHEREAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -COMMAAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) +IFAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RPTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +WHILEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +INAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CLLCTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +LSTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +EXITAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RETAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +SEGAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +SEQAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +PRTDAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CRCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RSTRCAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +LETAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +RDUCEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +SUCHTAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +COLONAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +ADDAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CAPSLAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +HASEAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +ISAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +CATAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +WHEREAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +COMMAAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) QQUTAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -DEFAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) -MACROAST.NRLIB/code.$(FASLEXT): $(OUT)/SASTCAT.$(FASLEXT) +DEFAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) +MACROAST.NRLIB/code.$(FASLEXT): $(OUT)/SPADXPT.$(FASLEXT) @ \section{Broken Files} diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index fe76c79f..8f50526d 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -440,6 +440,7 @@ (|VectorFunctions2| . VECTOR2) (|ViewDefaultsPackage| . VIEWDEF) (|Void| . VOID) + (|WhereAst| . WHEREAST) (|WhileAst| . WHILEAST) (|WuWenTsunTriangularSet| . WUTSET) ) @@ -746,6 +747,7 @@ (|SetAggregate| . SETAGG) (|SetCategory| . SETCAT) (|SExpressionCategory| . SEXCAT) + (|SpadAstExports| . SPADXPT) (|SpadSyntaxCategory| . SASTCAT) (|SpecialFunctionCategory| . SPFCAT) (|SquareFreeNormalizedTriangularSetCategory| . SNTSCAT) diff --git a/src/algebra/syntax.spad.pamphlet b/src/algebra/syntax.spad.pamphlet index b8d68f84..e38347eb 100644 --- a/src/algebra/syntax.spad.pamphlet +++ b/src/algebra/syntax.spad.pamphlet @@ -545,6 +545,188 @@ SpadSyntaxCategory(): Category == AbstractSyntaxCategory renderSyntax(x::Syntax) @ +\subsection{The Exports of SpadAst} + +<<category SPADXPT SpadAstExports>>= +)abbrev category SPADXPT SpadAstExports +++ Author: Gabriel Dos Reis +++ Date Created: September 20, 2008 +++ Date Last Modified: September 21, 2008 +++ Description: This category describes the exported +++ signatures of the SpadAst domain. +SpadAstExports(): Category == Join(SpadSyntaxCategory, UnionType) with + _case: (%, ImportAst()) -> Boolean + ++ s case ImportAst holds if `s' represents an `import' statement. + autoCoerce: % -> ImportAst() + ++ autoCoerce(s) returns the ImportAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, DefinitionAst()) -> Boolean + ++ s case DefinitionAst holds if `s' represents a definition. + autoCoerce: % -> DefinitionAst() + ++ autoCoerce(s) returns the DefinitionAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, MacroAst()) -> Boolean + ++ s case MacroAst holds if `s' represents a macro definition. + autoCoerce: % -> MacroAst() + ++ autoCoerce(s) returns the MacroAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, WhereAst()) -> Boolean + ++ s case WhereAst holds if `s' represents an expression with + ++ local definitions. + autoCoerce: % -> WhereAst() + ++ autoCoerce(s) returns the WhereAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, CategoryAst()) -> Boolean + ++ s case CategoryAst holds if `s' represents an unnamed category. + autoCoerce: % -> CategoryAst() + ++ autoCoerce(s) returns the CategoryAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, CapsuleAst()) -> Boolean + ++ s case CapsuleAst holds if `s' represents a domain capsule. + autoCoerce: % -> CapsuleAst() + ++ autoCoerce(s) returns the CapsuleAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, SignatureAst()) -> Boolean + ++ s case SignatureAst holds if `s' represents a signature export. + autoCoerce: % -> SignatureAst() + ++ autoCoerce(s) returns the SignatureAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, AttributeAst()) -> Boolean + ++ s case AttributeAst holds if `s' represents an attribute. + autoCoerce: % -> AttributeAst() + ++ autoCoerce(s) returns the AttributeAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, MappingAst()) -> Boolean + ++ s case MappingAst holds if `s' represents a mapping type. + autoCoerce: % -> MappingAst() + ++ autoCoerce(s) returns the MappingAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, IfAst()) -> Boolean + ++ s case IfAst holds if `s' represents an if-statement. + autoCoerce: % -> IfAst() + ++ autoCoerce(s) returns the IfAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, RepeatAst()) -> Boolean + ++ s case RepeatAst holds if `s' represents an repeat-loop. + autoCoerce: % -> RepeatAst() + ++ autoCoerce(s) returns the RepeatAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, WhileAst()) -> Boolean + ++ s case WhileAst holds if `s' represents a while-iterator + autoCoerce: % -> WhileAst() + ++ autoCoerce(s) returns the WhileAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, InAst()) -> Boolean + ++ s case InAst holds if `s' represents a in-iterator + autoCoerce: % -> InAst() + ++ autoCoerce(s) returns the InAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, CollectAst()) -> Boolean + ++ s case CollectAst holds if `s' represents a list-comprehension. + autoCoerce: % -> CollectAst() + ++ autoCoerce(s) returns the CollectAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, ConstructAst()) -> Boolean + ++ s case ConstructAst holds if `s' represents a list-expression. + autoCoerce: % -> ConstructAst() + ++ autoCoerce(s) returns the ConstructAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, ExitAst()) -> Boolean + ++ s case ExitAst holds if `s' represents an exit-expression. + autoCoerce: % -> ExitAst() + ++ autoCoerce(s) returns the ExitAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, ReturnAst()) -> Boolean + ++ s case ReturnAst holds if `s' represents a return-statement. + autoCoerce: % -> ReurnAst() + ++ autoCoerce(s) returns the ReturnAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, CoerceAst()) -> Boolean + ++ s case ReturnAst holds if `s' represents a coerce-expression. + autoCoerce: % -> CoerceAst() + ++ autoCoerce(s) returns the CoerceAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, PretendAst()) -> Boolean + ++ s case PretendAst holds if `s' represents a pretend-expression. + autoCoerce: % -> PretendAst() + ++ autoCoerce(s) returns the PretendAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, RestrictAst()) -> Boolean + ++ s case RestrictAst holds if `s' represents a restrict-expression. + autoCoerce: % -> RestrictAst() + ++ autoCoerce(s) returns the RestrictAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, SegmentAst()) -> Boolean + ++ s case SegmentAst holds if `s' represents a segment-expression. + autoCoerce: % -> SegmentAst() + ++ autoCoerce(s) returns the SegmentAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, SequenceAst()) -> Boolean + ++ s case SequenceAst holds if `s' represents a sequence-of-statements. + autoCoerce: % -> SequenceAst() + ++ autoCoerce(s) returns the SequenceAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, LetAst()) -> Boolean + ++ s case LetAst holds if `s' represents an assignment-expression. + autoCoerce: % -> LetAst() + ++ autoCoerce(s) returns the LetAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, SuchThatAst()) -> Boolean + ++ s case SuchThatAst holds if `s' represents a qualified-expression. + autoCoerce: % -> SuchThatAst() + ++ autoCoerce(s) returns the SuchThatAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, ColonAst()) -> Boolean + ++ s case ColonAst holds if `s' represents a colon-expression. + autoCoerce: % -> ColonAst() + ++ autoCoerce(s) returns the ColoonAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, CaseAst()) -> Boolean + ++ s case CaseAst holds if `s' represents a case-expression. + autoCoerce: % -> CaseAst() + ++ autoCoerce(s) returns the CaseAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, HasAst()) -> Boolean + ++ s case HasAst holds if `s' represents a has-expression. + autoCoerce: % -> HasAst() + ++ autoCoerce(s) returns the HasAst view of `s'. Left at the + ++ discretion of the compiler. + + _case: (%, IsAst()) -> Boolean + ++ s case IsAst holds if `s' represents an is-expression. + autoCoerce: % -> IsAst() + ++ autoCoerce(s) returns the IsAst view of `s'. Left at the + ++ discretion of the compiler. + +@ + + \subsection{The Literal domain} <<domain LITERAL Literal>>= @@ -1423,6 +1605,7 @@ MacroAst(): Public == Private where <<category ASTCAT AbstractSyntaxCategory>> <<category SASTCAT SpadSyntaxCategory>> +<<category SPADXPT SpadAstExports>> <<domain LITERAL Literal>> <<domain HEADAST HeadAst>> diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index b5166231..e8511cb7 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2255670 . 3430962939) +(2257516 . 3431009356) (-18 A S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) NIL NIL (-19 S) ((|constructor| (NIL "One-dimensional-array aggregates serves as models for one-dimensional arrays. Categorically,{} these aggregates are finite linear aggregates with the \\spadatt{shallowlyMutable} property,{} that is,{} any component of the array may be changed without affecting the identity of the overall array. Array data structures are typically represented by a fixed area in storage and therefore cannot efficiently grow or shrink on demand as can list structures (see however \\spadtype{FlexibleArray} for a data structure which is a cross between a list and an array). Iteration over,{} and access to,{} elements of arrays is extremely fast (and often can be optimized to open-code). Insertion and deletion however is generally slow since an entirely new data structure must be created for the result."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4325 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4321 . T) (-4326 . T) (-4320 . T) (-2609 . T)) +((-4326 . T) (-4324 . T) (-4323 . T) ((-4331 "*") . T) (-4322 . T) (-4327 . T) (-4321 . T) (-2618 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,17 +56,17 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|Syntax|) $) "base(\\spad{d}) returns the actual body of the add-domain expression \\spad{`d'}.")) (|base| (((|Syntax|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -1410) +(-32 R -1415) ((|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 -1007) (QUOTE (-547))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4328))) +((|HasAttribute| |#1| (QUOTE -4329))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2609 . T)) +((-2618 . T)) NIL (-35) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -82,17 +82,17 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-40 -1410 UP UPUP -1830) +(-40 -1415 UP UPUP -2580) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4321 |has| (-398 |#2|) (-354)) (-4326 |has| (-398 |#2|) (-354)) (-4320 |has| (-398 |#2|) (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1525 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1525 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1525 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1525 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) -(-41 R -1410) +((-4322 |has| (-398 |#2|) (-354)) (-4327 |has| (-398 |#2|) (-354)) (-4321 |has| (-398 |#2|) (-354)) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1530 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1530 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1530 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1530 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) +(-41 R -1415) ((|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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -421) (|devaluate| |#1|))))) @@ -106,23 +106,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-298)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4325 |has| |#1| (-539)) (-4323 . T) (-4322 . T)) +((-4326 |has| |#1| (-539)) (-4324 . T) (-4323 . T)) ((|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-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."))) -((-4328 . T) (-4329 . T)) -((-1525 (-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|))))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-1530 (-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|))))))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-354)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| $ (QUOTE (-1016))) (|HasCategory| $ (LIST (QUOTE -1007) (QUOTE (-547))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -130,7 +130,7 @@ NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,{}...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,{}u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-4325 . T)) +((-4326 . T)) NIL (-51 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p,{} f,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -1410) +(-54 |Base| R -1415) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -154,7 +154,7 @@ NIL NIL (-56 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-57 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -162,65 +162,65 @@ NIL NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-59 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-60 -2465) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-60 -2473) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-61 -2465) +(-61 -2473) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-62 -2465) +(-62 -2473) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-63 -2465) +(-63 -2473) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-64 -2465) +(-64 -2473) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-65 -2465) +(-65 -2473) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-66 -2465) +(-66 -2473) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -2465) +(-67 -2473) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-68 -2465) +(-68 -2473) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-69 -2465) +(-69 -2473) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-70 -2465) +(-70 -2473) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-71 -2465) +(-71 -2473) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-72 -2465) +(-72 -2473) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-73 -2465) +(-73 -2473) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -232,55 +232,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-76 -2465) +(-76 -2473) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -2465) +(-77 -2473) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-78 -2465) +(-78 -2473) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -2465) +(-79 -2473) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -2465) +(-80 -2473) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -2465) +(-81 -2473) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -2465) +(-82 -2473) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -2465) +(-83 -2473) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -2465) +(-84 -2473) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -2465) +(-85 -2473) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -2465) +(-86 -2473) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-87 -2465) +(-87 -2473) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-88 -2465) +(-88 -2473) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -290,8 +290,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-354)))) (-90 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-91 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -314,15 +314,15 @@ NIL NIL (-96) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4328 . T)) +((-4329 . T)) NIL (-97) ((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,{}b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-4328 . T) ((-4330 "*") . T) (-4329 . T) (-4325 . T) (-4323 . T) (-4322 . T) (-4321 . T) (-4326 . T) (-4320 . T) (-4319 . T) (-4318 . T) (-4317 . T) (-4316 . T) (-4324 . T) (-4327 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4315 . T)) +((-4329 . T) ((-4331 "*") . T) (-4330 . T) (-4326 . T) (-4324 . T) (-4323 . T) (-4322 . T) (-4327 . T) (-4321 . T) (-4320 . T) (-4319 . T) (-4318 . T) (-4317 . T) (-4325 . T) (-4328 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4316 . T)) NIL (-98 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,{}n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f,{} g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-4325 . T)) +((-4326 . T)) NIL (-99 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) @@ -338,15 +338,15 @@ NIL NIL (-102 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-103 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4330 "*")))) +((|HasAttribute| |#1| (QUOTE (-4331 "*")))) (-104) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4328 . T)) +((-4329 . T)) NIL (-105 A S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) @@ -354,12 +354,12 @@ NIL NIL (-106 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL (-107) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1525 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1530 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1112))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1136)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-108) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -370,11 +370,11 @@ NIL NIL (-110) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1063))) (|HasCategory| (-112) (LIST (QUOTE -300) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-112) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-112) (QUOTE (-1063))) (|HasCategory| (-112) (LIST (QUOTE -591) (QUOTE (-832))))) (-111 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL (-112) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (($ $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -388,25 +388,25 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-115 -1410 UP) +(-115 -1415 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-116 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-117 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-116 |#1|) (QUOTE (-878))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-116 |#1|) (QUOTE (-991))) (|HasCategory| (-116 |#1|) (QUOTE (-794))) (-1525 (|HasCategory| (-116 |#1|) (QUOTE (-794))) (|HasCategory| (-116 |#1|) (QUOTE (-821)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-1111))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-225))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-298))) (|HasCategory| (-116 |#1|) (QUOTE (-532))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-116 |#1|) (QUOTE (-878))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-145))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-116 |#1|) (QUOTE (-991))) (|HasCategory| (-116 |#1|) (QUOTE (-794))) (-1530 (|HasCategory| (-116 |#1|) (QUOTE (-794))) (|HasCategory| (-116 |#1|) (QUOTE (-821)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-1112))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-116 |#1|) (QUOTE (-225))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -503) (QUOTE (-1136)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -116) (|devaluate| |#1|)) (LIST (QUOTE -116) (|devaluate| |#1|)))) (|HasCategory| (-116 |#1|) (QUOTE (-298))) (|HasCategory| (-116 |#1|) (QUOTE (-532))) (|HasCategory| (-116 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-116 |#1|) (QUOTE (-878)))) (|HasCategory| (-116 |#1|) (QUOTE (-143))))) (-118 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4329))) +((|HasAttribute| |#1| (QUOTE -4330))) (-119 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-2609 . T)) +((-2618 . T)) NIL (-120 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -414,15 +414,15 @@ NIL NIL (-121 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-122 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-123) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL (-124 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -430,20 +430,20 @@ NIL NIL (-125 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-126 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-127 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-128) ((|constructor| (NIL "ByteArray provides datatype for fix-sized buffer of bytes."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129)))))) (-1525 (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-129) (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063)))) (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129)))))) (-1530 (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-129) (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063)))) (|HasCategory| (-129) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-129) (QUOTE (-1063))) (-12 (|HasCategory| (-129) (QUOTE (-1063))) (|HasCategory| (-129) (LIST (QUOTE -300) (QUOTE (-129))))) (|HasCategory| (-129) (LIST (QUOTE -591) (QUOTE (-832))))) (-129) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of \\spad{`x'} and \\spad{`y'}.")) (|bitand| (($ $ $) "\\spad{bitand(x,{}y)} returns the bitwise `and' of \\spad{`x'} and \\spad{`y'}.")) (|coerce| (($ (|NonNegativeInteger|)) "\\spad{coerce(x)} has the same effect as byte(\\spad{x}).")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value \\spad{`v'} into the Byte algebra. \\spad{`v'} must be non-negative and less than 256."))) NIL @@ -462,13 +462,13 @@ NIL NIL (-133) ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4330 "*") . T)) +(((-4331 "*") . T)) NIL -(-134 |minix| -2713 S T$) +(-134 |minix| -2721 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-135 |minix| -2713 R) +(-135 |minix| -2721 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL @@ -486,8 +486,8 @@ NIL NIL (-139) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\spad{alphanumeric()} returns the class of all characters for which \\spadfunFrom{alphanumeric?}{Character} is \\spad{true}.")) (|alphabetic| (($) "\\spad{alphabetic()} returns the class of all characters for which \\spadfunFrom{alphabetic?}{Character} is \\spad{true}.")) (|lowerCase| (($) "\\spad{lowerCase()} returns the class of all characters for which \\spadfunFrom{lowerCase?}{Character} is \\spad{true}.")) (|upperCase| (($) "\\spad{upperCase()} returns the class of all characters for which \\spadfunFrom{upperCase?}{Character} is \\spad{true}.")) (|hexDigit| (($) "\\spad{hexDigit()} returns the class of all characters for which \\spadfunFrom{hexDigit?}{Character} is \\spad{true}.")) (|digit| (($) "\\spad{digit()} returns the class of all characters for which \\spadfunFrom{digit?}{Character} is \\spad{true}.")) (|charClass| (($ (|List| (|Character|))) "\\spad{charClass(l)} creates a character class which contains exactly the characters given in the list \\spad{l}.") (($ (|String|)) "\\spad{charClass(s)} creates a character class which contains exactly the characters given in the string \\spad{s}."))) -((-4328 . T) (-4318 . T) (-4329 . T)) -((-1525 (-12 (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4319 . T) (-4330 . T)) +((-1530 (-12 (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-359))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) (-140 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -502,7 +502,7 @@ NIL NIL (-143) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4325 . T)) +((-4326 . T)) NIL (-144 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -510,9 +510,9 @@ NIL NIL (-145) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4325 . T)) +((-4326 . T)) NIL -(-146 -1410 UP UPUP) +(-146 -1415 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,{}y),{} p(x,{}y))} returns \\spad{[g(z,{}t),{} q(z,{}t),{} c1(z),{} c2(z),{} n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,{}y) = g(z,{}t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z,{} t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,{}y),{} f(x),{} g(x))} returns \\spad{p(f(x),{} y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p,{} q)} returns an integer a such that a is neither a pole of \\spad{p(x,{}y)} nor a branch point of \\spad{q(x,{}y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g,{} n)} returns \\spad{[m,{} c,{} P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x,{} y))} returns \\spad{[c(x),{} n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,{}y))} returns \\spad{[c(x),{} q(x,{}z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x,{} y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x,{} z) = 0}."))) NIL NIL @@ -523,14 +523,14 @@ NIL (-148 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasAttribute| |#1| (QUOTE -4328))) +((|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasAttribute| |#1| (QUOTE -4329))) (-149 S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-2609 . T)) +((-2618 . T)) NIL (-150 |n| K Q) ((|constructor| (NIL "CliffordAlgebra(\\spad{n},{} \\spad{K},{} \\spad{Q}) defines a vector space of dimension \\spad{2**n} over \\spad{K},{} given a quadratic form \\spad{Q} on \\spad{K**n}. \\blankline If \\spad{e[i]},{} \\spad{1<=i<=n} is a basis for \\spad{K**n} then \\indented{3}{1,{} \\spad{e[i]} (\\spad{1<=i<=n}),{} \\spad{e[i1]*e[i2]}} (\\spad{1<=i1<i2<=n}),{}...,{}\\spad{e[1]*e[2]*..*e[n]} is a basis for the Clifford Algebra. \\blankline The algebra is defined by the relations \\indented{3}{\\spad{e[i]*e[j] = -e[j]*e[i]}\\space{2}(\\spad{i \\~~= j}),{}} \\indented{3}{\\spad{e[i]*e[i] = Q(e[i])}} \\blankline Examples of Clifford Algebras are: gaussians,{} quaternions,{} exterior algebras and spin algebras.")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} computes the multiplicative inverse of \\spad{x} or \"failed\" if \\spad{x} is not invertible.")) (|coefficient| ((|#2| $ (|List| (|PositiveInteger|))) "\\spad{coefficient(x,{}[i1,{}i2,{}...,{}iN])} extracts the coefficient of \\spad{e(i1)*e(i2)*...*e(iN)} in \\spad{x}.")) (|monomial| (($ |#2| (|List| (|PositiveInteger|))) "\\spad{monomial(c,{}[i1,{}i2,{}...,{}iN])} produces the value given by \\spad{c*e(i1)*e(i2)*...*e(iN)}.")) (|e| (($ (|PositiveInteger|)) "\\spad{e(n)} produces the appropriate unit element."))) -((-4323 . T) (-4322 . T) (-4325 . T)) +((-4324 . T) (-4323 . T) (-4326 . T)) NIL (-151) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,{}xMin,{}xMax,{}yMin,{}yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,{}frac,{}sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -548,7 +548,7 @@ 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 -(-155 R -1410) +(-155 R -1415) ((|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 @@ -579,10 +579,10 @@ NIL (-162 S R) ((|constructor| (NIL "This category represents the extension of a ring by a square root of \\spad{-1}.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} or \"failed\" if \\spad{x} is not a rational number.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(x)} returns \\spad{x} as a rational number. Error: if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(x)} tests if \\spad{x} is a rational number.")) (|polarCoordinates| (((|Record| (|:| |r| |#2|) (|:| |phi| |#2|)) $) "\\spad{polarCoordinates(x)} returns (\\spad{r},{} phi) such that \\spad{x} = \\spad{r} * exp(\\%\\spad{i} * phi).")) (|argument| ((|#2| $) "\\spad{argument(x)} returns the angle made by (0,{}1) and (0,{}\\spad{x}).")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x} = sqrt(norm(\\spad{x})).")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(x,{} r)} returns the exact quotient of \\spad{x} by \\spad{r},{} or \"failed\" if \\spad{r} does not divide \\spad{x} exactly.")) (|norm| ((|#2| $) "\\spad{norm(x)} returns \\spad{x} * conjugate(\\spad{x})")) (|real| ((|#2| $) "\\spad{real(x)} returns real part of \\spad{x}.")) (|imag| ((|#2| $) "\\spad{imag(x)} returns imaginary part of \\spad{x}.")) (|conjugate| (($ $) "\\spad{conjugate(x + \\%i y)} returns \\spad{x} - \\%\\spad{i} \\spad{y}.")) (|imaginary| (($) "\\spad{imaginary()} = sqrt(\\spad{-1}) = \\%\\spad{i}.")) (|complex| (($ |#2| |#2|) "\\spad{complex(x,{}y)} constructs \\spad{x} + \\%i*y.") ((|attribute|) "indicates that \\% has sqrt(\\spad{-1})"))) NIL -((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasAttribute| |#2| (QUOTE -4324)) (|HasAttribute| |#2| (QUOTE -4327)) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-821)))) +((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-1158))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasAttribute| |#2| (QUOTE -4325)) (|HasAttribute| |#2| (QUOTE -4328)) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-821)))) (-163 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})"))) -((-4321 -1525 (|has| |#1| (-539)) (-12 (|has| |#1| (-298)) (|has| |#1| (-878)))) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4324 |has| |#1| (-6 -4324)) (-4327 |has| |#1| (-6 -4327)) (-3398 . T) (-2609 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 -1530 (|has| |#1| (-539)) (-12 (|has| |#1| (-298)) (|has| |#1| (-878)))) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4325 |has| |#1| (-6 -4325)) (-4328 |has| |#1| (-6 -4328)) (-3402 . T) (-2618 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-164 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."))) @@ -594,8 +594,8 @@ NIL NIL (-166 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}."))) -((-4321 -1525 (|has| |#1| (-539)) (-12 (|has| |#1| (-298)) (|has| |#1| (-878)))) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4324 |has| |#1| (-6 -4324)) (-4327 |has| |#1| (-6 -4327)) (-3398 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . 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T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-340)))) (-12 (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-225))) (-12 (|HasCategory| |#1| 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(|HasCategory| |#1| (QUOTE (-878)))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-878))))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1158)))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (QUOTE (-539)))) (-1530 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-802))) (|HasCategory| |#1| (QUOTE (-1025))) (-12 (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1158)))) (|HasCategory| |#1| (QUOTE (-532))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-225))) (-12 (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasAttribute| |#1| (QUOTE -4325)) (|HasAttribute| |#1| (QUOTE -4328)) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136))))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-340))))) (-167 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -606,7 +606,7 @@ NIL NIL (-169) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-170) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -614,7 +614,7 @@ NIL NIL (-171 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0,{} x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialQuotients(x) = [b0,{}b1,{}b2,{}b3,{}...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialDenominators(x) = [b1,{}b2,{}b3,{}...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0,{} [a1,{}a2,{}a3,{}...],{} [b1,{}b2,{}b3,{}...])},{} then \\spad{partialNumerators(x) = [a1,{}a2,{}a3,{}...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,{}b)} constructs a continued fraction in the following way: if \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,{}[1,{}1,{}1,{}...],{}[b1,{}b2,{}b3,{}...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,{}a,{}b)} constructs a continued fraction in the following way: if \\spad{a = [a1,{}a2,{}...]} and \\spad{b = [b1,{}b2,{}...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-4330 "*") . T) (-4321 . T) (-4326 . T) (-4320 . T) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") . T) (-4322 . T) (-4327 . T) (-4321 . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-172) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -648,7 +648,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-180 R -1410) +(-180 R -1415) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -756,23 +756,23 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-207 -1410 UP UPUP R) +(-207 -1415 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 -(-208 -1410 FP) +(-208 -1415 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 (-209) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1525 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1530 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1112))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1136)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-210) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|Syntax|) $) "\\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| (((|List| (|Identifier|)) $) "\\spad{head(d)} returns the head of the definition \\spad{`d'}. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-211 R -1410) +(-211 R -1415) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -786,19 +786,19 @@ NIL NIL (-214 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-215 |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}."))) -((-4325 . T)) +((-4326 . T)) NIL -(-216 R -1410) +(-216 R -1415) ((|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 (-217) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2654 . T) (-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-218) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -806,23 +806,23 @@ NIL NIL (-219 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}"))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4331 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-220 A S) ((|constructor| (NIL "A dictionary is an aggregate in which entries can be inserted,{} searched for and removed. Duplicates are thrown away on insertion. This category models the usual notion of dictionary which involves large amounts of data where copying is impractical. Principal operations are thus destructive (non-copying) ones."))) NIL NIL (-221 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."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL (-222 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-225)))) (-223 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4325 . T)) +((-4326 . T)) NIL (-224 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -830,36 +830,36 @@ NIL NIL (-225) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4325 . T)) +((-4326 . T)) NIL (-226 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -4328))) +((|HasAttribute| |#1| (QUOTE -4329))) (-227 S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#1| $) "\\spad{remove!(x,{}d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#1|)) "\\spad{dictionary([x,{}y,{}...,{}z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL (-228) ((|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 -(-229 S -2713 R) +(-229 S -2721 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (QUOTE (-819))) (|HasAttribute| |#3| (QUOTE -4325)) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (QUOTE (-701))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-1063)))) -(-230 -2713 R) +((|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (QUOTE (-819))) (|HasAttribute| |#3| (QUOTE -4326)) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (QUOTE (-701))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-1063)))) +(-230 -2721 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4322 |has| |#2| (-1016)) (-4323 |has| |#2| (-1016)) (-4325 |has| |#2| (-6 -4325)) ((-4330 "*") |has| |#2| (-169)) (-4328 . T) (-2609 . T)) +((-4323 |has| |#2| (-1016)) (-4324 |has| |#2| (-1016)) (-4326 |has| |#2| (-6 -4326)) ((-4331 "*") |has| |#2| (-169)) (-4329 . T) (-2618 . T)) NIL -(-231 -2713 A B) +(-231 -2721 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 -(-232 -2713 R) +(-232 -2721 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. 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(((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -870,47 +870,47 @@ NIL NIL (-235) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4321 . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-236 S) ((|constructor| (NIL "A doubly-linked aggregate serves as a model for a doubly-linked list,{} that is,{} a list which can has links to both next and previous nodes and thus can be efficiently traversed in both directions.")) (|setnext!| (($ $ $) "\\spad{setnext!(u,{}v)} destructively sets the next node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|setprevious!| (($ $ $) "\\spad{setprevious!(u,{}v)} destructively sets the previous node of doubly-linked aggregate \\spad{u} to \\spad{v},{} returning \\spad{v}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates doubly-linked aggregate \\spad{v} to the end of doubly-linked aggregate \\spad{u}.")) (|next| (($ $) "\\spad{next(l)} returns the doubly-linked aggregate beginning with its next element. Error: if \\spad{l} has no next element. Note: \\axiom{next(\\spad{l}) = rest(\\spad{l})} and \\axiom{previous(next(\\spad{l})) = \\spad{l}}.")) (|previous| (($ $) "\\spad{previous(l)} returns the doubly-link list beginning with its previous element. Error: if \\spad{l} has no previous element. Note: \\axiom{next(previous(\\spad{l})) = \\spad{l}}.")) (|tail| (($ $) "\\spad{tail(l)} returns the doubly-linked aggregate \\spad{l} starting at its second element. Error: if \\spad{l} is empty.")) (|head| (($ $) "\\spad{head(l)} returns the first element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty.")) (|last| ((|#1| $) "\\spad{last(l)} returns the last element of a doubly-linked aggregate \\spad{l}. Error: if \\spad{l} is empty."))) -((-2609 . T)) +((-2618 . T)) NIL (-237 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-238 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-239 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) 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Date Last Updated: January 19,{} 2008. Basic Operations: coerce,{} reify Related Constructors: Type,{} Syntax,{} OutputForm Also See: Type,{} ConstructorCall")) (|showSummary| (((|Void|) $) "\\spad{showSummary(d)} prints out implementation detail information of domain \\spad{`d'}.")) (|reflect| (($ (|ConstructorCall|)) "\\spad{reflect cc} returns the domain object designated by the ConstructorCall syntax `cc'. The constructor implied by `cc' must be known to the system since it is instantiated.")) (|reify| (((|ConstructorCall|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 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(-547))))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-701))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-819))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (|HasCategory| (-547) (QUOTE (-821))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1136))))) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (-1530 (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (|HasCategory| |#3| (QUOTE (-701))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1136)))))) (-1530 (|HasCategory| |#3| (QUOTE (-1016))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#3| (QUOTE (-1063)))) (-1530 (|HasAttribute| |#3| (QUOTE -4326)) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1136)))))) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832))))) (-243 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-225)))) (-244 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL (-245 S) ((|constructor| (NIL "A dequeue is a doubly ended stack,{} that is,{} a bag where first items inserted are the first items extracted,{} at either the front or the back end of the data structure.")) (|reverse!| (($ $) "\\spad{reverse!(d)} destructively replaces \\spad{d} by its reverse dequeue,{} \\spadignore{i.e.} the top (front) element is now the bottom (back) element,{} and so on.")) (|extractBottom!| ((|#1| $) "\\spad{extractBottom!(d)} destructively extracts the bottom (back) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|extractTop!| ((|#1| $) "\\spad{extractTop!(d)} destructively extracts the top (front) element from the dequeue \\spad{d}. Error: if \\spad{d} is empty.")) (|insertBottom!| ((|#1| |#1| $) "\\spad{insertBottom!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d} at the bottom (back) of the dequeue.")) (|insertTop!| ((|#1| |#1| $) "\\spad{insertTop!(x,{}d)} destructively inserts \\spad{x} into the dequeue \\spad{d},{} that is,{} at the top (front) of the dequeue. The element previously at the top of the dequeue becomes the second in the dequeue,{} and so on.")) (|bottom!| ((|#1| $) "\\spad{bottom!(d)} returns the element at the bottom (back) of the dequeue.")) (|top!| ((|#1| $) "\\spad{top!(d)} returns the element at the top (front) of the dequeue.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(d)} returns the number of elements in dequeue \\spad{d}. Note: \\axiom{height(\\spad{d}) = \\# \\spad{d}}.")) (|dequeue| (($ (|List| |#1|)) "\\spad{dequeue([x,{}y,{}...,{}z])} creates a dequeue with first (top or front) element \\spad{x},{} second element \\spad{y},{}...,{}and last (bottom or back) element \\spad{z}.") (($) "\\spad{dequeue()}\\$\\spad{D} creates an empty dequeue of type \\spad{D}."))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-246) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -950,8 +950,8 @@ NIL NIL (-255 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"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#3| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-256 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -996,11 +996,11 @@ 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 -(-267 R -1410) +(-267 R -1415) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-268 R -1410) +(-268 R -1415) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -1022,7 +1022,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063)))) (-273 S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#1| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#1| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL (-274 S) ((|constructor| (NIL "Category for the elementary functions.")) (** (($ $ $) "\\spad{x**y} returns \\spad{x} to the power \\spad{y}.")) (|exp| (($ $) "\\spad{exp(x)} returns \\%\\spad{e} to the power \\spad{x}.")) (|log| (($ $) "\\spad{log(x)} returns the natural logarithm of \\spad{x}."))) @@ -1043,18 +1043,18 @@ NIL (-278 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -4329))) +((|HasAttribute| |#1| (QUOTE -4330))) (-279 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-280 S R |Mod| -2129 -2037 |exactQuo|) +(-280 S R |Mod| -2378 -2777 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-281) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4321 . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-282) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1070,21 +1070,21 @@ NIL NIL (-285 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."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-287) ((|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 -(-288 -1410 S) +(-288 -1415 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 -(-289 E -1410) +(-289 E -1415) ((|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 @@ -1122,7 +1122,7 @@ NIL NIL (-298) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-299 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1132,7 +1132,7 @@ 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 -(-301 -1410) +(-301 -1415) ((|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 @@ -1146,8 +1146,8 @@ NIL NIL (-304 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))}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-991))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (-1525 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-1111))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-225))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -300) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (LIST (QUOTE -277) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1204) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-298))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-532))) (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-12 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))) (-1525 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1204 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-991))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (-1530 (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-794))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-1112))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-225))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -503) (QUOTE (-1136)) (LIST (QUOTE -1205) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -300) (LIST (QUOTE -1205) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (LIST (QUOTE -277) (LIST (QUOTE -1205) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1205) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-298))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-532))) (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (-12 (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))) (-1530 (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-143))) (-12 (|HasCategory| (-1205 |#1| |#2| |#3| |#4|) (QUOTE (-878))) (|HasCategory| $ (QUOTE (-143)))))) (-305 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 @@ -1158,9 +1158,9 @@ NIL NIL (-307 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."))) -((-4325 -1525 (-1807 (|has| |#1| (-1016)) (|has| |#1| (-615 (-547)))) (-12 (|has| |#1| (-539)) (-1525 (-1807 (|has| |#1| (-1016)) (|has| |#1| (-615 (-547)))) (|has| |#1| (-1016)) (|has| |#1| (-463)))) (|has| |#1| (-1016)) (|has| |#1| (-463))) (-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4326 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(|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))))) (-1530 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#1| (QUOTE (-1016)))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1075))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| $ (QUOTE (-1016))) (|HasCategory| $ (LIST (QUOTE -1007) (QUOTE (-547))))) +(-308 R -1415) ((|constructor| (NIL "Taylor series solutions of explicit ODE\\spad{'s}.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1170,8 +1170,8 @@ NIL NIL (-310 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."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . 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(|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1182,7 +1182,7 @@ NIL NIL (-313 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) ((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-766)))) (-314 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1198,19 +1198,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169)))) (-317 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-318 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."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-319 S -1410) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-319 S -1415) ((|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 (-359)))) -(-320 -1410) +(-320 -1415) ((|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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-321) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) @@ -1228,54 +1228,54 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-325 S -1410 UP UPUP R) +(-325 S -1415 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 -(-326 -1410 UP UPUP R) +(-326 -1415 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 -(-327 -1410 UP UPUP R) +(-327 -1415 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|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL (-328 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|)))) (-329 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{} ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-330 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-370)))) (|HasCategory| $ (QUOTE (-1016))) (|HasCategory| $ (LIST (QUOTE -1007) (QUOTE (-547))))) (-331 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-332 S -1410 UP UPUP) +(-332 S -1415 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-354)))) -(-333 -1410 UP UPUP) +(-333 -1415 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,{}...,{}vn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,{}...,{}vn) = M (1,{} y,{} ...,{} y**(n-1))} where \\spad{(v1,{}...,{}vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,{}...,{}wn) = (1,{} y,{} ...,{} y**(n-1))} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,{}...,{}wn) = M (1,{} y,{} ...,{} y**(n-1))},{} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,{}...,{}bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,{}...,{}bn)} returns the complementary basis \\spad{(b1',{}...,{}bn')} of \\spad{(b1,{}...,{}bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f,{} p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f,{} a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a,{} b)} tests if \\spad{(x=a,{}y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-4321 |has| (-398 |#2|) (-354)) (-4326 |has| (-398 |#2|) (-354)) (-4320 |has| (-398 |#2|) (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 |has| (-398 |#2|) (-354)) (-4327 |has| (-398 |#2|) (-354)) (-4321 |has| (-398 |#2|) (-354)) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-334 |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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) (-335 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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-336 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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-337 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 @@ -1290,33 +1290,33 @@ NIL NIL (-340) ((|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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-341 R UP -1410) +(-341 R UP -1415) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-342 |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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) (-343 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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-344 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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-345 |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}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| (-879 |#1|) (QUOTE (-143))) (|HasCategory| (-879 |#1|) (QUOTE (-359)))) (|HasCategory| (-879 |#1|) (QUOTE (-145))) (|HasCategory| (-879 |#1|) (QUOTE (-359))) (|HasCategory| (-879 |#1|) (QUOTE (-143)))) (-346 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."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) -(-347 -1410 GF) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +(-347 -1415 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 @@ -1324,21 +1324,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-349 -1410 FP FPP) +(-349 -1415 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-350 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}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-143)))) (-351 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-352 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4325 . T)) +((-4326 . T)) NIL (-353 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1346,7 +1346,7 @@ NIL NIL (-354) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-355 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1362,7 +1362,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-539)))) (-358 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4325 |has| |#1| (-539)) (-4323 . T) (-4322 . T)) +((-4326 |has| |#1| (-539)) (-4324 . T) (-4323 . T)) NIL (-359) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1374,7 +1374,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-354)))) (-361 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL (-362 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1383,14 +1383,14 @@ NIL (-363 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063)))) +((|HasAttribute| |#1| (QUOTE -4330)) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063)))) (-364 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4328 . T) (-2609 . T)) +((-4329 . T) (-2618 . T)) NIL (-365 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4323 . T) (-4322 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4324 . T) (-4323 . T)) NIL (-366 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f,{} agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1402,7 +1402,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-368 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) -((-4325 . T)) +((-4326 . T)) NIL (-369 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1410,7 +1410,7 @@ NIL NIL (-370) ((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4311 . T) (-4319 . T) (-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4312 . T) (-4320 . T) (-2654 . T) (-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-371 |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}."))) @@ -1418,23 +1418,23 @@ NIL NIL (-372 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) ((|HasCategory| |#1| (QUOTE (-169)))) (-373 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL (-374) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2609 . T)) +((-2618 . T)) NIL (-375) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2609 . T)) +((-2618 . T)) NIL (-376 R S) ((|constructor| (NIL "A \\spad{bi}-module is a free module over a ring with generators indexed by an ordered set. Each element can be expressed as a finite linear combination of generators. Only non-zero terms are stored."))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) ((|HasCategory| |#1| (QUOTE (-169)))) (-377 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1442,7 +1442,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-821)))) (-378) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-379) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1454,13 +1454,13 @@ NIL NIL (-381 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL (-382) ((|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 -(-383 -1410 UP UPUP R) +(-383 -1415 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 @@ -1474,27 +1474,27 @@ NIL NIL (-386) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-2609 . T)) +((-2618 . T)) NIL (-387) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2609 . T)) +((-2618 . T)) NIL (-388) ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-389 -2465 |returnType| -2857 |symbols|) +(-389 -2473 |returnType| -2865 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-390 -1410 UP) +(-390 -1415 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-391 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-2609 . T)) +((-2618 . T)) NIL (-392 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1502,15 +1502,15 @@ NIL NIL (-393) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-394 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4311)) (|HasAttribute| |#1| (QUOTE -4319))) +((|HasAttribute| |#1| (QUOTE -4312)) (|HasAttribute| |#1| (QUOTE -4320))) (-395) ((|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\"."))) -((-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2654 . T) (-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-396 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."))) @@ -1522,15 +1522,15 @@ NIL NIL (-398 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."))) -((-4315 -12 (|has| |#1| (-6 -4326)) (|has| |#1| (-442)) (|has| |#1| (-6 -4315))) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (QUOTE (-794))) (-1525 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#1| (QUOTE (-821)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1111))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-532))) (-12 (|HasAttribute| |#1| (QUOTE -4326)) (|HasAttribute| |#1| (QUOTE -4315)) (|HasCategory| |#1| (QUOTE (-442)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +((-4316 -12 (|has| |#1| (-6 -4327)) (|has| |#1| (-442)) (|has| |#1| (-6 -4316))) (-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (QUOTE (-794))) (-1530 (|HasCategory| |#1| (QUOTE (-794))) (|HasCategory| |#1| (QUOTE (-821)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1112))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-802)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-532))) (-12 (|HasAttribute| |#1| (QUOTE -4327)) (|HasAttribute| |#1| (QUOTE -4316)) (|HasCategory| |#1| (QUOTE (-442)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-399 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-400 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL (-401 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1544,11 +1544,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-404 R -1410 UP A) +(-404 R -1415 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4325 . T)) +((-4326 . T)) NIL -(-405 R -1410 UP A |ibasis|) +(-405 R -1415 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -1007) (|devaluate| |#2|)))) @@ -1562,12 +1562,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-354)))) (-408 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4325 |has| |#1| (-539)) (-4323 . T) (-4322 . T)) +((-4326 |has| |#1| (-539)) (-4324 . T) (-4323 . T)) NIL (-409 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."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -300) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -277) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-1176))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-1176)))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-442)))) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -300) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -277) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-1177))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-1177)))) (|HasCategory| |#1| (QUOTE (-991))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-442)))) (-410 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 @@ -1594,17 +1594,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-359)))) (-416 S) ((|constructor| (NIL "A finite-set aggregate models the notion of a finite set,{} that is,{} a collection of elements characterized by membership,{} but not by order or multiplicity. See \\spadtype{Set} for an example.")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#1| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\spad{universe()}\\$\\spad{D} returns the universal set for finite set aggregate \\spad{D}.")) (|complement| (($ $) "\\spad{complement(u)} returns the complement of the set \\spad{u},{} \\spadignore{i.e.} the set of all values not in \\spad{u}.")) (|cardinality| (((|NonNegativeInteger|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4328 . T) (-4318 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4319 . T) (-4330 . T) (-2618 . T)) NIL -(-417 R -1410) +(-417 R -1415) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-418 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,{}r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,{}r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-4315 -12 (|has| |#1| (-6 -4315)) (|has| |#2| (-6 -4315))) (-4322 . T) (-4323 . T) (-4325 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4315)) (|HasAttribute| |#2| (QUOTE -4315)))) -(-419 R -1410) +((-4316 -12 (|has| |#1| (-6 -4316)) (|has| |#2| (-6 -4316))) (-4323 . T) (-4324 . T) (-4326 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4316)) (|HasAttribute| |#2| (QUOTE -4316)))) +(-419 R -1415) ((|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 @@ -1614,17 +1614,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-1075))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (-421 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4325 -1525 (|has| |#1| (-1016)) (|has| |#1| (-463))) (-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-539)) (-4320 |has| |#1| (-539)) (-2609 . T)) +((-4326 -1530 (|has| |#1| (-1016)) (|has| |#1| (-463))) (-4324 |has| |#1| (-169)) (-4323 |has| |#1| (-169)) ((-4331 "*") |has| |#1| (-539)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-2618 . T)) NIL -(-422 R -1410) +(-422 R -1415) ((|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 -(-423 R -1410) +(-423 R -1415) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-424 R -1410) +(-424 R -1415) ((|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 @@ -1632,7 +1632,7 @@ 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 -(-426 R -1410 UP) +(-426 R -1415 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 -1007) (QUOTE (-48))))) @@ -1650,17 +1650,17 @@ NIL NIL (-430) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-2609 . T)) +((-2618 . T)) NIL (-431) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-2609 . T)) +((-2618 . T)) NIL (-432 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-433 R UP -1410) +(-433 R UP -1415) ((|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 @@ -1698,16 +1698,16 @@ NIL NIL (-442) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-443 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGenericElementPackage allows you to create generic elements of an algebra,{} \\spadignore{i.e.} the scalars are extended to include symbolic coefficients")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis") (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}")) (|genericRightDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericRightDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericRightTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericRightTraceForm (a,{}b)} is defined to be \\spadfun{genericRightTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericLeftDiscriminant| (((|Fraction| (|Polynomial| |#1|))) "\\spad{genericLeftDiscriminant()} is the determinant of the generic left trace forms of all products of basis element,{} if the generic left trace form is associative,{} an algebra is separable if the generic left discriminant is invertible,{} if it is non-zero,{} there is some ring extension which makes the algebra separable")) (|genericLeftTraceForm| (((|Fraction| (|Polynomial| |#1|)) $ $) "\\spad{genericLeftTraceForm (a,{}b)} is defined to be \\spad{genericLeftTrace (a*b)},{} this defines a symmetric bilinear form on the algebra")) (|genericRightNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{rightRankPolynomial} and changes the sign if the degree of this polynomial is odd")) (|genericRightTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericRightTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{rightRankPolynomial} and changes the sign")) (|genericRightMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericRightMinimalPolynomial(a)} substitutes the coefficients of \\spad{a} for the generic coefficients in \\spadfun{rightRankPolynomial}")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{rightRankPolynomial()} returns the right minimimal polynomial of the generic element")) (|genericLeftNorm| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftNorm(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the constant term in \\spadfun{leftRankPolynomial} and changes the sign if the degree of this polynomial is odd. This is a form of degree \\spad{k}")) (|genericLeftTrace| (((|Fraction| (|Polynomial| |#1|)) $) "\\spad{genericLeftTrace(a)} substitutes the coefficients of \\spad{a} for the generic coefficients into the coefficient of the second highest term in \\spadfun{leftRankPolynomial} and changes the sign. \\indented{1}{This is a linear form}")) (|genericLeftMinimalPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|))) $) "\\spad{genericLeftMinimalPolynomial(a)} substitutes the coefficients of {em a} for the generic coefficients in \\spad{leftRankPolynomial()}")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) "\\spad{leftRankPolynomial()} returns the left minimimal polynomial of the generic element")) (|generic| (($ (|Vector| (|Symbol|)) (|Vector| $)) "\\spad{generic(vs,{}ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} with the symbolic coefficients \\spad{vs} error,{} if the vector of symbols is shorter than the vector of elements") (($ (|Symbol|) (|Vector| $)) "\\spad{generic(s,{}v)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{v} with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($ (|Vector| $)) "\\spad{generic(ve)} returns a generic element,{} \\spadignore{i.e.} the linear combination of \\spad{ve} basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}") (($ (|Vector| (|Symbol|))) "\\spad{generic(vs)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{vs}; error,{} if the vector of symbols is too short") (($ (|Symbol|)) "\\spad{generic(s)} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{s1,{}s2,{}..}") (($) "\\spad{generic()} returns a generic element,{} \\spadignore{i.e.} the linear combination of the fixed basis with the symbolic coefficients \\spad{\\%x1,{}\\%x2,{}..}")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none")) (|coerce| (($ (|Vector| (|Fraction| (|Polynomial| |#1|)))) "\\spad{coerce(v)} assumes that it is called with a vector of length equal to the dimension of the algebra,{} then a linear combination with the basis element is formed"))) -((-4325 |has| (-398 (-921 |#1|)) (-539)) (-4323 . T) (-4322 . T)) +((-4326 |has| (-398 (-921 |#1|)) (-539)) (-4324 . T) (-4323 . T)) ((|HasCategory| (-398 (-921 |#1|)) (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| (-398 (-921 |#1|)) (QUOTE (-539)))) (-444 |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"))) -(((-4330 "*") |has| |#2| (-169)) (-4321 |has| |#2| (-539)) (-4326 |has| |#2| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-878))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1525 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +(((-4331 "*") |has| |#2| (-169)) (-4322 |has| |#2| (-539)) (-4327 |has| |#2| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#2| (QUOTE (-878))) (-1530 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1530 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1530 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4327)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-445 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 @@ -1734,7 +1734,7 @@ NIL NIL (-451 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,{}e,{}x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,{}i,{}e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,{}x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL (-452 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1742,7 +1742,7 @@ NIL NIL (-453 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#4| (LIST (QUOTE -300) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#4| (LIST (QUOTE -591) (QUOTE (-832))))) (-454 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1772,7 +1772,7 @@ 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| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-461 |lv| -1410 R) +(-461 |lv| -1415 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1782,23 +1782,23 @@ NIL NIL (-463) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4325 . T)) +((-4326 . T)) NIL (-464 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1136)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3694) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1136))))) (|HasSignature| |#1| (LIST (QUOTE -2267) (LIST (LIST (QUOTE -619) (QUOTE (-1136))) (|devaluate| |#1|))))))) (-465 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-466 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)}"))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#4| (LIST (QUOTE -300) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#4| (LIST (QUOTE -591) (QUOTE (-832))))) (-467) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-468) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|Syntax|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|Syntax|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1806,29 +1806,29 @@ NIL NIL (-469 |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."))) -((-4328 . T) (-4329 . 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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. 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T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1530 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1112))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1136)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-478 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4328)) (|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) +((|HasAttribute| |#1| (QUOTE -4329)) (|HasAttribute| |#1| (QUOTE -4330)) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (-479 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,{}u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,{}u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,{}u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,{}u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,{}u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2609 . T)) +((-2618 . T)) NIL (-480) ((|constructor| (NIL "This domain represents hostnames on computer network.")) (|host| (($ (|String|)) "\\spad{host(n)} constructs a Hostname from the name \\spad{`n'}."))) @@ -1860,33 +1860,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-483 -1410 UP |AlExt| |AlPol|) +(-483 -1415 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-484) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| $ (QUOTE (-1016))) (|HasCategory| $ (LIST (QUOTE -1007) (QUOTE (-547))))) (-485 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-486 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."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-487 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 -(-488 R UP -1410) +(-488 R UP -1415) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-489 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| (-112) (QUOTE (-1063))) (|HasCategory| (-112) (LIST (QUOTE -300) (QUOTE (-112))))) (|HasCategory| (-112) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-112) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-112) (QUOTE (-1063))) (|HasCategory| (-112) (LIST (QUOTE -591) (QUOTE (-832))))) (-490 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) @@ -1900,10 +1900,10 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-493 -1410 |Expon| |VarSet| |DPoly|) +(-493 -1415 |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 -592) (QUOTE (-1135))))) +((|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-1136))))) (-494 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,{}lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL @@ -1950,36 +1950,36 @@ NIL ((|HasCategory| |#2| (QUOTE (-766)))) (-505 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}"))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-506) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|Syntax|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|Syntax|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|Syntax|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL (-507 |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}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| (-561 |#1|) (QUOTE (-143))) (|HasCategory| (-561 |#1|) (QUOTE (-359)))) (|HasCategory| (-561 |#1|) (QUOTE (-145))) (|HasCategory| (-561 |#1|) (QUOTE (-359))) (|HasCategory| (-561 |#1|) (QUOTE (-143)))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((-1530 (|HasCategory| (-561 |#1|) (QUOTE (-143))) (|HasCategory| (-561 |#1|) (QUOTE (-359)))) (|HasCategory| (-561 |#1|) (QUOTE (-145))) (|HasCategory| (-561 |#1|) (QUOTE (-359))) (|HasCategory| (-561 |#1|) (QUOTE (-143)))) (-508 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}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-509 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."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-510 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4329))) +((|HasAttribute| |#3| (QUOTE -4330))) (-511 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -4329))) +((|HasAttribute| |#7| (QUOTE -4330))) (-512 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."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4331 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-513) ((|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 @@ -2008,7 +2008,7 @@ 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 -(-520 K -1410 |Par|) +(-520 K -1415 |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 @@ -2028,7 +2028,7 @@ 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 -(-525 K -1410 |Par|) +(-525 K -1415 |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 @@ -2058,17 +2058,17 @@ NIL NIL (-532) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4326 . T) (-4327 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4327 . T) (-4328 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-533 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) -(-534 R -1410) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +(-534 R -1415) ((|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 -(-535 R0 -1410 UP UPUP R) +(-535 R0 -1415 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 @@ -2078,7 +2078,7 @@ NIL NIL (-537 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."))) -((-2646 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2654 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-538 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."))) @@ -2086,9 +2086,9 @@ NIL NIL (-539) ((|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."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-540 R -1410) +(-540 R -1415) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2100,7 +2100,7 @@ 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 -(-543 R -1410 L) +(-543 R -1415 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -630) (|devaluate| |#2|)))) @@ -2108,31 +2108,31 @@ NIL ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,{}k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,{}p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,{}p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,{}b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,{}b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,{}k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,{}1/2)},{} where \\spad{E(n,{}x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,{}m1,{}x2,{}m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,{}0)},{} where \\spad{B(n,{}x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-545 -1410 UP UPUP R) +(-545 -1415 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 -(-546 -1410 UP) +(-546 -1415 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 (-547) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4310 . T) (-4316 . T) (-4320 . T) (-4315 . T) (-4326 . T) (-4327 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4311 . T) (-4317 . T) (-4321 . T) (-4316 . T) (-4327 . T) (-4328 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-548) ((|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 -(-549 R -1410 L) +(-549 R -1415 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -630) (|devaluate| |#2|)))) -(-550 R -1410) +(-550 R -1415) ((|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 -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1099)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-605))))) -(-551 -1410 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1100)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-605))))) +(-551 -1415 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2140,27 +2140,27 @@ 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 -(-553 -1410) +(-553 -1415) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-554 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This domain is an implementation of interval arithmetic and transcendental + functions over intervals."))) -((-2646 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2654 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-555) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-556 R -1410) +(-556 R -1415) ((|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 -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-275))) (|HasCategory| |#2| (QUOTE (-605))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135))))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-275)))) (|HasCategory| |#1| (QUOTE (-539)))) -(-557 -1410 UP) +((-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-275))) (|HasCategory| |#2| (QUOTE (-605))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1136))))) (-12 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-275)))) (|HasCategory| |#1| (QUOTE (-539)))) +(-557 -1415 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-558 R -1410) +(-558 R -1415) ((|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 @@ -2170,28 +2170,28 @@ NIL NIL (-560 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-561 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-359)))) (-562) ((|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 -(-563 R -1410) +(-563 R -1415) ((|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 -(-564 E -1410) +(-564 E -1415) ((|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 -(-565 -1410) +(-565 -1415) ((|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}."))) -((-4323 . T) (-4322 . T)) -((|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1135))))) +((-4324 . T) (-4323 . T)) +((|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-1136))))) (-566 I) ((|constructor| (NIL "The \\spadtype{IntegerRoots} package computes square roots and \\indented{2}{\\spad{n}th roots of integers efficiently.}")) (|approxSqrt| ((|#1| |#1|) "\\spad{approxSqrt(n)} returns an approximation \\spad{x} to \\spad{sqrt(n)} such that \\spad{-1 < x - sqrt(n) < 1}. Compute an approximation \\spad{s} to \\spad{sqrt(n)} such that \\indented{10}{\\spad{-1 < s - sqrt(n) < 1}} A variable precision Newton iteration is used. The running time is \\spad{O( log(n)**2 )}.")) (|perfectSqrt| (((|Union| |#1| "failed") |#1|) "\\spad{perfectSqrt(n)} returns the square root of \\spad{n} if \\spad{n} is a perfect square and returns \"failed\" otherwise")) (|perfectSquare?| (((|Boolean|) |#1|) "\\spad{perfectSquare?(n)} returns \\spad{true} if \\spad{n} is a perfect square and \\spad{false} otherwise")) (|approxNthRoot| ((|#1| |#1| (|NonNegativeInteger|)) "\\spad{approxRoot(n,{}r)} returns an approximation \\spad{x} to \\spad{n**(1/r)} such that \\spad{-1 < x - n**(1/r) < 1}")) (|perfectNthRoot| (((|Record| (|:| |base| |#1|) (|:| |exponent| (|NonNegativeInteger|))) |#1|) "\\spad{perfectNthRoot(n)} returns \\spad{[x,{}r]},{} where \\spad{n = x\\^r} and \\spad{r} is the largest integer such that \\spad{n} is a perfect \\spad{r}th power") (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{perfectNthRoot(n,{}r)} returns the \\spad{r}th root of \\spad{n} if \\spad{n} is an \\spad{r}th power and returns \"failed\" otherwise")) (|perfectNthPower?| (((|Boolean|) |#1| (|NonNegativeInteger|)) "\\spad{perfectNthPower?(n,{}r)} returns \\spad{true} if \\spad{n} is an \\spad{r}th power and \\spad{false} otherwise"))) NIL @@ -2218,19 +2218,19 @@ NIL NIL (-572 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (-1525 (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (-1530 (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) (-573 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n),{} n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n),{} n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL (-574 |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}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|)))) (|HasCategory| (-547) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547)))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-547)) (|devaluate| |#1|)))) (|HasCategory| (-547) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1136)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-547)))))) (-575 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4323 |has| |#1| (-539)) (-4322 |has| |#1| (-539)) ((-4330 "*") |has| |#1| (-539)) (-4321 |has| |#1| (-539)) (-4325 . T)) +((-4324 |has| |#1| (-539)) (-4323 |has| |#1| (-539)) ((-4331 "*") |has| |#1| (-539)) (-4322 |has| |#1| (-539)) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-539)))) (-576 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[f(x0),{}f(x1),{}f(x2),{}..]}."))) @@ -2240,7 +2240,7 @@ 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 -(-578 R -1410 FG) +(-578 R -1415 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2250,15 +2250,15 @@ NIL NIL (-580 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-581 S |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#2| |#2|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#3|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#3| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#2| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#2| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#3| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#2|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#2| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#3|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL -((|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (QUOTE (-821))) (|HasAttribute| |#1| (QUOTE -4328)) (|HasCategory| |#3| (QUOTE (-1063)))) +((|HasAttribute| |#1| (QUOTE -4330)) (|HasCategory| |#2| (QUOTE (-821))) (|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#3| (QUOTE (-1063)))) (-582 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,{}i,{}j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,{}x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,{}u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,{}u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2609 . T)) +((-2618 . T)) NIL (-583) ((|constructor| (NIL "\\indented{1}{This domain defines the datatype for the Java} Virtual Machine byte codes.")) (|coerce| (($ (|Byte|)) "\\spad{coerce(x)} the numerical byte value into a \\spad{JVM} bytecode."))) @@ -2270,19 +2270,19 @@ NIL NIL (-585 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)."))) -((-4325 -1525 (-1807 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4323 . T) (-4322 . T)) -((-1525 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) +((-4326 -1530 (-1814 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4324 . T) (-4323 . T)) +((-1530 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-586 |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."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| (-1118) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (QUOTE (-1119))) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| (-1119) (QUOTE (-821))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-587 S |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#3| "failed") |#2| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#3| "failed") |#2| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#2|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#2| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) NIL NIL (-588 |Key| |Entry|) ((|constructor| (NIL "A keyed dictionary is a dictionary of key-entry pairs for which there is a unique entry for each key.")) (|search| (((|Union| |#2| "failed") |#1| $) "\\spad{search(k,{}t)} searches the table \\spad{t} for the key \\spad{k},{} returning the entry stored in \\spad{t} for key \\spad{k}. If \\spad{t} has no such key,{} \\axiom{search(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|remove!| (((|Union| |#2| "failed") |#1| $) "\\spad{remove!(k,{}t)} searches the table \\spad{t} for the key \\spad{k} removing (and return) the entry if there. If \\spad{t} has no such key,{} \\axiom{remove!(\\spad{k},{}\\spad{t})} returns \"failed\".")) (|keys| (((|List| |#1|) $) "\\spad{keys(t)} returns the list the keys in table \\spad{t}.")) (|key?| (((|Boolean|) |#1| $) "\\spad{key?(k,{}t)} tests if \\spad{k} is a key in table \\spad{t}."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL (-589 R S) ((|constructor| (NIL "This package exports some auxiliary functions on kernels")) (|constantIfCan| (((|Union| |#1| "failed") (|Kernel| |#2|)) "\\spad{constantIfCan(k)} \\undocumented")) (|constantKernel| (((|Kernel| |#2|) |#1|) "\\spad{constantKernel(r)} \\undocumented"))) @@ -2300,12 +2300,12 @@ 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| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-593 -1410 UP) +(-593 -1415 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$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 (-594) -((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic."))) +((|constructor| (NIL "This domain implements Kleene\\spad{'s} 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of \\spad{`x'} is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of \\spad{`x'} is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of \\spad{`x'} is `false'")) (|true| (($) "the definite truth value")) (|unknown| (($) "the indefinite `unknown'")) (|false| (($) "the definite falsehood value"))) NIL NIL (-595 S R) @@ -2314,20 +2314,20 @@ NIL NIL (-596 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-4325 . T)) +((-4326 . T)) NIL (-597 A R S) ((|constructor| (NIL "LocalAlgebra produces the localization of an algebra,{} \\spadignore{i.e.} fractions whose numerators come from some \\spad{R} algebra.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{a / d} divides the element \\spad{a} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-819)))) -(-598 R -1410) +(-598 R -1415) ((|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 (-599 R UP) ((|constructor| (NIL "\\indented{1}{Univariate polynomials with negative and positive exponents.} Author: Manuel Bronstein Date Created: May 1988 Date Last Updated: 26 Apr 1990")) (|separate| (((|Record| (|:| |polyPart| $) (|:| |fracPart| (|Fraction| |#2|))) (|Fraction| |#2|)) "\\spad{separate(x)} \\undocumented")) (|monomial| (($ |#1| (|Integer|)) "\\spad{monomial(x,{}n)} \\undocumented")) (|coefficient| ((|#1| $ (|Integer|)) "\\spad{coefficient(x,{}n)} \\undocumented")) (|trailingCoefficient| ((|#1| $) "\\spad{trailingCoefficient }\\undocumented")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient }\\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|order| (((|Integer|) $) "\\spad{order(x)} \\undocumented")) (|degree| (((|Integer|) $) "\\spad{degree(x)} \\undocumented")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} \\undocumented"))) -((-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4321 . T) (-4325 . T)) -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) +((-4324 . T) (-4323 . T) ((-4331 "*") . T) (-4322 . T) (-4326 . T)) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (-600 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) NIL @@ -2342,7 +2342,7 @@ NIL NIL (-603 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4325 . T)) +((-4326 . T)) NIL (-604 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2352,30 +2352,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-606 R -1410) +(-606 R -1415) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-607 |lv| -1410) +(-607 |lv| -1415) ((|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 (-608) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1778) (QUOTE (-52))))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-1118) (QUOTE (-821))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (QUOTE (-1119))) (LIST (QUOTE |:|) (QUOTE -1786) (QUOTE (-52))))))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-1119) (QUOTE (-821))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) (-609 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-354)))) (-610 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4323 . T) (-4322 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4324 . T) (-4323 . T)) NIL (-611 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4325 -1525 (-1807 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4323 . T) (-4322 . T)) -((-1525 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) +((-4326 -1530 (-1814 (|has| |#2| (-358 |#1|)) (|has| |#1| (-539))) (-12 (|has| |#2| (-408 |#1|)) (|has| |#1| (-539)))) (-4324 . T) (-4323 . T)) +((-1530 (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -408) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -358) (|devaluate| |#1|)))) (-612 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 @@ -2387,10 +2387,10 @@ NIL (-614 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 -((-3998 (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-354)))) +((-4000 (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-354)))) (-615 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4325 . T)) +((-4326 . T)) NIL (-616 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) @@ -2406,16 +2406,16 @@ NIL NIL (-619 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-802))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-802))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-620 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL (-621 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-622 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2427,22 +2427,22 @@ NIL (-624 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4329))) +((|HasAttribute| |#1| (QUOTE -4330))) (-625 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-2609 . T)) +((-2618 . T)) NIL -(-626 R -1410 L) +(-626 R -1415 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 (-627 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-354)))) (-628 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-354)))) (-629 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) @@ -2450,15 +2450,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-354)))) (-630 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,{}n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-631 -1410 UP) +(-631 -1415 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)))) -(-632 A -1341) +(-632 A -4256) ((|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}}"))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-354)))) (-633 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,{}n,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,{}b,{}D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) @@ -2474,7 +2474,7 @@ NIL NIL (-636 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) ((|HasCategory| |#1| (QUOTE (-765)))) (-637 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2482,7 +2482,7 @@ NIL NIL (-638 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4323 . T) (-4322 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4324 . T) (-4323 . T)) ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-169)))) (-639 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) @@ -2490,13 +2490,13 @@ NIL NIL (-640 S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#1|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL -(-641 -1410) +(-641 -1415) ((|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 -(-642 -1410 |Row| |Col| M) +(-642 -1415 |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 @@ -2506,8 +2506,8 @@ NIL NIL (-644 |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."))) -((-4325 . T) (-4328 . T) (-4322 . T) (-4323 . T)) -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1525 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539))) (-1525 (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) +((-4326 . T) (-4329 . T) (-4323 . T) (-4324 . T)) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4331 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1530 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539))) (-1530 (|HasAttribute| |#2| (QUOTE (-4331 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) (-645) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|Syntax|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL @@ -2522,12 +2522,12 @@ NIL NIL (-648 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-2609 . T)) +((-2618 . T)) NIL (-649 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 -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-650) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|Syntax|) $) "\\spad{body(m)} returns the right hand side of the definition \\spad{`m'}.")) (|head| (((|List| (|Identifier|)) $) "\\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 @@ -2571,10 +2571,10 @@ NIL (-660 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539)))) +((|HasAttribute| |#2| (QUOTE (-4331 "*"))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-539)))) (-661 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,{}i1,{}j1,{}y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,{}j)} is set to \\spad{y(i-i1+1,{}j-j1+1)} for \\spad{i = i1,{}...,{}i1-1+nrows y} and \\spad{j = j1,{}...,{}j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,{}i1,{}i2,{}j1,{}j2)} extracts the submatrix \\spad{[x(i,{}j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,{}i,{}j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,{}rowList,{}colList,{}y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then \\spad{x(i<k>,{}j<l>)} is set to \\spad{y(k,{}l)} for \\spad{k = 1,{}...,{}m} and \\spad{l = 1,{}...,{}n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,{}rowList,{}colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,{}i<2>,{}...,{}i<m>]} and \\spad{colList = [j<1>,{}j<2>,{}...,{}j<n>]},{} then the \\spad{(k,{}l)}th entry of \\spad{elt(x,{}rowList,{}colList)} is \\spad{x(i<k>,{}j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,{}y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,{}y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-662 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) @@ -2582,8 +2582,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539)))) (-663 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."))) -((-4328 . T) (-4329 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4330 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-298))) (|HasCategory| |#1| (QUOTE (-539))) (|HasAttribute| |#1| (QUOTE (-4331 "*"))) (|HasCategory| |#1| (QUOTE (-354))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-664 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 @@ -2592,7 +2592,7 @@ NIL ((|constructor| (NIL "This domain implements the notion of optional vallue,{} where a computation may fail to produce expected value.")) (|nothing| (($) "represents failure.")) (|autoCoerce| ((|#1| $) "same as above but implicitly called by the compiler.")) (|coerce| ((|#1| $) "x::T tries to extract the value of \\spad{T} from the computation \\spad{x}. Produces a runtime error when the computation fails.") (($ |#1|) "x::T injects the value \\spad{x} into \\%.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} evaluates \\spad{true} if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}."))) NIL NIL -(-666 S -1410 FLAF FLAS) +(-666 S -1415 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2602,11 +2602,11 @@ NIL NIL (-668) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4321 . T) (-4326 |has| (-673) (-354)) (-4320 |has| (-673) (-354)) (-3398 . T) (-4327 |has| (-673) (-6 -4327)) (-4324 |has| (-673) (-6 -4324)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . 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T)) +((|HasCategory| (-673) (QUOTE (-145))) (|HasCategory| (-673) (QUOTE (-143))) (|HasCategory| (-673) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-673) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-673) (QUOTE (-359))) (|HasCategory| (-673) (QUOTE (-354))) (|HasCategory| (-673) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-673) (QUOTE (-225))) (-1530 (|HasCategory| (-673) (QUOTE (-354))) (|HasCategory| (-673) (QUOTE (-340)))) (|HasCategory| (-673) (QUOTE (-340))) (|HasCategory| (-673) (LIST (QUOTE -277) (QUOTE (-673)) (QUOTE (-673)))) (|HasCategory| (-673) (LIST (QUOTE -300) (QUOTE (-673)))) (|HasCategory| (-673) (LIST (QUOTE -503) (QUOTE (-1136)) (QUOTE (-673)))) (|HasCategory| (-673) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-673) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-673) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-673) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (-1530 (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-354))) (|HasCategory| (-673) (QUOTE (-340)))) (|HasCategory| (-673) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-673) (QUOTE (-991))) (|HasCategory| (-673) (QUOTE (-1158))) (-12 (|HasCategory| (-673) (QUOTE (-971))) (|HasCategory| (-673) (QUOTE (-1158)))) (-1530 (-12 (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (|HasCategory| (-673) (QUOTE (-354))) (-12 (|HasCategory| (-673) (QUOTE (-340))) (|HasCategory| (-673) (QUOTE (-878))))) (-1530 (-12 (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (-12 (|HasCategory| (-673) (QUOTE (-354))) (|HasCategory| (-673) (QUOTE (-878)))) (-12 (|HasCategory| (-673) (QUOTE (-340))) (|HasCategory| (-673) (QUOTE (-878))))) (|HasCategory| (-673) (QUOTE (-532))) (-12 (|HasCategory| (-673) (QUOTE (-1025))) (|HasCategory| (-673) (QUOTE (-1158)))) (|HasCategory| (-673) (QUOTE (-1025))) (-1530 (|HasCategory| (-673) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-673) (QUOTE (-354)))) (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878))) (-1530 (-12 (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (|HasCategory| (-673) (QUOTE (-354)))) (-1530 (-12 (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (|HasCategory| (-673) (QUOTE (-539)))) (-12 (|HasCategory| (-673) (QUOTE (-225))) (|HasCategory| (-673) (QUOTE (-354)))) (-12 (|HasCategory| (-673) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-673) (QUOTE (-354)))) (|HasCategory| (-673) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-673) (QUOTE (-821))) (|HasCategory| (-673) (QUOTE (-539))) (|HasAttribute| (-673) (QUOTE -4328)) (|HasAttribute| (-673) (QUOTE -4325)) (-12 (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (|HasCategory| (-673) (QUOTE (-143)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-673) (QUOTE (-298))) (|HasCategory| (-673) (QUOTE (-878)))) (|HasCategory| (-673) (QUOTE (-340))))) (-669 S) ((|constructor| (NIL "A multi-dictionary is a dictionary which may contain duplicates. As for any dictionary,{} its size is assumed large so that copying (non-destructive) operations are generally to be avoided.")) (|duplicates| (((|List| (|Record| (|:| |entry| |#1|) (|:| |count| (|NonNegativeInteger|)))) $) "\\spad{duplicates(d)} returns a list of values which have duplicates in \\spad{d}")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(d)} destructively removes any duplicate values in dictionary \\spad{d}.")) (|insert!| (($ |#1| $ (|NonNegativeInteger|)) "\\spad{insert!(x,{}d,{}n)} destructively inserts \\spad{n} copies of \\spad{x} into dictionary \\spad{d}."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL (-670 U) ((|constructor| (NIL "This package supports factorization and gcds of univariate polynomials over the integers modulo different primes. The inputs are given as polynomials over the integers with the prime passed explicitly as an extra argument.")) (|exptMod| ((|#1| |#1| (|Integer|) |#1| (|Integer|)) "\\spad{exptMod(f,{}n,{}g,{}p)} raises the univariate polynomial \\spad{f} to the \\spad{n}th power modulo the polynomial \\spad{g} and the prime \\spad{p}.")) (|separateFactors| (((|List| |#1|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) (|Integer|)) "\\spad{separateFactors(ddl,{} p)} refines the distinct degree factorization produced by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} to give a complete list of factors.")) (|ddFact| (((|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|)))) |#1| (|Integer|)) "\\spad{ddFact(f,{}p)} computes a distinct degree factorization of the polynomial \\spad{f} modulo the prime \\spad{p},{} \\spadignore{i.e.} such that each factor is a product of irreducibles of the same degrees. The input polynomial \\spad{f} is assumed to be square-free modulo \\spad{p}.")) (|factor| (((|List| |#1|) |#1| (|Integer|)) "\\spad{factor(f1,{}p)} returns the list of factors of the univariate polynomial \\spad{f1} modulo the integer prime \\spad{p}. Error: if \\spad{f1} is not square-free modulo \\spad{p}.")) (|linears| ((|#1| |#1| (|Integer|)) "\\spad{linears(f,{}p)} returns the product of all the linear factors of \\spad{f} modulo \\spad{p}. Potentially incorrect result if \\spad{f} is not square-free modulo \\spad{p}.")) (|gcd| ((|#1| |#1| |#1| (|Integer|)) "\\spad{gcd(f1,{}f2,{}p)} computes the \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2616,13 +2616,13 @@ 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 -(-672 OV E -1410 PG) +(-672 OV E -1415 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 (-673) ((|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|)) "\\spad{base()} returns the base of the model") (((|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}"))) -((-2646 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2654 . T) (-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-674 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."))) @@ -2630,7 +2630,7 @@ NIL NIL (-675) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4327 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4328 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-676 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,{}x,{}y)} returns a function \\spad{f: (D1,{} D2) -> I} defined by \\spad{f(x,{} y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1,{} D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) @@ -2652,7 +2652,7 @@ 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 -(-681 S -1686 I) +(-681 S -1695 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 @@ -2662,7 +2662,7 @@ NIL NIL (-683 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i,{} i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL (-684 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f,{} p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) @@ -2672,25 +2672,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-686 R |Mod| -2129 -2037 |exactQuo|) +(-686 R |Mod| -2378 -2777 |exactQuo|) ((|constructor| (NIL "\\indented{1}{These domains are used for the factorization and gcds} of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{EuclideanModularRing}")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#1| |#2|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#1| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#2| $) "\\spad{modulus(x)} \\undocumented"))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-687 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4324 |has| |#1| (-354)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-340))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4325 |has| |#1| (-354)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-340))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-688 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-689 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) +((-4324 |has| |#1| (-169)) (-4323 |has| |#1| (-169)) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145)))) -(-690 R |Mod| -2129 -2037 |exactQuo|) +(-690 R |Mod| -2378 -2777 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4325 . T)) +((-4326 . T)) NIL (-691 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2698,11 +2698,11 @@ NIL NIL (-692 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL -(-693 -1410) +(-693 -1415) ((|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]]}."))) -((-4325 . T)) +((-4326 . T)) NIL (-694 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,{}n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,{}n) := a * leftPower(a,{}n-1)} and \\spad{leftPower(a,{}1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,{}n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,{}n) := rightPower(a,{}n-1) * a} and \\spad{rightPower(a,{}1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) @@ -2726,7 +2726,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-340))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-359)))) (-699 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b,{} ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-4321 |has| |#1| (-354)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 |has| |#1| (-354)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-700 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) ((|One|) (($) "1 is the multiplicative identity."))) @@ -2736,7 +2736,7 @@ 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 -(-702 -1410 UP) +(-702 -1415 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 @@ -2754,8 +2754,8 @@ NIL NIL (-706 |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."))) -(((-4330 "*") |has| |#2| (-169)) (-4321 |has| |#2| (-539)) (-4326 |has| |#2| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-878))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1525 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1525 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +(((-4331 "*") |has| |#2| (-169)) (-4322 |has| |#2| (-539)) (-4327 |has| |#2| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#2| (QUOTE (-878))) (-1530 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1530 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-834 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (-1530 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#2| (QUOTE -4327)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-707 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2770,15 +2770,15 @@ NIL NIL (-710 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\spad{reductum(f)} is \\spad{f} minus its leading monomial.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} gives the coefficient of \\spad{f},{} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(f)} gives the monomial of \\spad{f} whose corresponding monoid element is the greatest among all those with non-zero coefficients.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(f)} is the number of non-zero coefficients with respect to the canonical basis.")) (|monomials| (((|List| $) $) "\\spad{monomials(f)} gives the list of all monomials whose sum is \\spad{f}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(f)} lists all non-zero coefficients.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(f)} tests if \\spad{f} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|terms| (((|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|))) $) "\\spad{terms(f)} gives the list of non-zero coefficients combined with their corresponding basis element as records. This is the internal representation.")) (|coerce| (($ (|List| (|Record| (|:| |coef| |#1|) (|:| |monom| |#2|)))) "\\spad{coerce(lt)} converts a list of terms and coefficients to a member of the domain.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(f,{}m)} extracts the coefficient of \\spad{m} in \\spad{f} with respect to the canonical basis \\spad{M}.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,{}m)} creates a scalar multiple of the basis element \\spad{m}."))) -((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) +((-4324 |has| |#1| (-169)) (-4323 |has| |#1| (-169)) (-4326 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-359)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-821)))) (-711 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4318 . T) (-4329 . T) (-2609 . T)) +((-4319 . T) (-4330 . T) (-2618 . T)) NIL (-712 S) ((|constructor| (NIL "A multiset is a set with multiplicities.")) (|remove!| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove!(p,{}ms,{}number)} removes destructively at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove!(x,{}ms,{}number)} removes destructively at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $ (|Integer|)) "\\spad{remove(p,{}ms,{}number)} removes at most \\spad{number} copies of elements \\spad{x} such that \\spad{p(x)} is \\spadfun{\\spad{true}} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.") (($ |#1| $ (|Integer|)) "\\spad{remove(x,{}ms,{}number)} removes at most \\spad{number} copies of element \\spad{x} if \\spad{number} is positive,{} all of them if \\spad{number} equals zero,{} and all but at most \\spad{-number} if \\spad{number} is negative.")) (|members| (((|List| |#1|) $) "\\spad{members(ms)} returns a list of the elements of \\spad{ms} {\\em without} their multiplicity. See also \\spadfun{parts}.")) (|multiset| (($ (|List| |#1|)) "\\spad{multiset(ls)} creates a multiset with elements from \\spad{ls}.") (($ |#1|) "\\spad{multiset(s)} creates a multiset with singleton \\spad{s}.") (($) "\\spad{multiset()}\\$\\spad{D} creates an empty multiset of domain \\spad{D}."))) -((-4328 . T) (-4318 . T) (-4329 . T)) +((-4329 . T) (-4319 . T) (-4330 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-713) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) @@ -2790,7 +2790,7 @@ NIL NIL (-715 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,{}x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,{}x,{}n)} returns \\spad{min(n,{}order(f,{}x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,{}x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,{}[x1,{}x2,{}...,{}xk],{}[n1,{}n2,{}...,{}nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,{}x,{}n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4323 . T) (-4322 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL (-716 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) @@ -2806,7 +2806,7 @@ NIL NIL (-719 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL (-720) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -2888,15 +2888,15 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-740 -1410) +(-740 -1415) ((|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 -(-741 P -1410) +(-741 P -1415) ((|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 -(-742 UP -1410) +(-742 UP -1415) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2910,9 +2910,9 @@ NIL NIL (-745) ((|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."))) -(((-4330 "*") . T)) +(((-4331 "*") . T)) NIL -(-746 R -1410) +(-746 R -1415) ((|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 @@ -2932,7 +2932,7 @@ 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 -(-751 -1410 |ExtF| |SUEx| |ExtP| |n|) +(-751 -1415 |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 @@ -2946,23 +2946,23 @@ NIL NIL (-754 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."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-756 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)}"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4324 |has| |#1| (-354)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1111))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4325 |has| |#1| (-354)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-1112))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-757 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-758 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL (-759 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) @@ -3014,25 +3014,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-359)))) (-771 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-772 -1525 R OS S) +(-772 -1530 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-773 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-1525 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) +((-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (-1530 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1530 (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-968 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (-774) ((|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 -(-775 R -1410 L) +(-775 R -1415 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-776 R -1410) +(-776 R -1415) ((|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 @@ -3040,7 +3040,7 @@ 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 -(-778 R -1410) +(-778 R -1415) ((|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 @@ -3048,11 +3048,11 @@ 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 -(-780 -1410 UP UPUP R) +(-780 -1415 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 -(-781 -1410 UP L LQ) +(-781 -1415 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 @@ -3060,41 +3060,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-783 -1410 UP L LQ) +(-783 -1415 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-784 -1410 UP) +(-784 -1415 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 -(-785 -1410 L UP A LO) +(-785 -1415 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 -(-786 -1410 UP) +(-786 -1415 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-787 -1410 LO) +(-787 -1415 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 -(-788 -1410 LODO) +(-788 -1415 LODO) ((|constructor| (NIL "\\spad{ODETools} provides tools for the linear ODE solver.")) (|particularSolution| (((|Union| |#1| "failed") |#2| |#1| (|List| |#1|) (|Mapping| |#1| |#1|)) "\\spad{particularSolution(op,{} g,{} [f1,{}...,{}fm],{} I)} returns a particular solution \\spad{h} of the equation \\spad{op y = g} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op,{} g,{} [f1,{}...,{}fm])} returns \\spad{[u1,{}...,{}um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,{}...,{}fm]} are linearly independent and \\spad{op(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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(QUOTE (-547)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-1063)))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (-790 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"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-792 (-1135)) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-792 (-1135)) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-792 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-792 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-792 (-1135)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-792 (-1136)) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-792 (-1136)) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-792 (-1136)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-792 (-1136)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-792 (-1136)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-791 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) -(((-4330 "*") |has| |#2| (-354)) (-4321 |has| |#2| (-354)) (-4326 |has| |#2| (-354)) (-4320 |has| |#2| (-354)) (-4325 . T) (-4323 . T) (-4322 . T)) +(((-4331 "*") |has| |#2| (-354)) (-4322 |has| |#2| (-354)) (-4327 |has| |#2| (-354)) (-4321 |has| |#2| (-354)) (-4326 . T) (-4324 . T) (-4323 . T)) ((|HasCategory| |#2| (QUOTE (-354)))) (-792 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used orderly ranking to the set of derivatives of an ordered list of differential indeterminates. An orderly ranking is a ranking \\spadfun{<} of the derivatives with the property that for two derivatives \\spad{u} and \\spad{v},{} \\spad{u} \\spadfun{<} \\spad{v} if the \\spadfun{order} of \\spad{u} is less than that of \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines an orderly ranking \\spadfun{<} on derivatives \\spad{u} via the lexicographic order on the pair (\\spadfun{order}(\\spad{u}),{} \\spadfun{variable}(\\spad{u}))."))) @@ -3106,7 +3106,7 @@ NIL NIL (-794) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-795) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -3134,7 +3134,7 @@ NIL NIL (-801 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-225)))) (-802) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3146,7 +3146,7 @@ NIL NIL (-804 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4328 . T) (-4318 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4319 . T) (-4330 . T) (-2618 . T)) NIL (-805) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3158,11 +3158,11 @@ NIL NIL (-807 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."))) -((-4325 |has| |#1| (-819))) -((|HasCategory| |#1| (QUOTE (-819))) (-1525 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1525 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4326 |has| |#1| (-819))) +((|HasCategory| |#1| (QUOTE (-819))) (-1530 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1530 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) (-808 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) +((-4324 |has| |#1| (-169)) (-4323 |has| |#1| (-169)) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145)))) (-809) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3186,13 +3186,13 @@ NIL NIL (-814 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."))) -((-4325 |has| |#1| (-819))) -((|HasCategory| |#1| (QUOTE (-819))) (-1525 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1525 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4326 |has| |#1| (-819))) +((|HasCategory| |#1| (QUOTE (-819))) (-1530 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-819)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-532))) (-1530 (|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-21)))) (-815) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-816 -2713 S) +(-816 -2721 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 @@ -3206,7 +3206,7 @@ NIL NIL (-819) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4325 . T)) +((-4326 . T)) NIL (-820 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3222,19 +3222,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169)))) (-823 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL (-824 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) -(-825 R |sigma| -2647) +(-825 R |sigma| -2655) ((|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."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-354)))) -(-826 |x| R |sigma| -2647) +(-826 |x| R |sigma| -2655) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-354)))) (-827 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) @@ -3270,7 +3270,7 @@ NIL NIL (-835 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) -((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) +((-4324 |has| |#1| (-169)) (-4323 |has| |#1| (-169)) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354)))) (-836 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3282,24 +3282,24 @@ NIL NIL (-838 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{root(f,{}a)} returns a root of the polynomial \\spad{f}. Argument \\spad{a} must be a root of \\spad{f} \\spad{(mod p)}.")) (|sqrt| (($ $ (|Integer|)) "\\spad{sqrt(b,{}a)} returns a square root of \\spad{b}. Argument \\spad{a} is a square root of \\spad{b} \\spad{(mod p)}.")) (|approximate| (((|Integer|) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns an integer \\spad{y} such that \\spad{y = x (mod p^n)} when \\spad{n} is positive,{} and 0 otherwise.")) (|quotientByP| (($ $) "\\spad{quotientByP(x)} returns \\spad{b},{} where \\spad{x = a + b p}.")) (|moduloP| (((|Integer|) $) "\\spad{modulo(x)} returns a,{} where \\spad{x = a + b p}.")) (|modulus| (((|Integer|)) "\\spad{modulus()} returns the value of \\spad{p}.")) (|complete| (($ $) "\\spad{complete(x)} forces the computation of all digits.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,{}n)} forces the computation of digits up to order \\spad{n}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the exponent of the highest power of \\spad{p} dividing \\spad{x}.")) (|digits| (((|Stream| (|Integer|)) $) "\\spad{digits(x)} returns a stream of \\spad{p}-adic digits of \\spad{x}."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-839 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-840 |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)."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-878))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-145))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-839 |#1|) (QUOTE (-991))) (|HasCategory| (-839 |#1|) (QUOTE (-794))) (-1525 (|HasCategory| (-839 |#1|) (QUOTE (-794))) (|HasCategory| (-839 |#1|) (QUOTE (-821)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-1111))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-225))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -503) (QUOTE (-1135)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -839) (|devaluate| |#1|)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (QUOTE (-298))) (|HasCategory| (-839 |#1|) (QUOTE (-532))) (|HasCategory| (-839 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-839 |#1|) (QUOTE (-878))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-145))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-839 |#1|) (QUOTE (-991))) (|HasCategory| (-839 |#1|) (QUOTE (-794))) (-1530 (|HasCategory| (-839 |#1|) (QUOTE (-794))) (|HasCategory| (-839 |#1|) (QUOTE (-821)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-1112))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-839 |#1|) (QUOTE (-225))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -503) (QUOTE (-1136)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -300) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (LIST (QUOTE -277) (LIST (QUOTE -839) (|devaluate| |#1|)) (LIST (QUOTE -839) (|devaluate| |#1|)))) (|HasCategory| (-839 |#1|) (QUOTE (-298))) (|HasCategory| (-839 |#1|) (QUOTE (-532))) (|HasCategory| (-839 |#1|) (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-839 |#1|) (QUOTE (-878)))) (|HasCategory| (-839 |#1|) (QUOTE (-143))))) (-841 |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)}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (-1525 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1111))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (-1530 (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1112))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-821))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) (-842 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 (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))))) (-843) ((|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 @@ -3355,7 +3355,7 @@ NIL (-856 |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 (-3998 (|HasCategory| |#2| (QUOTE (-1016)))) (-3998 (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (-3998 (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135))))) +((-12 (-4000 (|HasCategory| |#2| (QUOTE (-1016)))) (-4000 (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1136)))))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (-4000 (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1136)))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1136))))) (-857 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 @@ -3364,7 +3364,7 @@ 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 -(-859 R -1686) +(-859 R -1695) ((|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 @@ -3388,7 +3388,7 @@ 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 -(-865 UP -1410) +(-865 UP -1415) ((|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 @@ -3406,19 +3406,19 @@ NIL NIL (-869 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4325 . T)) +((-4326 . T)) NIL (-870 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-871 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (-872 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4325 . T)) +((-4326 . T)) NIL (-873 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3426,8 +3426,8 @@ NIL NIL (-874 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4325 . T)) -((-1525 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) +((-4326 . T)) +((-1530 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-821)))) (-875 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3442,13 +3442,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-143)))) (-878) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-879 |p|) ((|constructor| (NIL "PrimeField(\\spad{p}) implements the field with \\spad{p} elements if \\spad{p} is a prime number. Error: if \\spad{p} is not prime. Note: this domain does not check that argument is a prime."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) ((|HasCategory| $ (QUOTE (-145))) (|HasCategory| $ (QUOTE (-143))) (|HasCategory| $ (QUOTE (-359)))) -(-880 R0 -1410 UP UPUP R) +(-880 R0 -1415 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 @@ -3462,7 +3462,7 @@ NIL NIL (-883 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-884 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) @@ -3476,7 +3476,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-887 -1410) +(-887 -1415) ((|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 @@ -3486,17 +3486,17 @@ NIL NIL (-889) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-890) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4330 "*") . T)) +(((-4331 "*") . T)) NIL -(-891 -1410 P) +(-891 -1415 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-892 |xx| -1410) +(-892 |xx| -1415) ((|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 @@ -3520,7 +3520,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-898 R -1410) +(-898 R -1415) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3532,7 +3532,7 @@ 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 -(-901 S R -1410) +(-901 S R -1415) ((|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 @@ -3552,11 +3552,11 @@ 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 -855) (|devaluate| |#1|)))) -(-906 R -1410 -1686) +(-906 R -1415 -1695) ((|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 -(-907 -1686) +(-907 -1695) ((|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 @@ -3578,8 +3578,8 @@ NIL NIL (-912 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-913 |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 @@ -3599,12 +3599,12 @@ NIL (-917 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-878))) (|HasAttribute| |#2| (QUOTE -4326)) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#4| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#4| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#4| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#4| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-821)))) +((|HasCategory| |#2| (QUOTE (-878))) (|HasAttribute| |#2| (QUOTE -4327)) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#4| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#4| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#4| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#4| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-821)))) (-918 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL -(-919 E V R P -1410) +(-919 E V R P -1415) ((|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 @@ -3614,9 +3614,9 @@ NIL NIL (-921 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}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1135) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) -(-922 E V R P -1410) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1136) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1136) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1136) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1136) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1136) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(-922 E V R P -1415) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-442)))) @@ -3638,13 +3638,13 @@ NIL NIL (-927 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"))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-928) ((|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 -(-929 -1410) +(-929 -1415) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3658,12 +3658,12 @@ NIL NIL (-932 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}"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-130)))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-130)))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327))) (-933 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"))) -((-4325 -12 (|has| |#2| (-463)) (|has| |#1| (-463)))) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-821))))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701))))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-359)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-821))))) +((-4326 -12 (|has| |#2| (-463)) (|has| |#1| (-463)))) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-821))))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701))))) (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-359)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-463))) (|HasCategory| |#2| (QUOTE (-463)))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701)))) (-12 (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#2| (QUOTE (-767))))) (-12 (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-701)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-130))) (|HasCategory| |#2| (QUOTE (-130)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-821))))) (-934) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3678,7 +3678,7 @@ NIL NIL (-937 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\spad{merge(q1,{}q2)} returns combines priority queues \\spad{q1} and \\spad{q2} to return a single priority queue \\spad{q}.")) (|max| ((|#1| $) "\\spad{max(q)} returns the maximum element of priority queue \\spad{q}."))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-938 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3698,7 +3698,7 @@ NIL NIL (-942 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,{}[x1,{}..,{}xk],{}[n1,{}..,{}nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,{}x,{}n)} computes \\spad{a*x**n}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-943) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3710,7 +3710,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-539)))) (-945 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4328 . T) (-2609 . T)) +((-4329 . T) (-2618 . T)) NIL (-946 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3726,7 +3726,7 @@ NIL NIL (-949 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL (-950 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3744,7 +3744,7 @@ 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 -(-954 K R UP -1410) +(-954 K R UP -1415) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3771,10 +3771,10 @@ NIL (-960 A S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#2| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#2| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#2| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#2| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#2| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#2| |#2|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) NIL -((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1111)))) +((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-991))) (|HasCategory| |#2| (QUOTE (-794))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-1112)))) (-961 S) ((|constructor| (NIL "QuotientField(\\spad{S}) is the category of fractions of an Integral Domain \\spad{S}.")) (|floor| ((|#1| $) "\\spad{floor(x)} returns the largest integral element below \\spad{x}.")) (|ceiling| ((|#1| $) "\\spad{ceiling(x)} returns the smallest integral element above \\spad{x}.")) (|random| (($) "\\spad{random()} returns a random fraction.")) (|fractionPart| (($ $) "\\spad{fractionPart(x)} returns the fractional part of \\spad{x}. \\spad{x} = wholePart(\\spad{x}) + fractionPart(\\spad{x})")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} returns the whole part of the fraction \\spad{x} \\spadignore{i.e.} the truncated quotient of the numerator by the denominator.")) (|denominator| (($ $) "\\spad{denominator(x)} is the denominator of the fraction \\spad{x} converted to \\%.")) (|numerator| (($ $) "\\spad{numerator(x)} is the numerator of the fraction \\spad{x} converted to \\%.")) (|denom| ((|#1| $) "\\spad{denom(x)} returns the denominator of the fraction \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer(x)} returns the numerator of the fraction \\spad{x}.")) (/ (($ |#1| |#1|) "\\spad{d1 / d2} returns the fraction \\spad{d1} divided by \\spad{d2}."))) -((-2609 . T) (-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2618 . T) (-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-962 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3786,7 +3786,7 @@ NIL NIL (-964 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-965 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) @@ -3794,7 +3794,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-281)))) (-966 R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#1| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#1| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#1| |#1| |#1| |#1|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#1| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#1| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-4321 |has| |#1| (-281)) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 |has| |#1| (-281)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-967 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) @@ -3802,12 +3802,12 @@ NIL NIL (-968 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.}"))) -((-4321 |has| |#1| (-281)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))))) +((-4322 |has| |#1| (-281)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-281))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -503) (QUOTE (-1136)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -277) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-532))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))))) (-969 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}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-970 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3816,14 +3816,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|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 -(-972 -1410 UP UPUP |radicnd| |n|) +(-972 -1415 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4321 |has| (-398 |#2|) (-354)) (-4326 |has| (-398 |#2|) (-354)) (-4320 |has| (-398 |#2|) (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1525 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1525 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1525 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1525 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) +((-4322 |has| (-398 |#2|) (-354)) (-4327 |has| (-398 |#2|) (-354)) (-4321 |has| (-398 |#2|) (-354)) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-398 |#2|) (QUOTE (-143))) (|HasCategory| (-398 |#2|) (QUOTE (-145))) (|HasCategory| (-398 |#2|) (QUOTE (-340))) (-1530 (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (|HasCategory| (-398 |#2|) (QUOTE (-354))) (|HasCategory| (-398 |#2|) (QUOTE (-359))) (-1530 (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (|HasCategory| (-398 |#2|) (QUOTE (-340)))) (-1530 (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-398 |#2|) (QUOTE (-340))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1530 (|HasCategory| (-398 |#2|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-398 |#2|) (QUOTE (-354)))) (-12 (|HasCategory| (-398 |#2|) (QUOTE (-225))) (|HasCategory| (-398 |#2|) (QUOTE (-354))))) (-973 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1135)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1525 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1111))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1135)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-547) (QUOTE (-878))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-1136)))) (|HasCategory| (-547) (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-145))) (|HasCategory| (-547) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-991))) (|HasCategory| (-547) (QUOTE (-794))) (-1530 (|HasCategory| (-547) (QUOTE (-794))) (|HasCategory| (-547) (QUOTE (-821)))) (|HasCategory| (-547) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-1112))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| (-547) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| (-547) (QUOTE (-225))) (|HasCategory| (-547) (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| (-547) (LIST (QUOTE -503) (QUOTE (-1136)) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -300) (QUOTE (-547)))) (|HasCategory| (-547) (LIST (QUOTE -277) (QUOTE (-547)) (QUOTE (-547)))) (|HasCategory| (-547) (QUOTE (-298))) (|HasCategory| (-547) (QUOTE (-532))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-547) (LIST (QUOTE -615) (QUOTE (-547)))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| (-547) (QUOTE (-878)))) (|HasCategory| (-547) (QUOTE (-143))))) (-974) ((|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 @@ -3843,10 +3843,10 @@ NIL (-978 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4329)) (|HasCategory| |#2| (QUOTE (-1063)))) +((|HasAttribute| |#1| (QUOTE -4330)) (|HasCategory| |#2| (QUOTE (-1063)))) (-979 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-2609 . T)) +((-2618 . T)) NIL (-980 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3854,21 +3854,21 @@ NIL NIL (-981) ((|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}}"))) -((-4321 . T) (-4326 . T) (-4320 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4325 . T)) +((-4322 . T) (-4327 . T) (-4321 . T) (-4324 . T) (-4323 . T) ((-4331 "*") . T) (-4326 . T)) NIL -(-982 R -1410) +(-982 R -1415) ((|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 -(-983 R -1410) +(-983 R -1415) ((|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 -(-984 -1410 UP) +(-984 -1415 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 -(-985 -1410 UP) +(-985 -1415 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 @@ -3902,9 +3902,9 @@ NIL NIL (-993 |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"))) -((-4321 . T) (-4326 . T) (-4320 . T) (-4323 . T) (-4322 . T) ((-4330 "*") . T) (-4325 . T)) -((-1525 (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547))))) -(-994 -1410 L) +((-4322 . T) (-4327 . T) (-4321 . T) (-4324 . T) (-4323 . T) ((-4331 "*") . T) (-4326 . T)) +((-1530 (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-398 (-547)) (LIST (QUOTE -1007) (QUOTE (-547))))) +(-994 -1415 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -3914,12 +3914,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1063)))) (-996 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#4| (LIST (QUOTE -300) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#4| (LIST (QUOTE -591) (QUOTE (-832))))) (-997 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4330 "*")))) +((|HasAttribute| |#1| (QUOTE (-4331 "*")))) (-998 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -3940,14 +3940,14 @@ 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 -(-1003 -1410 |Expon| |VarSet| |FPol| |LFPol|) +(-1003 -1415 |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"))) -(((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-1004) ((|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.}"))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -1778) (QUOTE (-52))))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-1135) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (QUOTE (-1136))) (LIST (QUOTE |:|) (QUOTE -1786) (QUOTE (-52))))))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-1136) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) (-1005) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|Syntax|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL @@ -3982,7 +3982,7 @@ NIL NIL (-1013 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| (-754 |#1| (-834 |#2|)) (QUOTE (-1063))) (|HasCategory| (-754 |#1| (-834 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -754) (|devaluate| |#1|) (LIST (QUOTE -834) (|devaluate| |#2|)))))) (|HasCategory| (-754 |#1| (-834 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-754 |#1| (-834 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| (-834 |#2|) (QUOTE (-359))) (|HasCategory| (-754 |#1| (-834 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) (-1014) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) @@ -3994,9 +3994,9 @@ NIL NIL (-1016) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4325 . T)) +((-4326 . T)) NIL -(-1017 |xx| -1410) +(-1017 |xx| -1415) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -4006,12 +4006,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-298))) (|HasCategory| |#4| (QUOTE (-354))) (|HasCategory| |#4| (QUOTE (-539))) (|HasCategory| |#4| (QUOTE (-169)))) (-1019 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4328 . T) (-2609 . T) (-4323 . T) (-4322 . T)) +((-4329 . T) (-2618 . T) (-4324 . T) (-4323 . T)) NIL (-1020 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4328 . T) (-4323 . T) (-4322 . T)) -((-1525 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-354)))) (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (QUOTE (-298))) (|HasCategory| |#3| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) +((-4329 . T) (-4324 . T) (-4323 . T)) +((-1530 (-12 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (QUOTE (-354)))) (|HasCategory| |#3| (QUOTE (-354))) (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (QUOTE (-298))) (|HasCategory| |#3| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-169))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|))))) (-1021 |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 @@ -4030,7 +4030,7 @@ NIL NIL (-1025) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-1026 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -4038,19 +4038,19 @@ NIL NIL (-1027) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4316 . T) (-4320 . T) (-4315 . T) (-4326 . T) (-4327 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4317 . T) (-4321 . T) (-4316 . T) (-4327 . T) (-4328 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-1028) ((|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}"))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1135))) (LIST (QUOTE |:|) (QUOTE -1778) (QUOTE (-52))))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (QUOTE (-1063))) (|HasCategory| (-1135) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (QUOTE (-1136))) (LIST (QUOTE |:|) (QUOTE -1786) (QUOTE (-52))))))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-52) (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| (-52) (QUOTE (-1063))) (|HasCategory| (-52) (LIST (QUOTE -300) (QUOTE (-52))))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (QUOTE (-1063))) (|HasCategory| (-1136) (QUOTE (-821))) (|HasCategory| (-52) (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-52) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (LIST (QUOTE -591) (QUOTE (-832))))) (-1029 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-1135))))) +((|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-532))) (|HasCategory| |#2| (LIST (QUOTE -38) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-1136))))) (-1030 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL (-1031) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|Syntax|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|Syntax|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) @@ -4074,7 +4074,7 @@ NIL NIL (-1036 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL (-1037 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -4084,11 +4084,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-1039 |Base| R -1410) +(-1039 |Base| R -1415) ((|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 -(-1040 |Base| R -1410) +(-1040 |Base| R -1415) ((|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 @@ -4102,8 +4102,8 @@ NIL NIL (-1043 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."))) -((-4321 |has| |#1| (-354)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-340)))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135))))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354))))) +((-4322 |has| |#1| (-354)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-340))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-340)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-359))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354)))) (|HasCategory| |#1| (QUOTE (-340)))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136))))) (-12 (|HasCategory| |#1| (QUOTE (-340))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136))))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354)))) (-12 (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (QUOTE (-354))))) (-1044 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 @@ -4134,8 +4134,8 @@ NIL NIL (-1051 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"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1052 (-1135)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| (-1052 (-1136)) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1052 (-1136)) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1052 (-1136)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1052 (-1136)) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1052 (-1136)) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-225))) (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1052 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 @@ -4158,7 +4158,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1063)))) (-1057 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-2609 . T)) +((-2618 . T)) NIL (-1058 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -4166,7 +4166,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (QUOTE (-1063)))) (-1059 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l),{} f(l+k),{} ...,{} f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l,{} l+k,{} ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,{}3,{}5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2609 . T)) +((-2618 . T)) NIL (-1060 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -4174,7 +4174,7 @@ NIL NIL (-1061 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4318 . T) (-2609 . T)) +((-4319 . T) (-2618 . T)) NIL (-1062 S) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) @@ -4190,8 +4190,8 @@ NIL NIL (-1065 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)}}"))) -((-4328 . T) (-4318 . T) (-4329 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +((-4329 . T) (-4319 . T) (-4330 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-359))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1066 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4218,7 +4218,7 @@ NIL NIL (-1072 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL (-1073) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). 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(|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-767))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-819))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (|HasCategory| (-547) (QUOTE (-821))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#3| (QUOTE (-225))) (|HasCategory| |#3| (QUOTE (-1016)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -869) (QUOTE (-1136))))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547))))) (-1530 (|HasCategory| |#3| (QUOTE (-1016))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -1007) (QUOTE (-547)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#3| (QUOTE (-1063)))) (|HasAttribute| |#3| (QUOTE -4326)) (|HasCategory| |#3| (QUOTE (-130))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1063))) (|HasCategory| |#3| (LIST (QUOTE -300) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -591) (QUOTE (-832))))) (-1077 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-442)))) -(-1078 R -1410) +(-1078 R -1415) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4258,19 +4258,19 @@ NIL NIL (-1082) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4316 . T) (-4320 . T) (-4315 . T) (-4326 . T) (-4327 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4317 . T) (-4321 . T) (-4316 . T) (-4327 . T) (-4328 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-1083 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4328 . T) (-4329 . T) (-2609 . T)) +((-4329 . T) (-4330 . T) (-2618 . T)) NIL (-1084 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#3| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#3| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#4| |#4| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#5| $ |#5|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#3| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#3| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#4| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#3|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#3|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-354))) (|HasAttribute| |#3| (QUOTE (-4330 "*"))) (|HasCategory| |#3| (QUOTE (-169)))) +((|HasCategory| |#3| (QUOTE (-354))) (|HasAttribute| |#3| (QUOTE (-4331 "*"))) (|HasCategory| |#3| (QUOTE (-169)))) (-1085 |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if the matrix is not invertible.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m},{} if that matrix is invertible and returns \"failed\" otherwise.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.")) (|diagonalProduct| ((|#2| $) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}.")) (|trace| ((|#2| $) "\\spad{trace(m)} returns the trace of the matrix \\spad{m}. this is the sum of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonal| ((|#3| $) "\\spad{diagonal(m)} returns a row consisting of the elements on the diagonal of the matrix \\spad{m}.")) (|diagonalMatrix| (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ |#2|) "\\spad{scalarMatrix(r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-2609 . T) (-4328 . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-2618 . T) (-4329 . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL (-1086 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,{}B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) @@ -4278,17 +4278,17 @@ NIL NIL (-1087 R |VarSet|) ((|constructor| (NIL "\\indented{2}{This type is the basic representation of sparse recursive multivariate} polynomials. It is parameterized by the coefficient ring and the variable set which may be infinite. The variable ordering is determined by the variable set parameter. The coefficient ring may be non-commutative,{} but the variables are assumed to commute."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-878))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1525 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-878))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (|HasCategory| |#1| (QUOTE (-442))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327)) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-878)))) (|HasCategory| |#1| (QUOTE (-143))))) (-1088 |Coef| |Var| SMP) ((|constructor| (NIL "This domain provides multivariate Taylor series with variables from an arbitrary ordered set. A Taylor series is represented by a stream of polynomials from the polynomial domain \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) (-1089 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}"))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL -(-1090 UP -1410) +(-1090 UP -1415) ((|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 @@ -4321,600 +4321,604 @@ NIL NIL NIL (-1098) +((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|case| (((|Boolean| (SEQ (|Mapping| (|Boolean|) $ (|DefinitionAst|)) (|Mapping| (|Boolean|) $ (|MacroAst|)) (|Mapping| (|Boolean|) $ (|WhereAst|)) (|Mapping| (|Boolean|) $ (|CategoryAst|)) (|Mapping| (|Boolean|) $ (|CapsuleAst|)) (|Mapping| (|Boolean|) $ (|SignatureAst|)) (|Mapping| (|Boolean|) $ (|AttributeAst|)) (|Mapping| (|Boolean|) $ (|MappingAst|)) (|Mapping| (|Boolean|) $ (|IfAst|)) (|Mapping| (|Boolean|) $ (|RepeatAst|)) (|Mapping| (|Boolean|) $ (|WhileAst|)) (|Mapping| (|Boolean|) $ (|InAst|)) (|Mapping| (|Boolean|) $ (|CollectAst|)) (|Mapping| (|Boolean|) $ (|ConstructAst|)) (|Mapping| (|Boolean|) $ (|ExitAst|)) (|Mapping| (|Boolean|) $ (|ReturnAst|)) (|Mapping| (|Boolean|) $ (|CoerceAst|)) (|Mapping| (|Boolean|) $ (|PretendAst|)) (|Mapping| (|Boolean|) $ (|RestrictAst|)) (|Mapping| (|Boolean|) $ (|SegmentAst|)) (|Mapping| (|Boolean|) $ (|SequenceAst|)) (|Mapping| (|Boolean|) $ (|LetAst|)) (|Mapping| (|Boolean|) $ (|SuchThatAst|)) (|Mapping| (|Boolean|) $ (|ColonAst|)) (|Mapping| (|Boolean|) $ (|CaseAst|)) (|Mapping| (|Boolean|) $ (|HasAst|)) (|Mapping| (|Boolean|) $ (|IsAst|)) (|exit| (|Mapping| (|IsAst|) $)))) $ (|ImportAst|)) "\\spad{s case ImportAst} holds if \\spad{`s'} represents an `import' statement."))) +((-2618 . T)) +NIL +(-1099) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,{}o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1099) +(-1100) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,{}z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,{}z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,{}z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,{}z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,{}x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,{}x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,{}x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1100 V C) +(-1101 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}o2)} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}o1,{}o2)} returns \\spad{true} iff \\axiom{o1(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{o2(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}\\spad{lt})} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in \\spad{lt}]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(\\spad{lvt})} returns the same as \\axiom{[construct(\\spad{vt}.val,{}\\spad{vt}.tower) for \\spad{vt} in \\spad{lvt}]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(\\spad{vt})} returns the same as \\axiom{construct(\\spad{vt}.val,{}\\spad{vt}.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1101 V C) +(-1102 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."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1100) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063))) (-1525 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1100) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1100 |#1| |#2|) (QUOTE (-1063))))) (|HasCategory| (-1100 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832))))) -(-1102 |ndim| R) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-1101 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1101) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1101 |#1| |#2|) (QUOTE (-1063)))) (|HasCategory| (-1101 |#1| |#2|) (QUOTE (-1063))) (-1530 (|HasCategory| (-1101 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832)))) (-12 (|HasCategory| (-1101 |#1| |#2|) (LIST (QUOTE -300) (LIST (QUOTE -1101) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1101 |#1| |#2|) (QUOTE (-1063))))) (|HasCategory| (-1101 |#1| |#2|) (LIST (QUOTE -591) (QUOTE (-832))))) +(-1103 |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.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|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}."))) -((-4325 . T) (-4317 |has| |#2| (-6 (-4330 "*"))) (-4328 . T) (-4322 . T) (-4323 . T)) -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1525 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (-1525 (|HasAttribute| |#2| (QUOTE (-4330 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) -(-1103 S) +((-4326 . T) (-4318 |has| |#2| (-6 (-4331 "*"))) (-4329 . T) (-4323 . T) (-4324 . T)) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE (-4331 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (-1530 (-12 (|HasCategory| |#2| (QUOTE (-225))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-298))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-354))) (-1530 (|HasAttribute| |#2| (QUOTE (-4331 "*"))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasCategory| |#2| (QUOTE (-225)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-169)))) +(-1104 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1104) +(-1105) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL -(-1105 R E V P TS) +(-1106 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1106 R E V P) +(-1107 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#4| (LIST (QUOTE -300) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#4| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1107 S) +(-1108 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}."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1108 A S) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-1109 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL -(-1109 S) +(-1110 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})}."))) -((-2609 . T)) +((-2618 . T)) NIL -(-1110 |Key| |Ent| |dent|) +(-1111 |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."))) -((-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) -(-1111) +((-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-821))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +(-1112) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1112 |Coef|) +(-1113 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1113 S) +(-1114 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,{}u)}."))) NIL NIL -(-1114 A B) +(-1115 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,{}f,{}u)},{} where \\spad{u} is a finite stream \\spad{[x0,{}x1,{}...,{}xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,{}b),{} r1 = f(x1,{}r0),{}...,{} r(n) = f(xn,{}r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,{}h,{}[x0,{}x1,{}x2,{}...])} returns \\spad{[y0,{}y1,{}y2,{}...]},{} where \\spad{y0 = h(x0,{}b)},{} \\spad{y1 = h(x1,{}y0)},{}\\spad{...} \\spad{yn = h(xn,{}y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,{}s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}...]) = [f(x0),{}f(x1),{}f(x2),{}..]}."))) NIL NIL -(-1115 A B C) +(-1116 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}st1,{}st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,{}[x0,{}x1,{}x2,{}..],{}[y0,{}y1,{}y2,{}..]) = [f(x0,{}y0),{}f(x1,{}y1),{}..]}."))) NIL NIL -(-1116 S) +(-1117 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4329 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1117) +((-4330 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-1118) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL -(-1118) +(-1119) NIL -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) -(-1119 |Entry|) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142)))))) (|HasCategory| (-142) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| (-142) (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| (-142) (QUOTE (-1063))) (-12 (|HasCategory| (-142) (QUOTE (-1063))) (|HasCategory| (-142) (LIST (QUOTE -300) (QUOTE (-142))))) (|HasCategory| (-142) (LIST (QUOTE -591) (QUOTE (-832))))) +(-1120 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (QUOTE (-1118))) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#1|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (QUOTE (-1063))) (|HasCategory| (-1118) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) -(-1120 A) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (QUOTE (-1119))) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#1|)))))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (QUOTE (-1063))) (|HasCategory| (-1119) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (LIST (QUOTE -591) (QUOTE (-832))))) +(-1121 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL ((|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) -(-1121 |Coef|) +(-1122 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1122 |Coef|) +(-1123 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1123 R UP) +(-1124 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p,{} q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p,{} q)} returns \\spad{[p0,{}...,{}pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p,{} q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-298)))) -(-1124 |n| R) +(-1125 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,{}\\spad{li})} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,{}\\spad{li},{}p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,{}\\spad{li},{}b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,{}ind,{}p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,{}\\spad{li},{}i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,{}\\spad{li},{}p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,{}s2,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,{}p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,{}\\spad{li},{}i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,{}\\spad{li},{}p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It\\spad{'s} length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) 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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}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . 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T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1136)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3694) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1136))))) (|HasSignature| |#1| (LIST (QUOTE -2267) (LIST (LIST (QUOTE -619) (QUOTE (-1136))) (|devaluate| |#1|))))))) +(-1135) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL NIL -(-1135) +(-1136) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,{}[a1,{}...,{}an])} or \\spad{s}([a1,{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s,{} [a1,{}...,{}an])} returns \\spad{s} arg-scripted by \\spad{[a1,{}...,{}an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s,{} [a1,{}...,{}an])} returns \\spad{s} superscripted by \\spad{[a1,{}...,{}an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s,{} [a1,{}...,{}an])} returns \\spad{s} subscripted by \\spad{[a1,{}...,{}an]}.")) 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(|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r,{} n)} returns the vector of the elementary symmetric functions in \\spad{[r,{}r,{}...,{}r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,{}...,{}rn])} returns the vector of the elementary symmetric functions in the \\spad{\\spad{ri}'s}: \\spad{[r1 + ... + rn,{} r1 r2 + ... + r(n-1) rn,{} ...,{} r1 r2 ... rn]}."))) NIL NIL -(-1137 R) +(-1138 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-6 -4326)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| (-940) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4326))) -(-1138) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-6 -4327)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-442))) (-12 (|HasCategory| (-940) (QUOTE (-130))) (|HasCategory| |#1| (QUOTE (-539)))) (-1530 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasAttribute| |#1| (QUOTE -4327))) +(-1139) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1139) +(-1140) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,{}tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,{}tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,{}t,{}tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,{}t,{}tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1140) +(-1141) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} building complete representation of Spad programs as objects of a term algebra built from ground terms of type integers,{} foats,{} symbols,{} and strings. This domain differs from InputForm in that it represents any entity in a Spad program,{} not just expressions. Related Constructors: Boolean,{} Integer,{} Float,{} Symbol,{} String,{} SExpression. See Also: SExpression,{} SetCategory. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if \\spad{`x'} really is a String") (((|Boolean|) $ (|[\|\|]| (|Symbol|))) "\\spad{x case Symbol} is \\spad{true} if \\spad{`x'} really is a Symbol") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if \\spad{`x'} really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if \\spad{`x'} really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when \\spad{`x'} is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in \\spad{`x'}.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Symbol|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax \\spad{`x'}. The value returned is itself a syntax if \\spad{`x'} really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when \\spad{`s'} is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).") (($ (|Symbol|) (|List| $)) "\\spad{buildSyntax(op,{} [a1,{} ...,{} an])} builds a syntax object for \\spad{op}(a1,{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.") (((|Symbol|) $) "\\spad{autoCoerce(s)} forcibly extracts a symbo from the Syntax domain \\spad{`s'}; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax \\spad{`s'}; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax \\spad{`s'}.") (($ (|String|)) "\\spad{coerce(s)} injects the string value \\spad{`s'} into the syntax domain") (((|Symbol|) $) "\\spad{coerce(s)} extracts a symbol from the syntax \\spad{`s'}.") (($ (|Symbol|)) "\\spad{coerce(s)} injects the symbol \\spad{`s'} into the Syntax domain.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax \\spad{`s'}.") (($ (|DoubleFloat|)) "\\spad{coerce(f)} injects the float value \\spad{`f'} into the Syntax domain") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax \\spad{`s'}") (($ (|Integer|)) "\\spad{coerce(i)} injects the integer value `i' into the Syntax domain.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when \\spad{`s'} is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1141 R) +(-1142 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,{}lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,{}v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,{}v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,{}lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,{}lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1142) +(-1143) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1143 S) +(-1144 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1144 S) +(-1145 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1145 |Key| |Entry|) +(-1146 |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}"))) -((-4328 . T) (-4329 . T)) -((-12 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3327) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1778) (|devaluate| |#2|)))))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1525 (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) -(-1146 R) +((-4329 . T) (-4330 . T)) +((-12 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -300) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3331) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -1786) (|devaluate| |#2|)))))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#2| (QUOTE (-1063)))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -592) (QUOTE (-523)))) (-12 (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-1063))) (-1530 (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#2| (LIST (QUOTE -591) (QUOTE (-832)))) (|HasCategory| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (LIST (QUOTE -591) (QUOTE (-832))))) +(-1147 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL NIL -(-1147 S |Key| |Entry|) +(-1148 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1148 |Key| |Entry|) +(-1149 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4329 . T) (-2609 . T)) +((-4330 . T) (-2618 . T)) NIL -(-1149 |Key| |Entry|) +(-1150 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1150) +(-1151) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1151 S) +(-1152 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1152) +(-1153) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL -(-1153) +(-1154) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,{}\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,{}s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1154 R) +(-1155 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1155) +(-1156) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1156 S) +(-1157 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1157) +(-1158) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1158 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}."))) -((-4329 . T) (-4328 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (-1159 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4330 . T) (-4329 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1063))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-1160 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1160) +(-1161) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1161 R -1410) +(-1162 R -1415) ((|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 -(-1162 R |Row| |Col| M) +(-1163 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,{}d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1163 R -1410) +(-1164 R -1415) ((|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 -592) (LIST (QUOTE -861) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -855) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -855) (|devaluate| |#1|))))) -(-1164 S R E V P) +(-1165 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-359)))) -(-1165 R E V P) +(-1166 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL -(-1166 |Coef|) +(-1167 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) -(-1167 |Curve|) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-145))) (|HasCategory| |#1| (QUOTE (-143))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-354)))) +(-1168 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,{}ll,{}b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,{}b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1168) +(-1169) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,{}n,{}b,{}r,{}lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,{}sin(n - 1) a],{}...,{}[cos 2 a,{}sin 2 a],{}[cos a,{}sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,{}q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,{}x2,{}x3,{}c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1169 S) +(-1170 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL ((|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1170 -1410) +(-1171 -1415) ((|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 -(-1171) +(-1172) ((|constructor| (NIL "This domain represents a type AST.")) (|coerce| (($ (|Syntax|)) "s::TypeAst injects \\spad{`s'} into the TypeAst domain."))) NIL NIL -(-1172) +(-1173) ((|constructor| (NIL "The fundamental Type."))) -((-2609 . T)) +((-2618 . T)) NIL -(-1173 S) +(-1174 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-821)))) -(-1174) +(-1175) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1175 S) +(-1176 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1176) +(-1177) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1177 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1178 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1178 |Coef|) +(-1179 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1179 S |Coef| UTS) +(-1180 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-354)))) -(-1180 |Coef| UTS) +(-1181 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-2609 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-2618 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1181 |Coef| UTS) +(-1182 |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)}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((-1525 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -277) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -503) (QUOTE (-1135)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-794)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-821)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-878)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-991)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-1111)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -300) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#2| (LIST (QUOTE -1007) 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for the factorization of univariate polynomials with integer coefficients. The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,{}flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1184 R S) +(-1185 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-819)))) -(-1185 S) +(-1186 S) ((|constructor| (NIL "This domain provides segments which may be half open. That is,{} ranges of the form \\spad{a..} or \\spad{a..b}.")) (|hasHi| (((|Boolean|) $) "\\spad{hasHi(s)} tests whether the segment \\spad{s} has an upper bound.")) (|coerce| (($ (|Segment| |#1|)) "\\spad{coerce(x)} allows \\spadtype{Segment} values to be used as \\%.")) (|segment| (($ |#1|) "\\spad{segment(l)} is an alternate way to construct the segment \\spad{l..}.")) (SEGMENT (($ |#1|) "\\spad{l..} produces a half open segment,{} that is,{} one with no upper bound."))) NIL ((|HasCategory| |#1| (QUOTE (-819))) (|HasCategory| |#1| (QUOTE (-1063)))) -(-1186 |x| R |y| S) +(-1187 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func,{} poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1187 R Q UP) +(-1188 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1188 R UP) +(-1189 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1189 R UP) +(-1190 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,{}g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1190 R U) +(-1191 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. 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T)) +((|HasCategory| |#2| (QUOTE (-878))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (-1530 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-539)))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-370)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-370))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -855) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -855) (QUOTE (-547))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-370)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -592) (LIST (QUOTE -861) (QUOTE (-547)))))) (-12 (|HasCategory| (-1045) (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -592) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (LIST (QUOTE -615) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-145))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (-1530 (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-1112))) (|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (-1530 (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| |#2| (QUOTE (-225))) (|HasAttribute| |#2| (QUOTE -4327)) (|HasCategory| |#2| (QUOTE (-442))) (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (-1530 (-12 (|HasCategory| $ (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-878)))) (|HasCategory| |#2| (QUOTE (-143))))) +(-1193 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{} p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1193 S R) +(-1194 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-1111)))) -(-1194 R) +((|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354))) (|HasCategory| |#2| (QUOTE (-442))) (|HasCategory| |#2| (QUOTE (-539))) (|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (QUOTE (-1112)))) +(-1195 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4324 |has| |#1| (-354)) (-4326 |has| |#1| (-6 -4326)) (-4323 . T) (-4322 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4325 |has| |#1| (-354)) (-4327 |has| |#1| (-6 -4327)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL -(-1195 S |Coef| |Expon|) +(-1196 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1075))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3835) (LIST (|devaluate| |#2|) (QUOTE (-1135)))))) -(-1196 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1075))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -3838) (LIST (|devaluate| |#2|) (QUOTE (-1136)))))) +(-1197 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1197 RC P) +(-1198 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1198 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1199 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1199 |Coef|) +(-1200 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,{}r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,{}st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1200 S |Coef| ULS) +(-1201 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1201 |Coef| ULS) +(-1202 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1202 |Coef| ULS) +(-1203 |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)}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) -(-1203 |Coef| |var| |cen|) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1136)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3694) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1136))))) (|HasSignature| |#1| (LIST (QUOTE -2267) (LIST (LIST (QUOTE -619) (QUOTE (-1136))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) +(-1204 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4326 |has| |#1| (-354)) (-4320 |has| |#1| (-354)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1525 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) -(-1204 R FE |var| |cen|) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4327 |has| |#1| (-354)) (-4321 |has| |#1| (-354)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#1| (QUOTE (-169))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547))) (|devaluate| |#1|)))) (|HasCategory| (-398 (-547)) (QUOTE (-1075))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-1530 (|HasCategory| |#1| (QUOTE (-354))) (|HasCategory| |#1| (QUOTE (-539)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1136)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -398) (QUOTE (-547)))))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3694) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1136))))) (|HasSignature| |#1| (LIST (QUOTE -2267) (LIST (LIST (QUOTE -619) (QUOTE (-1136))) (|devaluate| |#1|))))))) +(-1205 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))}."))) -(((-4330 "*") |has| (-1203 |#2| |#3| |#4|) (-169)) (-4321 |has| (-1203 |#2| |#3| |#4|) (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-354))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-442))) (-1525 (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| (-1203 |#2| |#3| |#4|) (QUOTE (-539)))) -(-1205 A S) +(((-4331 "*") |has| (-1204 |#2| |#3| |#4|) (-169)) (-4322 |has| (-1204 |#2| |#3| |#4|) (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| (-1204 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1204 |#2| |#3| |#4|) (QUOTE (-143))) (|HasCategory| (-1204 |#2| |#3| |#4|) (QUOTE (-145))) (|HasCategory| (-1204 |#2| |#3| |#4|) (QUOTE (-169))) (|HasCategory| (-1204 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1204 |#2| |#3| |#4|) (LIST (QUOTE -1007) (QUOTE (-547)))) (|HasCategory| (-1204 |#2| |#3| |#4|) (QUOTE (-354))) (|HasCategory| (-1204 |#2| |#3| |#4|) (QUOTE (-442))) (-1530 (|HasCategory| (-1204 |#2| |#3| |#4|) (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| (-1204 |#2| |#3| |#4|) (LIST (QUOTE -1007) (LIST (QUOTE -398) (QUOTE (-547)))))) (|HasCategory| (-1204 |#2| |#3| |#4|) (QUOTE (-539)))) +(-1206 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4329))) -(-1206 S) +((|HasAttribute| |#1| (QUOTE -4330))) +(-1207 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2609 . T)) +((-2618 . T)) NIL -(-1207 |Coef1| |Coef2| UTS1 UTS2) +(-1208 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1208 S |Coef|) +(-1209 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-547)))) (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-1157))) (|HasSignature| |#2| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2963) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1135))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354)))) -(-1209 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#2| (QUOTE (-928))) (|HasCategory| |#2| (QUOTE (-1158))) (|HasSignature| |#2| (LIST (QUOTE -2267) (LIST (LIST (QUOTE -619) (QUOTE (-1136))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3694) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1136))))) (|HasCategory| |#2| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#2| (QUOTE (-354)))) +(-1210 |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."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1210 |Coef| |var| |cen|) +(-1211 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4330 "*") |has| |#1| (-169)) (-4321 |has| |#1| (-539)) (-4322 . T) (-4323 . T) (-4325 . T)) -((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1525 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1135)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3835) (LIST (|devaluate| |#1|) (QUOTE (-1135)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1525 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1157))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -2963) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1135))))) (|HasSignature| |#1| (LIST (QUOTE -2259) (LIST (LIST (QUOTE -619) (QUOTE (-1135))) (|devaluate| |#1|))))))) -(-1211 |Coef| UTS) +(((-4331 "*") |has| |#1| (-169)) (-4322 |has| |#1| (-539)) (-4323 . T) (-4324 . T) (-4326 . T)) +((|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasCategory| |#1| (QUOTE (-539))) (-1530 (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-539)))) (|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-143))) (|HasCategory| |#1| (QUOTE (-145))) (-12 (|HasCategory| |#1| (LIST (QUOTE -869) (QUOTE (-1136)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-745)) (|devaluate| |#1|)))) (|HasCategory| (-745) (QUOTE (-1075))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasSignature| |#1| (LIST (QUOTE -3838) (LIST (|devaluate| |#1|) (QUOTE (-1136)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-745))))) (|HasCategory| |#1| (QUOTE (-354))) (-1530 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-547)))) (|HasCategory| |#1| (QUOTE (-928))) (|HasCategory| |#1| (QUOTE (-1158))) (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -38) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasSignature| |#1| (LIST (QUOTE -3694) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1136))))) (|HasSignature| |#1| (LIST (QUOTE -2267) (LIST (LIST (QUOTE -619) (QUOTE (-1136))) (|devaluate| |#1|))))))) +(-1212 |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 -(-1212 -1410 UP L UTS) +(-1213 -1415 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 (-539)))) -(-1213) +(-1214) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) -((-2609 . T)) +((-2618 . T)) NIL -(-1214 |sym|) +(-1215 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1215 S R) +(-1216 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL ((|HasCategory| |#2| (QUOTE (-971))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-701))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1216 R) +(-1217 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4329 . T) (-4328 . T) (-2609 . T)) +((-4330 . T) (-4329 . T) (-2618 . T)) NIL -(-1217 A B) +(-1218 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1218 R) +(-1219 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4329 . T) (-4328 . T)) -((-1525 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1525 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1525 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1219) +((-4330 . T) (-4329 . T)) +((-1530 (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|))))) (-1530 (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) (|HasCategory| |#1| (LIST (QUOTE -592) (QUOTE (-523)))) (-1530 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063)))) (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| (-547) (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-701))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-971))) (|HasCategory| |#1| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -300) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -591) (QUOTE (-832))))) +(-1220) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1220) +(-1221) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,{}c1,{}c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,{}i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,{}x,{}y,{}z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,{}s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,{}s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,{}s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,{}h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,{}d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,{}s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,{}dx,{}dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,{}sx,{}sy,{}sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,{}s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,{}th,{}phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,{}s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,{}s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,{}s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,{}s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}rotx,{}roty,{}rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,{}viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,{}th,{}phi,{}s,{}dx,{}dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,{}ind,{}pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,{}sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,{}lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,{}s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1221) +(-1222) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,{}h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,{}y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1222) +(-1223) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1223) +(-1224) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1224 A S) +(-1225 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1225 S) +(-1226 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-4323 . T) (-4322 . T)) +((-4324 . T) (-4323 . T)) NIL -(-1226 R) +(-1227 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1227 K R UP -1410) +(-1228 K R UP -1415) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-1228) +(-1229) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|Syntax|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|Syntax|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1229) +(-1230) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|Syntax|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1230 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1231 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) -((-4323 |has| |#1| (-169)) (-4322 |has| |#1| (-169)) (-4325 . T)) +((-4324 |has| |#1| (-169)) (-4323 |has| |#1| (-169)) (-4326 . T)) ((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354)))) -(-1231 R E V P) +(-1232 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4329 . T) (-4328 . T)) +((-4330 . T) (-4329 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#4| (LIST (QUOTE -300) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -592) (QUOTE (-523)))) (|HasCategory| |#4| (QUOTE (-1063))) (|HasCategory| |#1| (QUOTE (-539))) (|HasCategory| |#3| (QUOTE (-359))) (|HasCategory| |#4| (LIST (QUOTE -591) (QUOTE (-832))))) -(-1232 R) +(-1233 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) -((-4322 . T) (-4323 . T) (-4325 . T)) +((-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1233 |vl| R) +(-1234 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-4325 . T) (-4321 |has| |#2| (-6 -4321)) (-4323 . T) (-4322 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4321))) -(-1234 R |VarSet| XPOLY) +((-4326 . T) (-4322 |has| |#2| (-6 -4322)) (-4324 . T) (-4323 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4322))) +(-1235 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1235 |vl| R) +(-1236 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,{}n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,{}y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,{}r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,{}y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,{}w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,{}v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,{}y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,{}w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,{}v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,{}y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,{}w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4321 |has| |#2| (-6 -4321)) (-4323 . T) (-4322 . T) (-4325 . T)) +((-4322 |has| |#2| (-6 -4322)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL -(-1236 S -1410) +(-1237 S -1415) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-359))) (|HasCategory| |#2| (QUOTE (-143))) (|HasCategory| |#2| (QUOTE (-145)))) -(-1237 -1410) +(-1238 -1415) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4320 . T) (-4326 . T) (-4321 . T) ((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +((-4321 . T) (-4327 . T) (-4322 . T) ((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL -(-1238 |VarSet| R) +(-1239 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4321 |has| |#2| (-6 -4321)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -692) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasAttribute| |#2| (QUOTE -4321))) -(-1239 |vl| R) +((-4322 |has| |#2| (-6 -4322)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasCategory| |#2| (LIST (QUOTE -692) (LIST (QUOTE -398) (QUOTE (-547))))) (|HasAttribute| |#2| (QUOTE -4322))) +(-1240 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,{}n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4321 |has| |#2| (-6 -4321)) (-4323 . T) (-4322 . T) (-4325 . T)) +((-4322 |has| |#2| (-6 -4322)) (-4324 . T) (-4323 . T) (-4326 . T)) NIL -(-1240 R) +(-1241 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4321 |has| |#1| (-6 -4321)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasAttribute| |#1| (QUOTE -4321))) -(-1241 R E) +((-4322 |has| |#1| (-6 -4322)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasAttribute| |#1| (QUOTE -4322))) +(-1242 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4325 . T) (-4326 |has| |#1| (-6 -4326)) (-4321 |has| |#1| (-6 -4321)) (-4323 . T) (-4322 . T)) -((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasAttribute| |#1| (QUOTE -4325)) (|HasAttribute| |#1| (QUOTE -4326)) (|HasAttribute| |#1| (QUOTE -4321))) -(-1242 |VarSet| R) +((-4326 . T) (-4327 |has| |#1| (-6 -4327)) (-4322 |has| |#1| (-6 -4322)) (-4324 . T) (-4323 . T)) +((|HasCategory| |#1| (QUOTE (-169))) (|HasCategory| |#1| (QUOTE (-354))) (|HasAttribute| |#1| (QUOTE -4326)) (|HasAttribute| |#1| (QUOTE -4327)) (|HasAttribute| |#1| (QUOTE -4322))) +(-1243 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-4321 |has| |#2| (-6 -4321)) (-4323 . T) (-4322 . T) (-4325 . T)) -((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4321))) -(-1243 A) +((-4322 |has| |#2| (-6 -4322)) (-4324 . T) (-4323 . T) (-4326 . T)) +((|HasCategory| |#2| (QUOTE (-169))) (|HasAttribute| |#2| (QUOTE -4322))) +(-1244 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,{}n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1244 R |ls| |ls2|) +(-1245 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1245 R) +(-1246 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1246 |p|) +(-1247 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4330 "*") . T) (-4322 . T) (-4323 . T) (-4325 . T)) +(((-4331 "*") . T) (-4323 . T) (-4324 . T) (-4326 . T)) NIL NIL NIL @@ -4932,4 +4936,4 @@ NIL NIL NIL NIL -((-3 NIL 2255650 2255655 2255660 2255665) (-2 NIL 2255630 2255635 2255640 2255645) (-1 NIL 2255610 2255615 2255620 2255625) (0 NIL 2255590 2255595 2255600 2255605) (-1246 "ZMOD.spad" 2255399 2255412 2255528 2255585) (-1245 "ZLINDEP.spad" 2254443 2254454 2255389 2255394) (-1244 "ZDSOLVE.spad" 2244292 2244314 2254433 2254438) (-1243 "YSTREAM.spad" 2243785 2243796 2244282 2244287) (-1242 "XRPOLY.spad" 2243005 2243025 2243641 2243710) (-1241 "XPR.spad" 2240734 2240747 2242723 2242822) (-1240 "XPOLY.spad" 2240289 2240300 2240590 2240659) (-1239 "XPOLYC.spad" 2239606 2239622 2240215 2240284) (-1238 "XPBWPOLY.spad" 2238043 2238063 2239386 2239455) (-1237 "XF.spad" 2236504 2236519 2237945 2238038) (-1236 "XF.spad" 2234945 2234962 2236388 2236393) (-1235 "XFALG.spad" 2231969 2231985 2234871 2234940) (-1234 "XEXPPKG.spad" 2231220 2231246 2231959 2231964) (-1233 "XDPOLY.spad" 2230834 2230850 2231076 2231145) (-1232 "XALG.spad" 2230432 2230443 2230790 2230829) (-1231 "WUTSET.spad" 2226271 2226288 2230078 2230105) (-1230 "WP.spad" 2225285 2225329 2226129 2226196) (-1229 "WHILEAST.spad" 2225084 2225093 2225275 2225280) (-1228 "WHEREAST.spad" 2224757 2224766 2225074 2225079) (-1227 "WFFINTBS.spad" 2222320 2222342 2224747 2224752) (-1226 "WEIER.spad" 2220534 2220545 2222310 2222315) (-1225 "VSPACE.spad" 2220207 2220218 2220502 2220529) (-1224 "VSPACE.spad" 2219900 2219913 2220197 2220202) (-1223 "VOID.spad" 2219490 2219499 2219890 2219895) (-1222 "VIEW.spad" 2217112 2217121 2219480 2219485) (-1221 "VIEWDEF.spad" 2212309 2212318 2217102 2217107) (-1220 "VIEW3D.spad" 2196144 2196153 2212299 2212304) (-1219 "VIEW2D.spad" 2183881 2183890 2196134 2196139) (-1218 "VECTOR.spad" 2182556 2182567 2182807 2182834) (-1217 "VECTOR2.spad" 2181183 2181196 2182546 2182551) (-1216 "VECTCAT.spad" 2179071 2179082 2181139 2181178) (-1215 "VECTCAT.spad" 2176779 2176792 2178849 2178854) (-1214 "VARIABLE.spad" 2176559 2176574 2176769 2176774) (-1213 "UTYPE.spad" 2176193 2176202 2176539 2176554) (-1212 "UTSODETL.spad" 2175486 2175510 2176149 2176154) (-1211 "UTSODE.spad" 2173674 2173694 2175476 2175481) (-1210 "UTS.spad" 2168463 2168491 2172141 2172238) (-1209 "UTSCAT.spad" 2165914 2165930 2168361 2168458) (-1208 "UTSCAT.spad" 2163009 2163027 2165458 2165463) (-1207 "UTS2.spad" 2162602 2162637 2162999 2163004) (-1206 "URAGG.spad" 2157224 2157235 2162582 2162597) (-1205 "URAGG.spad" 2151820 2151833 2157180 2157185) (-1204 "UPXSSING.spad" 2149463 2149489 2150901 2151034) (-1203 "UPXS.spad" 2146490 2146518 2147595 2147744) (-1202 "UPXSCONS.spad" 2144247 2144267 2144622 2144771) (-1201 "UPXSCCA.spad" 2142705 2142725 2144093 2144242) (-1200 "UPXSCCA.spad" 2141305 2141327 2142695 2142700) (-1199 "UPXSCAT.spad" 2139886 2139902 2141151 2141300) (-1198 "UPXS2.spad" 2139427 2139480 2139876 2139881) (-1197 "UPSQFREE.spad" 2137839 2137853 2139417 2139422) (-1196 "UPSCAT.spad" 2135432 2135456 2137737 2137834) (-1195 "UPSCAT.spad" 2132731 2132757 2135038 2135043) (-1194 "UPOLYC.spad" 2127709 2127720 2132573 2132726) (-1193 "UPOLYC.spad" 2122579 2122592 2127445 2127450) (-1192 "UPOLYC2.spad" 2122048 2122067 2122569 2122574) (-1191 "UP.spad" 2119090 2119105 2119598 2119751) (-1190 "UPMP.spad" 2117980 2117993 2119080 2119085) (-1189 "UPDIVP.spad" 2117543 2117557 2117970 2117975) (-1188 "UPDECOMP.spad" 2115780 2115794 2117533 2117538) (-1187 "UPCDEN.spad" 2114987 2115003 2115770 2115775) (-1186 "UP2.spad" 2114349 2114370 2114977 2114982) (-1185 "UNISEG.spad" 2113702 2113713 2114268 2114273) (-1184 "UNISEG2.spad" 2113195 2113208 2113658 2113663) (-1183 "UNIFACT.spad" 2112296 2112308 2113185 2113190) (-1182 "ULS.spad" 2102850 2102878 2103943 2104372) (-1181 "ULSCONS.spad" 2096889 2096909 2097261 2097410) (-1180 "ULSCCAT.spad" 2094486 2094506 2096709 2096884) (-1179 "ULSCCAT.spad" 2092217 2092239 2094442 2094447) (-1178 "ULSCAT.spad" 2090433 2090449 2092063 2092212) (-1177 "ULS2.spad" 2089945 2089998 2090423 2090428) (-1176 "UFD.spad" 2089010 2089019 2089871 2089940) (-1175 "UFD.spad" 2088137 2088148 2089000 2089005) (-1174 "UDVO.spad" 2086984 2086993 2088127 2088132) (-1173 "UDPO.spad" 2084411 2084422 2086940 2086945) (-1172 "TYPE.spad" 2084333 2084342 2084391 2084406) (-1171 "TYPEAST.spad" 2084166 2084175 2084323 2084328) (-1170 "TWOFACT.spad" 2082816 2082831 2084156 2084161) (-1169 "TUPLE.spad" 2082202 2082213 2082715 2082720) (-1168 "TUBETOOL.spad" 2079039 2079048 2082192 2082197) (-1167 "TUBE.spad" 2077680 2077697 2079029 2079034) (-1166 "TS.spad" 2076269 2076285 2077245 2077342) (-1165 "TSETCAT.spad" 2063384 2063401 2076225 2076264) (-1164 "TSETCAT.spad" 2050497 2050516 2063340 2063345) (-1163 "TRMANIP.spad" 2044863 2044880 2050203 2050208) (-1162 "TRIMAT.spad" 2043822 2043847 2044853 2044858) (-1161 "TRIGMNIP.spad" 2042339 2042356 2043812 2043817) (-1160 "TRIGCAT.spad" 2041851 2041860 2042329 2042334) (-1159 "TRIGCAT.spad" 2041361 2041372 2041841 2041846) (-1158 "TREE.spad" 2039932 2039943 2040968 2040995) (-1157 "TRANFUN.spad" 2039763 2039772 2039922 2039927) (-1156 "TRANFUN.spad" 2039592 2039603 2039753 2039758) (-1155 "TOPSP.spad" 2039266 2039275 2039582 2039587) (-1154 "TOOLSIGN.spad" 2038929 2038940 2039256 2039261) (-1153 "TEXTFILE.spad" 2037486 2037495 2038919 2038924) (-1152 "TEX.spad" 2034503 2034512 2037476 2037481) (-1151 "TEX1.spad" 2034059 2034070 2034493 2034498) (-1150 "TEMUTL.spad" 2033614 2033623 2034049 2034054) (-1149 "TBCMPPK.spad" 2031707 2031730 2033604 2033609) (-1148 "TBAGG.spad" 2030731 2030754 2031675 2031702) (-1147 "TBAGG.spad" 2029775 2029800 2030721 2030726) (-1146 "TANEXP.spad" 2029151 2029162 2029765 2029770) (-1145 "TABLE.spad" 2027562 2027585 2027832 2027859) (-1144 "TABLEAU.spad" 2027043 2027054 2027552 2027557) (-1143 "TABLBUMP.spad" 2023826 2023837 2027033 2027038) (-1142 "SYSTEM.spad" 2023100 2023109 2023816 2023821) (-1141 "SYSSOLP.spad" 2020573 2020584 2023090 2023095) (-1140 "SYNTAX.spad" 2016765 2016774 2020563 2020568) (-1139 "SYMTAB.spad" 2014821 2014830 2016755 2016760) (-1138 "SYMS.spad" 2010806 2010815 2014811 2014816) (-1137 "SYMPOLY.spad" 2009813 2009824 2009895 2010022) (-1136 "SYMFUNC.spad" 2009288 2009299 2009803 2009808) (-1135 "SYMBOL.spad" 2006624 2006633 2009278 2009283) (-1134 "SWITCH.spad" 2003381 2003390 2006614 2006619) (-1133 "SUTS.spad" 2000280 2000308 2001848 2001945) (-1132 "SUPXS.spad" 1997294 1997322 1998412 1998561) (-1131 "SUP.spad" 1994063 1994074 1994844 1994997) (-1130 "SUPFRACF.spad" 1993168 1993186 1994053 1994058) (-1129 "SUP2.spad" 1992558 1992571 1993158 1993163) (-1128 "SUMRF.spad" 1991524 1991535 1992548 1992553) (-1127 "SUMFS.spad" 1991157 1991174 1991514 1991519) (-1126 "SULS.spad" 1981698 1981726 1982804 1983233) (-1125 "SUCH.spad" 1981378 1981393 1981688 1981693) (-1124 "SUBSPACE.spad" 1973385 1973400 1981368 1981373) (-1123 "SUBRESP.spad" 1972545 1972559 1973341 1973346) (-1122 "STTF.spad" 1968644 1968660 1972535 1972540) (-1121 "STTFNC.spad" 1965112 1965128 1968634 1968639) (-1120 "STTAYLOR.spad" 1957510 1957521 1964993 1964998) (-1119 "STRTBL.spad" 1956015 1956032 1956164 1956191) (-1118 "STRING.spad" 1955424 1955433 1955438 1955465) (-1117 "STRICAT.spad" 1955200 1955209 1955380 1955419) (-1116 "STREAM.spad" 1951968 1951979 1954725 1954740) (-1115 "STREAM3.spad" 1951513 1951528 1951958 1951963) (-1114 "STREAM2.spad" 1950581 1950594 1951503 1951508) (-1113 "STREAM1.spad" 1950285 1950296 1950571 1950576) (-1112 "STINPROD.spad" 1949191 1949207 1950275 1950280) (-1111 "STEP.spad" 1948392 1948401 1949181 1949186) (-1110 "STBL.spad" 1946918 1946946 1947085 1947100) (-1109 "STAGG.spad" 1945983 1945994 1946898 1946913) (-1108 "STAGG.spad" 1945056 1945069 1945973 1945978) (-1107 "STACK.spad" 1944407 1944418 1944663 1944690) (-1106 "SREGSET.spad" 1942111 1942128 1944053 1944080) (-1105 "SRDCMPK.spad" 1940656 1940676 1942101 1942106) (-1104 "SRAGG.spad" 1935741 1935750 1940612 1940651) (-1103 "SRAGG.spad" 1930858 1930869 1935731 1935736) (-1102 "SQMATRIX.spad" 1928482 1928500 1929390 1929477) (-1101 "SPLTREE.spad" 1923034 1923047 1927918 1927945) (-1100 "SPLNODE.spad" 1919622 1919635 1923024 1923029) (-1099 "SPFCAT.spad" 1918399 1918408 1919612 1919617) (-1098 "SPECOUT.spad" 1916949 1916958 1918389 1918394) (-1097 "spad-parser.spad" 1916414 1916423 1916939 1916944) (-1096 "SPACEC.spad" 1900427 1900438 1916404 1916409) (-1095 "SPACE3.spad" 1900203 1900214 1900417 1900422) (-1094 "SORTPAK.spad" 1899748 1899761 1900159 1900164) (-1093 "SOLVETRA.spad" 1897505 1897516 1899738 1899743) (-1092 "SOLVESER.spad" 1896025 1896036 1897495 1897500) (-1091 "SOLVERAD.spad" 1892035 1892046 1896015 1896020) (-1090 "SOLVEFOR.spad" 1890455 1890473 1892025 1892030) (-1089 "SNTSCAT.spad" 1890043 1890060 1890411 1890450) (-1088 "SMTS.spad" 1888303 1888329 1889608 1889705) (-1087 "SMP.spad" 1885742 1885762 1886132 1886259) (-1086 "SMITH.spad" 1884585 1884610 1885732 1885737) (-1085 "SMATCAT.spad" 1882683 1882713 1884517 1884580) (-1084 "SMATCAT.spad" 1880725 1880757 1882561 1882566) (-1083 "SKAGG.spad" 1879674 1879685 1880681 1880720) (-1082 "SINT.spad" 1877982 1877991 1879540 1879669) (-1081 "SIMPAN.spad" 1877710 1877719 1877972 1877977) (-1080 "SIG.spad" 1877038 1877047 1877700 1877705) (-1079 "SIGNRF.spad" 1876146 1876157 1877028 1877033) (-1078 "SIGNEF.spad" 1875415 1875432 1876136 1876141) (-1077 "SHP.spad" 1873333 1873348 1875371 1875376) (-1076 "SHDP.spad" 1864318 1864345 1864827 1864958) (-1075 "SGROUP.spad" 1863926 1863935 1864308 1864313) (-1074 "SGROUP.spad" 1863532 1863543 1863916 1863921) (-1073 "SGCF.spad" 1856413 1856422 1863522 1863527) (-1072 "SFRTCAT.spad" 1855329 1855346 1856369 1856408) (-1071 "SFRGCD.spad" 1854392 1854412 1855319 1855324) (-1070 "SFQCMPK.spad" 1849029 1849049 1854382 1854387) (-1069 "SFORT.spad" 1848464 1848478 1849019 1849024) (-1068 "SEXOF.spad" 1848307 1848347 1848454 1848459) (-1067 "SEX.spad" 1848199 1848208 1848297 1848302) (-1066 "SEXCAT.spad" 1845303 1845343 1848189 1848194) (-1065 "SET.spad" 1843603 1843614 1844724 1844763) (-1064 "SETMN.spad" 1842037 1842054 1843593 1843598) (-1063 "SETCAT.spad" 1841522 1841531 1842027 1842032) (-1062 "SETCAT.spad" 1841005 1841016 1841512 1841517) (-1061 "SETAGG.spad" 1837514 1837525 1840973 1841000) (-1060 "SETAGG.spad" 1834043 1834056 1837504 1837509) (-1059 "SEGXCAT.spad" 1833155 1833168 1834023 1834038) (-1058 "SEG.spad" 1832968 1832979 1833074 1833079) (-1057 "SEGCAT.spad" 1831787 1831798 1832948 1832963) (-1056 "SEGBIND.spad" 1830859 1830870 1831742 1831747) (-1055 "SEGBIND2.spad" 1830555 1830568 1830849 1830854) (-1054 "SEGAST.spad" 1830270 1830279 1830545 1830550) (-1053 "SEG2.spad" 1829695 1829708 1830226 1830231) (-1052 "SDVAR.spad" 1828971 1828982 1829685 1829690) (-1051 "SDPOL.spad" 1826361 1826372 1826652 1826779) (-1050 "SCPKG.spad" 1824440 1824451 1826351 1826356) (-1049 "SCOPE.spad" 1823585 1823594 1824430 1824435) (-1048 "SCACHE.spad" 1822267 1822278 1823575 1823580) (-1047 "SASTCAT.spad" 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"FLOAT.spad" 615288 615296 621990 622119) (-369 "FLOATCP.spad" 612705 612719 615278 615283) (-368 "FLINEXP.spad" 612417 612427 612685 612700) (-367 "FLINEXP.spad" 612083 612095 612353 612358) (-366 "FLASORT.spad" 611403 611415 612073 612078) (-365 "FLALG.spad" 609049 609068 611329 611398) (-364 "FLAGG.spad" 606055 606065 609017 609044) (-363 "FLAGG.spad" 602974 602986 605938 605943) (-362 "FLAGG2.spad" 601655 601671 602964 602969) (-361 "FINRALG.spad" 599684 599697 601611 601650) (-360 "FINRALG.spad" 597639 597654 599568 599573) (-359 "FINITE.spad" 596791 596799 597629 597634) (-358 "FINAALG.spad" 585772 585782 596733 596786) (-357 "FINAALG.spad" 574765 574777 585728 585733) (-356 "FILE.spad" 574348 574358 574755 574760) (-355 "FILECAT.spad" 572866 572883 574338 574343) (-354 "FIELD.spad" 572272 572280 572768 572861) (-353 "FIELD.spad" 571764 571774 572262 572267) (-352 "FGROUP.spad" 570373 570383 571744 571759) (-351 "FGLMICPK.spad" 569160 569175 570363 570368) (-350 "FFX.spad" 568535 568550 568876 568969) (-349 "FFSLPE.spad" 568024 568045 568525 568530) (-348 "FFPOLY.spad" 559276 559287 568014 568019) (-347 "FFPOLY2.spad" 558336 558353 559266 559271) (-346 "FFP.spad" 557733 557753 558052 558145) (-345 "FF.spad" 557181 557197 557414 557507) (-344 "FFNBX.spad" 555693 555713 556897 556990) (-343 "FFNBP.spad" 554206 554223 555409 555502) (-342 "FFNB.spad" 552671 552692 553887 553980) (-341 "FFINTBAS.spad" 550085 550104 552661 552666) (-340 "FFIELDC.spad" 547660 547668 549987 550080) (-339 "FFIELDC.spad" 545321 545331 547650 547655) (-338 "FFHOM.spad" 544069 544086 545311 545316) (-337 "FFF.spad" 541504 541515 544059 544064) (-336 "FFCGX.spad" 540351 540371 541220 541313) (-335 "FFCGP.spad" 539240 539260 540067 540160) (-334 "FFCG.spad" 538032 538053 538921 539014) (-333 "FFCAT.spad" 531059 531081 537871 538027) (-332 "FFCAT.spad" 524165 524189 530979 530984) (-331 "FFCAT2.spad" 523910 523950 524155 524160) (-330 "FEXPR.spad" 515619 515665 523666 523705) (-329 "FEVALAB.spad" 515325 515335 515609 515614) (-328 "FEVALAB.spad" 514816 514828 515102 515107) (-327 "FDIV.spad" 514258 514282 514806 514811) (-326 "FDIVCAT.spad" 512300 512324 514248 514253) (-325 "FDIVCAT.spad" 510340 510366 512290 512295) (-324 "FDIV2.spad" 509994 510034 510330 510335) (-323 "FCPAK1.spad" 508547 508555 509984 509989) (-322 "FCOMP.spad" 507926 507936 508537 508542) (-321 "FC.spad" 497751 497759 507916 507921) (-320 "FAXF.spad" 490686 490700 497653 497746) (-319 "FAXF.spad" 483673 483689 490642 490647) (-318 "FARRAY.spad" 481819 481829 482856 482883) (-317 "FAMR.spad" 479939 479951 481717 481814) (-316 "FAMR.spad" 478043 478057 479823 479828) (-315 "FAMONOID.spad" 477693 477703 477997 478002) (-314 "FAMONC.spad" 475915 475927 477683 477688) (-313 "FAGROUP.spad" 475521 475531 475811 475838) (-312 "FACUTIL.spad" 473717 473734 475511 475516) (-311 "FACTFUNC.spad" 472893 472903 473707 473712) (-310 "EXPUPXS.spad" 469726 469749 471025 471174) (-309 "EXPRTUBE.spad" 466954 466962 469716 469721) (-308 "EXPRODE.spad" 463826 463842 466944 466949) (-307 "EXPR.spad" 459101 459111 459815 460222) (-306 "EXPR2UPS.spad" 455193 455206 459091 459096) (-305 "EXPR2.spad" 454896 454908 455183 455188) (-304 "EXPEXPAN.spad" 451835 451860 452469 452562) (-303 "EXIT.spad" 451506 451514 451825 451830) (-302 "EXITAST.spad" 451243 451251 451496 451501) (-301 "EVALCYC.spad" 450701 450715 451233 451238) (-300 "EVALAB.spad" 450265 450275 450691 450696) (-299 "EVALAB.spad" 449827 449839 450255 450260) (-298 "EUCDOM.spad" 447369 447377 449753 449822) (-297 "EUCDOM.spad" 444973 444983 447359 447364) (-296 "ESTOOLS.spad" 436813 436821 444963 444968) (-295 "ESTOOLS2.spad" 436414 436428 436803 436808) (-294 "ESTOOLS1.spad" 436099 436110 436404 436409) (-293 "ES.spad" 428646 428654 436089 436094) (-292 "ES.spad" 421099 421109 428544 428549) (-291 "ESCONT.spad" 417872 417880 421089 421094) (-290 "ESCONT1.spad" 417621 417633 417862 417867) (-289 "ES2.spad" 417116 417132 417611 417616) (-288 "ES1.spad" 416682 416698 417106 417111) (-287 "ERROR.spad" 414003 414011 416672 416677) (-286 "EQTBL.spad" 412475 412497 412684 412711) (-285 "EQ.spad" 407349 407359 410148 410260) (-284 "EQ2.spad" 407065 407077 407339 407344) (-283 "EP.spad" 403379 403389 407055 407060) (-282 "ENV.spad" 402081 402089 403369 403374) (-281 "ENTIRER.spad" 401749 401757 402025 402076) (-280 "EMR.spad" 400950 400991 401675 401744) (-279 "ELTAGG.spad" 399190 399209 400940 400945) (-278 "ELTAGG.spad" 397394 397415 399146 399151) (-277 "ELTAB.spad" 396841 396859 397384 397389) (-276 "ELFUTS.spad" 396220 396239 396831 396836) (-275 "ELEMFUN.spad" 395909 395917 396210 396215) (-274 "ELEMFUN.spad" 395596 395606 395899 395904) (-273 "ELAGG.spad" 393527 393537 395564 395591) (-272 "ELAGG.spad" 391407 391419 393446 393451) (-271 "ELABEXPR.spad" 390338 390346 391397 391402) (-270 "EFUPXS.spad" 387114 387144 390294 390299) (-269 "EFULS.spad" 383950 383973 387070 387075) (-268 "EFSTRUC.spad" 381905 381921 383940 383945) (-267 "EF.spad" 376671 376687 381895 381900) (-266 "EAB.spad" 374947 374955 376661 376666) (-265 "E04UCFA.spad" 374483 374491 374937 374942) (-264 "E04NAFA.spad" 374060 374068 374473 374478) (-263 "E04MBFA.spad" 373640 373648 374050 374055) (-262 "E04JAFA.spad" 373176 373184 373630 373635) (-261 "E04GCFA.spad" 372712 372720 373166 373171) (-260 "E04FDFA.spad" 372248 372256 372702 372707) (-259 "E04DGFA.spad" 371784 371792 372238 372243) (-258 "E04AGNT.spad" 367626 367634 371774 371779) (-257 "DVARCAT.spad" 364311 364321 367616 367621) (-256 "DVARCAT.spad" 360994 361006 364301 364306) (-255 "DSMP.spad" 358425 358439 358730 358857) (-254 "DROPT.spad" 352370 352378 358415 358420) (-253 "DROPT1.spad" 352033 352043 352360 352365) (-252 "DROPT0.spad" 346860 346868 352023 352028) (-251 "DRAWPT.spad" 345015 345023 346850 346855) (-250 "DRAW.spad" 337615 337628 345005 345010) (-249 "DRAWHACK.spad" 336923 336933 337605 337610) (-248 "DRAWCX.spad" 334365 334373 336913 336918) (-247 "DRAWCURV.spad" 333902 333917 334355 334360) (-246 "DRAWCFUN.spad" 323074 323082 333892 333897) (-245 "DQAGG.spad" 321230 321240 323030 323069) (-244 "DPOLCAT.spad" 316571 316587 321098 321225) (-243 "DPOLCAT.spad" 311998 312016 316527 316532) (-242 "DPMO.spad" 305301 305317 305439 305740) (-241 "DPMM.spad" 298617 298635 298742 299043) (-240 "DOMAIN.spad" 297888 297896 298607 298612) (-239 "DMP.spad" 295110 295125 295682 295809) (-238 "DLP.spad" 294458 294468 295100 295105) (-237 "DLIST.spad" 292870 292880 293641 293668) (-236 "DLAGG.spad" 291271 291281 292850 292865) (-235 "DIVRING.spad" 290813 290821 291215 291266) (-234 "DIVRING.spad" 290399 290409 290803 290808) (-233 "DISPLAY.spad" 288579 288587 290389 290394) (-232 "DIRPROD.spad" 279433 279449 280073 280204) (-231 "DIRPROD2.spad" 278241 278259 279423 279428) (-230 "DIRPCAT.spad" 277171 277187 278093 278236) (-229 "DIRPCAT.spad" 275842 275860 276766 276771) (-228 "DIOSP.spad" 274667 274675 275832 275837) (-227 "DIOPS.spad" 273639 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"BTOURN.spad" 141460 141470 142064 142091) (-125 "BTCAT.spad" 140836 140846 141416 141455) (-124 "BTCAT.spad" 140244 140256 140826 140831) (-123 "BTAGG.spad" 139354 139362 140200 140239) (-122 "BTAGG.spad" 138496 138506 139344 139349) (-121 "BSTREE.spad" 137231 137241 138103 138130) (-120 "BRILL.spad" 135426 135437 137221 137226) (-119 "BRAGG.spad" 134340 134350 135406 135421) (-118 "BRAGG.spad" 133228 133240 134296 134301) (-117 "BPADICRT.spad" 131210 131222 131465 131558) (-116 "BPADIC.spad" 130874 130886 131136 131205) (-115 "BOUNDZRO.spad" 130530 130547 130864 130869) (-114 "BOP.spad" 125994 126002 130520 130525) (-113 "BOP1.spad" 123380 123390 125950 125955) (-112 "BOOLEAN.spad" 122704 122712 123370 123375) (-111 "BMODULE.spad" 122416 122428 122672 122699) (-110 "BITS.spad" 121835 121843 122052 122079) (-109 "BINFILE.spad" 121178 121186 121825 121830) (-108 "BINDING.spad" 120597 120605 121168 121173) (-107 "BINARY.spad" 118488 118496 119065 119158) (-106 "BGAGG.spad" 117673 117683 118456 118483) (-105 "BGAGG.spad" 116878 116890 117663 117668) (-104 "BFUNCT.spad" 116442 116450 116858 116873) (-103 "BEZOUT.spad" 115576 115603 116392 116397) (-102 "BBTREE.spad" 112395 112405 115183 115210) (-101 "BASTYPE.spad" 112067 112075 112385 112390) (-100 "BASTYPE.spad" 111737 111747 112057 112062) (-99 "BALFACT.spad" 111177 111189 111727 111732) (-98 "AUTOMOR.spad" 110624 110633 111157 111172) (-97 "ATTREG.spad" 107343 107350 110376 110619) (-96 "ATTRBUT.spad" 103366 103373 107323 107338) (-95 "ATTRAST.spad" 103084 103091 103356 103361) (-94 "ATRIG.spad" 102554 102561 103074 103079) (-93 "ATRIG.spad" 102022 102031 102544 102549) (-92 "ASTCAT.spad" 101926 101933 102012 102017) (-91 "ASTCAT.spad" 101828 101837 101916 101921) (-90 "ASTACK.spad" 101161 101170 101435 101462) (-89 "ASSOCEQ.spad" 99961 99972 101117 101122) (-88 "ASP9.spad" 99042 99055 99951 99956) (-87 "ASP8.spad" 98085 98098 99032 99037) (-86 "ASP80.spad" 97407 97420 98075 98080) (-85 "ASP7.spad" 96567 96580 97397 97402) (-84 "ASP78.spad" 96018 96031 96557 96562) (-83 "ASP77.spad" 95387 95400 96008 96013) (-82 "ASP74.spad" 94479 94492 95377 95382) (-81 "ASP73.spad" 93750 93763 94469 94474) (-80 "ASP6.spad" 92382 92395 93740 93745) (-79 "ASP55.spad" 90891 90904 92372 92377) (-78 "ASP50.spad" 88708 88721 90881 90886) (-77 "ASP4.spad" 88003 88016 88698 88703) (-76 "ASP49.spad" 87002 87015 87993 87998) (-75 "ASP42.spad" 85409 85448 86992 86997) (-74 "ASP41.spad" 83988 84027 85399 85404) (-73 "ASP35.spad" 82976 82989 83978 83983) (-72 "ASP34.spad" 82277 82290 82966 82971) (-71 "ASP33.spad" 81837 81850 82267 82272) (-70 "ASP31.spad" 80977 80990 81827 81832) (-69 "ASP30.spad" 79869 79882 80967 80972) (-68 "ASP29.spad" 79335 79348 79859 79864) (-67 "ASP28.spad" 70608 70621 79325 79330) (-66 "ASP27.spad" 69505 69518 70598 70603) (-65 "ASP24.spad" 68592 68605 69495 69500) (-64 "ASP20.spad" 67808 67821 68582 68587) (-63 "ASP1.spad" 67189 67202 67798 67803) (-62 "ASP19.spad" 61875 61888 67179 67184) (-61 "ASP12.spad" 61289 61302 61865 61870) (-60 "ASP10.spad" 60560 60573 61279 61284) (-59 "ARRAY2.spad" 59920 59929 60167 60194) (-58 "ARRAY1.spad" 58755 58764 59103 59130) (-57 "ARRAY12.spad" 57424 57435 58745 58750) (-56 "ARR2CAT.spad" 53074 53095 57380 57419) (-55 "ARR2CAT.spad" 48756 48779 53064 53069) (-54 "APPRULE.spad" 48000 48022 48746 48751) (-53 "APPLYORE.spad" 47615 47628 47990 47995) (-52 "ANY.spad" 45957 45964 47605 47610) (-51 "ANY1.spad" 45028 45037 45947 45952) (-50 "ANTISYM.spad" 43467 43483 45008 45023) (-49 "ANON.spad" 43164 43171 43457 43462) (-48 "AN.spad" 41465 41472 42980 43073) (-47 "AMR.spad" 39644 39655 41363 41460) (-46 "AMR.spad" 37660 37673 39381 39386) (-45 "ALIST.spad" 35072 35093 35422 35449) (-44 "ALGSC.spad" 34195 34221 34944 34997) (-43 "ALGPKG.spad" 29904 29915 34151 34156) (-42 "ALGMFACT.spad" 29093 29107 29894 29899) (-41 "ALGMANIP.spad" 26513 26528 28890 28895) (-40 "ALGFF.spad" 24828 24855 25045 25201) (-39 "ALGFACT.spad" 23949 23959 24818 24823) (-38 "ALGEBRA.spad" 23680 23689 23905 23944) (-37 "ALGEBRA.spad" 23443 23454 23670 23675) (-36 "ALAGG.spad" 22941 22962 23399 23438) (-35 "AHYP.spad" 22322 22329 22931 22936) (-34 "AGG.spad" 20621 20628 22302 22317) (-33 "AGG.spad" 18894 18903 20577 20582) (-32 "AF.spad" 17319 17334 18829 18834) (-31 "ADDAST.spad" 16999 17006 17309 17314) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2257496 2257501 2257506 2257511) (-2 NIL 2257476 2257481 2257486 2257491) (-1 NIL 2257456 2257461 2257466 2257471) (0 NIL 2257436 2257441 2257446 2257451) (-1247 "ZMOD.spad" 2257245 2257258 2257374 2257431) (-1246 "ZLINDEP.spad" 2256289 2256300 2257235 2257240) (-1245 "ZDSOLVE.spad" 2246138 2246160 2256279 2256284) (-1244 "YSTREAM.spad" 2245631 2245642 2246128 2246133) (-1243 "XRPOLY.spad" 2244851 2244871 2245487 2245556) (-1242 "XPR.spad" 2242580 2242593 2244569 2244668) (-1241 "XPOLY.spad" 2242135 2242146 2242436 2242505) (-1240 "XPOLYC.spad" 2241452 2241468 2242061 2242130) (-1239 "XPBWPOLY.spad" 2239889 2239909 2241232 2241301) (-1238 "XF.spad" 2238350 2238365 2239791 2239884) (-1237 "XF.spad" 2236791 2236808 2238234 2238239) (-1236 "XFALG.spad" 2233815 2233831 2236717 2236786) (-1235 "XEXPPKG.spad" 2233066 2233092 2233805 2233810) (-1234 "XDPOLY.spad" 2232680 2232696 2232922 2232991) (-1233 "XALG.spad" 2232278 2232289 2232636 2232675) (-1232 "WUTSET.spad" 2228117 2228134 2231924 2231951) (-1231 "WP.spad" 2227131 2227175 2227975 2228042) (-1230 "WHILEAST.spad" 2226930 2226939 2227121 2227126) (-1229 "WHEREAST.spad" 2226603 2226612 2226920 2226925) (-1228 "WFFINTBS.spad" 2224166 2224188 2226593 2226598) (-1227 "WEIER.spad" 2222380 2222391 2224156 2224161) (-1226 "VSPACE.spad" 2222053 2222064 2222348 2222375) (-1225 "VSPACE.spad" 2221746 2221759 2222043 2222048) (-1224 "VOID.spad" 2221336 2221345 2221736 2221741) (-1223 "VIEW.spad" 2218958 2218967 2221326 2221331) (-1222 "VIEWDEF.spad" 2214155 2214164 2218948 2218953) (-1221 "VIEW3D.spad" 2197990 2197999 2214145 2214150) (-1220 "VIEW2D.spad" 2185727 2185736 2197980 2197985) (-1219 "VECTOR.spad" 2184402 2184413 2184653 2184680) (-1218 "VECTOR2.spad" 2183029 2183042 2184392 2184397) (-1217 "VECTCAT.spad" 2180917 2180928 2182985 2183024) (-1216 "VECTCAT.spad" 2178625 2178638 2180695 2180700) (-1215 "VARIABLE.spad" 2178405 2178420 2178615 2178620) (-1214 "UTYPE.spad" 2178039 2178048 2178385 2178400) (-1213 "UTSODETL.spad" 2177332 2177356 2177995 2178000) (-1212 "UTSODE.spad" 2175520 2175540 2177322 2177327) (-1211 "UTS.spad" 2170309 2170337 2173987 2174084) (-1210 "UTSCAT.spad" 2167760 2167776 2170207 2170304) (-1209 "UTSCAT.spad" 2164855 2164873 2167304 2167309) (-1208 "UTS2.spad" 2164448 2164483 2164845 2164850) (-1207 "URAGG.spad" 2159070 2159081 2164428 2164443) (-1206 "URAGG.spad" 2153666 2153679 2159026 2159031) (-1205 "UPXSSING.spad" 2151309 2151335 2152747 2152880) (-1204 "UPXS.spad" 2148336 2148364 2149441 2149590) (-1203 "UPXSCONS.spad" 2146093 2146113 2146468 2146617) (-1202 "UPXSCCA.spad" 2144551 2144571 2145939 2146088) (-1201 "UPXSCCA.spad" 2143151 2143173 2144541 2144546) (-1200 "UPXSCAT.spad" 2141732 2141748 2142997 2143146) (-1199 "UPXS2.spad" 2141273 2141326 2141722 2141727) (-1198 "UPSQFREE.spad" 2139685 2139699 2141263 2141268) (-1197 "UPSCAT.spad" 2137278 2137302 2139583 2139680) (-1196 "UPSCAT.spad" 2134577 2134603 2136884 2136889) (-1195 "UPOLYC.spad" 2129555 2129566 2134419 2134572) (-1194 "UPOLYC.spad" 2124425 2124438 2129291 2129296) (-1193 "UPOLYC2.spad" 2123894 2123913 2124415 2124420) (-1192 "UP.spad" 2120936 2120951 2121444 2121597) (-1191 "UPMP.spad" 2119826 2119839 2120926 2120931) (-1190 "UPDIVP.spad" 2119389 2119403 2119816 2119821) (-1189 "UPDECOMP.spad" 2117626 2117640 2119379 2119384) (-1188 "UPCDEN.spad" 2116833 2116849 2117616 2117621) (-1187 "UP2.spad" 2116195 2116216 2116823 2116828) (-1186 "UNISEG.spad" 2115548 2115559 2116114 2116119) (-1185 "UNISEG2.spad" 2115041 2115054 2115504 2115509) (-1184 "UNIFACT.spad" 2114142 2114154 2115031 2115036) (-1183 "ULS.spad" 2104696 2104724 2105789 2106218) (-1182 "ULSCONS.spad" 2098735 2098755 2099107 2099256) (-1181 "ULSCCAT.spad" 2096332 2096352 2098555 2098730) (-1180 "ULSCCAT.spad" 2094063 2094085 2096288 2096293) (-1179 "ULSCAT.spad" 2092279 2092295 2093909 2094058) (-1178 "ULS2.spad" 2091791 2091844 2092269 2092274) (-1177 "UFD.spad" 2090856 2090865 2091717 2091786) (-1176 "UFD.spad" 2089983 2089994 2090846 2090851) (-1175 "UDVO.spad" 2088830 2088839 2089973 2089978) (-1174 "UDPO.spad" 2086257 2086268 2088786 2088791) (-1173 "TYPE.spad" 2086179 2086188 2086237 2086252) (-1172 "TYPEAST.spad" 2086012 2086021 2086169 2086174) (-1171 "TWOFACT.spad" 2084662 2084677 2086002 2086007) (-1170 "TUPLE.spad" 2084048 2084059 2084561 2084566) (-1169 "TUBETOOL.spad" 2080885 2080894 2084038 2084043) (-1168 "TUBE.spad" 2079526 2079543 2080875 2080880) (-1167 "TS.spad" 2078115 2078131 2079091 2079188) (-1166 "TSETCAT.spad" 2065230 2065247 2078071 2078110) (-1165 "TSETCAT.spad" 2052343 2052362 2065186 2065191) (-1164 "TRMANIP.spad" 2046709 2046726 2052049 2052054) (-1163 "TRIMAT.spad" 2045668 2045693 2046699 2046704) (-1162 "TRIGMNIP.spad" 2044185 2044202 2045658 2045663) (-1161 "TRIGCAT.spad" 2043697 2043706 2044175 2044180) (-1160 "TRIGCAT.spad" 2043207 2043218 2043687 2043692) (-1159 "TREE.spad" 2041778 2041789 2042814 2042841) (-1158 "TRANFUN.spad" 2041609 2041618 2041768 2041773) (-1157 "TRANFUN.spad" 2041438 2041449 2041599 2041604) (-1156 "TOPSP.spad" 2041112 2041121 2041428 2041433) (-1155 "TOOLSIGN.spad" 2040775 2040786 2041102 2041107) (-1154 "TEXTFILE.spad" 2039332 2039341 2040765 2040770) (-1153 "TEX.spad" 2036349 2036358 2039322 2039327) (-1152 "TEX1.spad" 2035905 2035916 2036339 2036344) (-1151 "TEMUTL.spad" 2035460 2035469 2035895 2035900) (-1150 "TBCMPPK.spad" 2033553 2033576 2035450 2035455) (-1149 "TBAGG.spad" 2032577 2032600 2033521 2033548) (-1148 "TBAGG.spad" 2031621 2031646 2032567 2032572) (-1147 "TANEXP.spad" 2030997 2031008 2031611 2031616) (-1146 "TABLE.spad" 2029408 2029431 2029678 2029705) (-1145 "TABLEAU.spad" 2028889 2028900 2029398 2029403) (-1144 "TABLBUMP.spad" 2025672 2025683 2028879 2028884) (-1143 "SYSTEM.spad" 2024946 2024955 2025662 2025667) (-1142 "SYSSOLP.spad" 2022419 2022430 2024936 2024941) (-1141 "SYNTAX.spad" 2018611 2018620 2022409 2022414) (-1140 "SYMTAB.spad" 2016667 2016676 2018601 2018606) (-1139 "SYMS.spad" 2012652 2012661 2016657 2016662) (-1138 "SYMPOLY.spad" 2011659 2011670 2011741 2011868) (-1137 "SYMFUNC.spad" 2011134 2011145 2011649 2011654) (-1136 "SYMBOL.spad" 2008470 2008479 2011124 2011129) (-1135 "SWITCH.spad" 2005227 2005236 2008460 2008465) (-1134 "SUTS.spad" 2002126 2002154 2003694 2003791) (-1133 "SUPXS.spad" 1999140 1999168 2000258 2000407) (-1132 "SUP.spad" 1995909 1995920 1996690 1996843) (-1131 "SUPFRACF.spad" 1995014 1995032 1995899 1995904) (-1130 "SUP2.spad" 1994404 1994417 1995004 1995009) (-1129 "SUMRF.spad" 1993370 1993381 1994394 1994399) (-1128 "SUMFS.spad" 1993003 1993020 1993360 1993365) (-1127 "SULS.spad" 1983544 1983572 1984650 1985079) (-1126 "SUCH.spad" 1983224 1983239 1983534 1983539) (-1125 "SUBSPACE.spad" 1975231 1975246 1983214 1983219) (-1124 "SUBRESP.spad" 1974391 1974405 1975187 1975192) (-1123 "STTF.spad" 1970490 1970506 1974381 1974386) (-1122 "STTFNC.spad" 1966958 1966974 1970480 1970485) (-1121 "STTAYLOR.spad" 1959356 1959367 1966839 1966844) (-1120 "STRTBL.spad" 1957861 1957878 1958010 1958037) (-1119 "STRING.spad" 1957270 1957279 1957284 1957311) (-1118 "STRICAT.spad" 1957046 1957055 1957226 1957265) (-1117 "STREAM.spad" 1953814 1953825 1956571 1956586) (-1116 "STREAM3.spad" 1953359 1953374 1953804 1953809) (-1115 "STREAM2.spad" 1952427 1952440 1953349 1953354) (-1114 "STREAM1.spad" 1952131 1952142 1952417 1952422) (-1113 "STINPROD.spad" 1951037 1951053 1952121 1952126) (-1112 "STEP.spad" 1950238 1950247 1951027 1951032) (-1111 "STBL.spad" 1948764 1948792 1948931 1948946) (-1110 "STAGG.spad" 1947829 1947840 1948744 1948759) (-1109 "STAGG.spad" 1946902 1946915 1947819 1947824) (-1108 "STACK.spad" 1946253 1946264 1946509 1946536) (-1107 "SREGSET.spad" 1943957 1943974 1945899 1945926) (-1106 "SRDCMPK.spad" 1942502 1942522 1943947 1943952) (-1105 "SRAGG.spad" 1937587 1937596 1942458 1942497) (-1104 "SRAGG.spad" 1932704 1932715 1937577 1937582) (-1103 "SQMATRIX.spad" 1930328 1930346 1931236 1931323) (-1102 "SPLTREE.spad" 1924880 1924893 1929764 1929791) (-1101 "SPLNODE.spad" 1921468 1921481 1924870 1924875) (-1100 "SPFCAT.spad" 1920245 1920254 1921458 1921463) (-1099 "SPECOUT.spad" 1918795 1918804 1920235 1920240) (-1098 "SPADXPT.spad" 1917411 1917420 1918775 1918790) (-1097 "spad-parser.spad" 1916876 1916885 1917401 1917406) (-1096 "SPACEC.spad" 1900889 1900900 1916866 1916871) (-1095 "SPACE3.spad" 1900665 1900676 1900879 1900884) (-1094 "SORTPAK.spad" 1900210 1900223 1900621 1900626) (-1093 "SOLVETRA.spad" 1897967 1897978 1900200 1900205) (-1092 "SOLVESER.spad" 1896487 1896498 1897957 1897962) (-1091 "SOLVERAD.spad" 1892497 1892508 1896477 1896482) (-1090 "SOLVEFOR.spad" 1890917 1890935 1892487 1892492) (-1089 "SNTSCAT.spad" 1890505 1890522 1890873 1890912) (-1088 "SMTS.spad" 1888765 1888791 1890070 1890167) (-1087 "SMP.spad" 1886204 1886224 1886594 1886721) (-1086 "SMITH.spad" 1885047 1885072 1886194 1886199) (-1085 "SMATCAT.spad" 1883145 1883175 1884979 1885042) (-1084 "SMATCAT.spad" 1881187 1881219 1883023 1883028) (-1083 "SKAGG.spad" 1880136 1880147 1881143 1881182) (-1082 "SINT.spad" 1878444 1878453 1880002 1880131) (-1081 "SIMPAN.spad" 1878172 1878181 1878434 1878439) (-1080 "SIG.spad" 1877500 1877509 1878162 1878167) (-1079 "SIGNRF.spad" 1876608 1876619 1877490 1877495) (-1078 "SIGNEF.spad" 1875877 1875894 1876598 1876603) (-1077 "SHP.spad" 1873795 1873810 1875833 1875838) (-1076 "SHDP.spad" 1864780 1864807 1865289 1865420) (-1075 "SGROUP.spad" 1864388 1864397 1864770 1864775) (-1074 "SGROUP.spad" 1863994 1864005 1864378 1864383) (-1073 "SGCF.spad" 1856875 1856884 1863984 1863989) (-1072 "SFRTCAT.spad" 1855791 1855808 1856831 1856870) (-1071 "SFRGCD.spad" 1854854 1854874 1855781 1855786) (-1070 "SFQCMPK.spad" 1849491 1849511 1854844 1854849) (-1069 "SFORT.spad" 1848926 1848940 1849481 1849486) (-1068 "SEXOF.spad" 1848769 1848809 1848916 1848921) (-1067 "SEX.spad" 1848661 1848670 1848759 1848764) (-1066 "SEXCAT.spad" 1845765 1845805 1848651 1848656) (-1065 "SET.spad" 1844065 1844076 1845186 1845225) (-1064 "SETMN.spad" 1842499 1842516 1844055 1844060) (-1063 "SETCAT.spad" 1841984 1841993 1842489 1842494) (-1062 "SETCAT.spad" 1841467 1841478 1841974 1841979) (-1061 "SETAGG.spad" 1837976 1837987 1841435 1841462) (-1060 "SETAGG.spad" 1834505 1834518 1837966 1837971) (-1059 "SEGXCAT.spad" 1833617 1833630 1834485 1834500) (-1058 "SEG.spad" 1833430 1833441 1833536 1833541) (-1057 "SEGCAT.spad" 1832249 1832260 1833410 1833425) (-1056 "SEGBIND.spad" 1831321 1831332 1832204 1832209) (-1055 "SEGBIND2.spad" 1831017 1831030 1831311 1831316) (-1054 "SEGAST.spad" 1830732 1830741 1831007 1831012) (-1053 "SEG2.spad" 1830157 1830170 1830688 1830693) (-1052 "SDVAR.spad" 1829433 1829444 1830147 1830152) (-1051 "SDPOL.spad" 1826823 1826834 1827114 1827241) (-1050 "SCPKG.spad" 1824902 1824913 1826813 1826818) (-1049 "SCOPE.spad" 1824047 1824056 1824892 1824897) (-1048 "SCACHE.spad" 1822729 1822740 1824037 1824042) (-1047 "SASTCAT.spad" 1822638 1822647 1822719 1822724) (-1046 "SASTCAT.spad" 1822545 1822556 1822628 1822633) (-1045 "SAOS.spad" 1822417 1822426 1822535 1822540) (-1044 "SAERFFC.spad" 1822130 1822150 1822407 1822412) (-1043 "SAE.spad" 1820305 1820321 1820916 1821051) (-1042 "SAEFACT.spad" 1820006 1820026 1820295 1820300) (-1041 "RURPK.spad" 1817647 1817663 1819996 1820001) (-1040 "RULESET.spad" 1817088 1817112 1817637 1817642) (-1039 "RULE.spad" 1815292 1815316 1817078 1817083) (-1038 "RULECOLD.spad" 1815144 1815157 1815282 1815287) (-1037 "RSETGCD.spad" 1811522 1811542 1815134 1815139) (-1036 "RSETCAT.spad" 1801294 1801311 1811478 1811517) (-1035 "RSETCAT.spad" 1791098 1791117 1801284 1801289) (-1034 "RSDCMPK.spad" 1789550 1789570 1791088 1791093) (-1033 "RRCC.spad" 1787934 1787964 1789540 1789545) (-1032 "RRCC.spad" 1786316 1786348 1787924 1787929) (-1031 "RPTAST.spad" 1786020 1786029 1786306 1786311) (-1030 "RPOLCAT.spad" 1765380 1765395 1785888 1786015) (-1029 "RPOLCAT.spad" 1744454 1744471 1764964 1764969) (-1028 "ROUTINE.spad" 1740317 1740326 1743101 1743128) (-1027 "ROMAN.spad" 1739549 1739558 1740183 1740312) (-1026 "ROIRC.spad" 1738629 1738661 1739539 1739544) (-1025 "RNS.spad" 1737532 1737541 1738531 1738624) (-1024 "RNS.spad" 1736521 1736532 1737522 1737527) (-1023 "RNG.spad" 1736256 1736265 1736511 1736516) (-1022 "RMODULE.spad" 1735894 1735905 1736246 1736251) (-1021 "RMCAT2.spad" 1735302 1735359 1735884 1735889) (-1020 "RMATRIX.spad" 1733981 1734000 1734469 1734508) (-1019 "RMATCAT.spad" 1729502 1729533 1733925 1733976) (-1018 "RMATCAT.spad" 1724925 1724958 1729350 1729355) (-1017 "RINTERP.spad" 1724813 1724833 1724915 1724920) (-1016 "RING.spad" 1724170 1724179 1724793 1724808) (-1015 "RING.spad" 1723535 1723546 1724160 1724165) (-1014 "RIDIST.spad" 1722919 1722928 1723525 1723530) (-1013 "RGCHAIN.spad" 1721498 1721514 1722404 1722431) (-1012 "RF.spad" 1719112 1719123 1721488 1721493) (-1011 "RFFACTOR.spad" 1718574 1718585 1719102 1719107) 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1483272 1483491 1483584) (-878 "PFECAT.spad" 1480926 1480934 1483186 1483255) (-877 "PFECAT.spad" 1478620 1478630 1480882 1480887) (-876 "PFBRU.spad" 1476490 1476502 1478610 1478615) (-875 "PFBR.spad" 1474028 1474051 1476480 1476485) (-874 "PERM.spad" 1469709 1469719 1473858 1473873) (-873 "PERMGRP.spad" 1464445 1464455 1469699 1469704) (-872 "PERMCAT.spad" 1462997 1463007 1464425 1464440) (-871 "PERMAN.spad" 1461529 1461543 1462987 1462992) (-870 "PENDTREE.spad" 1460802 1460812 1461158 1461163) (-869 "PDRING.spad" 1459293 1459303 1460782 1460797) (-868 "PDRING.spad" 1457792 1457804 1459283 1459288) (-867 "PDEPROB.spad" 1456749 1456757 1457782 1457787) (-866 "PDEPACK.spad" 1450751 1450759 1456739 1456744) (-865 "PDECOMP.spad" 1450213 1450230 1450741 1450746) (-864 "PDECAT.spad" 1448567 1448575 1450203 1450208) (-863 "PCOMP.spad" 1448418 1448431 1448557 1448562) (-862 "PBWLB.spad" 1447000 1447017 1448408 1448413) (-861 "PATTERN.spad" 1441431 1441441 1446990 1446995) (-860 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(-804 "OMSAGG.spad" 1362852 1362862 1363020 1363071) (-803 "OMPKG.spad" 1361464 1361472 1362842 1362847) (-802 "OM.spad" 1360429 1360437 1361454 1361459) (-801 "OMLO.spad" 1359854 1359866 1360315 1360354) (-800 "OMEXPR.spad" 1359688 1359698 1359844 1359849) (-799 "OMERR.spad" 1359231 1359239 1359678 1359683) (-798 "OMERRK.spad" 1358265 1358273 1359221 1359226) (-797 "OMENC.spad" 1357609 1357617 1358255 1358260) (-796 "OMDEV.spad" 1351898 1351906 1357599 1357604) (-795 "OMCONN.spad" 1351307 1351315 1351888 1351893) (-794 "OINTDOM.spad" 1351070 1351078 1351233 1351302) (-793 "OFMONOID.spad" 1347257 1347267 1351060 1351065) (-792 "ODVAR.spad" 1346518 1346528 1347247 1347252) (-791 "ODR.spad" 1345966 1345992 1346330 1346479) (-790 "ODPOL.spad" 1343312 1343322 1343652 1343779) (-789 "ODP.spad" 1334433 1334453 1334806 1334937) (-788 "ODETOOLS.spad" 1333016 1333035 1334423 1334428) (-787 "ODESYS.spad" 1330666 1330683 1333006 1333011) (-786 "ODERTRIC.spad" 1326607 1326624 1330623 1330628) (-785 "ODERED.spad" 1325994 1326018 1326597 1326602) (-784 "ODERAT.spad" 1323545 1323562 1325984 1325989) (-783 "ODEPRRIC.spad" 1320436 1320458 1323535 1323540) (-782 "ODEPROB.spad" 1319635 1319643 1320426 1320431) (-781 "ODEPRIM.spad" 1316909 1316931 1319625 1319630) (-780 "ODEPAL.spad" 1316285 1316309 1316899 1316904) (-779 "ODEPACK.spad" 1302887 1302895 1316275 1316280) (-778 "ODEINT.spad" 1302318 1302334 1302877 1302882) (-777 "ODEIFTBL.spad" 1299713 1299721 1302308 1302313) (-776 "ODEEF.spad" 1295080 1295096 1299703 1299708) (-775 "ODECONST.spad" 1294599 1294617 1295070 1295075) (-774 "ODECAT.spad" 1293195 1293203 1294589 1294594) (-773 "OCT.spad" 1291333 1291343 1292049 1292088) (-772 "OCTCT2.spad" 1290977 1290998 1291323 1291328) (-771 "OC.spad" 1288751 1288761 1290933 1290972) (-770 "OC.spad" 1286250 1286262 1288434 1288439) (-769 "OCAMON.spad" 1286098 1286106 1286240 1286245) (-768 "OASGP.spad" 1285913 1285921 1286088 1286093) (-767 "OAMONS.spad" 1285433 1285441 1285903 1285908) (-766 "OAMON.spad" 1285294 1285302 1285423 1285428) (-765 "OAGROUP.spad" 1285156 1285164 1285284 1285289) (-764 "NUMTUBE.spad" 1284743 1284759 1285146 1285151) (-763 "NUMQUAD.spad" 1272605 1272613 1284733 1284738) (-762 "NUMODE.spad" 1263741 1263749 1272595 1272600) (-761 "NUMINT.spad" 1261299 1261307 1263731 1263736) (-760 "NUMFMT.spad" 1260139 1260147 1261289 1261294) (-759 "NUMERIC.spad" 1252211 1252221 1259944 1259949) (-758 "NTSCAT.spad" 1250701 1250717 1252167 1252206) (-757 "NTPOLFN.spad" 1250246 1250256 1250618 1250623) (-756 "NSUP.spad" 1243256 1243266 1247796 1247949) (-755 "NSUP2.spad" 1242648 1242660 1243246 1243251) (-754 "NSMP.spad" 1238843 1238862 1239151 1239278) (-753 "NREP.spad" 1237215 1237229 1238833 1238838) (-752 "NPCOEF.spad" 1236461 1236481 1237205 1237210) (-751 "NORMRETR.spad" 1236059 1236098 1236451 1236456) (-750 "NORMPK.spad" 1233961 1233980 1236049 1236054) (-749 "NORMMA.spad" 1233649 1233675 1233951 1233956) (-748 "NONE.spad" 1233390 1233398 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T)) ((((-547) (-129)) . T)) ((((-832)) . T)) @@ -657,30 +657,30 @@ ((((-832)) . T)) ((((-832)) . T)) ((((-547) |#2|) . T)) -(((|#1| (-1116 |#1|)) |has| |#1| (-819))) +(((|#1| (-1117 |#1|)) |has| |#1| (-819))) (|has| |#1| (-1063)) (((|#1|) . T)) -(-12 (|has| |#1| (-354)) (|has| |#2| (-1111))) +(-12 (|has| |#1| (-354)) (|has| |#2| (-1112))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (|has| |#1| (-1063)) (((|#2|) . T)) ((((-523)) |has| |#2| (-592 (-523))) (((-861 (-370))) |has| |#2| (-592 (-861 (-370)))) (((-861 (-547))) |has| |#2| (-592 (-861 (-547))))) -(((|#4|) -1525 (|has| |#4| (-169)) (|has| |#4| (-354)))) -(((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)))) +(((|#4|) -1530 (|has| |#4| (-169)) (|has| |#4| (-354)))) +(((|#3|) -1530 (|has| |#3| (-169)) (|has| |#3| (-354)))) ((((-832)) . T)) (((|#1|) . 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T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -((($) -1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016)))) +((($) -1530 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((|#3|) -1530 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016)))) ((((-547) |#1|) . T)) (|has| (-398 |#2|) (-145)) (|has| (-398 |#2|) (-143)) @@ -693,31 +693,31 @@ (|has| |#1| (-539)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((((-832)) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) (|has| |#1| (-38 (-398 (-547)))) -((((-379) (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-379) (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . 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T)) (((|#2|) |has| |#2| (-169))) -((((-1135) (-52)) . T)) +((((-1136) (-52)) . T)) (((|#1|) . T)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) @@ -725,17 +725,17 @@ (((|#1|) |has| |#1| (-169))) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1530 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#2|) |has| |#2| (-300 |#2|))) (((#0=(-547) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) (((|#1|) . T)) -(((|#1| (-1131 |#1|)) . T)) +(((|#1| (-1132 |#1|)) . T)) (|has| $ (-145)) (((|#2|) . T)) (((#0=(-547) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) ((($) . T) (((-547)) . T) (((-398 (-547))) . T)) (|has| |#2| (-359)) -(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1530 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) @@ -743,27 +743,27 @@ (((|#1| |#2|) . 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T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(((#0=(-1210 |#1| |#2| |#3|) #0#) -12 (|has| (-1210 |#1| |#2| |#3|) (-300 (-1210 |#1| |#2| |#3|))) (|has| |#1| (-354))) (((-1135) #0#) -12 (|has| (-1210 |#1| |#2| |#3|) (-503 (-1135) (-1210 |#1| |#2| |#3|))) (|has| |#1| (-354)))) +(((#0=(-1211 |#1| |#2| |#3|) #0#) -12 (|has| (-1211 |#1| |#2| |#3|) (-300 (-1211 |#1| |#2| |#3|))) (|has| |#1| (-354))) (((-1136) #0#) -12 (|has| (-1211 |#1| |#2| |#3|) (-503 (-1136) (-1211 |#1| |#2| |#3|))) (|has| |#1| (-354)))) (-12 (|has| |#1| (-1063)) (|has| |#2| (-1063))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1530 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-398 (-547))) . T) (((-547)) . T)) ((((-547) (-142)) . T)) ((((-142)) . T)) (((|#1|) . T)) -(-1525 (|has| |#1| (-21)) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1530 (|has| |#1| (-21)) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((((-112)) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-112)) . T)) @@ -771,38 +771,38 @@ ((((-523)) |has| |#1| (-592 (-523))) (((-217)) . #0=(|has| |#1| (-991))) (((-370)) . #0#)) ((((-832)) . T)) (|has| |#1| (-794)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#1| (-821)) -(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-169)) (|has| |#1| (-539))) (|has| |#1| (-539)) (|has| |#1| (-878)) (((|#1|) . T)) (|has| |#1| (-1063)) ((((-832)) . 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T) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) . T)) +((($) . T) (((-398 (-547))) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) . T)) (|has| |#1| (-802)) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) (|has| |#1| (-1063)) @@ -828,10 +828,10 @@ (((|#3|) |has| |#3| (-1063))) (|has| |#3| (-359)) (((|#1|) . T) (((-832)) . T)) -((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1210 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) +((((-398 (-547))) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1530 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-1211 |#1| |#2| |#3|)) |has| |#1| (-354)) ((|#1|) |has| |#1| (-169))) ((((-832)) . T)) (((|#2|) . 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T)) -(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) -(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1530 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1530 (|has| |#2| (-767)) (|has| |#2| (-819))) (-12 (|has| |#1| (-767)) (|has| |#2| (-767))) (((|#1|) . T)) (-12 (|has| |#1| (-767)) (|has| |#2| (-767))) -(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1530 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -(|has| |#1| (-1157)) +(((|#2|) . T) (((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +(|has| |#1| (-1158)) (((#0=(-547) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) ((((-398 (-547))) . T) (($) . T)) (((|#4|) |has| |#4| (-1016))) @@ -1067,8 +1067,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-398 (-547)) #0#) . T)) (|has| |#1| (-354)) ((((-547)) . T) (((-398 (-547))) . T) (($) . T)) -((($ $) . T) ((#0=(-398 (-547)) #0#) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1| |#1|) . T)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((($ $) . T) ((#0=(-398 (-547)) #0#) -1530 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1| |#1|) . T)) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1|) . T) (($) . T) (((-398 (-547))) . T)) ((((-832)) . T)) ((((-832)) . T)) @@ -1083,25 +1083,25 @@ (((|#1| |#2|) . T)) (|has| |#1| (-819)) (|has| |#1| (-819)) -((($) . T) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) -(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) -(((#0=(-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) #0#) |has| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))))) +((($) . T) (((-398 (-547))) -1530 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . 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T)) ((((-547)) |has| #0=(-398 |#2|) (-615 (-547))) ((#0#) . T)) ((((-547) (-142)) . T)) -((((-547) (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T) ((|#1| |#2|) . T)) +((((-547) (-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T) ((|#1| |#2|) . T)) ((((-398 (-547))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((((-832)) . T)) ((((-879 |#1|)) . T)) (|has| |#1| (-354)) @@ -1113,45 +1113,45 @@ (|has| |#1| (-819)) (((|#1|) . T) (($) . T)) (|has| |#1| (-819)) -((((-1135)) |has| |#1| (-869 (-1135)))) -(((|#1| (-1135)) . T)) -(((|#1| (-1218 |#1|) (-1218 |#1|)) . T)) -((((-832)) . T) (((-1140)) . T)) +((((-1136)) |has| |#1| (-869 (-1136)))) +(((|#1| (-1136)) . T)) +(((|#1| (-1219 |#1|) (-1219 |#1|)) . T)) +((((-832)) . T) (((-1141)) . T)) (((|#1| |#2|) . T)) ((($ $) . T)) (|has| |#1| (-1063)) -(((|#1| (-1135) (-792 (-1135)) (-519 (-792 (-1135)))) . T)) +(((|#1| (-1136) (-792 (-1136)) (-519 (-792 (-1136)))) . 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T)) (|has| |#2| (-819)) (-12 (|has| |#2| (-225)) (|has| |#2| (-1016))) (|has| |#1| (-539)) -(|has| |#1| (-1111)) -((((-1118) |#1|) . T)) -(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -(((#0=(-398 (-547)) #0#) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1| |#1|) . T)) -((((-398 (-547))) |has| |#1| (-1007 (-547))) (((-547)) |has| |#1| (-1007 (-547))) (((-1135)) |has| |#1| (-1007 (-1135))) ((|#1|) . T)) +(|has| |#1| (-1112)) +((((-1119) |#1|) . T)) +(-1530 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(((#0=(-398 (-547)) #0#) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($ $) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1| |#1|) . T)) +((((-398 (-547))) |has| |#1| (-1007 (-547))) (((-547)) |has| |#1| (-1007 (-547))) (((-1136)) |has| |#1| (-1007 (-1136))) ((|#1|) . T)) ((((-547) |#2|) . T)) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) ((((-547)) |has| |#1| (-855 (-547))) (((-370)) |has| |#1| (-855 (-370)))) -((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1|) . T)) +((((-398 (-547))) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) ((|#1|) . T)) (((|#1|) . T)) ((((-619 |#4|)) . T) (((-832)) . T)) ((((-523)) |has| |#4| (-592 (-523)))) @@ -1163,21 +1163,21 @@ ((((-523)) |has| |#4| (-592 (-523)))) (((|#1|) . T)) (((|#2|) . T)) -((((-1135)) |has| (-398 |#2|) (-869 (-1135)))) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) +((((-1136)) |has| (-398 |#2|) (-869 (-1136)))) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) #0#) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-832)) -1525 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-591 (-832))) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) (((-1218 |#3|)) . T)) +((((-832)) -1530 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-591 (-832))) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) (((-1219 |#3|)) . T)) ((((-547) |#2|) . T)) -(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) -(((|#2| |#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($ $) |has| |#2| (-169))) +(-1530 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(((|#2| |#2|) -1530 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($ $) |has| |#2| (-169))) ((((-832)) . T)) ((((-832)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T) ((|#2|) . T)) ((((-832)) . T)) ((((-832)) . T)) -((((-1118) (-1135) (-547) (-217) (-832)) . T)) +((((-1119) (-1136) (-547) (-217) (-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) @@ -1209,8 +1209,8 @@ (|has| |#1| (-38 (-398 (-547)))) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($) |has| |#2| (-169))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +(((|#2|) -1530 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-1016))) (($) |has| |#2| (-169))) (|has| $ (-145)) ((((-398 |#2|)) . T)) ((((-398 (-547))) |has| #0=(-398 |#2|) (-1007 (-398 (-547)))) (((-547)) |has| #0# (-1007 (-547))) ((#0#) . T)) @@ -1221,20 +1221,20 @@ (((|#3|) |has| |#3| (-169))) (|has| |#1| (-145)) (|has| |#1| (-143)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-225)) -((((-832)) . T) (((-1140)) . T)) -((((-1135) (-52)) . T)) +((((-832)) . T) (((-1141)) . T)) +((((-1136) (-52)) . T)) ((((-832)) . T)) (((|#1| |#1|) . T)) -((((-1135)) |has| |#2| (-869 (-1135)))) +((((-1136)) |has| |#2| (-869 (-1136)))) ((((-547) (-112)) . T)) (|has| |#1| (-539)) (((|#2|) . T)) @@ -1257,23 +1257,23 @@ ((((-968 |#1|)) . T) ((|#1|) . T)) ((((-832)) . T)) ((((-832)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((((-398 (-547))) . T) (((-398 |#1|)) . T) ((|#1|) . T) (($) . T)) -(((|#1| (-1131 |#1|)) . T)) +(((|#1| (-1132 |#1|)) . T)) ((((-547)) . T) (($) . T) (((-398 (-547))) . T)) (((|#3|) . T) (($) . T)) (|has| |#1| (-821)) (((|#2|) . T)) ((((-547)) . T) (($) . T) (((-398 (-547))) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) ((((-547) |#2|) . T)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#2|) . T)) ((((-547) |#3|) . T)) (((|#2|) . T)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) +((((-1211 |#1| |#2| |#3|)) |has| |#1| (-354))) (|has| |#1| (-38 (-398 (-547)))) ((((-832)) . T)) (|has| |#1| (-1063)) @@ -1282,12 +1282,12 @@ (|has| |#1| (-38 (-398 (-547)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((#0=(-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) #0#) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-354)) (((|#2|) . T) (((-547)) |has| |#2| (-1007 (-547))) (((-398 (-547))) |has| |#2| (-1007 (-398 (-547))))) (((|#2|) . T)) -((((-1118) (-52)) . T)) +((((-1119) (-52)) . T)) (((|#2|) |has| |#2| (-169))) ((((-547) |#3|) . T)) ((((-547) (-142)) . T)) @@ -1307,27 +1307,27 @@ ((((-547)) |has| |#1| (-615 (-547))) ((|#1|) . T)) ((((-547)) |has| |#1| (-615 (-547))) ((|#1|) . T)) ((((-547)) |has| |#1| (-615 (-547))) ((|#1|) . T)) -((((-1118) (-52)) . T)) +((((-1119) (-52)) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1| |#2|) . T)) ((((-547) (-142)) . T)) -(((#0=(-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) #0#) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) -((($) -1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +(((#0=(-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) #0#) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) +((($) -1530 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (|has| |#1| (-821)) (((|#2| (-745) (-1045)) . T)) (((|#1| |#2|) . T)) -(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-169)) (|has| |#1| (-539))) (|has| |#1| (-765)) (((|#1|) |has| |#1| (-169))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-1525 (|has| |#1| (-145)) (-12 (|has| |#1| (-354)) (|has| |#2| (-145)))) -(-1525 (|has| |#1| (-143)) (-12 (|has| |#1| (-354)) (|has| |#2| (-143)))) +(-1530 (|has| |#1| (-145)) (-12 (|has| |#1| (-354)) (|has| |#2| (-145)))) +(-1530 (|has| |#1| (-143)) (-12 (|has| |#1| (-354)) (|has| |#2| (-143)))) (((|#4|) . T)) (|has| |#1| (-143)) -((((-1118) |#1|) . T)) +((((-1119) |#1|) . T)) (|has| |#1| (-145)) (((|#1|) . T)) ((((-547)) . T)) @@ -1336,25 +1336,25 @@ ((((-832)) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#3|) . T)) -((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) -(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) +((((-1211 |#1| |#2| |#3|)) |has| |#1| (-354))) +(-1530 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . 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T)) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) @@ -1362,7 +1362,7 @@ (|has| |#2| (-143)) (|has| |#2| (-145)) (|has| |#1| (-463)) -(-1525 (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +(-1530 (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1136))) (|has| |#1| (-1016))) (|has| |#1| (-354)) ((((-832)) . T)) (|has| |#1| (-38 (-398 (-547)))) @@ -1371,18 +1371,18 @@ (|has| |#1| (-819)) (|has| |#1| (-819)) ((((-832)) . 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T)) ((((-832)) . T)) ((((-832)) . T)) (|has| |#1| (-1063)) -(((|#2| (-472 (-3764 |#1|) (-745)) (-834 |#1|)) . T)) +(((|#2| (-472 (-3767 |#1|) (-745)) (-834 |#1|)) . T)) ((((-398 (-547))) . #0=(|has| |#2| (-354))) (($) . #0#)) -(((|#1| (-519 (-1135)) (-1135)) . T)) +(((|#1| (-519 (-1136)) (-1136)) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-832)) . T)) @@ -1400,22 +1400,22 @@ (|has| |#1| (-145)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) -((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-1135) (-52)) . T)) +(((|#1|) . T) (((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-2 (|:| -3331 (-1136)) (|:| -1786 (-52)))) . T)) +((((-1134 |#1| |#2| |#3|)) |has| |#1| (-354))) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . 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T)) @@ -1424,13 +1424,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) (((|#1|) |has| |#1| (-169))) (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) -(((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)))) +(((|#3|) -1530 (|has| |#3| (-169)) (|has| |#3| (-354)))) (|has| |#2| (-821)) (|has| |#1| (-821)) -(-1525 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-878))) +(-1530 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-878))) ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) ((((-547) |#2|) . T)) -(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)))) +(((|#2|) -1530 (|has| |#2| (-169)) (|has| |#2| (-354)))) (|has| |#1| (-340)) (((|#3| |#3|) -12 (|has| |#3| (-300 |#3|)) (|has| |#3| (-1063)))) ((($) . T) (((-398 (-547))) . T)) @@ -1438,7 +1438,7 @@ (|has| |#1| (-794)) (|has| |#1| (-794)) (((|#1|) . T)) -(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-819)) (|has| |#1| (-819)) (|has| |#1| (-819)) @@ -1447,16 +1447,16 @@ ((((-547)) . T) (($) . T) (((-398 (-547))) . T)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-38 (-398 (-547)))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-1135)) |has| |#1| (-869 (-1135))) (((-1045)) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-1136)) |has| |#1| (-869 (-1136))) (((-1045)) . T)) (((|#1|) . 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T)) (|has| |#1| (-1063)) -(-1525 (|has| |#2| (-794)) (|has| |#2| (-821))) +(-1530 (|has| |#2| (-794)) (|has| |#2| (-821))) (((|#1|) . T)) (((|#1|) |has| |#1| (-169)) (($) . T)) -((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) -1530 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1530 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((($) . T)) -((((-1133 |#1| |#2| |#3|)) -12 (|has| (-1133 |#1| |#2| |#3|) (-300 (-1133 |#1| |#2| |#3|))) (|has| |#1| (-354)))) +((((-1134 |#1| |#2| |#3|)) -12 (|has| (-1134 |#1| |#2| |#3|) (-300 (-1134 |#1| |#2| |#3|))) (|has| |#1| (-354)))) ((((-832)) . T)) -(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1530 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) ((($) . 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T)) (|has| |#1| (-878)) (|has| |#1| (-878)) (|has| |#1| (-878)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-878))) -(-1525 (|has| |#1| (-821)) (|has| |#1| (-1063))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-878))) +(-1530 (|has| |#1| (-821)) (|has| |#1| (-1063))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) ((($ $) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((($ $) . T)) ((((-547) (-112)) . T)) ((($) . T)) (((|#1|) . T)) ((((-547)) . T)) ((((-112)) . T)) -(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-38 (-398 (-547)))) (((|#1| (-547)) . T)) ((($) . T)) @@ -1597,30 +1597,30 @@ (((|#1|) . T)) ((((-547)) . T)) (((|#1| |#2|) . T)) -((((-1135)) |has| |#1| (-1016))) +((((-1136)) |has| |#1| (-1016))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (((|#1|) . T)) ((((-832)) . T)) (((|#1| (-547)) . T)) -(((|#1| (-1210 |#1| |#2| |#3|)) . T)) +(((|#1| (-1211 |#1| |#2| |#3|)) . T)) (((|#1|) . T)) (((|#1| (-398 (-547))) . T)) -(((|#1| (-1182 |#1| |#2| |#3|)) . T)) +(((|#1| (-1183 |#1| |#2| |#3|)) . T)) (((|#1| (-745)) . T)) (((|#1|) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((((-832)) . T)) (|has| |#1| (-1063)) -((((-1118) |#1|) . T)) +((((-1119) |#1|) . T)) ((($) . T)) (|has| |#2| (-145)) (|has| |#2| (-143)) -(((|#1| (-519 (-792 (-1135))) (-792 (-1135))) . T)) +(((|#1| (-519 (-792 (-1136))) (-792 (-1136))) . T)) ((((-832)) . T)) -((((-1204 |#1| |#2| |#3| |#4|)) . T)) -((((-1204 |#1| |#2| |#3| |#4|)) . T)) +((((-1205 |#1| |#2| |#3| |#4|)) . T)) +((((-1205 |#1| |#2| |#3| |#4|)) . T)) (((|#1|) |has| |#1| (-1016))) ((((-547) (-112)) . T)) ((((-832)) |has| |#1| (-1063))) @@ -1630,34 +1630,34 @@ (((|#1|) . T)) ((((-547)) . T)) ((((-832)) . T)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-340))) (|has| |#1| (-145)) ((((-832)) . T)) (((|#3|) . T)) -(-1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +(-1530 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((((-832)) . T)) -((((-1203 |#2| |#3| |#4|)) . T) (((-1204 |#1| |#2| |#3| |#4|)) . T)) +((((-1204 |#2| |#3| |#4|)) . T) (((-1205 |#1| |#2| |#3| |#4|)) . T)) ((((-832)) . T)) -((((-48)) -12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547)))) (((-590 $)) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) -1525 (-12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547)))) (|has| |#1| (-1007 (-398 (-547))))) (((-398 (-921 |#1|))) |has| |#1| (-539)) (((-921 |#1|)) |has| |#1| (-1016)) (((-1135)) . 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T)) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|))))) (((|#1|) |has| |#1| (-169))) ((($) |has| |#1| (-539)) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1063))) -(((|#2|) -1525 (|has| |#2| (-169)) (|has| |#2| (-354)))) -((((-1203 |#2| |#3| |#4|)) . T)) +(((|#2|) -1530 (|has| |#2| (-169)) (|has| |#2| (-354)))) +((((-1204 |#2| |#3| |#4|)) . T)) ((((-112)) . T)) (|has| |#1| (-794)) (|has| |#1| (-794)) @@ -1666,8 +1666,8 @@ (|has| |#1| (-819)) (|has| |#1| (-819)) (((|#1| (-547) (-1045)) . T)) -(-1525 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +(-1530 (|has| |#1| (-869 (-1136))) (|has| |#1| (-1016))) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#1| (-398 (-547)) (-1045)) . T)) (((|#1| (-745) (-1045)) . T)) (|has| |#1| (-821)) @@ -1683,28 +1683,28 @@ (((|#1|) . T)) (|has| |#1| (-1063)) ((((-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-615 (-547)))) ((|#2|) |has| |#1| (-354))) -(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1530 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) (((|#2|) |has| |#2| (-169))) (((|#1|) |has| |#1| (-169))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) ((((-832)) . T)) (|has| |#3| (-819)) ((((-832)) . T)) -((((-1203 |#2| |#3| |#4|) (-310 |#2| |#3| |#4|)) . T)) +((((-1204 |#2| |#3| |#4|) (-310 |#2| |#3| |#4|)) . T)) ((((-832)) . T)) -(((|#1| |#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) +(((|#1| |#1|) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) (((|#1|) . T)) ((((-547)) . T)) ((((-547)) . T)) -(((|#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) +(((|#1|) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-1016)))) (((|#2|) |has| |#2| (-354))) ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-354))) (|has| |#1| (-821)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) |has| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))))) -(-1525 (|has| |#1| (-442)) (|has| |#1| (-878))) +((((-2 (|:| -3331 (-1136)) (|:| -1786 (-52)))) |has| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (-300 (-2 (|:| -3331 (-1136)) (|:| -1786 (-52)))))) +(-1530 (|has| |#1| (-442)) (|has| |#1| (-878))) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) ((((-832)) . T)) ((((-832)) . T)) @@ -1718,13 +1718,13 @@ (((|#1|) . T)) (((|#1| (-547)) . T)) (|has| |#1| (-819)) -(((|#1| (-1133 |#1| |#2| |#3|)) . T)) +(((|#1| (-1134 |#1| |#2| |#3|)) . T)) (((|#1| |#1|) . T)) (((|#1| |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| (-398 (-547))) . T)) -(((|#1| (-1126 |#1| |#2| |#3|)) . T)) +(((|#1| (-1127 |#1| |#2| |#3|)) . T)) (((|#1| (-745)) . T)) (((|#1|) . T)) (((|#1| |#1| |#2| (-232 |#1| |#2|) (-232 |#1| |#2|)) . T)) @@ -1740,18 +1740,18 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (((|#1|) . T)) -(-1525 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1530 (|has| |#2| (-169)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) . T) (($ $) . T)) ((((-832)) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (|has| |#1| (-354)) (|has| |#1| (-354)) (|has| (-398 |#2|) (-225)) (|has| |#1| (-878)) (((|#2|) |has| |#2| (-1016))) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|))))) (|has| |#1| (-354)) (((|#1|) |has| |#1| (-169))) (((|#1| |#1|) . T)) @@ -1776,7 +1776,7 @@ (((|#1| (-398 (-547)) (-1045)) . T)) (((|#1| (-745) (-1045)) . T)) (((#0=(-398 |#2|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-547)) -1525 (|has| (-398 (-547)) (-1007 (-547))) (|has| |#1| (-1007 (-547)))) (((-398 (-547))) . T)) +(((|#1|) . T) (((-547)) -1530 (|has| (-398 (-547)) (-1007 (-547))) (|has| |#1| (-1007 (-547)))) (((-398 (-547))) . T)) (((|#1| (-580 |#1| |#3|) (-580 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) @@ -1795,24 +1795,24 @@ ((((-673)) . T)) (((|#2|) |has| |#2| (-169))) (|has| |#2| (-819)) -((((-112)) |has| |#1| (-1063)) (((-832)) -1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063)))) +((((-112)) |has| |#1| (-1063)) (((-832)) -1530 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1136))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 (-52)))) . T)) ((((-832)) . T)) ((((-547) |#1|) . T)) ((((-673)) . T) (((-398 (-547))) . T) (((-547)) . T)) (((|#1| |#1|) |has| |#1| (-169))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|))))) +(((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) (((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|))))) ((((-370)) . T)) ((((-673)) . T)) ((((-398 (-547))) . #0=(|has| |#2| (-354))) (($) . #0#)) (((|#1|) |has| |#1| (-169))) ((((-398 (-921 |#1|))) . T)) (((|#2| |#2|) . T)) -(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1530 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#2|) . T)) (|has| |#2| (-821)) (((|#3|) |has| |#3| (-1016))) @@ -1820,16 +1820,16 @@ (|has| |#1| (-878)) (|has| |#1| (-354)) (|has| |#1| (-821)) -((((-1135)) |has| |#2| (-869 (-1135)))) +((((-1136)) |has| |#2| (-869 (-1136)))) ((((-832)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((((-398 (-547))) . T) (($) . T)) (|has| |#1| (-463)) (|has| |#1| (-359)) (|has| |#1| (-359)) (|has| |#1| (-359)) (|has| |#1| (-354)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-463)) (|has| |#1| (-539)) (|has| |#1| (-1016)) (|has| |#1| (-1075))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-463)) (|has| |#1| (-539)) (|has| |#1| (-1016)) (|has| |#1| (-1075))) (|has| |#1| (-38 (-398 (-547)))) ((((-116 |#1|)) . T)) ((((-116 |#1|)) . T)) @@ -1850,11 +1850,11 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-821)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-145)) (|has| |#1| (-143)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) |has| (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)) (-300 (-2 (|:| -3327 |#1|) (|:| -1778 |#2|)))) ((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) |has| (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)) (-300 (-2 (|:| -3331 |#1|) (|:| -1786 |#2|)))) ((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#2|) . T)) (((|#3|) . T)) ((((-116 |#1|)) . T)) @@ -1872,11 +1872,11 @@ ((((-523)) |has| |#1| (-592 (-523))) (((-861 (-547))) |has| |#1| (-592 (-861 (-547)))) (((-861 (-370))) |has| |#1| (-592 (-861 (-370)))) (((-370)) . #0=(|has| |#1| (-991))) (((-217)) . #0#)) (((|#1|) |has| |#1| (-354))) ((((-832)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((($ $) . T) (((-590 $) $) . T)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) -((($) . T) (((-1204 |#1| |#2| |#3| |#4|)) . T) (((-398 (-547))) . T)) -((($) -1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) +((($) . T) (((-1205 |#1| |#2| |#3| |#4|)) . T) (((-398 (-547))) . T)) +((($) -1530 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-539))) (|has| |#1| (-354)) (|has| |#1| (-354)) (|has| |#1| (-354)) @@ -1887,27 +1887,27 @@ ((((-370)) . T)) (((|#3|) -12 (|has| |#3| (-300 |#3|)) (|has| |#3| (-1063)))) ((((-832)) . T)) -(-1525 (|has| |#2| (-442)) (|has| |#2| (-878))) +(-1530 (|has| |#2| (-442)) (|has| |#2| (-878))) (((|#1|) . T)) (|has| |#1| (-821)) (|has| |#1| (-821)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-523)) |has| |#1| (-592 (-523)))) (((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (|has| |#1| (-1063)) ((((-832)) . T)) -((((-1135)) . T) (((-832)) . T) (((-1140)) . T)) +((((-1136)) . T) (((-832)) . T) (((-1141)) . T)) ((((-398 (-547))) . T) (((-547)) . T) (((-590 $)) . T)) (|has| |#1| (-143)) (|has| |#1| (-145)) ((((-547)) . T)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) -(((#0=(-1203 |#2| |#3| |#4|)) . T) (((-398 (-547))) |has| #0# (-38 (-398 (-547)))) (($) . T)) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) +(((#0=(-1204 |#2| |#3| |#4|)) . T) (((-398 (-547))) |has| #0# (-38 (-398 (-547)))) (($) . T)) ((((-547)) . T)) (|has| |#1| (-354)) -(-1525 (-12 (|has| (-1210 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) -(-1525 (-12 (|has| (-1210 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) +(-1530 (-12 (|has| (-1211 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) +(-1530 (-12 (|has| (-1211 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) (|has| |#1| (-354)) (|has| |#1| (-143)) (|has| |#1| (-145)) @@ -1924,19 +1924,19 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) (((|#3|) |has| |#3| (-169))) -(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(-1530 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) ((((-832)) . T)) ((((-547)) . T)) (((|#1| $) |has| |#1| (-277 |#1| |#1|))) ((((-398 (-547))) . T) (($) . T) (((-398 |#1|)) . T) ((|#1|) . T)) ((((-832)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -1525 (|has| |#1| (-281)) (|has| |#1| (-354))) ((#0=(-398 (-547)) #0#) |has| |#1| (-354))) -((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) +(((|#1| |#1|) . T) (($ $) -1530 (|has| |#1| (-281)) (|has| |#1| (-354))) ((#0=(-398 (-547)) #0#) |has| |#1| (-354))) +((((-2 (|:| -3331 (-1136)) (|:| -1786 (-52)))) . T)) ((($) . T)) ((((-547) |#1|) . T)) -((((-1135)) |has| (-398 |#2|) (-869 (-1135)))) -(((|#1|) . T) (($) -1525 (|has| |#1| (-281)) (|has| |#1| (-354))) (((-398 (-547))) |has| |#1| (-354))) +((((-1136)) |has| (-398 |#2|) (-869 (-1136)))) +(((|#1|) . T) (($) -1530 (|has| |#1| (-281)) (|has| |#1| (-354))) (((-398 (-547))) |has| |#1| (-354))) ((((-523)) |has| |#2| (-592 (-523)))) ((((-663 |#2|)) . T) (((-832)) . T)) (((|#1|) . T)) @@ -1944,8 +1944,8 @@ (((|#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) ((((-839 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1525 (|has| |#4| (-767)) (|has| |#4| (-819))) -(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1530 (|has| |#4| (-767)) (|has| |#4| (-819))) +(-1530 (|has| |#3| (-767)) (|has| |#3| (-819))) ((((-832)) . T)) ((((-832)) . T)) (((|#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) @@ -1961,17 +1961,17 @@ ((((-398 (-547))) . T) (($) . T)) ((((-398 (-547))) . T) (($) . T)) ((((-398 (-547))) . T) (($) . T)) -(-1525 (|has| |#1| (-442)) (|has| |#1| (-1176))) +(-1530 (|has| |#1| (-442)) (|has| |#1| (-1177))) ((($) . T)) ((((-398 (-547))) |has| #0=(-398 |#2|) (-1007 (-398 (-547)))) (((-547)) |has| #0# (-1007 (-547))) ((#0#) . T)) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) (((|#1| (-745)) . T)) (|has| |#1| (-821)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) -((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) +((($) -1530 (|has| |#1| (-354)) (|has| |#1| (-340))) (((-398 (-547))) -1530 (|has| |#1| (-354)) (|has| |#1| (-340))) ((|#1|) . T)) ((((-547)) . T)) (|has| |#1| (-38 (-398 (-547)))) -((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))))) +((((-2 (|:| -3331 (-1119)) (|:| -1786 (-52)))) |has| (-2 (|:| -3331 (-1119)) (|:| -1786 (-52))) (-300 (-2 (|:| -3331 (-1119)) (|:| -1786 (-52)))))) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (|has| |#1| (-819)) (|has| |#1| (-38 (-398 (-547)))) @@ -1996,24 +1996,24 @@ (((|#1| |#2|) . T)) ((((-142)) . T)) ((((-754 |#1| (-834 |#2|))) . T)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -(|has| |#1| (-1157)) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +(|has| |#1| (-1158)) (((|#1|) . T)) -(-1525 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) -((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|))) +(-1530 (|has| |#3| (-25)) (|has| |#3| (-130)) (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-359)) (|has| |#3| (-701)) (|has| |#3| (-767)) (|has| |#3| (-819)) (|has| |#3| (-1016)) (|has| |#3| (-1063))) +((((-1136) |#1|) |has| |#1| (-503 (-1136) |#1|))) (((|#2|) . T)) -((($ $) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) -((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($ $) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) |has| |#1| (-38 (-398 (-547))))) +((($) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-879 |#1|)) . T)) ((($) . T)) ((((-398 (-921 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-523)) |has| |#4| (-592 (-523)))) ((((-832)) . T) (((-619 |#4|)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-819)) -(((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) (((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) |has| (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|)) (-300 (-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))))) +(((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063))) (((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) |has| (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|)) (-300 (-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))))) (|has| |#1| (-1063)) (|has| |#1| (-354)) (|has| |#1| (-821)) @@ -2021,17 +2021,17 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-398 (-547))) . T)) -((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) +((($) -1530 (|has| |#1| (-354)) (|has| |#1| (-539))) (((-398 (-547))) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#1|) |has| |#1| (-169))) (|has| |#1| (-143)) (|has| |#1| (-145)) -(-1525 (-12 (|has| (-1133 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) -(-1525 (-12 (|has| (-1133 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) +(-1530 (-12 (|has| (-1134 |#1| |#2| |#3|) (-145)) (|has| |#1| (-354))) (|has| |#1| (-145))) +(-1530 (-12 (|has| (-1134 |#1| |#2| |#3|) (-143)) (|has| |#1| (-354))) (|has| |#1| (-143))) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-145)) (|has| |#1| (-143)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-1211 |#1| |#2| |#3|)) |has| |#1| (-354))) (|has| |#1| (-819)) (((|#1| |#2|) . T)) (((|#1|) . T) (((-547)) |has| |#1| (-615 (-547)))) @@ -2053,9 +2053,9 @@ ((((-832)) . T)) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) -(((|#1|) -1525 (|has| |#1| (-169)) (|has| |#1| (-354)))) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-1136) |#1|) |has| |#1| (-503 (-1136) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) +(((|#1|) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)))) ((((-307 |#1|)) . T)) (((|#2|) |has| |#2| (-354))) (((|#2|) . T)) @@ -2066,8 +2066,8 @@ (((|#2|) |has| |#2| (-169))) (((|#1|) |has| |#1| (-169))) (((|#2|) . T)) -((((-1135)) |has| |#1| (-869 (-1135))) (((-1045)) . T)) -((((-1135)) |has| |#1| (-869 (-1135))) (((-1052 (-1135))) . T)) +((((-1136)) |has| |#1| (-869 (-1136))) (((-1045)) . T)) +((((-1136)) |has| |#1| (-869 (-1136))) (((-1052 (-1136))) . T)) (((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (|has| |#1| (-38 (-398 (-547)))) @@ -2076,13 +2076,13 @@ (|has| |#1| (-143)) (|has| |#1| (-145)) ((($ $) . T)) -(-1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) +(-1530 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1136))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) (|has| |#1| (-539)) (((|#2|) . T)) ((((-547)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#1|) . T)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) ((((-561 |#1|)) . T)) ((($) . T)) (((|#1| (-58 |#1|) (-58 |#1|)) . T)) @@ -2091,7 +2091,7 @@ ((($) . T)) (((|#1|) . T)) ((((-832)) . T)) -(((|#2|) |has| |#2| (-6 (-4330 "*")))) +(((|#2|) |has| |#2| (-6 (-4331 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2099,26 +2099,26 @@ ((((-398 (-547))) |has| |#2| (-1007 (-398 (-547)))) (((-547)) |has| |#2| (-1007 (-547))) ((|#2|) . T) (((-834 |#1|)) . T)) ((($) . T) (((-116 |#1|)) . T) (((-398 (-547))) . T)) ((((-1087 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) -((((-1131 |#1|)) . T) (((-1045)) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) -((((-1087 |#1| (-1135))) . T) (((-1052 (-1135))) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-1135)) . T)) +((((-1132 |#1|)) . T) (((-1045)) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) +((((-1087 |#1| (-1136))) . T) (((-1052 (-1136))) . T) ((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-1136)) . T)) (|has| |#1| (-1063)) ((($) . T)) (|has| |#1| (-1063)) ((((-547)) -12 (|has| |#1| (-855 (-547))) (|has| |#2| (-855 (-547)))) (((-370)) -12 (|has| |#1| (-855 (-370))) (|has| |#2| (-855 (-370))))) (((|#1| |#2|) . T)) -((((-1135) |#1|) . T)) +((((-1136) |#1|) . T)) (((|#4|) . T)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) -((((-1135) (-52)) . T)) -((((-1203 |#2| |#3| |#4|) (-310 |#2| |#3| |#4|)) . T)) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-340))) +((((-1136) (-52)) . T)) +((((-1204 |#2| |#3| |#4|) (-310 |#2| |#3| |#4|)) . T)) ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T)) ((((-832)) . T)) -(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) -(((#0=(-1204 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) +(-1530 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-359)) (|has| |#2| (-701)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016)) (|has| |#2| (-1063))) +(((#0=(-1205 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-169)) ((#0=(-398 (-547)) #0#) |has| |#1| (-539)) (($ $) |has| |#1| (-539))) (((|#1|) . T) (($) . T) (((-398 (-547))) . T)) (((|#1| $) |has| |#1| (-277 |#1| |#1|))) -((((-1204 |#1| |#2| |#3| |#4|)) . T) (((-398 (-547))) . T) (($) . T)) +((((-1205 |#1| |#2| |#3| |#4|)) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-539)) (($) |has| |#1| (-539))) (|has| |#1| (-354)) (|has| |#1| (-143)) @@ -2128,33 +2128,33 @@ ((((-398 (-547))) . T) (($) . T)) (((|#3|) |has| |#3| (-354))) (((|#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) -((((-1135)) . T)) +((((-1136)) . T)) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063)))) (((|#2| |#3|) . T)) -(-1525 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1530 (|has| |#2| (-354)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) (((|#1| (-519 |#2|)) . T)) (((|#1| (-745)) . T)) -(((|#1| (-519 (-1052 (-1135)))) . T)) +(((|#1| (-519 (-1052 (-1136)))) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) (|has| |#2| (-878)) -(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1530 (|has| |#2| (-767)) (|has| |#2| (-819))) ((((-832)) . T)) -((($ $) . T) ((#0=(-1203 |#2| |#3| |#4|) #0#) . T) ((#1=(-398 (-547)) #1#) |has| #0# (-38 (-398 (-547))))) +((($ $) . T) ((#0=(-1204 |#2| |#3| |#4|) #0#) . T) ((#1=(-398 (-547)) #1#) |has| #0# (-38 (-398 (-547))))) ((((-879 |#1|)) . T)) (-12 (|has| |#1| (-354)) (|has| |#2| (-794))) ((($) . T) (((-398 (-547))) . T)) ((($) . T)) ((($) . T)) (|has| |#1| (-354)) -(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340)) (|has| |#1| (-539))) (|has| |#1| (-354)) -((($) . T) ((#0=(-1203 |#2| |#3| |#4|)) . T) (((-398 (-547))) |has| #0# (-38 (-398 (-547))))) +((($) . T) ((#0=(-1204 |#2| |#3| |#4|)) . T) (((-398 (-547))) |has| #0# (-38 (-398 (-547))))) (((|#1| |#2|) . T)) -((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) -(-1525 (-12 (|has| |#1| (-298)) (|has| |#1| (-878))) (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1525 (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016))) +((((-1134 |#1| |#2| |#3|)) |has| |#1| (-354))) +(-1530 (-12 (|has| |#1| (-298)) (|has| |#1| (-878))) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-869 (-1136))) (|has| |#1| (-1016))) ((((-547)) |has| |#1| (-615 (-547))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-832)) . T)) @@ -2182,31 +2182,31 @@ ((($ $) . T)) ((($) . T)) ((((-832)) . T)) -(((|#1| (-519 (-1135))) . T)) +(((|#1| (-519 (-1136))) . T)) (((|#1|) |has| |#1| (-169))) ((((-832)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) -(((|#2|) -1525 (|has| |#2| (-6 (-4330 "*"))) (|has| |#2| (-169)))) -(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) -(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(((|#2|) -1530 (|has| |#2| (-6 (-4331 "*"))) (|has| |#2| (-169)))) +(-1530 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1530 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#2| (-821)) (|has| |#2| (-878)) (|has| |#1| (-878)) (((|#2|) |has| |#2| (-169))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-1210 |#1| |#2| |#3|)) |has| |#1| (-354))) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-1211 |#1| |#2| |#3|)) |has| |#1| (-354))) ((((-832)) . T)) ((((-832)) . T)) ((((-523)) . T) (((-547)) . T) (((-861 (-547))) . T) (((-370)) . T) (((-217)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 (-52)))) . T)) (((|#1|) . T)) ((((-832)) . T)) (((|#1| |#2|) . T)) (((|#1| (-398 (-547))) . T)) (((|#1|) . T)) -(-1525 (|has| |#1| (-281)) (|has| |#1| (-354))) +(-1530 (|has| |#1| (-281)) (|has| |#1| (-354))) ((((-142)) . T)) ((((-398 |#2|)) . T) (((-398 (-547))) . T) (($) . T)) (|has| |#1| (-819)) @@ -2221,19 +2221,19 @@ ((((-398 (-547))) . T) (($) . T)) ((((-832)) . T)) ((((-832)) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-832)) . T)) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523))) (((-861 (-547))) |has| |#1| (-592 (-861 (-547)))) (((-861 (-370))) |has| |#1| (-592 (-861 (-370))))) -((((-1135) (-52)) . T)) +((((-1136) (-52)) . T)) (((|#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-832)) . T)) -((((-619 (-142))) . T) (((-1118)) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) -((((-1135) |#1|) |has| |#1| (-503 (-1135) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) +((((-619 (-142))) . T) (((-1119)) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) +((((-1136) |#1|) |has| |#1| (-503 (-1136) |#1|)) ((|#1| |#1|) |has| |#1| (-300 |#1|))) (|has| |#1| (-821)) ((((-832)) . T)) ((((-523)) |has| |#1| (-592 (-523)))) @@ -2244,16 +2244,16 @@ ((((-832)) . T) (((-619 |#4|)) . T)) (((|#2|) . T)) ((((-879 |#1|)) . T) (((-398 (-547))) . T) (($) . T)) -(-1525 (|has| |#4| (-169)) (|has| |#4| (-701)) (|has| |#4| (-819)) (|has| |#4| (-1016))) -(-1525 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) -((((-1135) (-52)) . T)) -(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#4| (-169)) (|has| |#4| (-701)) (|has| |#4| (-819)) (|has| |#4| (-1016))) +(-1530 (|has| |#3| (-169)) (|has| |#3| (-701)) (|has| |#3| (-819)) (|has| |#3| (-1016))) +((((-1136) (-52)) . T)) +(-1530 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-1525 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -(-1525 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1530 (|has| |#2| (-25)) (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1530 (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (|has| |#1| (-878)) (|has| |#1| (-878)) (((|#2|) . T)) @@ -2268,12 +2268,12 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (|has| |#1| (-794)) (((#0=(-879 |#1|) #0#) . T) (($ $) . T) ((#1=(-398 (-547)) #1#) . T)) ((((-398 |#2|)) . T)) (|has| |#1| (-819)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) (((|#1| |#1|) . T) ((#0=(-398 (-547)) #0#) . T) ((#1=(-547) #1#) . T) (($ $) . T)) ((((-879 |#1|)) . T) (($) . T) (((-398 (-547))) . T)) (((|#2|) |has| |#2| (-1016)) (((-547)) -12 (|has| |#2| (-615 (-547))) (|has| |#2| (-1016)))) @@ -2283,33 +2283,33 @@ (|has| |#1| (-143)) (((|#2|) . T)) ((((-832)) . T)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) -((((-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))) . T)) -(((#0=(-52)) . T) (((-2 (|:| -3327 (-1135)) (|:| -1778 #0#))) . T)) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) +((((-2 (|:| -3331 (-1136)) (|:| -1786 (-52)))) . T)) +(((#0=(-52)) . T) (((-2 (|:| -3331 (-1136)) (|:| -1786 #0#))) . T)) (|has| |#1| (-340)) ((((-547)) . T)) ((((-832)) . T)) -(((#0=(-1204 |#1| |#2| |#3| |#4|) $) |has| #0# (-277 #0# #0#))) +(((#0=(-1205 |#1| |#2| |#3| |#4|) $) |has| #0# (-277 #0# #0#))) (|has| |#1| (-354)) (((#0=(-1045) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-340))) (((#0=(-398 (-547)) #0#) . T) ((#1=(-673) #1#) . T) (($ $) . T)) ((((-307 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) |has| |#1| (-354))) (|has| |#1| (-1063)) (((|#1|) . T)) -(((|#1|) -1525 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) -(((|#1|) -1525 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) +(((|#1|) -1530 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) +(((|#1|) -1530 (|has| |#2| (-358 |#1|)) (|has| |#2| (-408 |#1|)))) (((|#2|) . T)) ((((-398 (-547))) . T) (((-673)) . T) (($) . T)) (((|#3| |#3|) . T)) (|has| |#2| (-225)) ((((-834 |#1|)) . T)) -((((-1135)) |has| |#1| (-869 (-1135))) ((|#3|) . T)) +((((-1136)) |has| |#1| (-869 (-1136))) ((|#3|) . T)) (-12 (|has| |#1| (-354)) (|has| |#2| (-991))) -((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) +((((-1134 |#1| |#2| |#3|)) |has| |#1| (-354))) ((((-832)) . T)) (|has| |#1| (-354)) (|has| |#1| (-354)) @@ -2320,7 +2320,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-547)) . T)) -(-1525 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) (((|#2|) . T) (((-547)) |has| |#2| (-615 (-547)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2328,7 +2328,7 @@ ((($) . T) (((-398 (-547))) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T) (($) . T)) -(((|#1| (-1218 |#1|) (-1218 |#1|)) . T)) +(((|#1| (-1219 |#1|) (-1219 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) ((((-832)) . T)) ((((-832)) . T)) @@ -2357,7 +2357,7 @@ (|has| |#2| (-991)) ((($) . T)) (|has| |#1| (-878)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2365,24 +2365,24 @@ ((($) . T)) (|has| |#1| (-354)) ((((-879 |#1|)) . T)) -((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1530 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) -(-1525 (|has| |#1| (-359)) (|has| |#1| (-821))) +(-1530 (|has| |#1| (-359)) (|has| |#1| (-821))) (((|#1|) . T)) ((((-832)) . T)) -((((-1135)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1135))))) +((((-1136)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1136))))) ((((-398 |#2|) |#3|) . T)) ((($) . T) (((-398 (-547))) . T)) ((((-745) |#1|) . T)) -(((|#2| (-232 (-3764 |#1|) (-745))) . T)) +(((|#2| (-232 (-3767 |#1|) (-745))) . T)) (((|#1| (-519 |#3|)) . T)) ((((-398 (-547))) . T)) -(-1525 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) +(-1530 (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((((-832)) . T)) -(((#0=(-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) #0#) |has| (-2 (|:| -3327 (-1135)) (|:| -1778 (-52))) (-300 (-2 (|:| -3327 (-1135)) (|:| -1778 (-52)))))) +(((#0=(-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) #0#) |has| (-2 (|:| -3331 (-1136)) (|:| -1786 (-52))) (-300 (-2 (|:| -3331 (-1136)) (|:| -1786 (-52)))))) (|has| |#1| (-878)) (|has| |#2| (-354)) -(-1525 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1530 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) ((((-166 (-370))) . T) (((-217)) . T) (((-370)) . T)) ((((-832)) . T)) (((|#1|) . T)) @@ -2399,13 +2399,13 @@ (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-38 (-398 (-547)))) (-12 (|has| |#1| (-532)) (|has| |#1| (-802))) ((((-832)) . T)) -((((-1135)) -1525 (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1135)))) (-12 (|has| |#1| (-354)) (|has| |#2| (-869 (-1135)))))) +((((-1136)) -1530 (-12 (|has| |#1| (-15 * (|#1| (-547) |#1|))) (|has| |#1| (-869 (-1136)))) (-12 (|has| |#1| (-354)) (|has| |#2| (-869 (-1136)))))) (|has| |#1| (-354)) -((((-1135)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1135))))) +((((-1136)) -12 (|has| |#1| (-15 * (|#1| (-398 (-547)) |#1|))) (|has| |#1| (-869 (-1136))))) (|has| |#1| (-354)) ((((-398 (-547))) . T) (($) . T)) ((($) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) . T)) @@ -2413,22 +2413,22 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-354))) (((|#2|) |has| |#1| (-354))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) -(((|#2|) . T) (((-1135)) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-1135)))) (((-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-547)))) (((-398 (-547))) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-547))))) +(((|#2|) . T) (((-1136)) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-1136)))) (((-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-547)))) (((-398 (-547))) -12 (|has| |#1| (-354)) (|has| |#2| (-1007 (-547))))) (((|#2|) . T)) -((((-1135) #0=(-1204 |#1| |#2| |#3| |#4|)) |has| #0# (-503 (-1135) #0#)) ((#0# #0#) |has| #0# (-300 #0#))) +((((-1136) #0=(-1205 |#1| |#2| |#3| |#4|)) |has| #0# (-503 (-1136) #0#)) ((#0# #0#) |has| #0# (-300 #0#))) ((((-590 $) $) . T) (($ $) . T)) -((((-166 (-217))) . T) (((-166 (-370))) . T) (((-1131 (-673))) . T) (((-861 (-370))) . T)) +((((-166 (-217))) . T) (((-166 (-370))) . T) (((-1132 (-673))) . T) (((-861 (-370))) . T)) ((((-832)) . T)) (|has| |#1| (-539)) (|has| |#1| (-539)) (|has| (-398 |#2|) (-225)) (((|#1| (-398 (-547))) . T)) ((($ $) . T)) -((((-1135)) |has| |#2| (-869 (-1135)))) +((((-1136)) |has| |#2| (-869 (-1136)))) ((($) . T)) ((((-832)) . T)) ((((-398 (-547))) . T) (($) . T)) @@ -2438,30 +2438,30 @@ ((((-370)) -12 (|has| |#1| (-354)) (|has| |#2| (-855 (-370)))) (((-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-855 (-547))))) (|has| |#1| (-354)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-354)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) (|has| |#1| (-354)) (|has| |#1| (-539)) (((|#4| |#4|) -12 (|has| |#4| (-300 |#4|)) (|has| |#4| (-1063)))) (((|#3|) . T)) (((|#1|) . T)) -(-1525 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +(-1530 (|has| |#2| (-130)) (|has| |#2| (-169)) (|has| |#2| (-354)) (|has| |#2| (-767)) (|has| |#2| (-819)) (|has| |#2| (-1016))) (((|#2|) . T)) (((|#2|) . T)) -(-1525 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) -((((-2 (|:| -3327 |#1|) (|:| -1778 |#2|))) . T)) +(-1530 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) +((((-2 (|:| -3331 |#1|) (|:| -1786 |#2|))) . T)) (|has| |#1| (-38 (-398 (-547)))) (((|#1| |#2|) . T)) (|has| |#1| (-38 (-398 (-547)))) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -((((-1118) |#1|) . T)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +((((-1119) |#1|) . T)) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-359))) (|has| |#1| (-145)) ((((-561 |#1|)) . T)) ((($) . T)) @@ -2469,13 +2469,13 @@ (|has| |#1| (-539)) (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-38 (-398 (-547)))) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-340))) (|has| |#1| (-145)) ((((-832)) . T)) ((($) . T)) -((((-398 (-547))) |has| |#2| (-1007 (-547))) (((-547)) |has| |#2| (-1007 (-547))) (((-1135)) |has| |#2| (-1007 (-1135))) ((|#2|) . T)) +((((-398 (-547))) |has| |#2| (-1007 (-547))) (((-547)) |has| |#2| (-1007 (-547))) (((-1136)) |has| |#2| (-1007 (-1136))) ((|#2|) . T)) (((#0=(-398 |#2|) #0#) . T) ((#1=(-398 (-547)) #1#) . T) (($ $) . T)) -((((-1100 |#1| |#2|)) . T)) +((((-1101 |#1| |#2|)) . T)) (((|#1| (-547)) . T)) (((|#1| (-398 (-547))) . T)) ((((-547)) |has| |#2| (-855 (-547))) (((-370)) |has| |#2| (-855 (-370)))) @@ -2486,7 +2486,7 @@ (((|#2|) . T)) ((((-832)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) -((((-1135) (-52)) . T)) +((((-1136) (-52)) . T)) ((((-398 |#2|)) . T)) ((((-832)) . T)) (((|#1|) . T)) @@ -2494,13 +2494,13 @@ (|has| |#1| (-765)) (|has| |#1| (-765)) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) ((((-114)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-217)) . T) (((-370)) . T) (((-861 (-370))) . T)) ((((-832)) . T)) -((((-1204 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-398 (-547))) . T)) +((((-1205 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-398 (-547))) . T)) (((|#1|) |has| |#1| (-169)) (($) |has| |#1| (-539)) (((-398 (-547))) |has| |#1| (-539))) ((((-832)) . T)) ((((-832)) . T)) @@ -2515,22 +2515,22 @@ ((((-547)) . T)) ((((-832)) . T)) ((((-547)) . T)) -(-1525 (|has| |#2| (-767)) (|has| |#2| (-819))) +(-1530 (|has| |#2| (-767)) (|has| |#2| (-819))) ((((-166 (-370))) . T) (((-217)) . T) (((-370)) . T)) ((((-832)) . T)) ((((-832)) . T)) -((((-1118)) . T) (((-523)) . T) (((-547)) . T) (((-861 (-547))) . T) (((-370)) . T) (((-217)) . T)) +((((-1119)) . T) (((-523)) . T) (((-547)) . T) (((-861 (-547))) . T) (((-370)) . T) (((-217)) . T)) ((((-832)) . T)) (|has| |#1| (-145)) (|has| |#1| (-143)) -((($) . T) ((#0=(-1203 |#2| |#3| |#4|)) |has| #0# (-169)) (((-398 (-547))) |has| #0# (-38 (-398 (-547))))) +((($) . T) ((#0=(-1204 |#2| |#3| |#4|)) |has| #0# (-169)) (((-398 (-547))) |has| #0# (-38 (-398 (-547))))) (((|#1|) . T) (($) . T) (((-398 (-547))) . T)) (|has| |#1| (-354)) (|has| |#1| (-354)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) -(-1525 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1135))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) -(|has| |#1| (-1111)) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +(-1530 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-463)) (|has| |#1| (-701)) (|has| |#1| (-869 (-1136))) (|has| |#1| (-1016)) (|has| |#1| (-1075)) (|has| |#1| (-1063))) +(|has| |#1| (-1112)) ((((-547) |#1|) . T)) (((|#1|) . T)) (((#0=(-116 |#1|) $) |has| #0# (-277 #0# #0#))) @@ -2539,7 +2539,7 @@ ((((-114)) . T) ((|#1|) . T)) ((((-832)) . T)) (((|#1| |#2|) . T)) -((((-1135) |#1|) . T)) +((((-1136) |#1|) . T)) (((|#1|) |has| |#1| (-300 |#1|))) ((((-547) |#1|) . T)) (((|#1|) . T)) @@ -2547,8 +2547,8 @@ (((|#1|) . T)) (|has| |#1| (-539)) ((((-398 |#2|)) . T) (((-398 (-547))) . T) (($) . T)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) ((((-370)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2557,7 +2557,7 @@ (|has| |#1| (-539)) (|has| |#1| (-1063)) ((((-754 |#1| (-834 |#2|))) |has| (-754 |#1| (-834 |#2|)) (-300 (-754 |#1| (-834 |#2|))))) -(-1525 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) +(-1530 (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878))) (((|#1|) . T)) (((|#2| |#3|) . T)) (((|#1|) . T)) @@ -2565,14 +2565,14 @@ (((|#1| (-519 |#2|)) . T)) (((|#1| (-745)) . T)) (|has| |#1| (-225)) -(((|#1| (-519 (-1052 (-1135)))) . T)) +(((|#1| (-519 (-1052 (-1136)))) . T)) (|has| |#2| (-354)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 (-52)))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 (-52)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) ((((-832)) . T)) ((((-832)) . T)) -(-1525 (|has| |#3| (-767)) (|has| |#3| (-819))) +(-1530 (|has| |#3| (-767)) (|has| |#3| (-819))) ((((-832)) . T)) ((((-1082)) . T) (((-832)) . T)) ((((-832)) . T)) @@ -2582,21 +2582,21 @@ ((((-547)) . T)) (((|#3|) . T)) ((((-832)) . T)) -(-1525 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1525 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) +(-1530 (|has| |#1| (-298)) (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-169)) (|has| |#1| (-539)) (|has| |#1| (-1016))) (((#0=(-561 |#1|) #0#) . T) (($ $) . T) ((#1=(-398 (-547)) #1#) . T)) ((($ $) . T) ((#0=(-398 (-547)) #0#) . T)) (((|#1|) |has| |#1| (-169))) -(((|#1| (-1218 |#1|) (-1218 |#1|)) . T)) +(((|#1| (-1219 |#1|) (-1219 |#1|)) . T)) ((((-561 |#1|)) . T) (($) . T) (((-398 (-547))) . T)) ((($) . T) (((-398 (-547))) . T)) ((($) . T) (((-398 (-547))) . T)) -(((|#2|) |has| |#2| (-6 (-4330 "*")))) +(((|#2|) |has| |#2| (-6 (-4331 "*")))) (((|#1|) . T)) (((|#1|) . T)) ((((-832)) . T)) ((((-285 |#3|)) . T)) -(((#0=(-398 (-547)) #0#) |has| |#2| (-38 (-398 (-547)))) ((|#2| |#2|) . T) (($ $) -1525 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) +(((#0=(-398 (-547)) #0#) |has| |#2| (-38 (-398 (-547)))) ((|#2| |#2|) . T) (($ $) -1530 (|has| |#2| (-169)) (|has| |#2| (-442)) (|has| |#2| (-539)) (|has| |#2| (-878)))) (((|#2| |#2|) . T) ((|#6| |#6|) . T)) (((|#1|) . T)) ((($) . T) (((-398 (-547))) |has| |#2| (-38 (-398 (-547)))) ((|#2|) . T)) @@ -2604,20 +2604,20 @@ (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . T) (((-398 (-547))) . T) (($) . T)) (((|#1|) . 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T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1530 (|has| |#1| (-169)) (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (|has| |#2| (-878)) (|has| |#1| (-878)) -((($) -1525 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1530 (|has| |#1| (-169)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#1|) . T)) -((((-2 (|:| -3327 (-1118)) (|:| -1778 |#1|))) . T)) +((((-2 (|:| -3331 (-1119)) (|:| -1786 |#1|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1| |#1|) . T)) @@ -2625,42 +2625,42 @@ (((|#1|) . T)) (|has| |#1| (-1063)) (((|#1|) . T)) -((((-1135)) . T) ((|#1|) . T)) +((((-1136)) . T) ((|#1|) . T)) ((((-832)) . T)) ((((-832)) . 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T)) (|has| |#2| (-794)) (|has| |#2| (-794)) -((((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#2|) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-398 (-547))) -1525 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) . T)) +((((-398 (-547))) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) ((|#2|) |has| |#1| (-354)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-398 (-547))) -1530 (|has| |#1| (-38 (-398 (-547)))) (|has| |#1| (-354))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1|) . T) (((-547)) |has| |#1| (-1007 (-547))) (((-398 (-547))) |has| |#1| (-1007 (-398 (-547))))) ((((-547)) |has| |#1| (-855 (-547))) (((-370)) |has| |#1| (-855 (-370)))) @@ -2698,14 +2698,14 @@ (((|#1|) . T)) (((|#1|) . T)) (((|#2| (-745)) . T)) -((((-1135)) . T)) +((((-1136)) . T)) ((((-839 |#1|)) . 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T)) -((($) -1525 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) +((($) -1530 (|has| |#1| (-354)) (|has| |#1| (-442)) (|has| |#1| (-539)) (|has| |#1| (-878))) ((|#1|) |has| |#1| (-169)) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) ((((-832)) . T)) ((((-142)) . T)) (((|#1|) . T) (((-398 (-547))) . T)) @@ -2789,7 +2789,7 @@ (((|#1|) . T)) ((((-832)) . T)) (((|#1|) . T)) -(|has| |#1| (-1111)) +(|has| |#1| (-1112)) (((|#1| (-519 (-834 |#2|)) (-834 |#2|) (-754 |#1| (-834 |#2|))) . T)) (((|#1|) . T)) ((((-398 $) (-398 $)) |has| |#1| (-539)) (($ $) . T) ((|#1| |#1|) . T)) @@ -2798,7 +2798,7 @@ ((((-398 (-547))) |has| |#1| (-1007 (-398 (-547)))) (((-547)) |has| |#1| (-1007 (-547))) ((|#1|) . T) ((|#2|) . T)) ((((-1045)) . T) ((|#1|) . 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T)) (((|#2| |#2|) . T) ((#0=(-398 (-547)) #0#) . T) (($ $) . T)) ((((-547)) . T)) @@ -2998,8 +2998,8 @@ ((((-398 (-547))) . T) (($) . T)) ((((-547) |#1|) . T)) ((((-832)) . T)) -((($ $) . T) (((-1135) $) . T)) -((((-1210 |#1| |#2| |#3|)) . T)) +((($ $) . T) (((-1136) $) . T)) +((((-1211 |#1| |#2| |#3|)) . T)) ((((-523)) |has| |#2| (-592 (-523))) (((-861 (-370))) |has| |#2| (-592 (-861 (-370)))) (((-861 (-547))) |has| |#2| (-592 (-861 (-547))))) ((((-832)) . T)) ((((-832)) . T)) @@ -3007,42 +3007,42 @@ ((((-832)) . T)) ((((-832)) . T)) ((((-832)) . T)) -(((|#1|) . T) (((-832)) . T) (((-1140)) . T)) +(((|#1|) . T) (((-832)) . T) (((-1141)) . T)) ((((-832)) . T)) (((|#1|) -12 (|has| |#1| (-300 |#1|)) (|has| |#1| (-1063)))) (((|#1| (-519 (-834 |#2|)) (-834 |#2|) (-754 |#1| (-834 |#2|))) . T)) (((|#1| |#2| (-232 |#1| |#2|) (-232 |#1| |#2|)) . T)) ((((-832)) . 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T)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-340))) (|has| |#1| (-354)) (|has| |#1| (-354)) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-340))) -(-1525 (|has| |#1| (-169)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-340))) +(-1530 (|has| |#1| (-169)) (|has| |#1| (-539))) (((|#1| (-547)) . T)) (((|#1| (-398 (-547))) . T)) (((|#1| (-745)) . T)) @@ -3054,19 +3054,19 @@ ((((-547) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-861 (-370))) . T) (((-861 (-547))) . T) (((-1135)) . T) (((-523)) . T)) +((((-861 (-370))) . T) (((-861 (-547))) . T) (((-1136)) . T) (((-523)) . T)) (((|#1|) . T)) ((((-832)) . 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T)) -(-1525 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) -((((-1135)) -12 (|has| |#2| (-869 (-1135))) (|has| |#2| (-1016)))) -(-1525 (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) (-12 (|has| |#1| (-701)) (|has| |#2| (-701)))) +(-1530 (|has| |#2| (-169)) (|has| |#2| (-701)) (|has| |#2| (-819)) (|has| |#2| (-1016))) +((((-1136)) -12 (|has| |#2| (-869 (-1136))) (|has| |#2| (-1016)))) +(-1530 (-12 (|has| |#1| (-463)) (|has| |#2| (-463))) (-12 (|has| |#1| (-701)) (|has| |#2| (-701)))) (|has| |#1| (-143)) (|has| |#1| (-145)) (|has| |#1| (-354)) @@ -3087,10 +3087,10 @@ ((((-398 (-547))) |has| |#1| (-38 (-398 (-547)))) ((|#1|) |has| |#1| (-169)) (($) |has| |#1| (-539))) ((((-547)) . T)) ((((-547)) . T)) -((((-1118) (-1135) (-547) (-217) (-832)) . T)) +((((-1119) (-1136) (-547) (-217) (-832)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-1525 (|has| |#1| (-340)) (|has| |#1| (-359))) +(-1530 (|has| |#1| (-340)) (|has| |#1| (-359))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-832)) . T)) @@ -3098,7 +3098,7 @@ ((($) . T) ((|#1|) . T) (((-398 (-547))) |has| |#1| (-38 (-398 (-547))))) (((|#2|) |has| |#2| (-1063)) (((-547)) -12 (|has| |#2| (-1007 (-547))) (|has| |#2| (-1063))) (((-398 (-547))) -12 (|has| |#2| (-1007 (-398 (-547)))) (|has| |#2| (-1063)))) ((((-523)) |has| |#1| (-592 (-523)))) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-821)) (|has| |#1| (-1063)))) ((($) . T) (((-398 (-547))) . T)) (|has| |#1| (-878)) (|has| |#1| (-878)) @@ -3107,14 +3107,14 @@ ((((-832)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-169))) -(-1525 (|has| |#1| (-354)) (|has| |#1| (-539))) -(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) +(-1530 (|has| |#1| (-354)) (|has| |#1| (-539))) +(-1530 (|has| |#1| (-21)) (|has| |#1| (-819))) (((|#2|) . T)) -(-1525 (|has| |#1| (-21)) (|has| |#1| (-819))) +(-1530 (|has| |#1| (-21)) (|has| |#1| (-819))) (((|#1|) |has| |#1| (-169))) (((|#1|) . T)) (((|#1|) . T)) -((((-832)) -1525 (-12 (|has| |#1| (-591 (-832))) (|has| |#2| (-591 (-832)))) (-12 (|has| |#1| (-1063)) (|has| |#2| (-1063))))) +((((-832)) -1530 (-12 (|has| |#1| (-591 (-832))) (|has| |#2| (-591 (-832)))) (-12 (|has| |#1| (-1063)) (|has| |#2| (-1063))))) ((((-398 |#2|) |#3|) . T)) ((((-398 (-547))) . T) (($) . T)) (|has| |#1| (-38 (-398 (-547)))) @@ -3126,20 +3126,20 @@ (((|#1|) . T) (((-398 (-547))) . T) (((-547)) . T) (($) . T)) (((#0=(-547) #0#) . T)) ((($) . T) (((-398 (-547))) . 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T)) -((((-1133 |#1| |#2| |#3|)) . T)) -((((-1133 |#1| |#2| |#3|)) . T) (((-1126 |#1| |#2| |#3|)) . T)) +((((-1134 |#1| |#2| |#3|)) . T)) +((((-1134 |#1| |#2| |#3|)) . T) (((-1127 |#1| |#2| |#3|)) . T)) ((((-832)) . T)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-547) |#1|) . T)) -((((-1133 |#1| |#2| |#3|)) |has| |#1| (-354))) +((((-1134 |#1| |#2| |#3|)) |has| |#1| (-354))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-354)) -(((|#3|) . T) ((|#2|) . T) (($) -1525 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) ((|#4|) -1525 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016)))) -(((|#2|) . T) (($) -1525 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((|#3|) -1525 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016)))) +(((|#3|) . T) ((|#2|) . T) (($) -1530 (|has| |#4| (-169)) (|has| |#4| (-819)) (|has| |#4| (-1016))) ((|#4|) -1530 (|has| |#4| (-169)) (|has| |#4| (-354)) (|has| |#4| (-1016)))) +(((|#2|) . T) (($) -1530 (|has| |#3| (-169)) (|has| |#3| (-819)) (|has| |#3| (-1016))) ((|#3|) -1530 (|has| |#3| (-169)) (|has| |#3| (-354)) (|has| |#3| (-1016)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-354)) @@ -3188,7 +3188,7 @@ ((((-832)) . T)) ((((-832)) . T)) (((|#1|) . T)) -((((-832)) -1525 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) +((((-832)) -1530 (|has| |#1| (-591 (-832))) (|has| |#1| (-1063)))) ((((-129)) . T) (((-832)) . T)) ((((-547) |#1|) . T)) (((|#1|) . T)) @@ -3196,37 +3196,37 @@ (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-354)) (|has| |#2| (-277 |#2| |#2|))) (($ $) . T)) ((($ $) . 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119329) ((-126 . -34) T) ((-791 . -130) T) ((-841 . -878) 119308) ((-623 . -591) 119290) ((-346 . -1237) 119274) ((-343 . -1237) 119258) ((-335 . -1237) 119242) ((-127 . -503) 119175) ((-121 . -503) 119108) ((-500 . -766) T) ((-500 . -769) T) ((-499 . -768) T) ((-102 . -300) 119046) ((-214 . -101) 119024) ((-668 . -1063) T) ((-673 . -169) T) ((-841 . -622) 118976) ((-64 . -375) T) ((-266 . -591) 118958) ((-64 . -386) T) ((-921 . -368) 118942) ((-839 . -281) T) ((-50 . -591) 118924) ((-968 . -38) 118872) ((-561 . -591) 118854) ((-471 . -368) 118838) ((-561 . -592) 118820) ((-507 . -591) 118802) ((-879 . -1237) 118789) ((-840 . -1172) T) ((-675 . -442) T) ((-484 . -503) 118755) ((-477 . -354) T) ((-346 . -359) 118734) ((-343 . -359) 118713) ((-335 . -359) 118692) ((-209 . -354) T) ((-689 . -701) T) ((-116 . -442) T) ((-1241 . -1232) 118676) ((-840 . -853) 118653) ((-840 . -855) NIL) ((-933 . -821) 118552) ((-789 . -821) 118503) ((-628 . -630) 118487) ((-1158 . -34) T) ((-168 . -591) 118469) ((-1076 . -21) 118379) ((-1076 . -25) 118230) ((-840 . -1007) 118207) ((-921 . -869) 118188) ((-1191 . -47) 118165) ((-879 . -359) T) ((-58 . -625) 118149) ((-505 . -625) 118133) ((-471 . -869) 118110) ((-70 . -431) T) ((-70 . -386) T) ((-485 . -625) 118094) ((-58 . -364) 118078) ((-599 . -169) T) ((-505 . -364) 118062) ((-485 . -364) 118046) ((-801 . -683) 118030) ((-1131 . -298) 118009) ((-1137 . -130) T) ((-117 . -169) T) ((-1106 . -300) 117947) ((-166 . -1172) T) ((-611 . -719) 117931) ((-585 . -719) 117915) ((-1230 . -130) T) ((-1203 . -889) 117894) ((-1182 . -889) 117873) ((-1182 . -794) NIL) ((-668 . -692) 117823) ((-1181 . -878) 117776) ((-993 . -1063) T) ((-840 . -368) 117753) ((-840 . -329) 117730) ((-874 . -1075) T) ((-166 . -853) 117714) ((-166 . -855) 117639) ((-477 . -1075) T) ((-345 . -1063) T) ((-209 . -1075) T) ((-75 . -431) T) ((-75 . -386) T) ((-166 . -1007) 117535) ((-310 . -821) T) ((-1218 . -503) 117468) ((-1202 . -622) 117365) ((-1181 . -622) 117235) 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-869) 115917) ((-673 . -281) T) ((-668 . -169) T) ((-686 . -111) 115873) ((-1246 . -1023) T) ((-1191 . -368) 115857) ((-409 . -1176) 115835) ((-1080 . -591) 115817) ((-304 . -819) NIL) ((-409 . -539) T) ((-217 . -298) T) ((-1181 . -765) 115770) ((-1181 . -768) 115723) ((-1202 . -701) T) ((-1181 . -701) T) ((-48 . -692) 115688) ((-217 . -991) T) ((-342 . -1225) 115665) ((-1204 . -402) 115631) ((-693 . -701) T) ((-1191 . -869) 115574) ((-112 . -591) 115556) ((-112 . -592) 115538) ((-693 . -463) T) ((-472 . -21) 115448) ((-127 . -479) 115432) ((-121 . -479) 115416) ((-472 . -25) 115267) ((-599 . -281) T) ((-565 . -1022) 115242) ((-428 . -1063) T) ((-1027 . -298) T) ((-117 . -281) T) ((-1067 . -101) T) ((-972 . -101) T) ((-565 . -111) 115210) ((-1102 . -300) 115148) ((-1166 . -1016) T) ((-1027 . -991) T) ((-65 . -1172) T) ((-1020 . -25) T) ((-1020 . -21) T) ((-686 . -1016) T) ((-376 . -21) T) ((-376 . -25) T) ((-668 . -503) NIL) ((-993 . -169) T) ((-686 . -235) T) ((-1027 . -532) T) ((-495 . -101) T) ((-491 . -101) T) ((-345 . -169) T) ((-334 . -591) 115130) ((-385 . -591) 115112) ((-464 . -701) T) ((-1082 . -819) T) ((-861 . -1007) 115080) ((-107 . -821) T) ((-632 . -1022) 115064) ((-477 . -130) T) ((-1204 . -1023) T) ((-209 . -130) T) ((-1116 . -101) 115042) ((-98 . -1063) T) ((-237 . -640) 115026) ((-237 . -625) 115010) ((-632 . -111) 114989) ((-307 . -402) 114973) ((-237 . -364) 114957) ((-1119 . -227) 114904) ((-968 . -223) 114888) ((-73 . -1172) T) ((-48 . -169) T) ((-675 . -378) T) ((-675 . -141) T) ((-1241 . -101) T) ((-1051 . -1022) 114731) ((-255 . -878) 114710) ((-239 . -878) 114689) ((-756 . -1022) 114512) ((-754 . -1022) 114355) ((-586 . -1172) T) ((-1124 . -591) 114337) ((-1051 . -111) 114166) ((-1013 . -101) T) ((-465 . -1172) T) ((-451 . -1022) 114137) ((-444 . -1022) 113980) ((-638 . -622) 113964) ((-840 . -298) T) ((-756 . -111) 113773) ((-754 . -111) 113602) ((-346 . -622) 113554) ((-343 . -622) 113506) ((-335 . -622) 113458) ((-255 . -622) 113383) 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95020) ((-304 . -1022) 94949) ((-968 . -277) 94907) ((-398 . -692) 94859) ((-128 . -821) T) ((-675 . -819) T) ((-1204 . -1016) T) ((-307 . -111) 94755) ((-304 . -111) 94668) ((-933 . -101) T) ((-789 . -101) 94458) ((-687 . -592) NIL) ((-687 . -591) 94440) ((-632 . -1007) 94336) ((-1204 . -317) 94280) ((-1004 . -279) 94255) ((-560 . -701) T) ((-547 . -768) T) ((-166 . -354) 94206) ((-547 . -765) T) ((-547 . -701) T) ((-484 . -701) T) ((-1106 . -479) 94190) ((-1051 . -855) NIL) ((-840 . -1075) T) ((-117 . -878) NIL) ((-1240 . -1239) 94166) ((-1238 . -1239) 94145) ((-756 . -855) NIL) ((-754 . -855) 94004) ((-1233 . -25) T) ((-1233 . -21) T) ((-1169 . -101) 93982) ((-1069 . -386) T) ((-599 . -622) 93969) ((-444 . -855) NIL) ((-649 . -101) 93947) ((-1051 . -1007) 93774) ((-840 . -23) T) ((-756 . -1007) 93633) ((-754 . -1007) 93490) ((-117 . -622) 93435) ((-444 . -1007) 93311) ((-623 . -1007) 93295) ((-603 . -101) T) ((-214 . -479) 93279) ((-1218 . -34) T) ((-611 . -692) 93263) ((-585 . -692) 93247) ((-644 . -38) 93207) ((-310 . -101) T) ((-84 . -591) 93189) ((-50 . -1007) 93173) ((-1082 . -1022) 93160) ((-1051 . -368) 93144) ((-756 . -368) 93128) ((-59 . -56) 93090) ((-673 . -768) T) ((-673 . -765) T) ((-561 . -1007) 93077) ((-507 . -1007) 93054) ((-673 . -701) T) ((-315 . -130) T) ((-307 . -1016) 92944) ((-304 . -1016) T) ((-166 . -1075) T) ((-754 . -368) 92928) ((-45 . -149) 92878) ((-973 . -961) 92860) ((-444 . -368) 92844) ((-398 . -169) T) ((-307 . -235) 92823) ((-304 . -235) T) ((-304 . -225) NIL) ((-285 . -1063) 92605) ((-217 . -130) T) ((-1082 . -111) 92590) ((-166 . -23) T) ((-773 . -145) 92569) ((-773 . -143) 92548) ((-242 . -615) 92454) ((-241 . -615) 92360) ((-310 . -275) 92326) ((-1116 . -503) 92259) ((-1095 . -1063) T) ((-217 . -1025) T) ((-789 . -300) 92197) ((-1051 . -869) 92132) ((-756 . -869) 92075) ((-754 . -869) 92059) ((-1240 . -38) 92029) ((-1238 . -38) 91999) ((-1191 . -1075) T) ((-826 . -1075) T) ((-444 . -869) 91976) ((-829 . -1063) T) ((-1191 . -23) T) ((-554 . -1075) T) ((-826 . -23) T) ((-599 . -701) T) ((-346 . -889) T) ((-343 . -889) T) ((-280 . -101) T) ((-335 . -889) T) ((-1027 . -130) T) ((-939 . -1047) T) ((-921 . -130) T) ((-117 . -768) NIL) ((-117 . -765) NIL) ((-117 . -701) T) ((-668 . -878) NIL) ((-1013 . -503) 91877) ((-471 . -130) T) ((-554 . -23) T) ((-649 . -300) 91815) ((-611 . -736) T) ((-585 . -736) T) ((-1182 . -821) NIL) ((-972 . -281) T) ((-242 . -21) T) ((-668 . -622) 91765) ((-342 . -1063) T) ((-242 . -25) T) ((-241 . -21) T) ((-241 . -25) T) ((-150 . -38) 91749) ((-2 . -101) T) ((-879 . -889) T) ((-472 . -1225) 91719) ((-215 . -1007) 91696) ((-1082 . -1016) T) ((-686 . -298) T) ((-285 . -692) 91638) ((-675 . -1023) T) ((-477 . -442) T) ((-398 . -503) 91550) ((-209 . -442) T) ((-1082 . -225) T) ((-286 . -149) 91500) ((-968 . -592) 91461) ((-968 . -591) 91443) ((-958 . -591) 91425) ((-116 . -1023) T) ((-628 . -1022) 91409) ((-217 . -482) T) ((-390 . -591) 91391) ((-390 . -592) 91368) ((-1020 . -1225) 91338) ((-628 . -111) 91317) ((-1102 . -479) 91301) ((-789 . -38) 91271) ((-62 . -431) T) ((-62 . -386) T) ((-1119 . -101) T) ((-840 . -130) T) ((-474 . -101) 91249) ((-1246 . -359) T) ((-1043 . -101) T) ((-1026 . -101) T) ((-342 . -692) 91194) ((-706 . -145) 91173) ((-706 . -143) 91152) ((-993 . -622) 91089) ((-512 . -1063) 91067) ((-350 . -101) T) ((-344 . -101) T) ((-336 . -101) T) ((-107 . -101) T) ((-493 . -1063) T) ((-345 . -622) 91012) ((-1131 . -615) 90960) ((-1087 . -615) 90908) ((-376 . -498) 90887) ((-807 . -819) 90866) ((-370 . -1176) T) ((-668 . -701) T) ((-330 . -1023) T) ((-1182 . -961) 90818) ((-171 . -1023) T) ((-102 . -591) 90750) ((-1133 . -143) 90729) ((-1133 . -145) 90708) ((-370 . -539) T) ((-1132 . -145) 90687) ((-1132 . -143) 90666) ((-1126 . -143) 90573) ((-398 . -281) T) ((-1126 . -145) 90480) ((-1088 . -145) 90459) ((-1088 . -143) 90438) ((-310 . -38) 90279) ((-166 . -130) T) ((-304 . -769) NIL) ((-304 . -766) NIL) ((-628 . -1016) T) ((-48 . -622) 90244) ((-963 . -101) T) ((-962 . -21) T) ((-127 . -979) 90228) ((-121 . -979) 90212) ((-962 . -25) T) ((-870 . -119) 90196) ((-1118 . -101) T) ((-790 . -821) 90175) ((-1191 . -130) T) ((-1131 . -25) T) ((-1131 . -21) T) ((-826 . -130) T) ((-1087 . -25) T) ((-1087 . -21) T) ((-825 . -25) T) ((-825 . -21) T) ((-756 . -298) 90154) ((-621 . -101) 90132) ((-608 . -101) T) ((-1119 . -300) 89927) ((-554 . -130) T) ((-597 . -819) 89906) ((-1116 . -479) 89890) ((-1110 . -149) 89840) ((-1106 . -591) 89802) ((-1106 . -592) 89763) ((-993 . -765) T) ((-993 . -768) T) ((-993 . -701) T) ((-474 . -300) 89701) ((-443 . -408) 89671) ((-342 . -169) T) ((-280 . -38) 89658) ((-265 . -101) T) ((-264 . -101) T) ((-263 . -101) T) ((-262 . -101) T) ((-261 . -101) T) ((-260 . -101) T) ((-259 . -101) T) ((-334 . -1007) 89635) ((-204 . -101) T) ((-203 . -101) T) ((-201 . -101) T) ((-200 . -101) T) ((-199 . -101) T) ((-198 . -101) T) ((-195 . -101) T) ((-194 . -101) T) ((-687 . -1022) 89458) ((-193 . -101) T) 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. -35) 88517) ((-1126 . -1157) 88483) ((-1126 . -1160) 88449) ((-1126 . -94) 88415) ((-352 . -1075) T) ((-350 . -1111) 88394) ((-344 . -1111) 88373) ((-336 . -1111) 88352) ((-1126 . -35) 88318) ((-1088 . -35) 88284) ((-1088 . -94) 88250) ((-107 . -1111) T) ((-1088 . -1160) 88216) ((-807 . -1023) 88195) ((-621 . -300) 88133) ((-608 . -300) 87984) ((-1088 . -1157) 87950) ((-687 . -1016) T) ((-1027 . -615) 87932) ((-1043 . -38) 87800) ((-921 . -615) 87748) ((-973 . -145) T) ((-973 . -143) NIL) ((-370 . -1075) T) ((-315 . -25) T) ((-313 . -23) T) ((-912 . -821) 87727) ((-687 . -317) 87704) ((-471 . -615) 87652) ((-40 . -1007) 87540) ((-675 . -692) 87527) ((-687 . -225) T) ((-330 . -1063) T) ((-171 . -1063) T) ((-322 . -821) T) ((-409 . -442) 87477) ((-370 . -23) T) ((-350 . -38) 87442) ((-344 . -38) 87407) ((-336 . -38) 87372) ((-79 . -431) T) ((-79 . -386) T) ((-217 . -25) T) ((-217 . -21) T) ((-808 . -1075) T) ((-107 . -38) 87322) ((-801 . -1075) T) ((-748 . -1063) T) ((-116 . -692) 87309) ((-646 . -1007) 87293) ((-590 . -101) T) ((-808 . -23) T) ((-801 . -23) T) ((-1116 . -277) 87270) ((-1076 . -300) 87208) ((-1065 . -227) 87192) ((-63 . -387) T) ((-63 . -386) T) ((-110 . -101) T) ((-40 . -368) 87169) ((-95 . -101) T) ((-627 . -823) 87153) ((-1027 . -21) T) ((-1027 . -25) T) ((-789 . -223) 87122) ((-921 . -25) T) ((-921 . -21) T) ((-597 . -1023) T) ((-471 . -25) T) ((-471 . -21) T) ((-996 . -300) 87060) ((-858 . -591) 87042) ((-854 . -591) 87024) ((-242 . -821) 86975) ((-241 . -821) 86926) ((-512 . -503) 86859) ((-840 . -615) 86836) ((-466 . -300) 86774) ((-453 . -300) 86712) ((-342 . -281) T) ((-1116 . -1206) 86696) ((-1102 . -591) 86658) ((-1102 . -592) 86619) ((-1100 . -101) T) ((-968 . -1022) 86515) ((-40 . -869) 86467) ((-1116 . -582) 86444) ((-1246 . -622) 86431) ((-1028 . -149) 86377) ((-841 . -1176) T) ((-968 . -111) 86259) ((-330 . -692) 86243) ((-835 . -591) 86225) ((-171 . -692) 86157) ((-398 . -277) 86115) ((-841 . -539) T) ((-107 . -391) 86097) ((-83 . -375) T) ((-83 . -386) T) ((-675 . -169) T) ((-594 . -591) 86079) ((-98 . -701) T) ((-472 . -101) 85869) ((-98 . -463) T) ((-116 . -169) T) ((-1076 . -38) 85839) ((-166 . -615) 85787) ((-1020 . -101) T) ((-840 . -25) T) ((-789 . -230) 85766) ((-840 . -21) T) ((-792 . -101) T) ((-405 . -101) T) ((-376 . -101) T) ((-110 . -300) NIL) ((-219 . -101) 85744) ((-127 . -1172) T) ((-121 . -1172) T) ((-1003 . -130) T) ((-644 . -358) 85728) ((-968 . -1016) T) ((-1191 . -615) 85676) ((-1067 . -591) 85658) ((-972 . -591) 85640) ((-504 . -23) T) ((-499 . -23) T) ((-334 . -298) T) ((-497 . -23) T) ((-313 . -130) T) ((-3 . -1063) T) ((-972 . -592) 85624) ((-968 . -235) 85603) ((-968 . -225) 85582) ((-1246 . -701) T) ((-1210 . -143) 85561) ((-807 . -1063) T) ((-1210 . -145) 85540) ((-1203 . -145) 85519) ((-1203 . -143) 85498) ((-1202 . -1176) 85477) ((-1182 . -143) 85384) ((-1182 . -145) 85291) ((-1181 . -1176) 85270) ((-370 . -130) T) ((-547 . -855) 85252) ((0 . -1063) T) ((-171 . -169) T) ((-166 . -21) T) ((-166 . -25) T) ((-49 . -1063) T) ((-1204 . -622) 85157) ((-1202 . -539) 85108) ((-689 . -1075) T) ((-1181 . -539) 85059) ((-547 . -1007) 85041) ((-574 . -145) 85020) ((-574 . -143) 84999) ((-484 . -1007) 84942) ((-86 . -375) T) ((-86 . -386) T) ((-841 . -354) T) ((-808 . -130) T) ((-801 . -130) T) ((-689 . -23) T) ((-495 . -591) 84892) ((-491 . -591) 84874) ((-1242 . -1023) T) ((-370 . -1025) T) ((-995 . -1063) 84852) ((-870 . -34) T) ((-472 . -300) 84790) ((-571 . -101) T) ((-1116 . -592) 84751) ((-1116 . -591) 84683) ((-1131 . -821) 84662) ((-45 . -101) T) ((-1087 . -821) 84641) ((-791 . -101) T) ((-1191 . -25) T) ((-1191 . -21) T) ((-826 . -25) T) ((-44 . -358) 84625) ((-826 . -21) T) ((-706 . -442) 84576) ((-1241 . -591) 84558) ((-584 . -1047) T) ((-1020 . -300) 84496) ((-554 . -25) T) ((-554 . -21) T) ((-381 . -1063) T) ((-645 . -1047) T) ((-158 . -1047) T) ((-153 . -1047) T) ((-597 . -1063) T) ((-673 . -855) 84478) ((-1218 . -1172) T) ((-219 . -300) 84416) ((-142 . -359) T) ((-1013 . -592) 84358) ((-1013 . -591) 84301) ((-304 . -878) NIL) ((-673 . -1007) 84246) ((-686 . -889) T) ((-464 . -1176) 84225) ((-1132 . -442) 84204) ((-1126 . -442) 84183) ((-321 . -101) T) ((-841 . -1075) T) ((-307 . -622) 84004) ((-304 . -622) 83933) ((-464 . -539) 83884) ((-330 . -503) 83850) ((-533 . -149) 83800) ((-40 . -298) T) ((-814 . -591) 83782) ((-675 . -281) T) ((-841 . -23) T) ((-370 . -482) T) ((-1043 . -223) 83752) ((-501 . -101) T) ((-398 . -592) 83560) ((-398 . -591) 83542) ((-254 . -591) 83524) ((-116 . -281) T) ((-1204 . -701) T) ((-1202 . -354) 83503) ((-1181 . -354) 83482) ((-1231 . -34) T) ((-117 . -1172) T) ((-107 . -223) 83464) ((-1137 . -101) T) ((-467 . -1063) T) ((-512 . -479) 83448) ((-712 . -34) T) ((-472 . -38) 83418) ((-139 . -34) T) ((-117 . -853) 83395) ((-117 . -855) NIL) ((-599 . -1007) 83278) ((-619 . -821) 83257) ((-1230 . -101) T) ((-286 . -101) T) ((-687 . -359) 83236) ((-117 . -1007) 83213) ((-381 . -692) 83197) ((-597 . -692) 83181) 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72964) ((-427 . -101) T) ((-45 . -1109) 72914) ((-116 . -111) 72899) ((-611 . -695) T) ((-585 . -695) T) ((-789 . -503) 72832) ((-1004 . -1172) T) ((-912 . -149) 72816) ((-514 . -101) T) ((-509 . -101) 72766) ((-1131 . -442) 72697) ((-1051 . -1176) 72676) ((-756 . -1176) 72655) ((-754 . -1176) 72634) ((-61 . -1172) T) ((-467 . -591) 72586) ((-467 . -592) 72508) ((-1118 . -1063) T) ((-1102 . -622) 72482) ((-1087 . -442) 72433) ((-1051 . -539) 72364) ((-472 . -402) 72333) ((-599 . -889) 72312) ((-444 . -1176) 72291) ((-963 . -1063) T) ((-756 . -539) 72202) ((-389 . -591) 72184) ((-754 . -539) 72115) ((-649 . -503) 72048) ((-706 . -300) 72035) ((-638 . -25) T) ((-638 . -21) T) ((-444 . -539) 71966) ((-117 . -889) T) ((-117 . -794) NIL) ((-346 . -25) T) ((-346 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-335 . -25) T) ((-335 . -21) T) ((-255 . -25) T) ((-255 . -21) T) ((-82 . -375) T) ((-82 . -386) T) ((-239 . -25) T) ((-239 . -21) T) ((-1220 . -591) 71948) ((-1166 . -1075) T) ((-1166 . 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. -38) 69670) ((-330 . -1016) T) ((-1126 . -38) 69466) ((-1043 . -169) T) ((-171 . -1016) T) ((-1088 . -38) 69363) ((-687 . -47) 69340) ((-350 . -169) T) ((-344 . -169) T) ((-508 . -56) 69314) ((-486 . -56) 69264) ((-342 . -1237) 69241) ((-217 . -442) T) ((-310 . -281) 69192) ((-336 . -169) T) ((-171 . -235) T) ((-1181 . -821) 69091) ((-107 . -169) T) ((-841 . -961) 69075) ((-632 . -1075) T) ((-561 . -354) T) ((-561 . -320) 69062) ((-507 . -320) 69039) ((-507 . -354) T) ((-307 . -298) 69018) ((-304 . -298) T) ((-580 . -821) 68997) ((-1076 . -692) 68939) ((-509 . -273) 68923) ((-632 . -23) T) ((-409 . -223) 68907) ((-304 . -991) NIL) ((-327 . -23) T) ((-102 . -979) 68891) ((-45 . -36) 68870) ((-590 . -1063) T) ((-342 . -359) T) ((-513 . -101) T) ((-484 . -27) T) ((-232 . -300) 68808) ((-1051 . -1075) T) ((-1241 . -622) 68782) ((-756 . -1075) T) ((-754 . -1075) T) ((-444 . -1075) T) ((-1027 . -442) T) ((-921 . -442) 68733) ((-110 . -1063) T) ((-1051 . -23) T) ((-791 . -1023) T) ((-756 . -23) T) ((-754 . -23) T) ((-471 . -442) 68684) ((-1119 . -503) 68467) ((-372 . -373) 68446) ((-1137 . -402) 68430) ((-451 . -23) T) ((-444 . -23) T) ((-95 . -1063) T) ((-474 . -503) 68363) ((-280 . -281) T) ((-1045 . -591) 68345) ((-398 . -878) 68324) ((-50 . -1075) T) ((-993 . -889) T) ((-972 . -701) T) ((-687 . -855) NIL) ((-561 . -1075) T) ((-507 . -1075) T) ((-814 . -622) 68297) ((-1166 . -130) T) ((-1126 . -391) 68249) ((-973 . -300) NIL) ((-789 . -479) 68233) ((-345 . -889) T) ((-1116 . -34) T) ((-398 . -622) 68185) ((-50 . -23) T) ((-686 . -130) T) ((-687 . -1007) 68065) ((-561 . -23) T) ((-107 . -503) NIL) ((-507 . -23) T) ((-166 . -400) 68036) ((-128 . -300) NIL) ((-1100 . -1063) T) ((-1233 . -1232) 68020) ((-675 . -769) T) ((-675 . -766) T) ((-1082 . -298) T) ((-370 . -145) T) ((-271 . -591) 68002) ((-1181 . -961) 67972) ((-48 . -889) T) ((-649 . -479) 67956) ((-242 . -1225) 67926) ((-241 . -1225) 67896) ((-1135 . -821) T) ((-1076 . -169) 67875) ((-1082 . -991) T) ((-1013 . 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. -1016) T) ((-1088 . -971) 35308) ((-1043 . -701) T) ((-687 . -1075) T) ((-575 . -281) 35287) ((-574 . -281) 35266) ((-477 . -235) T) ((-477 . -225) T) ((-209 . -235) T) ((-209 . -225) T) ((-1125 . -591) 35248) ((-841 . -38) 35200) ((-350 . -701) T) ((-344 . -701) T) ((-336 . -701) T) ((-107 . -768) T) ((-107 . -765) T) ((-509 . -1206) 35184) ((-107 . -701) T) ((-687 . -23) T) ((-1246 . -25) T) ((-464 . -275) 35150) ((-1246 . -21) T) ((-1181 . -300) 35089) ((-1135 . -101) T) ((-40 . -143) 35061) ((-40 . -145) 35033) ((-509 . -582) 35010) ((-1076 . -622) 34858) ((-580 . -300) 34796) ((-45 . -625) 34746) ((-45 . -640) 34696) ((-45 . -364) 34646) ((-1118 . -34) T) ((-840 . -819) NIL) ((-628 . -130) T) ((-475 . -591) 34628) ((-232 . -277) 34605) ((-621 . -34) T) ((-608 . -34) T) ((-1051 . -442) 34556) ((-790 . -503) 34430) ((-756 . -442) 34361) ((-754 . -442) 34312) ((-444 . -442) 34263) ((-921 . -402) 34247) ((-706 . -591) 34229) ((-242 . -692) 34171) ((-241 . -692) 34113) ((-706 . -592) 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. -101) T) ((-335 . -101) T) ((-255 . -101) T) ((-239 . -101) T) ((-467 . -298) T) ((-1027 . -1023) T) ((-921 . -1023) T) ((-307 . -615) 32963) ((-304 . -615) 32924) ((-471 . -1023) T) ((-469 . -101) T) ((-427 . -591) 32906) ((-1131 . -1063) T) ((-1087 . -1063) T) ((-825 . -1063) T) ((-1101 . -101) T) ((-790 . -281) 32837) ((-932 . -1022) 32720) ((-467 . -991) T) ((-128 . -19) 32702) ((-710 . -1022) 32672) ((-128 . -582) 32647) ((-443 . -1022) 32617) ((-1107 . -1083) 32601) ((-1065 . -503) 32534) ((-932 . -111) 32403) ((-879 . -101) T) ((-710 . -111) 32368) ((-514 . -591) 32334) ((-58 . -101) 32284) ((-509 . -592) 32245) ((-509 . -591) 32157) ((-508 . -101) 32135) ((-505 . -101) 32085) ((-486 . -101) 32063) ((-485 . -101) 32013) ((-443 . -111) 31976) ((-242 . -169) 31955) ((-241 . -169) 31934) ((-409 . -1022) 31908) ((-1166 . -942) 31870) ((-968 . -1075) T) ((-912 . -503) 31803) ((-477 . -769) T) ((-464 . -38) 31644) ((-409 . -111) 31611) ((-477 . -766) T) ((-969 . -300) 31549) ((-209 . -769) T) ((-209 . -766) T) ((-968 . -23) T) ((-687 . -130) T) ((-1181 . -391) 31519) ((-307 . -25) 31371) ((-166 . -402) 31355) ((-307 . -21) 31226) ((-304 . -25) T) ((-304 . -21) T) ((-834 . -359) T) ((-110 . -34) T) ((-472 . -622) 31074) ((-840 . -1023) T) ((-572 . -279) 31049) ((-560 . -145) T) ((-547 . -145) T) ((-484 . -145) T) ((-1131 . -692) 30878) ((-1087 . -692) 30727) ((-1082 . -615) 30709) ((-825 . -692) 30679) ((-644 . -1172) T) ((-1 . -101) T) ((-232 . -591) 30410) ((-1191 . -402) 30394) ((-1145 . -300) 30198) ((-932 . -1016) T) ((-710 . -1016) T) ((-690 . -1016) T) ((-619 . -1063) 30148) ((-1020 . -622) 30132) ((-826 . -402) 30116) ((-500 . -101) T) ((-496 . -101) T) ((-239 . -300) 30103) ((-255 . -300) 30090) ((-932 . -317) 30069) ((-376 . -622) 30053) ((-469 . -300) 29857) ((-242 . -503) 29790) ((-644 . -1007) 29686) ((-241 . -503) 29619) ((-1101 . -300) 29545) ((-793 . -1063) T) ((-773 . -1022) 29529) ((-1210 . -277) 29514) ((-1203 . -277) 29499) ((-1182 . -277) 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. -532) T) ((-495 . -101) T) ((-491 . -101) T) ((-345 . -169) T) ((-334 . -591) 115130) ((-385 . -591) 115112) ((-464 . -701) T) ((-1082 . -819) T) ((-861 . -1007) 115080) ((-107 . -821) T) ((-632 . -1022) 115064) ((-477 . -130) T) ((-1205 . -1023) T) ((-209 . -130) T) ((-1117 . -101) 115042) ((-98 . -1063) T) ((-237 . -640) 115026) ((-237 . -625) 115010) ((-632 . -111) 114989) ((-307 . -402) 114973) ((-237 . -364) 114957) ((-1120 . -227) 114904) ((-968 . -223) 114888) ((-73 . -1173) T) ((-48 . -169) T) ((-675 . -378) T) ((-675 . -141) T) ((-1242 . -101) T) ((-1051 . -1022) 114731) ((-255 . -878) 114710) ((-239 . -878) 114689) ((-756 . -1022) 114512) ((-754 . -1022) 114355) ((-586 . -1173) T) ((-1125 . -591) 114337) ((-1051 . -111) 114166) ((-1013 . -101) T) ((-465 . -1173) T) ((-451 . -1022) 114137) ((-444 . -1022) 113980) ((-638 . -622) 113964) ((-840 . -298) T) ((-756 . -111) 113773) ((-754 . -111) 113602) ((-346 . -622) 113554) ((-343 . -622) 113506) ((-335 . -622) 113458) ((-255 . 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-101) T) ((-345 . -1238) 95886) ((-1239 . -101) T) ((-1205 . -111) 95778) ((-142 . -591) 95760) ((-962 . -130) T) ((-44 . -101) T) ((-232 . -821) 95711) ((-1192 . -1177) 95690) ((-102 . -479) 95674) ((-1242 . -692) 95644) ((-1051 . -47) 95605) ((-1027 . -1075) T) ((-921 . -1075) T) ((-127 . -34) T) ((-121 . -34) T) ((-756 . -47) 95582) ((-754 . -47) 95554) ((-1192 . -539) 95465) ((-345 . -359) T) ((-471 . -1075) T) ((-1132 . -130) T) ((-1087 . -130) T) ((-444 . -47) 95444) ((-840 . -354) T) ((-825 . -130) T) ((-150 . -101) T) ((-1027 . -23) T) ((-921 . -23) T) ((-554 . -539) T) ((-790 . -25) T) ((-790 . -21) T) ((-1103 . -503) 95377) ((-571 . -1047) T) ((-565 . -1007) 95361) ((-471 . -23) T) ((-342 . -1023) T) ((-1167 . -869) 95342) ((-644 . -300) 95280) ((-1076 . -1226) 95250) ((-673 . -622) 95215) ((-972 . -169) T) ((-932 . -143) 95194) ((-611 . -1063) T) ((-585 . -1063) T) ((-932 . -145) 95173) ((-973 . -821) T) ((-710 . -145) 95152) ((-710 . -143) 95131) ((-940 . -821) T) ((-464 . -889) 95110) ((-307 . -1022) 95020) ((-304 . -1022) 94949) ((-968 . -277) 94907) ((-398 . -692) 94859) ((-128 . -821) T) ((-675 . -819) T) ((-1205 . -1016) T) ((-307 . -111) 94755) ((-304 . -111) 94668) ((-933 . -101) T) ((-789 . -101) 94458) ((-687 . -592) NIL) ((-687 . -591) 94440) ((-632 . -1007) 94336) ((-1205 . -317) 94280) ((-1004 . -279) 94255) ((-560 . -701) T) ((-547 . -768) T) ((-166 . -354) 94206) ((-547 . -765) T) ((-547 . -701) T) ((-484 . -701) T) ((-1107 . -479) 94190) ((-1051 . -855) NIL) ((-840 . -1075) T) ((-117 . -878) NIL) ((-1241 . -1240) 94166) ((-1239 . -1240) 94145) ((-756 . -855) NIL) ((-754 . -855) 94004) ((-1234 . -25) T) ((-1234 . -21) T) ((-1170 . -101) 93982) ((-1069 . -386) T) ((-599 . -622) 93969) ((-444 . -855) NIL) ((-649 . -101) 93947) ((-1051 . -1007) 93774) ((-840 . -23) T) ((-756 . -1007) 93633) ((-754 . -1007) 93490) ((-117 . -622) 93435) ((-444 . -1007) 93311) ((-623 . -1007) 93295) ((-603 . -101) T) ((-214 . -479) 93279) ((-1219 . -34) T) ((-611 . -692) 93263) ((-585 . -692) 93247) ((-644 . -38) 93207) ((-310 . -101) T) ((-84 . -591) 93189) ((-50 . -1007) 93173) ((-1082 . -1022) 93160) ((-1051 . -368) 93144) ((-756 . -368) 93128) ((-59 . -56) 93090) ((-673 . -768) T) ((-673 . -765) T) ((-561 . -1007) 93077) ((-507 . -1007) 93054) ((-673 . -701) T) ((-315 . -130) T) ((-307 . -1016) 92944) ((-304 . -1016) T) ((-166 . -1075) T) ((-754 . -368) 92928) ((-45 . -149) 92878) ((-973 . -961) 92860) ((-444 . -368) 92844) ((-398 . -169) T) ((-307 . -235) 92823) ((-304 . -235) T) ((-304 . -225) NIL) ((-285 . -1063) 92605) ((-217 . -130) T) ((-1082 . -111) 92590) ((-166 . -23) T) ((-773 . -145) 92569) ((-773 . -143) 92548) ((-242 . -615) 92454) ((-241 . -615) 92360) ((-310 . -275) 92326) ((-1117 . -503) 92259) ((-1095 . -1063) T) ((-217 . -1025) T) ((-789 . -300) 92197) ((-1051 . -869) 92132) ((-756 . -869) 92075) ((-754 . -869) 92059) ((-1241 . -38) 92029) ((-1239 . -38) 91999) ((-1192 . -1075) T) ((-826 . -1075) T) ((-444 . -869) 91976) 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-592) 91368) ((-1020 . -1226) 91338) ((-628 . -111) 91317) ((-1103 . -479) 91301) ((-789 . -38) 91271) ((-62 . -431) T) ((-62 . -386) T) ((-1120 . -101) T) ((-840 . -130) T) ((-474 . -101) 91249) ((-1247 . -359) T) ((-1043 . -101) T) ((-1026 . -101) T) ((-342 . -692) 91194) ((-706 . -145) 91173) ((-706 . -143) 91152) ((-993 . -622) 91089) ((-512 . -1063) 91067) ((-350 . -101) T) ((-344 . -101) T) ((-336 . -101) T) ((-107 . -101) T) ((-493 . -1063) T) ((-345 . -622) 91012) ((-1132 . -615) 90960) ((-1087 . -615) 90908) ((-376 . -498) 90887) ((-807 . -819) 90866) ((-370 . -1177) T) ((-668 . -701) T) ((-330 . -1023) T) ((-1183 . -961) 90818) ((-171 . -1023) T) ((-102 . -591) 90750) ((-1134 . -143) 90729) ((-1134 . -145) 90708) ((-370 . -539) T) ((-1133 . -145) 90687) ((-1133 . -143) 90666) ((-1127 . -143) 90573) ((-398 . -281) T) ((-1127 . -145) 90480) ((-1088 . -145) 90459) ((-1088 . -143) 90438) ((-310 . -38) 90279) ((-166 . -130) T) ((-304 . -769) NIL) ((-304 . -766) NIL) ((-628 . -1016) T) ((-48 . -622) 90244) ((-963 . -101) T) ((-962 . -21) T) ((-127 . -979) 90228) ((-121 . -979) 90212) ((-962 . -25) T) ((-870 . -119) 90196) ((-1119 . -101) T) ((-790 . -821) 90175) ((-1192 . -130) T) ((-1132 . -25) T) ((-1132 . -21) T) ((-826 . -130) T) ((-1087 . -25) T) ((-1087 . -21) T) ((-825 . -25) T) ((-825 . -21) T) ((-756 . -298) 90154) ((-621 . -101) 90132) ((-608 . -101) T) ((-1120 . -300) 89927) ((-554 . -130) T) ((-597 . -819) 89906) ((-1117 . -479) 89890) ((-1111 . -149) 89840) ((-1107 . -591) 89802) ((-1107 . -592) 89763) ((-993 . -765) T) ((-993 . -768) T) ((-993 . -701) T) ((-474 . -300) 89701) ((-443 . -408) 89671) ((-342 . -169) T) ((-280 . -38) 89658) ((-265 . -101) T) ((-264 . -101) T) ((-263 . -101) T) ((-262 . -101) T) ((-261 . -101) T) ((-260 . -101) T) ((-259 . -101) T) ((-334 . -1007) 89635) ((-204 . -101) T) ((-203 . -101) T) ((-201 . -101) T) ((-200 . -101) T) ((-199 . -101) T) ((-198 . -101) T) ((-195 . -101) T) ((-194 . -101) T) ((-687 . -1022) 89458) ((-193 . -101) T) ((-192 . -101) T) ((-191 . -101) T) ((-190 . -101) T) ((-189 . -101) T) ((-188 . -101) T) ((-187 . -101) T) ((-186 . -101) T) ((-185 . -101) T) ((-345 . -701) T) ((-687 . -111) 89267) ((-644 . -223) 89251) ((-561 . -298) T) ((-507 . -298) T) ((-285 . -503) 89200) ((-107 . -300) NIL) ((-71 . -386) T) ((-1076 . -101) 88990) ((-807 . -402) 88974) ((-1082 . -769) T) ((-1082 . -766) T) ((-675 . -1063) T) ((-370 . -354) T) ((-166 . -482) 88952) ((-205 . -1063) T) ((-214 . -591) 88884) ((-133 . -1063) T) ((-116 . -1063) T) ((-48 . -701) T) ((-1013 . -479) 88849) ((-495 . -92) T) ((-139 . -416) 88831) ((-139 . -359) T) ((-996 . -101) T) ((-501 . -498) 88810) ((-466 . -101) T) ((-453 . -101) T) ((-1003 . -1075) T) ((-1134 . -35) 88776) ((-1134 . -94) 88742) ((-1134 . -1161) 88708) ((-1134 . -1158) 88674) ((-1119 . -300) NIL) ((-88 . -387) T) ((-88 . -386) T) ((-1043 . -1112) 88653) ((-1133 . -1158) 88619) ((-1133 . -1161) 88585) ((-1003 . -23) T) ((-1133 . -94) 88551) 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-1063) T) ((-116 . -692) 87309) ((-646 . -1007) 87293) ((-590 . -101) T) ((-808 . -23) T) ((-801 . -23) T) ((-1117 . -277) 87270) ((-1076 . -300) 87208) ((-1065 . -227) 87192) ((-63 . -387) T) ((-63 . -386) T) ((-110 . -101) T) ((-40 . -368) 87169) ((-95 . -101) T) ((-627 . -823) 87153) ((-1027 . -21) T) ((-1027 . -25) T) ((-789 . -223) 87122) ((-921 . -25) T) ((-921 . -21) T) ((-597 . -1023) T) ((-471 . -25) T) ((-471 . -21) T) ((-996 . -300) 87060) ((-858 . -591) 87042) ((-854 . -591) 87024) ((-242 . -821) 86975) ((-241 . -821) 86926) ((-512 . -503) 86859) ((-840 . -615) 86836) ((-466 . -300) 86774) ((-453 . -300) 86712) ((-342 . -281) T) ((-1117 . -1207) 86696) ((-1103 . -591) 86658) ((-1103 . -592) 86619) ((-1101 . -101) T) ((-968 . -1022) 86515) ((-40 . -869) 86467) ((-1117 . -582) 86444) ((-1247 . -622) 86431) ((-1028 . -149) 86377) ((-841 . -1177) T) ((-968 . -111) 86259) ((-330 . -692) 86243) ((-835 . -591) 86225) ((-171 . -692) 86157) ((-398 . -277) 86115) ((-841 . -539) T) ((-107 . -391) 86097) ((-83 . -375) T) ((-83 . -386) T) ((-675 . -169) T) ((-594 . -591) 86079) ((-98 . -701) T) ((-472 . -101) 85869) ((-98 . -463) T) ((-116 . -169) T) ((-1076 . -38) 85839) ((-166 . -615) 85787) ((-1020 . -101) T) ((-840 . -25) T) ((-789 . -230) 85766) ((-840 . -21) T) ((-792 . -101) T) ((-405 . -101) T) ((-376 . -101) T) ((-110 . -300) NIL) ((-219 . -101) 85744) ((-127 . -1173) T) ((-121 . -1173) T) ((-1003 . -130) T) ((-644 . -358) 85728) ((-968 . -1016) T) ((-1192 . -615) 85676) ((-1067 . -591) 85658) ((-972 . -591) 85640) ((-504 . -23) T) ((-499 . -23) T) ((-334 . -298) T) ((-497 . -23) T) ((-313 . -130) T) ((-3 . -1063) T) ((-972 . -592) 85624) ((-968 . -235) 85603) ((-968 . -225) 85582) ((-1247 . -701) T) ((-1211 . -143) 85561) ((-807 . -1063) T) ((-1211 . -145) 85540) ((-1204 . -145) 85519) ((-1204 . -143) 85498) ((-1203 . -1177) 85477) ((-1183 . -143) 85384) ((-1183 . -145) 85291) ((-1182 . -1177) 85270) ((-370 . -130) T) ((-547 . -855) 85252) ((0 . -1063) T) 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-300) 84416) ((-142 . -359) T) ((-1013 . -592) 84358) ((-1013 . -591) 84301) ((-304 . -878) NIL) ((-673 . -1007) 84246) ((-686 . -889) T) ((-464 . -1177) 84225) ((-1133 . -442) 84204) ((-1127 . -442) 84183) ((-321 . -101) T) ((-841 . -1075) T) ((-307 . -622) 84004) ((-304 . -622) 83933) ((-464 . -539) 83884) ((-330 . -503) 83850) ((-533 . -149) 83800) ((-40 . -298) T) ((-814 . -591) 83782) ((-675 . -281) T) ((-841 . -23) T) ((-370 . -482) T) ((-1043 . -223) 83752) ((-501 . -101) T) ((-398 . -592) 83560) ((-398 . -591) 83542) ((-254 . -591) 83524) ((-116 . -281) T) ((-1205 . -701) T) ((-1203 . -354) 83503) ((-1182 . -354) 83482) ((-1232 . -34) T) ((-117 . -1173) T) ((-107 . -223) 83464) ((-1138 . -101) T) ((-467 . -1063) T) ((-512 . -479) 83448) ((-712 . -34) T) ((-472 . -38) 83418) ((-139 . -34) T) ((-117 . -853) 83395) ((-117 . -855) NIL) ((-599 . -1007) 83278) ((-619 . -821) 83257) ((-1231 . -101) T) ((-286 . -101) T) ((-687 . -359) 83236) ((-117 . -1007) 83213) ((-381 . -692) 83197) 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80262) ((-343 . -354) T) ((-335 . -320) 80246) ((-335 . -354) T) ((-477 . -101) T) ((-1231 . -38) 80216) ((-512 . -661) 80166) ((-209 . -101) T) ((-993 . -1007) 80046) ((-972 . -111) 79975) ((-1134 . -942) 79944) ((-1133 . -942) 79906) ((-509 . -149) 79890) ((-1043 . -361) 79869) ((-342 . -591) 79851) ((-313 . -21) T) ((-345 . -1007) 79828) ((-313 . -25) T) ((-1127 . -942) 79797) ((-1088 . -942) 79764) ((-75 . -591) 79746) ((-673 . -298) T) ((-166 . -821) 79725) ((-879 . -354) T) ((-370 . -25) T) ((-370 . -21) T) ((-879 . -320) 79712) ((-85 . -591) 79694) ((-673 . -991) T) ((-651 . -821) T) ((-1203 . -130) T) ((-1182 . -130) T) ((-870 . -979) 79678) ((-808 . -21) T) ((-48 . -1007) 79621) ((-808 . -25) T) ((-801 . -25) T) ((-801 . -21) T) ((-1241 . -1023) T) ((-1239 . -1023) T) ((-628 . -701) T) ((-1242 . -1022) 79605) ((-1192 . -821) 79584) ((-789 . -402) 79553) ((-102 . -119) 79537) ((-129 . -1063) T) ((-52 . -1063) T) ((-895 . -591) 79519) ((-840 . -961) 79496) ((-797 . -101) T) 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78624) ((-1132 . -143) 78603) ((-1132 . -145) 78582) ((-1087 . -145) 78561) ((-1087 . -143) 78540) ((-611 . -1022) 78524) ((-585 . -1022) 78508) ((-644 . -1063) T) ((-644 . -1019) 78448) ((-1134 . -1210) 78432) ((-1134 . -1197) 78409) ((-477 . -1112) T) ((-1133 . -1202) 78370) ((-1133 . -1197) 78340) ((-1133 . -1200) 78324) ((-209 . -1112) T) ((-334 . -889) T) ((-792 . -257) 78308) ((-611 . -111) 78287) ((-585 . -111) 78266) ((-1127 . -1181) 78227) ((-814 . -1016) 78206) ((-1127 . -1197) 78183) ((-504 . -25) T) ((-484 . -293) T) ((-500 . -23) T) ((-499 . -25) T) ((-497 . -25) T) ((-496 . -23) T) ((-1127 . -1179) 78167) ((-398 . -1016) T) ((-310 . -1023) T) ((-668 . -298) T) ((-107 . -819) T) ((-398 . -235) T) ((-398 . -225) 78146) ((-687 . -701) T) ((-477 . -38) 78096) ((-209 . -38) 78046) ((-464 . -482) 78012) ((-1119 . -1105) T) ((-1064 . -101) T) ((-675 . -591) 77994) ((-675 . -592) 77909) ((-689 . -21) T) ((-689 . -25) T) ((-205 . -591) 77891) ((-133 . -591) 77873) ((-116 . -591) 77855) ((-154 . -25) T) ((-1241 . -1063) T) ((-841 . -615) 77803) ((-1239 . -1063) T) ((-932 . -101) T) ((-710 . -101) T) ((-690 . -101) T) ((-443 . -101) T) ((-790 . -442) 77754) ((-44 . -1063) T) ((-1052 . -821) T) ((-638 . -130) T) ((-1028 . -300) 77605) ((-644 . -692) 77589) ((-280 . -1023) T) ((-346 . -130) T) ((-343 . -130) T) ((-335 . -130) T) ((-255 . -130) T) ((-239 . -130) T) ((-409 . -101) T) ((-150 . -1063) T) ((-45 . -221) 77539) ((-927 . -821) 77518) ((-968 . -622) 77456) ((-232 . -1226) 77426) ((-993 . -298) T) ((-285 . -1022) 77347) ((-879 . -130) T) ((-40 . -889) T) ((-477 . -391) 77329) ((-345 . -298) T) ((-209 . -391) 77311) ((-1043 . -402) 77295) ((-285 . -111) 77211) ((-841 . -25) T) ((-841 . -21) T) ((-330 . -591) 77193) ((-1205 . -47) 77137) ((-217 . -145) T) ((-171 . -591) 77119) ((-1076 . -819) 77098) ((-748 . -591) 77080) ((-586 . -227) 77027) ((-465 . -227) 76977) ((-1241 . -692) 76947) ((-48 . -298) T) ((-1239 . -692) 76917) ((-933 . -1063) T) ((-789 . -1063) 76707) ((-303 . -101) T) ((-870 . -1173) T) ((-48 . -991) T) ((-1182 . -615) 76615) ((-663 . -101) 76593) ((-44 . -692) 76577) ((-533 . -101) T) ((-66 . -374) T) ((-66 . -386) T) ((-636 . -23) T) ((-644 . -736) T) ((-1170 . -1063) 76555) ((-342 . -1022) 76500) ((-649 . -1063) 76478) ((-1027 . -145) T) ((-921 . -145) 76457) ((-921 . -143) 76436) ((-773 . -101) T) ((-150 . -692) 76420) ((-471 . -145) 76399) ((-471 . -143) 76378) ((-342 . -111) 76307) ((-1043 . -1023) T) ((-313 . -821) 76286) ((-1211 . -942) 76255) ((-603 . -1063) T) ((-1204 . -942) 76217) ((-500 . -130) T) ((-496 . -130) T) ((-286 . -221) 76167) ((-350 . -1023) T) ((-344 . -1023) T) ((-336 . -1023) T) ((-285 . -1016) 76109) ((-1183 . -942) 76078) ((-370 . -821) T) ((-107 . -1023) T) ((-968 . -701) T) ((-839 . -889) T) ((-814 . -769) 76057) ((-814 . -766) 76036) ((-409 . -300) 75975) ((-458 . -101) T) ((-574 . -942) 75944) ((-310 . -1063) T) ((-398 . -769) 75923) ((-398 . -766) 75902) ((-489 . -479) 75884) ((-1205 . -1007) 75850) ((-1203 . -21) T) ((-1203 . -25) T) ((-1182 . -21) T) ((-1182 . -25) T) ((-789 . -692) 75792) ((-673 . -395) T) ((-584 . -101) T) ((-1232 . -1173) T) ((-1076 . -402) 75761) ((-972 . -359) NIL) ((-645 . -101) T) ((-158 . -101) T) ((-153 . -101) T) ((-102 . -34) T) ((-712 . -1173) T) ((-44 . -736) T) ((-572 . -101) T) ((-76 . -387) T) ((-76 . -386) T) ((-627 . -630) 75745) ((-139 . -1173) T) ((-840 . -145) T) ((-840 . -143) NIL) ((-1172 . -92) T) ((-342 . -1016) T) ((-69 . -374) T) ((-69 . -386) T) ((-1126 . -101) T) ((-644 . -503) 75678) ((-663 . -300) 75616) ((-932 . -38) 75513) ((-710 . -38) 75483) ((-533 . -300) 75287) ((-307 . -1173) T) ((-342 . -225) T) ((-342 . -235) T) ((-304 . -1173) T) ((-280 . -1063) T) ((-1140 . -591) 75269) ((-686 . -1177) T) ((-1117 . -625) 75253) ((-1167 . -539) 75232) ((-686 . -539) T) ((-307 . -853) 75216) ((-307 . -855) 75141) ((-304 . -853) 75102) ((-304 . -855) NIL) ((-773 . -300) 75067) ((-310 . -692) 74908) ((-315 . -314) 74885) 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-1063) T) ((-1088 . -101) T) ((-214 . -34) T) ((-280 . -692) 73837) ((-1120 . -588) 73813) ((-572 . -300) NIL) ((-474 . -1063) 73791) ((-381 . -591) 73773) ((-499 . -821) T) ((-1111 . -221) 73723) ((-1211 . -1210) 73707) ((-1211 . -1197) 73684) ((-1204 . -1202) 73645) ((-1204 . -1197) 73615) ((-1204 . -1200) 73599) ((-1183 . -1181) 73560) ((-1183 . -1197) 73537) ((-597 . -591) 73519) ((-1183 . -1179) 73503) ((-673 . -889) T) ((-1134 . -275) 73469) ((-1133 . -275) 73435) ((-1127 . -275) 73401) ((-1043 . -1063) T) ((-1026 . -1063) T) ((-48 . -293) T) ((-307 . -869) 73367) ((-304 . -869) NIL) ((-1026 . -1033) 73346) ((-1082 . -855) 73328) ((-773 . -38) 73312) ((-255 . -615) 73260) ((-239 . -615) 73208) ((-675 . -1022) 73195) ((-574 . -1197) 73172) ((-1088 . -275) 73138) ((-310 . -169) 73069) ((-350 . -1063) T) ((-344 . -1063) T) ((-336 . -1063) T) ((-489 . -19) 73051) ((-1082 . -1007) 73033) ((-1065 . -149) 73017) ((-107 . -1063) T) ((-116 . -1022) 73004) ((-686 . -354) T) ((-489 . -582) 72979) ((-675 . -111) 72964) ((-427 . -101) T) ((-45 . -1110) 72914) ((-116 . -111) 72899) ((-611 . -695) T) ((-585 . -695) T) ((-789 . -503) 72832) ((-1004 . -1173) T) ((-912 . -149) 72816) ((-514 . -101) T) ((-509 . -101) 72766) ((-1132 . -442) 72697) ((-1051 . -1177) 72676) ((-756 . -1177) 72655) ((-754 . -1177) 72634) ((-61 . -1173) T) ((-467 . -591) 72586) ((-467 . -592) 72508) ((-1119 . -1063) T) ((-1103 . -622) 72482) ((-1087 . -442) 72433) ((-1051 . -539) 72364) ((-472 . -402) 72333) ((-599 . -889) 72312) ((-444 . -1177) 72291) ((-963 . -1063) T) ((-756 . -539) 72202) ((-389 . -591) 72184) ((-754 . -539) 72115) ((-649 . -503) 72048) ((-706 . -300) 72035) ((-638 . -25) T) ((-638 . -21) T) ((-444 . -539) 71966) ((-117 . -889) T) ((-117 . -794) NIL) ((-346 . -25) T) ((-346 . -21) T) ((-343 . -25) T) ((-343 . -21) T) ((-335 . -25) T) ((-335 . -21) T) ((-255 . -25) T) ((-255 . -21) T) ((-82 . -375) T) ((-82 . -386) T) ((-239 . -25) T) ((-239 . -21) T) ((-1221 . -591) 71948) ((-1167 . -1075) T) ((-1167 . -23) T) ((-1127 . -300) 71833) ((-1088 . -300) 71820) ((-1043 . -692) 71688) ((-835 . -622) 71648) ((-912 . -949) 71632) ((-879 . -21) T) ((-280 . -169) T) ((-879 . -25) T) ((-302 . -92) T) ((-841 . -821) 71583) ((-686 . -1075) T) ((-686 . -23) T) ((-621 . -1063) 71561) ((-608 . -588) 71536) ((-608 . -1063) T) ((-561 . -1177) T) ((-507 . -1177) T) ((-561 . -539) T) ((-507 . -539) T) ((-350 . -692) 71488) ((-344 . -692) 71440) ((-171 . -111) 71351) ((-330 . -1022) 71335) ((-171 . -1022) 71267) ((-107 . -692) 71217) ((-336 . -692) 71169) ((-330 . -111) 71148) ((-265 . -1063) T) ((-264 . -1063) T) ((-263 . -1063) T) ((-262 . -1063) T) ((-675 . -1016) T) ((-261 . -1063) T) ((-260 . -1063) T) ((-259 . -1063) T) ((-204 . -1063) T) ((-203 . -1063) T) ((-201 . -1063) T) ((-166 . -1161) 71126) ((-166 . -1158) 71104) ((-200 . -1063) T) ((-199 . -1063) T) ((-116 . -1016) T) ((-198 . -1063) T) ((-195 . -1063) T) ((-675 . -225) T) ((-194 . -1063) T) ((-193 . -1063) T) ((-192 . -1063) T) ((-191 . -1063) T) ((-190 . -1063) T) ((-189 . -1063) T) ((-188 . -1063) T) ((-187 . -1063) T) ((-186 . -1063) T) ((-185 . -1063) T) ((-232 . -101) 70894) ((-166 . -35) 70872) ((-166 . -94) 70850) ((-628 . -1007) 70746) ((-472 . -1023) 70676) ((-1076 . -1063) 70466) ((-1103 . -34) T) ((-644 . -479) 70450) ((-72 . -1173) T) ((-104 . -591) 70432) ((-1243 . -591) 70414) ((-372 . -591) 70396) ((-554 . -1161) T) ((-554 . -1158) T) ((-706 . -38) 70245) ((-519 . -591) 70227) ((-509 . -300) 70165) ((-489 . -591) 70147) ((-489 . -592) 70129) ((-1172 . -591) 70095) ((-1127 . -1112) NIL) ((-996 . -1036) 70064) ((-996 . -1063) T) ((-973 . -101) T) ((-940 . -101) T) ((-883 . -101) T) ((-862 . -1007) 70041) ((-1103 . -701) T) ((-972 . -622) 69986) ((-466 . -1063) T) ((-453 . -1063) T) ((-565 . -23) T) ((-554 . -35) T) ((-554 . -94) T) ((-418 . -101) T) ((-1028 . -221) 69932) ((-128 . -101) T) ((-1134 . -38) 69829) ((-835 . -701) T) ((-668 . -889) T) ((-500 . -25) T) ((-496 . -21) T) ((-496 . -25) T) ((-1133 . -38) 69670) ((-330 . -1016) T) ((-1127 . -38) 69466) ((-1043 . -169) T) ((-171 . -1016) T) ((-1088 . -38) 69363) ((-687 . -47) 69340) ((-350 . -169) T) ((-344 . -169) T) ((-508 . -56) 69314) ((-486 . -56) 69264) ((-342 . -1238) 69241) ((-217 . -442) T) ((-310 . -281) 69192) ((-336 . -169) T) ((-171 . -235) T) ((-1182 . -821) 69091) ((-107 . -169) T) ((-841 . -961) 69075) ((-632 . -1075) T) ((-561 . -354) T) ((-561 . -320) 69062) ((-507 . -320) 69039) ((-507 . -354) T) ((-307 . -298) 69018) ((-304 . -298) T) ((-580 . -821) 68997) ((-1076 . -692) 68939) ((-509 . -273) 68923) ((-632 . -23) T) ((-409 . -223) 68907) ((-304 . -991) NIL) ((-327 . -23) T) ((-102 . -979) 68891) ((-45 . -36) 68870) ((-590 . -1063) T) ((-342 . -359) T) ((-513 . -101) T) ((-484 . -27) T) ((-232 . -300) 68808) ((-1051 . -1075) T) ((-1242 . -622) 68782) ((-756 . -1075) T) ((-754 . -1075) T) ((-444 . -1075) T) ((-1027 . -442) T) ((-921 . -442) 68733) ((-110 . -1063) T) ((-1051 . -23) T) ((-791 . -1023) T) ((-756 . -23) T) ((-754 . -23) T) ((-471 . -442) 68684) ((-1120 . -503) 68467) ((-372 . -373) 68446) ((-1138 . -402) 68430) ((-451 . -23) T) ((-444 . -23) T) ((-95 . -1063) T) ((-474 . -503) 68363) ((-280 . -281) T) ((-1045 . -591) 68345) ((-398 . -878) 68324) ((-50 . -1075) T) ((-993 . -889) T) ((-972 . -701) T) ((-687 . -855) NIL) ((-561 . -1075) T) ((-507 . -1075) T) ((-814 . -622) 68297) ((-1167 . -130) T) ((-1127 . -391) 68249) ((-973 . -300) NIL) ((-789 . -479) 68233) ((-345 . -889) T) ((-1117 . -34) T) ((-398 . -622) 68185) ((-50 . -23) T) ((-686 . -130) T) ((-687 . -1007) 68065) ((-561 . -23) T) ((-107 . -503) NIL) ((-507 . -23) T) ((-166 . -400) 68036) ((-128 . -300) NIL) ((-1101 . -1063) T) ((-1234 . -1233) 68020) ((-675 . -769) T) ((-675 . -766) T) ((-1082 . -298) T) ((-370 . -145) T) ((-271 . -591) 68002) ((-1182 . -961) 67972) ((-48 . -889) T) ((-649 . -479) 67956) ((-242 . -1226) 67926) ((-241 . -1226) 67896) ((-1136 . -821) T) ((-1076 . -169) 67875) ((-1082 . 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. -768) NIL) ((-923 . -101) T) ((-890 . -101) T) ((-1088 . -701) T) ((-745 . -101) T) ((-646 . -101) T) ((-464 . -1063) T) ((-330 . -1075) T) ((-171 . -1075) T) ((-310 . -889) 9647) ((-1203 . -692) 9488) ((-841 . -169) T) ((-1182 . -692) 9302) ((-814 . -21) 9254) ((-814 . -25) 9206) ((-237 . -1110) 9190) ((-126 . -503) 9123) ((-398 . -25) T) ((-398 . -21) T) ((-330 . -23) T) ((-166 . -592) 8891) ((-166 . -591) 8873) ((-171 . -23) T) ((-619 . -279) 8850) ((-509 . -34) T) ((-867 . -591) 8832) ((-88 . -1173) T) ((-812 . -591) 8814) ((-782 . -591) 8796) ((-743 . -591) 8778) ((-651 . -591) 8760) ((-232 . -622) 8608) ((-1136 . -1063) T) ((-1132 . -1022) 8431) ((-1111 . -1173) T) ((-1087 . -1022) 8274) ((-825 . -1022) 8258) ((-1132 . -111) 8067) ((-1087 . -111) 7896) ((-825 . -111) 7875) ((-1192 . -592) NIL) ((-1192 . -591) 7857) ((-334 . -1112) T) ((-826 . -591) 7839) ((-1039 . -277) 7818) ((-79 . -1173) T) ((-973 . -878) NIL) ((-586 . -277) 7794) ((-1159 . -503) 7727) ((-477 . -1173) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index f716a8d6..372be482 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3430962937) -(4331 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3431009354) +(4332 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -406,9 +406,9 @@ |SquareFreeNormalizedTriangularSetCategory| |PolynomialSolveByFormulas| |RadicalSolvePackage| |TransSolvePackageService| |TransSolvePackage| |SortPackage| - |ThreeSpace| |ThreeSpaceCategory| |SpadParser| |SpecialOutputPackage| - |SpecialFunctionCategory| |SplittingNode| |SplittingTree| - |SquareMatrix| |StringAggregate&| |StringAggregate| + |ThreeSpace| |ThreeSpaceCategory| |SpadParser| |SpadAstExports| + |SpecialOutputPackage| |SpecialFunctionCategory| |SplittingNode| + |SplittingTree| |SquareMatrix| |StringAggregate&| |StringAggregate| |SquareFreeRegularSetDecompositionPackage| |SquareFreeRegularTriangularSet| |Stack| |StreamAggregate&| |StreamAggregate| |SparseTable| |StepThrough| |StreamInfiniteProduct| @@ -468,655 +468,656 @@ |XPolynomial| |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |separateDegrees| |maxColIndex| |rightLcm| |comment| - |bernoulliB| |lo| |karatsuba| |halfExtendedSubResultantGcd2| - |iteratedInitials| |physicalLength!| |innerSolve| |obj| - |normalizeAtInfinity| |f01qcf| |exprHasWeightCosWXorSinWX| |sinh2csch| - |balancedBinaryTree| |nextIrreduciblePoly| |belong?| |incr| - |setleaves!| |factorGroebnerBasis| |aspFilename| |cache| |nthFactor| - |logIfCan| |incrementKthElement| |iiacosh| |totalfract| |e02ddf| |hi| - |OMread| |shiftRoots| |listexp| |bubbleSort!| |charpol| - |removeSuperfluousQuasiComponents| |Hausdorff| |lllip| - |symmetricPower| |block| |cycleEntry| |antiCommutator| - |createThreeSpace| |contract| |returns| |leftTrace| |nthr| |char| - |eigenMatrix| |indices| |shift| |mkAnswer| |setPrologue!| |supersub| - |singularitiesOf| |rk4f| |lfinfieldint| |coefChoose| |s01eaf| - |symbolTableOf| |fortran| |depth| |morphism| |iiatan| |airyBi| - |basisOfRightAnnihilator| |s21bbf| |f04faf| |f01rcf| |zeroOf| - |trigs2explogs| |optpair| |bumprow| |semiResultantEuclideannaif| - |safetyMargin| |printStats!| |bumptab1| |s17agf| |identification| - |definingInequation| ~ |romberg| |empty| |tail| |leftScalarTimes!| - |isobaric?| |relativeApprox| |checkForZero| |Beta| |diff| |tube| - |inverseColeman| |factors| |ReduceOrder| |ScanFloatIgnoreSpacesIfCan| - |float| |xn| |critT| |square?| |open| |basis| |e04jaf| |limitedint| - |coord| |getCode| |cAtan| |expandTrigProducts| |int| |s18aef| - |rdregime| |UP2ifCan| |isPower| |f01qdf| |algebraicDecompose| - |rightRank| |jordanAlgebra?| |beauzamyBound| |OMputObject| |color| - |getButtonValue| |frst| |e01saf| |compBound| |pmintegrate| - |rectangularMatrix| |lastSubResultantElseSplit| |totalDifferential| - |selectFiniteRoutines| |external?| |semiDiscriminantEuclidean| - |linear| |s21baf| |numer| |irreducibleRepresentation| |chiSquare| - |useSingleFactorBound| |curve| |makeViewport2D| |perspective| |unary?| - |numberOfMonomials| |OMgetBind| |denom| |log2| |makeMulti| - |meshFun2Var| |rightDivide| |asechIfCan| |generate| |lexico| - |polynomial| |powmod| |solve| |dn| |setchildren!| |meshPar1Var| - |randnum| |patternMatch| F |clipParametric| |listLoops| |aQuartic| - |pi| |denomLODE| |lllp| |genericLeftNorm| |groebner?| |besselI| |erf| - |structuralConstants| |incrementBy| |crushedSet| |basisOfCenter| - |rightTrace| |isPlus| |lflimitedint| |infinity| |cSin| |union| - |processTemplate| |ParCondList| |reseed| |components| |script| - |permutationRepresentation| |expand| |mainSquareFreePart| |inRadical?| - |coordinate| |createNormalPoly| |s18acf| |showTheFTable| |csubst| - |leftExtendedGcd| |polyRDE| |squareFreePrim| |filterWhile| |mantissa| - |getConstant| |df2fi| |polCase| |status| |palgextint0| |OMUnknownCD?| - |divisor| |leastAffineMultiple| |dilog| |OMcloseConn| |splitNodeOf!| - |debug3D| |filterUntil| |shanksDiscLogAlgorithm| - |createMultiplicationMatrix| |kernel| |f01mcf| |radicalSimplify| - |separant| |normalizeIfCan| |f01brf| |selectfirst| |ParCond| |tex| - |sin| |options| |bottom!| |select| |draw| |interReduce| |row| |level| - |clearTheSymbolTable| |lexTriangular| |qroot| |e02adf| |result| - |untab| |cos| |viewZoomDefault| |shrinkable| |gcdPolynomial| |nthCoef| - |reduceBasisAtInfinity| |d02cjf| |cTanh| |stopTableInvSet!| - |setColumn!| |satisfy?| |po| |tan| |rightExtendedGcd| - |collectQuasiMonic| |s19aaf| |polyRicDE| |optimize| |composites| - |moduleSum| |makeUnit| |bivariatePolynomials| NOT - |initializeGroupForWordProblem| |lazyPremWithDefault| |string| |cot| - |tanintegrate| |restorePrecision| |dom| |integralCoordinates| - |toseSquareFreePart| |stoseInvertibleSetsqfreg| |c06frf| |OMputString| - |setRow!| |rowEchelonLocal| OR |sin?| |sec| |OMgetEndError| - |hdmpToDmp| |makeObject| |discreteLog| |sequence| |upperCase!| - |mapDown!| |trapezoidal| |e01bgf| |zag| AND |csc| |fintegrate| - |increase| |d02raf| |typeList| |bandedJacobian| |startStats!| - |outputForm| |qualifier| |simpleBounds?| |makeRecord| |mainVariable| - |float?| |asin| |OMputAttr| |failed?| |uncouplingMatrices| |setnext!| - |rightFactorIfCan| |coef| |pole?| |enqueue!| |elliptic| |acos| - |cycleLength| |monomial?| |headRemainder| |enterInCache| - |complexNumericIfCan| |leftQuotient| |lastSubResultantEuclidean| - |setelt!| |roughBase?| |scopes| |curry| |lazyPquo| |atan| - |innerSolve1| |fortranTypeOf| |constantOpIfCan| |cAtanh| - |minimalPolynomial| |mkPrim| |cyclicEntries| |title| |nthFlag| - |unitsColorDefault| |quotientByP| |acot| |normal?| |connect| - |hasSolution?| |exists?| |even?| |freeOf?| |ScanFloatIgnoreSpaces| - |size?| |groebgen| |OMunhandledSymbol| |asec| |tubePointsDefault| - |kmax| |isExpt| |numeric| |OMgetEndBind| |zeroDimensional?| - |updateStatus!| |reducedDiscriminant| |rischDEsys| |pointColorPalette| - |complexEigenvalues| |stoseInvertibleSet| |mix| |acsc| |npcoef| - |coth2tanh| |e| |radical| |key?| |leftRecip| |subResultantsChain| - |chebyshevT| |midpoints| |diagonalMatrix| |OMgetEndApp| |sinh| - |mathieu22| |companionBlocks| |internalDecompose| |printHeader| - |completeHermite| |medialSet| |showScalarValues| |replaceKthElement| - |squareFreeLexTriangular| |dominantTerm| |cosh| |complexNormalize| - |branchIfCan| |stripCommentsAndBlanks| |topFortranOutputStack| - |integral| |subQuasiComponent?| |linearAssociatedOrder| |tanSum| - |rangePascalTriangle| |tree| |mainMonomials| * |tanh| - |multiplyCoefficients| |pomopo!| |nativeModuleExtension| |f02abf| - |monomRDE| |extendedSubResultantGcd| |quickSort| |setValue!| - |alternating| |generalSqFr| |exprHasAlgebraicWeight| |coth| - |pseudoRemainder| |extensionDegree| |qPot| |spherical| |zerosOf| - |OMconnectTCP| |extractIndex| |tubeRadius| - |stoseIntegralLastSubResultant| |sech| |realSolve| |green| - |linkToFortran| |debug| |gderiv| |rationalPoint?| |algebraicVariables| - |OMputBVar| |writeBytes!| |iicosh| |intcompBasis| |mapGen| |csch| - |super| |semiResultantEuclidean2| D |atanhIfCan| |mergeFactors| - |lazyIrreducibleFactors| |fortranDoubleComplex| |and?| |rootSimp| - |getRef| |doubleDisc| |asinh| |euclideanGroebner| |ScanArabic| |li| - |binomial| |lowerPolynomial| |multisect| |diagonal?| |powern| - |pushdterm| |ceiling| |mathieu23| |acosh| |imagE| |errorInfo| - |insert!| |iicot| |constantCoefficientRicDE| |rightQuotient| - |baseRDEsys| |atanh| |htrigs| |removeZeroes| |graphs| |scaleRoots| - |oddInfiniteProduct| |complexSolve| |deleteProperty!| - |generalizedEigenvectors| |countable?| |associator| |setleft!| - |rightZero| |radicalEigenvectors| |acoth| |diagonals| - |linearAssociatedExp| |createLowComplexityNormalBasis| - |oblateSpheroidal| |distance| |unknown| |invertibleElseSplit?| - |rightTraceMatrix| |triangSolve| |basisOfLeftNucloid| |SFunction| - |pdf2df| |realZeros| |asech| |iiacos| |internalIntegrate0| |parabolic| - |rotatey| |rk4qc| |kovacic| |pastel| |printingInfo?| |palginfieldint| - |e02dcf| |integralAtInfinity?| |argument| |pow| |lifting1| - |gcdPrimitive| |setProperty!| |seriesSolve| |basisOfCommutingElements| - |permutation| |tanQ| |multiple| |basisOfRightNucloid| |updatF| |cubic| - |build| |sturmVariationsOf| |meshPar2Var| |getOperands| - |leftMinimalPolynomial| |totalGroebner| |applyQuote| - |mapUnivariateIfCan| |UnVectorise| |expint| |entry| |write!| - |safeFloor| |weighted| |bumptab| |stronglyReduce| |qinterval| |escape| - |isAbsolutelyIrreducible?| |numberOfNormalPoly| |setClosed| - |sparsityIF| |rightUnit| |print| |impliesOperands| |pade| |qelt| - |true| |d01bbf| |orthonormalBasis| |pleskenSplit| |distribute| - |e04gcf| |orOperands| |complement| |complexIntegrate| |imagi| - |OMencodingSGML| |cycles| |and| |lintgcd| |cycleRagits| - |toseLastSubResultant| |ruleset| |addiag| |direction| |inverseLaplace| - |reverseLex| |minIndex| |xRange| |solveid| |removeSinhSq| - |powerAssociative?| |palgextint| |dark| |ratpart| |LyndonWordsList| - |eulerPhi| |binaryFunction| |symmetricSquare| |yRange| - |validExponential| |modulus| |moebiusMu| |permutationGroup| - |unrankImproperPartitions1| |graphStates| |e02baf| |objects| - |plenaryPower| |s18adf| |retractable?| |sqfree| |zRange| |preprocess| - SEGMENT |ef2edf| |ksec| |commutativeEquality| |suchThat| |axes| - |c06ekf| |base| |map!| |f07aef| |sinhcosh| |scripted?| |nsqfree| - |mainDefiningPolynomial| |exprToGenUPS| |shufflein| |cyclotomic| - |atrapezoidal| |rename| |qsetelt!| |vconcat| |clipPointsDefault| - |showRegion| |inverseIntegralMatrixAtInfinity| |setMaxPoints| - |virtualDegree| |binding| |cRationalPower| |makeGraphImage| - |internal?| |leadingIndex| |prefix| |finiteBound| |s14aaf| F2FG - |reducedSystem| |reindex| |resultantReduitEuclidean| |bits| |pop!| - |quadratic?| |fullDisplay| |dec| |head| |sqfrFactor| - |lazyPseudoDivide| |wreath| |elliptic?| |setTopPredicate| |qfactor| - |negative?| |redPol| |definingPolynomial| |readBytes!| |e02gaf| - |subMatrix| |Lazard2| |OMgetObject| |d01gbf| |variable?| |iomode| - |explicitEntries?| |weights| |curryLeft| |recip| |readLine!| - |moreAlgebraic?| |addPoint| |multinomial| |condition| |iipow| - |lazyGintegrate| |genericLeftMinimalPolynomial| |modifyPoint| - |extractTop!| |outputFixed| |acsch| |factorsOfDegree| - |univariatePolynomial| |lexGroebner| |approxSqrt| |clearDenominator| - |cotIfCan| |geometric| |computePowers| |expIfCan| |coshIfCan| - |hexDigit| |f07fef| |splitLinear| |ldf2vmf| |setMaxPoints3D| - |certainlySubVariety?| |nextColeman| |concat| |sayLength| - |mainVariables| |exponential1| |varselect| |mainExpression| - |anticoord| |complexEigenvectors| |quasiMonicPolynomials| - |scanOneDimSubspaces| |enumerate| |rootOfIrreduciblePoly| |high| - |crest| |superHeight| |findBinding| |inf| |copyInto!| |rspace| - |cAcoth| |neglist| |numericalIntegration| |rational?| - |standardBasisOfCyclicSubmodule| |localIntegralBasis| - |OMsupportsSymbol?| |localUnquote| |elementary| |previous| |tower| - |s17dgf| |parent| |badValues| |partialNumerators| |s17adf| - |outputAsScript| |exponent| |mathieu12| |palgint| |orbit| |inv| - |outlineRender| |gethi| |rightPower| |extractIfCan| |bipolar| - |property| |iCompose| |SturmHabicht| |normalDenom| |radix| |setright!| - |drawComplexVectorField| |ground?| |trailingCoefficient| |d01anf| - |minrank| |maxint| |leviCivitaSymbol| |createNormalElement| - |rightCharacteristicPolynomial| |ground| |trueEqual| - |leftRankPolynomial| |backOldPos| |associative?| |nthExpon| - |minRowIndex| |infix| |fill!| |rk4a| |iilog| |e04ucf| |deleteRoutine!| - |rightMinimalPolynomial| |usingTable?| |primextintfrac| - |leadingMonomial| |constantLeft| |f04maf| |completeSmith| |leftRank| - |createGenericMatrix| |showClipRegion| |units| |subscriptedVariables| - |swapColumns!| |getProperty| |e02bef| |makeCrit| |exquo| - |leadingCoefficient| |monicCompleteDecompose| |complexNumeric| - |expenseOfEvaluation| |OMreceive| |f02aaf| |cylindrical| |polygamma| - |computeInt| |merge| |iiacsc| |tableForDiscreteLogarithm| |div| |move| - |cExp| |primitiveMonomials| |kernels| |allRootsOf| |leftRemainder| - |dmp2rfi| |gcdcofact| |goodnessOfFit| |univariatePolynomialsGcds| - |empty?| |getStream| |quo| |solveInField| |reductum| |d01alf| |create| - |combineFeatureCompatibility| |expPot| |rotatez| |output| - |factorsOfCyclicGroupSize| |bfKeys| |powerSum| |drawComplex| - |gramschmidt| |halfExtendedResultant2| |univariate| |tensorProduct| - |hostPlatform| |mainKernel| |nextPrimitivePoly| |curryRight| |formula| - |OMencodingBinary| |compile| |enterPointData| |setVariableOrder| |sh| - |rem| |simplify| |exp1| |badNum| |setFormula!| |target| |iitan| - |universe| |code| |complexExpand| |OMgetString| |nextsousResultant2| - |pascalTriangle| |prinshINFO| |setvalue!| |quartic| |alphabetic| - |acoshIfCan| |quoted?| |nodeOf?| |legendreP| |mainForm| |iroot| - |stFuncN| |gcdcofactprim| |rischDE| |insertTop!| |factor| BY - |integerBound| |split!| |regime| |bounds| |permanent| |unexpand| - |tracePowMod| |expintegrate| |pToDmp| |selectAndPolynomials| |sqrt| - |squareFreePolynomial| |extractBottom!| |leastMonomial| - |leftCharacteristicPolynomial| |minimumExponent| |mainValue| - |cyclicEqual?| |nrows| |f2df| |reduction| |real| |thetaCoord| - |leftLcm| |evenInfiniteProduct| |minPoly| |setOrder| |rational| - |sincos| |setCondition!| |getExplanations| |ncols| |exprToUPS| - |duplicates?| |f04mbf| |imag| |getMatch| |squareFreePart| - |rationalPoints| |leftRegularRepresentation| |insertMatch| |multMonom| - |palgint0| |delete| |sech2cosh| |paraboloidal| |tRange| - |directProduct| |HermiteIntegrate| |changeNameToObjf| |integral?| - |seriesToOutputForm| |B1solve| |lyndon?| |extendIfCan| |setPoly| - |integralBasis| |colorFunction| |d01gaf| |s19acf| |An| - |transcendenceDegree| |mapBivariate| |setsubMatrix!| |quadratic| |lhs| - |viewThetaDefault| |wholeRagits| |epilogue| |euclideanNormalForm| - |f02axf| |modularGcd| |imagK| |packageCall| |destruct| |drawToScale| - |iterationVar| |equiv?| |rhs| |readLineIfCan!| |monicModulo| - |addPoint2| |is?| |endSubProgram| |putGraph| |numberOfPrimitivePoly| - |scale| |generalizedEigenvector| |mightHaveRoots| |nullary| - |rightRemainder| |headReduce| |subHeight| |overlap| |e02daf| - |sylvesterSequence| |changeBase| |cot2tan| |stirling2| - |realElementary| |mat| |sinhIfCan| |fortranCharacter| |pr2dmp| - |wholeRadix| |perfectSqrt| |messagePrint| |cardinality| - |fortranLiteralLine| |createPrimitiveElement| |totalLex| |divisors| - |multiplyExponents| |lagrange| |nthRoot| |node| |polynomialZeros| - |iiasin| |jacobiIdentity?| |f02aef| |realEigenvectors| |monomial| - |poisson| |cyclotomicDecomposition| |perfectNthRoot| |hessian| - |firstDenom| |dimension| |lquo| |hspace| |setelt| |initial| |tValues| - |checkRur| |mapExpon| |OMgetApp| |OMParseError?| |multivariate| - |discriminant| |associatedSystem| |coerceP| |c06eaf| - |innerEigenvectors| |stoseInvertibleSetreg| |getProperties| - |factorSFBRlcUnit| |PollardSmallFactor| |c05adf| |screenResolution3D| - |areEquivalent?| |variables| |asimpson| |tryFunctionalDecomposition| - |consnewpol| |principalIdeal| |s13adf| |pquo| |roughSubIdeal?| |copy| - |s21bdf| |indicialEquation| |setScreenResolution3D| |positive?| - |birth| |applyRules| |nonLinearPart| |bringDown| |safeCeiling| - |minPol| |augment| |substring?| |addmod| |selectOrPolynomials| - |closedCurve?| |blue| |e04fdf| |var1Steps| |commutative?| - |subResultantGcd| |log10| |character?| |mathieu11| |nullity| - |basisOfRightNucleus| |contractSolve| |iibinom| |explicitlyEmpty?| - |showIntensityFunctions| |match?| |knownInfBasis| |bitand| - |fixedDivisor| |conjugate| |top| |viewPosDefault| - |showTheRoutinesTable| |suffix?| |autoCoerce| |getVariableOrder| - |pseudoDivide| |leadingTerm| |semiIndiceSubResultantEuclidean| - |infinityNorm| |omError| |bitior| |rootRadius| |intermediateResultsIF| - |simpsono| |continue| |primitiveElement| |s17aef| |removeCoshSq| - |jacobi| |overlabel| |blankSeparate| |commonDenominator| |c06ecf| - |taylor| |width| |extendedIntegrate| |monomialIntPoly| - |strongGenerators| |d01asf| |round| |prefix?| |bracket| |d02kef| - |newTypeLists| |subPolSet?| |unrankImproperPartitions0| |laurent| - |ListOfTerms| |matrixGcd| |lyndonIfCan| |getDatabase| |mainVariable?| - |asinIfCan| |lineColorDefault| |pointLists| |zeroDimPrime?| - |findCycle| |resetVariableOrder| |puiseux| |meatAxe| |dihedral| - |tan2cot| |gcdprim| |horizConcat| |more?| |subResultantChain| - |invertIfCan| |bezoutResultant| |delay| |sort!| |maxrank| |iicoth| - |part?| |solveLinear| |term?| |pushNewContour| |magnitude| |acotIfCan| - = |sechIfCan| |cyclicCopy| |remainder| |equation| |pointData| - |iidprod| |genericRightDiscriminant| |flagFactor| |create3Space| - |e01sef| |getGoodPrime| |symmetricDifference| |s19adf| |topPredicate| - |hMonic| |countRealRootsMultiple| |c06gbf| |makeViewport3D| |e02dff| - |janko2| |nextSublist| |drawStyle| |lepol| |lowerCase| < |tanNa| - |resultantEuclidean| |maxRowIndex| |optional| |credPol| |component| - |bitCoef| |c06gsf| |divergence| |infix?| |setButtonValue| |say| - |indicialEquations| > |degreeSubResultant| |e02akf| |nonQsign| - |makeVariable| |leadingIdeal| |normalize| |OMreadStr| |mask| - |factorSquareFreeByRecursion| |bindings| - |semiSubResultantGcdEuclidean2| <= |aLinear| |member?| - |prepareDecompose| |lfextlimint| |implies| |testDim| - |radicalEigenvalues| |factorOfDegree| |algebraicSort| |denominators| - |toroidal| |doubleFloatFormat| >= |setAdaptive| |setrest!| |traverse| - |wordInGenerators| |nthRootIfCan| |OMgetFloat| |makeop| |deepExpand| - |df2mf| |GospersMethod| |s17def| |removeRedundantFactors| |xor| |ode2| - |OMputEndAttr| |pile| |adaptive3D?| |interpolate| |euclideanSize| - |setLabelValue| |initials| |createNormalPrimitivePoly| - |compiledFunction| |presub| |match| |imaginary| |singleFactorBound| - |showTheIFTable| |polygon?| |name| |algebraic?| |linears| |d01fcf| - |totalDegree| |autoReduced?| + |viewDefaults| - |integralLastSubResultant| |recolor| |calcRanges| |prinpolINFO| - |changeThreshhold| |cyclicSubmodule| |body| |getlo| - |createPrimitiveNormalPoly| |selectPDERoutines| |reset| - |divideExponents| - |makeYoungTableau| |getOperator| |quasiRegular?| - |identitySquareMatrix| |csch2sinh| |splitSquarefree| |getGraph| - |makeSketch| |tubePlot| |integralMatrixAtInfinity| |getZechTable| - |leftUnit| / |ffactor| |lowerCase!| |constructorName| |clip| |every?| - |SturmHabichtCoefficients| |e04naf| |var1StepsDefault| - |radicalOfLeftTraceForm| |printStatement| |infinite?| |write| - |palgRDE0| |coerceListOfPairs| |mindeg| |octon| |f02fjf| |palgRDE| - |string?| |ignore?| |LazardQuotient2| |leftOne| - |constantToUnaryFunction| |save| |trunc| |host| |evaluate| |infLex?| - |tanhIfCan| |innerint| |explicitlyFinite?| |viewpoint| |lift| |dmpToP| - LODO2FUN |ran| |rightDiscriminant| |sample| |modTree| |OMputEndObject| - |sylvesterMatrix| |s17akf| |iifact| |setPredicates| |e02bdf| |reduce| - |indicialEquationAtInfinity| |testModulus| |transpose| |open?| - |clikeUniv| |unit?| |permutations| |setMinPoints| - |rightFactorCandidate| |expandLog| |fracPart| |cSinh| |argscript| - |nor| |bivariateSLPEBR| |rewriteIdealWithRemainder| |divide| |tab1| - |iiasec| |squareFreeFactors| |figureUnits| |ratDenom| |identityMatrix| - |mainContent| |primPartElseUnitCanonical!| |solid?| - |rightAlternative?| |solveLinearPolynomialEquation| |stronglyReduced?| - |constant| |genericRightTrace| |s19abf| |s15adf| |subTriSet?| |edf2df| - |cSec| |iiasech| |algSplitSimple| |center| |numberOfChildren| |real?| - |modularGcdPrimitive| |resetBadValues| |fortranLogical| - |deepestInitial| |rangeIsFinite| |d01amf| |bit?| |Ci| |coefficients| - |divisorCascade| |determinant| |specialTrigs| |primintfldpoly| |exQuo| - 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|systemSizeIF| |leastPower| |decimal| |karatsubaOnce| |scan| - |att2Result| |karatsubaDivide| |middle| |internalIntegrate| |null?| - |rombergo| |display| |rootPower| |rCoord| |atanIfCan| |limit| - |tanIfCan| |tanh2trigh| |eigenvector| |maxPoints3D| |kind| |iisqrt3| - |showAllElements| |leftTraceMatrix| |optAttributes| |minimize| - |retractIfCan| |fortranLinkerArgs| |collectUnder| |univariate?| - |forLoop| |exp| |flexibleArray| |op| |reverse!| |reorder| |lambda| - |powers| |partialQuotients| |quasiRegular| |dim| |changeMeasure| - |e01baf| |colorDef| |rootSplit| |positiveRemainder| |setImagSteps| - |shallowCopy| |dfRange| |ramifiedAtInfinity?| |baseRDE| |identity| - |groebner| |input| |unvectorise| |numberOfComponents| |noKaratsuba| - |changeName| |selectPolynomials| |extract!| |factorials| |showSummary| - |wholePart| |solveLinearlyOverQ| |genericLeftTrace| |library| - |getMultiplicationMatrix| |variationOfParameters| |setPosition| - |iiGamma| |psolve| |addMatch| |terms| |s17ajf| |fillPascalTriangle| - |commaSeparate| |showAttributes| |abs| |cup| |OMputApp| |hclf| - |doubleResultant| |c06gqf| |doublyTransitive?| |nextsubResultant2| - |properties| |wrregime| |linearPolynomials| |rur| |lowerCase?| - |mapSolve| |OMreadFile| |ptree| |anfactor| |removeSinSq| |translate| - |evaluateInverse| |factorial| |redPo| |ord| |primaryDecomp| |set| - |monomialIntegrate| |lp| |ideal| - |rewriteIdealWithQuasiMonicGenerators| |intChoose| |iFTable| - |supRittWu?| |map| |point| |extractPoint| |OMopenString| |csc2sin| - |perfectNthPower?| |cycleSplit!| |solveRetract| |delete!| |e04dgf| - |iiacoth| |s20adf| |OMputEndAtp| |genericRightNorm| |heap| - |principal?| |setFieldInfo| |parseString| |rootBound| |OMgetAttr| - |conditionP| |linearDependence| |transcendent?| |root| |sum| |orbits| - |resultant| |predicate| |update| |series| |zeroSquareMatrix| - |numberOfVariables| |fprindINFO| |second| |ratPoly| |red| - |genericLeftDiscriminant| |fortranLiteral| |rootDirectory| - |resetAttributeButtons| |invmod| |e02def| |third| |dequeue| |rarrow| - |viewDeltaYDefault| |critpOrder| |Frobenius| |convert| - |discriminantEuclidean| |prolateSpheroidal| |rst| |groebnerFactorize| - |numberOfFractionalTerms| |gbasis| |aromberg| |resize| |linearPart| - |zeroDim?| |symbol?| |d01aqf| UTS2UP |interpret| |viewDeltaXDefault| - |SturmHabichtMultiple| |child| |min| |flexible?| |shade| - |newSubProgram| |degreePartition| |hdmpToP| |primlimintfrac| - |quadraticNorm| |primes| |arguments| |internalZeroSetSplit| |airyAi| - |buildSyntax| |headReduced?| |functionIsOscillatory| |cscIfCan| - |cycle| |primintegrate| |stFunc2| |laplace| |position| |externalList| - |show| |OMgetError| |bat| |trigs| |charClass| |OMgetInteger| |Aleph| - |lazy?| |d02gbf| |leftNorm| |f04jgf| |useEisensteinCriterion| - |rightRankPolynomial| |f04arf| |setAdaptive3D| - |unprotectedRemoveRedundantFactors| |cosh2sech| |midpoint| |void| - |parameters| |monomials| |trace| |rightUnits| |dot| |updatD| - |createRandomElement| |contours| |ranges| |sts2stst| |e02agf| - |operator| |split| |makeEq| |lfextendedint| |taylorIfCan| |range| - |iicsc| |createMultiplicationTable| |SturmHabichtSequence| - |printInfo!| |e04mbf| |unitVector| |style| |complementaryBasis| - |f02awf| |extendedint| |f02agf| |column| |physicalLength| - |characteristicPolynomial| |f02xef| |sdf2lst| |someBasis| |mapCoef| - |semiDegreeSubResultantEuclidean| |squareFree| |supDimElseRittWu?| - |getPickedPoints| |toScale| |trace2PowMod| |primitivePart| - |sumOfSquares| |singRicDE| |basisOfNucleus| |withPredicates| |e02bcf| - |OMserve| |linGenPos| |e02ajf| |OMsupportsCD?| |printTypes| |nary?| - |integralMatrix| |readable?| |brillhartTrials| |idealiserMatrix| - |e04ycf| |normalForm| |removeSuperfluousCases| |constantOperator| - |irreducibleFactor| |critB| |iiacot| |setTex!| |phiCoord| - |startPolynomial| |minColIndex| |quote| |find| |lieAlgebra?| - |subtractIfCan| |llprop| |expr| |integrate| |OMputEndError| |light| - |minus!| |jacobian| |boundOfCauchy| |getBadValues| - |indiceSubResultant| |approximants| |submod| |s17dcf| |byte| - |numericIfCan| |parts| |algebraicOf| |unit| |minordet| |central?| - |extendedEuclidean| |radicalRoots| |coleman| |vedf2vef| |e01daf| - |leadingBasisTerm| |complete| |useSingleFactorBound?| |harmonic| - |cCsc| |solveLinearPolynomialEquationByFractions| |getIdentifier| - |branchPointAtInfinity?| |reify| |showAll?| |variable| |maxPoints| - |element?| |numFunEvals| |subst| |removeRoughlyRedundantFactorsInPol| - |f04qaf| |odd?| |rroot| |expandPower| |loadNativeModule| |iterators| - |mirror| |removeDuplicates!| |LowTriBddDenomInv| |entries| - |generalizedContinuumHypothesisAssumed?| |leadingCoefficientRicDE| - |ramified?| |nextPartition| |algintegrate| |rightOne| - |listYoungTableaus| |returnTypeOf| |aCubic| |vectorise| |makeSin| - |sumOfDivisors| |check| |inHallBasis?| |OMencodingUnknown| |error| - |next| |integralRepresents| |firstSubsetGray| |pushuconst| |simpson| - |plusInfinity| |bernoulli| |ref| |cyclePartition| |slex| |assert| - |balancedFactorisation| |showFortranOutputStack| |imports| |lifting| - |algDsolve| |minusInfinity| |palgintegrate| |init| |arrayStack| - |subNode?| |reverse| |getCurve| |f01maf| - |halfExtendedSubResultantGcd1| |measure2Result| |shiftRight| - |diagonal| |binarySearchTree| |subResultantGcdEuclidean| |routines| - |d02bhf| |surface| |createPrimitivePoly| |one?| |OMwrite| - |quadraticForm| |exactQuotient| |datalist| |deriv| |cAcot| - |extendedResultant| |primlimitedint| |OMconnOutDevice| |iisinh| - |edf2fi| |notelem| |socf2socdf| |completeEval| |removeConstantTerm| - |stopMusserTrials| |normalElement| |e01bff| |randomLC| |sign| - |OMgetEndAttr| |stoseInvertible?sqfreg| |invmultisect| |rightMult| - |ScanRoman| |changeWeightLevel| |plotPolar| |generalLambert| |type| - |uniform| |represents| |fortranReal| |edf2efi| |probablyZeroDim?| - |hexDigit?| |normalDeriv| |yCoordinates| |relerror| |listOfMonoms| - |rightRecip| |c06fqf| |extractClosed| |shuffle| |decreasePrecision| - |ratDsolve| |rank| |child?| |toseInvertibleSet| |subscript| |separate| - |commutator| |leaf?| |segment| |pdf2ef| |OMmakeConn| |leftDivide| - |shallowExpand| |primeFrobenius| |OMbindTCP| |s17acf| - |partialFraction| |linearAssociatedLog| |cCos| |resultantReduit| - |elRow2!| |dmpToHdmp| |noLinearFactor?| |iExquo| |transform| - |firstUncouplingMatrix| |deepestTail| |groebSolve| |matrixConcat3D| - |generalPosition| |alternatingGroup| |atom?| |normalized?| - |lieAdmissible?| |hermite| |monicRightFactorIfCan| |zCoord| - |purelyAlgebraic?| |cyclic?| |cAcosh| |cosIfCan| |goodPoint| - |cothIfCan| |frobenius| |quasiAlgebraicSet| - |internalSubQuasiComponent?| |number?| |compound?| |iiperm| - |stiffnessAndStabilityOfODEIF| |mergeDifference| |cons| |c02agf| - |alternative?| |biRank| |repeating| |d03faf| |andOperands| |atoms| - |stoseInternalLastSubResultant| |double?| |OMputAtp| |lists| |mapmult| - |problemPoints| |irreducibleFactors| |OMputVariable| |nlde| - |primeFactor| |entry?| |complexLimit| |e02aef| |outputGeneral| - |s18def| |sort| |cCoth| |showArrayValues| |schema| |mesh| |f02adf| - |symFunc| |removeRoughlyRedundantFactorsInPols| |normDeriv2| - |invertible?| |LiePoly| |elements| |diagonalProduct| |listBranches| - |bag| |parametersOf| |factorFraction| |normal01| |characteristicSet| - |dequeue!| |upDateBranches| |content| |lookup| |increment| - |selectSumOfSquaresRoutines| |reduceByQuasiMonic| - |rationalApproximation| |constantIfCan| |OMUnknownSymbol?| |genus| - |isTimes| |mapdiv| |sn| |source| |eyeDistance| |node?| |outputSpacing| - |positiveSolve| |s17dlf| |symmetric?| |whatInfinity| |modularFactor| - |normFactors| |acothIfCan| |integralDerivationMatrix| - |inverseIntegralMatrix| |critMonD1| |precision| |e01bhf| |random| - |unravel| |startTableInvSet!| |subset?| |rootNormalize| |binomThmExpt| - |saturate| |mr| |multiple?| |contains?| |makeSeries| |myDegree| - |patternVariable| |iisqrt2| |screenResolution| |whileLoop| - |createLowComplexityTable| |null| |chebyshevU| |rootOf| - |generalizedInverse| |uniform01| |reopen!| |listOfLists| - |bipolarCylindrical| |OMgetEndBVar| |case| |mulmod| |intPatternMatch| - |reducedQPowers| |swap!| |pushucoef| FG2F |symbolTable| |imagj| - |bright| |coerceL| |repeatUntilLoop| |Zero| |numberOfCycles| - |radicalSolve| |plus!| |mappingAst| |compactFraction| |exptMod| - |pushup| |fractRadix| |ricDsolve| |One| |rotatex| |hasPredicate?| - |stoseSquareFreePart| |mainCharacterization| |digamma| - |pushFortranOutputStack| |fractionFreeGauss!| |iflist2Result| |iisec| - |smith| |equality| |OMgetEndAtp| |bsolve| |subresultantSequence| - |varList| |popFortranOutputStack| |generalInfiniteProduct| - |lazyPseudoRemainder| |monicDecomposeIfCan| |leftPower| - |showTheSymbolTable| |weakBiRank| |addBadValue| |e02bbf| - |scalarMatrix| |fmecg| |outputAsFortran| |symmetricProduct| - |triangulate| |in?| |duplicates| |callForm?| |normalizedDivide| - |coerceImages| |complexElementary| |makeCos| |secIfCan| |sin2csc| - |categories| |FormatArabic| |subresultantVector| |rationalFunction| - |brillhartIrreducible?| |binaryTournament| |postfix| - |LyndonCoordinates| |makeSUP| |patternMatchTimes| |key| |LiePolyIfCan| - |implies?| |elt| |LyndonBasis| |e02zaf| |choosemon| |ptFunc| |moebius| - |mapExponents| |numberOfDivisors| |adaptive| |e01bef| |isMult| - |removeIrreducibleRedundantFactors| |filename| |redpps| |generic?| - |toseInvertible?| |semiResultantEuclidean1| |shiftLeft| - |selectODEIVPRoutines| |linSolve| |upperCase| |revert| GE - |setLegalFortranSourceExtensions| |prefixRagits| |port| |coordinates| - |not?| |extractProperty| |prod| |interpretString| - |associatedEquations| |order| GT |any| |operation| |unitNormalize| - |diag| |stoseLastSubResultant| |clipSurface| |push!| |parse| |mvar| - |polygon| |fibonacci| |semiLastSubResultantEuclidean| LE - |selectIntegrationRoutines| |getSyntaxFormsFromFile| |seed| - |createIrreduciblePoly| |FormatRoman| |oddintegers| |symbolIfCan| - |has?| |purelyAlgebraicLeadingMonomial?| LT |ocf2ocdf| |edf2ef| - |outputList| |useNagFunctions| |label| |d01apf| |or?| |btwFact| - |returnType!| |convergents| |multiEuclidean| |complex| |makingStats?| - |rootKerSimp| |exprHasLogarithmicWeights| |push| |continuedFraction| - |iiasinh| |basisOfLeftNucleus| |extension| |exactQuotient!| - |limitPlus| |vark| |viewPhiDefault| |c06fpf| |OMsend| |exponential| - |cLog| |readByteIfCan!| |countRealRoots| |arity| |mainCoefficients| - |digit?| |associatorDependence| |integralBasisAtInfinity| - |nextLatticePermutation| |dictionary| |argumentList!| - |stiffnessAndStabilityFactor| |lazyVariations| |plus| |characteristic| - |twoFactor| |invertibleSet| |possiblyNewVariety?| |decompose| |vector| - |s17aff| |sup| |keys| |OMencodingXML| |subCase?| |oneDimensionalArray| - |prime| |simplifyPower| |characteristicSerie| |constantKernel| - |differentiate| |hasoln| |compose| |absolutelyIrreducible?| - |fortranCarriageReturn| |basisOfCentroid| |antisymmetricTensors| - |differentialVariables| |functionIsFracPolynomial?| |currentEnv| - |root?| |quasiComponent| |stosePrepareSubResAlgo| |c02aff| - |inconsistent?| |pointSizeDefault| |rk4| |BumInSepFFE| |outputMeasure| - |Vectorise| |nextPrimitiveNormalPoly| |bezoutMatrix| |raisePolynomial| - |removeSquaresIfCan| |copies| |times| |splitDenominator| |rquo| - |matrixDimensions| |derivationCoordinates| |pmComplexintegrate| - |complexRoots| |elRow1!| |changeVar| |search| |cAsec| |norm| |index| - |lazyPrem| |imagk| |stopTable!| |e01sff| |nodes| |sortConstraints| - |symmetricGroup| |cAsech| |mapMatrixIfCan| |monomRDEsys| - |lazyIntegrate| |simplifyLog| |isOp| |parabolicCylindrical| |ldf2lst| - |exprex| |skewSFunction| |curveColorPalette| |option| |call| - |removeRedundantFactorsInPols| |leftMult| |hasHi| |rowEchLocal| - |realRoots| |relationsIdeal| |lazyPseudoQuotient| |numberOfOperations| - |localAbs| |fortranDouble| |totolex| |list| |monom| |OMputFloat| - |pair| |over| |box| |quatern| |prevPrime| |writeLine!| |position!| - |stirling1| |df2ef| |car| |representationType| |sorted?| |pol| - |reducedContinuedFraction| |factorAndSplit| |d02gaf| |declare| - |d02bbf| |expressIdealMember| |redmat| |cdr| GF2FG |setOfMinN| - |besselY| |read!| |factor1| |OMputEndBVar| |arg1| |weight| |common| - |solve1| |setDifference| |movedPoints| |cTan| |rename!| |f01qef| - |checkPrecision| |closeComponent| |low| |cfirst| |arg2| |function| - 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|internalSubPolSet?| |OMputInteger| |PDESolve| ** |defineProperty| - |OMputEndBind| |inR?| |basicSet| |prindINFO| - |removeRedundantFactorsInContents| |digits| |maxdeg| - |cyclotomicFactorization| |unparse| |mindegTerm| |irreducible?| - |generic| |internalAugment| |adaptive?| |userOrdered?| |latex| - |squareTop| |maximumExponent| |selectOptimizationRoutines| EQ - |nullary?| |s20acf| |sizeLess?| |setEmpty!| |summation| |lSpaceBasis| - |assign| |hasTopPredicate?| |finite?| |palgLODE0| |asecIfCan| |ddFact| - |algebraicCoefficients?| |LagrangeInterpolation| |f2st| |Gamma| - |lastSubResultant| |fortranCompilerName| |OMgetAtp| |curve?| |cCot| - |viewWriteDefault| |outputAsTex| |d01ajf| |queue| - |internalLastSubResultant| |difference| |triangular?| - |factorSquareFree| |power!| |coercePreimagesImages| |flatten| - |laguerre| |rewriteIdealWithHeadRemainder| |pointColorDefault| - |symbol| |laplacian| |matrix| |symmetricRemainder| |signAround| - |swapRows!| |roman| |startTable!| |genericPosition| |viewSizeDefault| - 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|declare!| |f01rdf| |writable?| |numberOfComputedEntries| - |categoryFrame| |hermiteH| |fixPredicate| |palgLODE| |denominator| - |cond| |fortranComplex| |dAndcExp| |expintfldpoly| |s18aff| - |expenseOfEvaluationIF| |unitNormal| |clipBoolean| |ipow| |primitive?| - |palglimint0| |brace| |minimumDegree| |OMputEndApp| - |initiallyReduced?| |clearTheFTable| |primextendedint| |replace| - |f02wef| |rubiksGroup| |linearDependenceOverZ| |var2StepsDefault| - |tan2trig| |halfExtendedResultant1| |nil?| |d03edf| |padicallyExpand| - |Ei| |bitTruth| |padecf| |rootPoly| |iiatanh| |binaryTree| |rightNorm| - |headAst| UP2UTS |pdct| |eigenvectors| |reduced?| |stop| |firstNumer| - |failed| |createZechTable| |branchPoint?| |charthRoot| |compdegd| - |rightGcd| |closed?| |noncommutativeJordanAlgebra?| |members| |cCosh| - |value| |highCommonTerms| |numberOfComposites| |coth2trigh| - |functionIsContinuousAtEndPoints| |region| |exteriorDifferential| - |OMsetEncoding| |wordInStrongGenerators| |iiabs| |reduceLODE| - |denomRicDE| |coefficient| - |rewriteSetByReducingWithParticularGenerators| |zoom| - |mainPrimitivePart| |leftUnits| |children| |measure| - |clearFortranOutputStack| |c06gcf| |aQuadratic| |f04adf| |removeZero| - |opeval| |e01sbf| |graphCurves| |genericRightMinimalPolynomial| - |s17ahf| |rowEchelon| |closedCurve| |homogeneous?| |groebnerIdeal| - |integerIfCan| |any?| |partitions| |graeffe| |particularSolution| - |generalizedContinuumHypothesisAssumed| |nextSubsetGray| - |linearlyDependent?| |xCoord| |dimensionsOf| |monicLeftDivide| - |linear?| |or| |trivialIdeal?| |critM| |eulerE| |length| |remove!| - |partition| |startTableGcd!| |algint| |doubleRank| |prinb| - |elseBranch| |corrPoly| |makeprod| |scripts| |bat1| |numFunEvals3D| - |roughUnitIdeal?| |insertionSort!| |lazyEvaluate| |dimensions| - |intensity| |bombieriNorm| |bandedHessian| |hue| - |currentCategoryFrame| |viewport2D| |deref| |critMTonD1| |prime?| - |idealSimplify| |infieldint| |repeating?| |cross| |yellow| |idealiser| - |setprevious!| |iprint| |Lazard| |c06fuf| |bezoutDiscriminant| - |directSum| |zeroVector| |generator| |top!| |removeCosSq| - |leadingSupport| |d02ejf| |quotedOperators| |cycleTail| |index?| - |exponentialOrder| |sizePascalTriangle| |eq?| |OMgetEndObject| - |cos2sec| |triangularSystems| |stFunc1| |thenBranch| |f04atf| - |argumentListOf| |useEisensteinCriterion?| |fixedPoints| |errorKind| - |mesh?| |decrease| |alphabetic?| |stoseInvertible?reg| |computeBasis| - |lighting| |linearMatrix| |leftDiscriminant| |integer?| |pToHdmp| - |lprop| |roughBasicSet| |clipWithRanges| |OMgetBVar| |rootProduct| - |besselK| |kroneckerDelta| |makeTerm| |leftZero| - |completeEchelonBasis| |transcendentalDecompose| |minPoints3D| - |leftFactorIfCan| |OMputError| |eigenvalues| |superscript| - |OMconnInDevice| |OMputBind| |inspect| |option?| |select!| |digit| - |coerceS| |chvar| |s15aef| |sub| |inGroundField?| |chainSubResultants| - |f02akf| |zeroSetSplitIntoTriangularSystems| |froot| |dioSolve| - |comparison| |nthExponent| |f01bsf| |reflect| |sPol| |conjugates| - |nil| |infinite| |arbitraryExponent| |approximate| |complex| - 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|retractable?| |primintfldpoly| |equivOperands| + |zeroSetSplitIntoTriangularSystems| |integralCoordinates| |integral?| + |critMonD1| |cAcos| |f02xef| |sqfree| |exQuo| |euler| |froot| + |toseSquareFreePart| |seriesToOutputForm| |e01bhf| ~ |sdf2lst| + |cosSinInfo| |tail| |preprocess| |dioSolve| |stoseInvertibleSetsqfreg| + |unravel| |B1solve| |someBasis| |univariateSolve| |ef2edf| |cyclic| + |changeThreshhold| |comparison| |float| |c06frf| |lyndon?| + |startTableInvSet!| |open| |mapCoef| |monicDivide| |xn| |ksec| + |addMatchRestricted| |cyclicSubmodule| |nthExponent| |OMputString| + |subset?| |extendIfCan| |zeroDimPrimary?| + |semiDegreeSubResultantEuclidean| |critT| |commutativeEquality| + |getlo| |power| |f01bsf| |setRow!| |rootNormalize| |setPoly| |axes| + |createPrimitiveNormalPoly| |graphImage| |isPower| |reflect| + |rowEchelonLocal| |binomThmExpt| |integralBasis| |setFieldInfo| + |unparse| |expextendedint| |c06ekf| |linear| |numer| + |selectPDERoutines| |f01qdf| |sPol| |sin?| |colorFunction| |saturate| + |parseString| |mindegTerm| |f07aef| |denom| |divideExponents| + |axesColorDefault| |conjugates| |irreducible?| |OMgetEndError| + |d01gaf| |multiple?| |rootBound| |generate| |sinhcosh| |polynomial| + |operators| |makeYoungTableau| |generic| |hdmpToDmp| |contains?| + |s19acf| |OMgetAttr| F |maxIndex| |scripted?| |getOperator| |pi| + |xCoord| |child?| |discreteLog| |incrementBy| |makeSeries| |erf| |An| + |conditionP| |internalAugment| |nsqfree| |dimensionsOf| |infinity| + |selectNonFiniteRoutines| |quasiRegular?| |toseInvertibleSet| |union| + |sequence| |linearDependence| |myDegree| |script| + |transcendenceDegree| |adaptive?| |expand| |mainDefiningPolynomial| + |polar| |identitySquareMatrix| |monicLeftDivide| |subscript| + |mapBivariate| |upperCase!| |userOrdered?| |patternVariable| + |transcendent?| |filterWhile| |mantissa| |exprToGenUPS| |status| + |csch2sinh| |infRittWu?| |linear?| |separate| |mapDown!| |iisqrt2| + |dilog| |setsubMatrix!| |root| |latex| 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+ |logIfCan| |e| |makeGraphImage| |radical| |e04naf| |stoseInvertible?| + |resultantReduit| |bat1| |intPatternMatch| |mainVariable| |sinh| + |readLineIfCan!| |palgLODE0| |e02def| |internal?| |squareMatrix| + |var1StepsDefault| |elRow2!| |numFunEvals3D| |reducedQPowers| |float?| + |monicModulo| |cosh| |dequeue| |asecIfCan| |leadingIndex| + |radicalOfLeftTraceForm| |cAsin| |dmpToHdmp| |roughUnitIdeal?| |swap!| + |tree| |OMputAttr| * |tanh| |addPoint2| |ddFact| |rarrow| + |finiteBound| |printStatement| |taylorQuoByVar| |noLinearFactor?| + |insertionSort!| |pushucoef| |failed?| |is?| |coth| + |algebraicCoefficients?| |viewDeltaYDefault| |s14aaf| |infinite?| + |wordsForStrongGenerators| |iExquo| |lazyEvaluate| + |uncouplingMatrices| FG2F |sech| |endSubProgram| |critpOrder| + |LagrangeInterpolation| F2FG |debug| |palgRDE0| |normalizedAssociate| + |transform| |dimensions| |setnext!| |imagj| |csch| |putGraph| |f2st| + |Frobenius| |reducedSystem| D |coerceListOfPairs| |polyred| + |firstUncouplingMatrix| |intensity| |numberOfPrimitivePoly| + |rightFactorIfCan| |coerceL| |asinh| |discriminantEuclidean| |Gamma| + |reindex| |li| |close!| |mindeg| |bombieriNorm| |deepestTail| + |repeatUntilLoop| |pole?| |acosh| |scale| |prolateSpheroidal| + |lastSubResultant| |resultantReduitEuclidean| |octon| |expt| + |groebSolve| |bandedHessian| |generalizedEigenvector| |enqueue!| + |numberOfCycles| |atanh| |rst| |fortranCompilerName| |bits| |f02fjf| + |RittWuCompare| |matrixConcat3D| |hue| |elliptic| |groebnerFactorize| + |mightHaveRoots| |radicalSolve| |acoth| |OMgetAtp| + |incrementKthElement| |printCode| |pop!| |palgRDE| |unknown| + |generalPosition| |currentCategoryFrame| |iiacosh| |nullary| + |cycleLength| |plus!| |asech| |numberOfFractionalTerms| |curve?| + |quadratic?| |complex?| |string?| |alternatingGroup| |viewport2D| + |monomial?| |mappingAst| |rightRemainder| |gbasis| |cCot| + |fullDisplay| |ignore?| |OMlistSymbols| |deref| |atom?| + |compactFraction| |headRemainder| |multiple| |headReduce| |aromberg| + |viewWriteDefault| |head| |OMgetType| |LazardQuotient2| |critMTonD1| + |normalized?| |applyQuote| |enterInCache| |exptMod| |subHeight| + |outputAsTex| |resize| |entry| |sqfrFactor| |leftOne| |asinhIfCan| + |lieAdmissible?| |prime?| |complexNumericIfCan| |overlap| |pushup| + |linearPart| |d01ajf| |constantToUnaryFunction| |true| |print| + |lazyPseudoDivide| |mathieu24| |qelt| |idealSimplify| |hermite| + |leftQuotient| |e02daf| |fractRadix| |zeroDim?| |queue| |wreath| + |infieldint| |addPointLast| |trunc| |and| |monicRightFactorIfCan| + |ricDsolve| |lastSubResultantEuclidean| |sylvesterSequence| |ruleset| + |internalLastSubResultant| |symbol?| |elliptic?| |host| |tableau| + |xRange| |zCoord| |repeating?| |setelt!| |rotatex| |changeBase| + |d01aqf| |difference| |setTopPredicate| |evaluate| |bivariate?| + |yRange| |purelyAlgebraic?| |cross| |hasPredicate?| |roughBase?| + |cot2tan| |objects| |triangular?| UTS2UP |yellow| |qfactor| + |makeFloatFunction| |infLex?| |zRange| |cyclic?| SEGMENT |stirling2| + |scopes| |suchThat| |stoseSquareFreePart| |base| |factorSquareFree| + |viewDeltaXDefault| |map!| |negative?| |legendre| |tanhIfCan| + |idealiser| |cAcosh| |curry| |realElementary| |mainCharacterization| + |power!| |SturmHabichtMultiple| |innerint| |redPol| |qsetelt!| |mdeg| + |setprevious!| |cosIfCan| |lazyPquo| |mat| |digamma| + |coercePreimagesImages| |child| |prefix| |definingPolynomial| + |listConjugateBases| |explicitlyFinite?| |goodPoint| |iprint| + |fractionFreeGauss!| |sinhIfCan| |flexible?| |laguerre| |readBytes!| + |dec| |s18dcf| |viewpoint| |Lazard| |cothIfCan| |ParCondList| + |iflist2Result| |fortranCharacter| |rewriteIdealWithHeadRemainder| + |shade| |frobenius| |e02gaf| |moduloP| |dmpToP| |c06fuf| |square?| + |reseed| |iisec| |pr2dmp| |newSubProgram| |pointColorDefault| + |bezoutDiscriminant| |subMatrix| |cSech| LODO2FUN |basis| + |quasiAlgebraicSet| |components| |condition| |wholeRadix| |smith| + |degreePartition| |laplacian| |ran| |separateFactors| |acsch| + |directSum| |internalSubQuasiComponent?| |permutationRepresentation| + |equality| |perfectSqrt| |symmetricRemainder| |hdmpToP| + |sturmVariationsOf| |rightDiscriminant| |rationalPower| |number?| + |zeroVector| |mainSquareFreePart| |signAround| |OMgetEndAtp| + |messagePrint| |primlimintfrac| |concat| |meshPar2Var| |setErrorBound| + |sample| |top!| |compound?| |inRadical?| |cardinality| |bsolve| + |quadraticNorm| |swapRows!| |getOperands| |modTree| |hconcat| |iiperm| + |removeCosSq| |coordinate| |primes| |roman| |leftMinimalPolynomial| + |stiffnessAndStabilityOfODEIF| |OMputEndObject| |integers| + |leadingSupport| |e04jaf| |createNormalPoly| |double?| |prinshINFO| + |previous| |tower| |startTable!| |internalZeroSetSplit| + |totalGroebner| |sylvesterMatrix| |iicos| |limitedint| + |mergeDifference| |d02ejf| |s18acf| |inv| |OMputAtp| |setvalue!| + |genericPosition| |airyAi| |mapUnivariateIfCan| |symmetricPower| + |property| |c05pbf| |s17akf| |c02agf| |quotedOperators| |ground?| + |showTheFTable| |quartic| |mapmult| |buildSyntax| |viewSizeDefault| + |UnVectorise| |block| |alternative?| |cycleTail| |alphabetic| |csubst| + |problemPoints| |ground| |fixedPoint| |int| |headReduced?| |expint| + |sortConstraints| |nonQsign| |cycleEntry| |biRank| |index?| + |leadingMonomial| |leftExtendedGcd| |irreducibleFactors| |acoshIfCan| + |functionIsOscillatory| |s18aef| |randomR| |makeVariable| |write!| + |symmetricGroup| |units| |exponentialOrder| |antiCommutator| |exquo| + |repeating| |OMputVariable| |polyRDE| |quoted?| |leadingCoefficient| + |complexNumeric| |cscIfCan| |decomposeFunc| |safeFloor| |leadingIdeal| + |cAsech| |sizePascalTriangle| |createThreeSpace| |squareFreePrim| + |d03faf| |div| |primitiveMonomials| |nodeOf?| |nlde| |eq?| |weighted| + |mapMatrixIfCan| |normalize| |extract!| |contract| |getConstant| + |andOperands| |primeFactor| |quo| |legendreP| |reductum| + |setRealSteps| |kernels| |OMreadStr| |bumptab| |monomRDEsys| |output| + |returns| |OMgetEndObject| |atoms| |factorials| |df2fi| |entry?| + |mainForm| |polarCoordinates| |univariate| |iroot| |leftTrace| + |stronglyReduce| |factorSquareFreeByRecursion| |lazyIntegrate| + |formula| |compile| |stoseInternalLastSubResultant| |cos2sec| + |polCase| |rem| |swap| |complexLimit| |wholePart| |target| |bindings| + |qinterval| |code| |simplifyLog| |nthr| |palgextint0| |e02aef| + |stFuncN| |mainMonomial| |solveLinearlyOverQ| |escape| |rightNorm| + |isOp| |semiSubResultantGcdEuclidean2| |getCurve| |eigenMatrix| + |outputGeneral| |OMUnknownCD?| |sumSquares| |gcdcofactprim| + |genericLeftTrace| |factor| BY |parabolicCylindrical| + |isAbsolutelyIrreducible?| |headAst| |aLinear| |indices| |f01maf| + |divisor| |getMultiplicationMatrix| |s18def| |rischDE| |sqrt| + |zeroSetSplit| |ldf2lst| |numberOfNormalPoly| |mkAnswer| |member?| + |halfExtendedSubResultantGcd1| UP2UTS |nrows| |insertTop!| + |leastAffineMultiple| |cCoth| |real| |variationOfParameters| |plot| + |measure2Result| |setClosed| |exprex| |prepareDecompose| |pdct| + |setPrologue!| |ncols| |integerBound| |OMcloseConn| |setPosition| + |showArrayValues| |fglmIfCan| |imag| |skewSFunction| |sparsityIF| + |eigenvectors| |lfextlimint| |delete| |shiftRight| |supersub| + |directProduct| |splitNodeOf!| |schema| |split!| |iiGamma| |unmakeSUP| + |curveColorPalette| |rightUnit| |singularitiesOf| |testDim| |diagonal| + |reduced?| |debug3D| |regime| |mesh| |computeCycleEntry| |psolve| + |binarySearchTree| |removeRedundantFactorsInPols| |impliesOperands| + |radicalEigenvalues| |lhs| |firstNumer| |rk4f| + |shanksDiscLogAlgorithm| |setProperties!| |f02adf| |bounds| |destruct| + |addMatch| |createZechTable| |factorOfDegree| |pade| |leftMult| |rhs| + |lfinfieldint| |subResultantGcdEuclidean| |createMultiplicationMatrix| + |permanent| |symFunc| |getOrder| |terms| |branchPoint?| |d01bbf| + |algebraicSort| |hasHi| |coefChoose| |routines| |f01mcf| + |removeRoughlyRedundantFactorsInPols| |unexpand| |curveColor| |s17ajf| + |denominators| |orthonormalBasis| |rowEchLocal| |d02bhf| |s01eaf| + |charthRoot| |radicalSimplify| |tracePowMod| |normDeriv2| |iisin| + |fillPascalTriangle| |toroidal| |pleskenSplit| |realRoots| |compdegd| + |surface| |symbolTableOf| |node| |coord| |separant| |quotient| + |expintegrate| |invertible?| |monomial| |commaSeparate| |morphism| + |doubleFloatFormat| |distribute| |createPrimitivePoly| + |relationsIdeal| |empty| |rightGcd| |setelt| |complexZeros| |getCode| + |initial| |normalizeIfCan| |LiePoly| |pToDmp| |multivariate| |abs| + |iiatan| |leftScalarTimes!| |e04gcf| |lazyPseudoQuotient| + |setAdaptive| |one?| |closed?| |cup| |f01brf| |selectAndPolynomials| + |elements| |variables| |currentScope| |numberOfOperations| + |noncommutativeJordanAlgebra?| |orOperands| |setrest!| |OMwrite| + |copy| |airyBi| |selectfirst| |squareFreePolynomial| |diagonalProduct| + |s14abf| |OMputApp| |basisOfRightAnnihilator| |localAbs| |complement| + |members| |traverse| |quadraticForm| |substring?| |ParCond| + |extractBottom!| |listBranches| |doubleComplex?| |hclf| |log10| + |fortranDouble| |complexIntegrate| |cCosh| |wordInGenerators| |s21bbf| + |exactQuotient| |bag| |bottom!| |doubleResultant| |leastMonomial| + |se2rfi| |match?| |bitand| |highCommonTerms| |totolex| |f04faf| + |nthRootIfCan| |imagi| |top| |suffix?| |deriv| |autoCoerce| + |interReduce| |leftCharacteristicPolynomial| |parametersOf| |c06gqf| + |f02bbf| |bitior| |continue| |cAcot| |OMencodingSGML| |OMputFloat| + |OMgetFloat| |f01rcf| |numberOfComposites| |doublyTransitive?| |row| + |minimumExponent| |factorFraction| |lfintegrate| |taylor| |width| + |zeroOf| |extendedResultant| |cycles| |makeop| |over| |prefix?| + |coth2trigh| |laurent| |clearTheSymbolTable| |mainValue| |normal01| + |nextsubResultant2| |divideIfCan| |functionIsContinuousAtEndPoints| + |lintgcd| |deepExpand| |quatern| |primlimitedint| |trigs2explogs| + |lexTriangular| |puiseux| |cyclicEqual?| |characteristicSet| + |wrregime| |roughEqualIdeals?| |df2mf| |cycleRagits| |prevPrime| + |OMconnOutDevice| |region| |optpair| |qroot| |f2df| |dequeue!| + |linearPolynomials| |points| |exteriorDifferential| + |toseLastSubResultant| |GospersMethod| |writeLine!| |iisinh| |bumprow| + |reduction| |BasicMethod| |e02adf| = |upDateBranches| |rur| |equation| + |position!| |addiag| |edf2fi| |s17def| |OMsetEncoding| + |semiResultantEuclideannaif| |untab| |content| |thetaCoord| + |lowerCase?| |nextNormalPoly| |stirling1| |direction| |safetyMargin| + |removeRedundantFactors| |notelem| |wordInStrongGenerators| |lookup| + |viewZoomDefault| |leftLcm| < |outputArgs| |mapSolve| |optional| + |socf2socdf| |inverseLaplace| |df2ef| |ode2| |iiabs| |infix?| |say| + |shrinkable| |increment| > |evenInfiniteProduct| |numerators| + |OMreadFile| |completeEval| |reverseLex| |representationType| + |OMputEndAttr| |mask| |reduceLODE| |minPoly| |gcdPolynomial| <= + |selectSumOfSquaresRoutines| |anfactor| |ODESolve| |minIndex| + |implies| |sorted?| |pile| |removeConstantTerm| |denomRicDE| |nthCoef| + >= |reduceByQuasiMonic| |setOrder| |wronskianMatrix| |removeSinSq| + |solveid| |pol| |adaptive3D?| |stopMusserTrials| |coefficient| + |reduceBasisAtInfinity| |rationalApproximation| |rational| + |evaluateInverse| |factorByRecursion| |xor| |removeSinhSq| + |reducedContinuedFraction| |interpolate| |normalElement| + |rewriteSetByReducingWithParticularGenerators| |factorial| + |constantIfCan| |d02cjf| |totalfract| |sincos| |rotate| |match| + |factorAndSplit| |powerAssociative?| |euclideanSize| |e01bff| |name| + |zoom| |redPo| |cTanh| |OMUnknownSymbol?| |setCondition!| + |e02ddf| + |factorset| |setLabelValue| |palgextint| |randomLC| |d02gaf| + |mainPrimitivePart| |body| |ord| |genus| |stopTableInvSet!| |reset| + |getExplanations| - |schwerpunkt| |OMread| |dark| |d02bbf| |initials| + |leftUnits| |sign| |setColumn!| |exprToUPS| |shiftRoots| + |primaryDecomp| |isTimes| / |frst| |nextPrime| |constructorName| + |ratpart| |createNormalPrimitivePoly| |expressIdealMember| + |OMgetEndAttr| |children| |monomialIntegrate| |duplicates?| |satisfy?| + |write| |listexp| |mapdiv| |inverseColeman| |pseudoQuotient| + |LyndonWordsList| |compiledFunction| |redmat| |measure| + |stoseInvertible?sqfreg| |cartesian| |sn| |save| |po| |ideal| |f04mbf| + |factors| |bubbleSort!| |clearFortranOutputStack| |eulerPhi| GF2FG + |presub| |lift| |invmultisect| |rightExtendedGcd| |getMatch| + |eyeDistance| |rewriteIdealWithQuasiMonicGenerators| |imagJ| + |imaginary| |binaryFunction| |rightMult| |setOfMinN| |c06gcf| |reduce| + |collectQuasiMonic| |node?| |squareFreePart| |intChoose| |refine| + |symmetricSquare| |singleFactorBound| |besselY| |ScanRoman| + |aQuadratic| |s19aaf| |rationalPoints| |outputSpacing| |iFTable| + |numericalOptimization| |validExponential| |read!| |showTheIFTable| + |f04adf| |changeWeightLevel| |polyRicDE| |leftRegularRepresentation| + |positiveSolve| |predicates| |supRittWu?| |isobaric?| |factor1| + |modulus| |polygon?| |constant| |plotPolar| |removeZero| |s17dlf| + |insertMatch| |hcrf| |extractPoint| |moebiusMu| |OMputEndBVar| + |center| |relativeApprox| |algebraic?| |opeval| |generalLambert| + |multMonom| |symmetric?| |cAcsc| |OMopenString| |permutationGroup| + |weight| |linears| |e01sbf| |uniform| |palgint0| |insert| + |whatInfinity| |internalSubPolSet?| |csc2sin| |s17agf| + |unrankImproperPartitions1| |solve1| |d01fcf| |represents| + |graphCurves| |modularFactor| |charpol| |nil| |sech2cosh| + |perfectNthPower?| |OMputInteger| |identification| |movedPoints| + |totalDegree| |t| |clearCache| |fortranReal| + |genericRightMinimalPolynomial| |paraboloidal| |normFactors| + |PDESolve| |cycleSplit!| |removeSuperfluousQuasiComponents| |imagE| + |cTan| |autoReduced?| |edf2efi| |s17ahf| |tRange| |acothIfCan| + |solveRetract| |defineProperty| |errorInfo| |eq| |rename!| + |viewDefaults| |probablyZeroDim?| |rowEchelon| |delete!| + |integralDerivationMatrix| |HermiteIntegrate| |retract| |OMputEndBind| + |approximate| |delta| Y |insert!| |iter| |f01qef| + |integralLastSubResultant| |hexDigit?| |closedCurve| |e04dgf| |inR?| + |iicot| |recolor| |closeComponent| |homogeneous?| |normalDeriv| + |subscriptedVariables| |iiacoth| |basicSet| |constantCoefficientRicDE| + |close| |yCoordinates| |calcRanges| |low| |groebnerIdeal| |eval| + |swapColumns!| |prindINFO| |s20adf| |rightQuotient| |prinpolINFO| + |cfirst| |relerror| |integerIfCan| |getProperty| |OMputEndAtp| + |removeRedundantFactorsInContents| |baseRDEsys| |display| |any?| + |listOfMonoms| |e02bef| |genericRightNorm| |digits| |htrigs| + |dictionary| |findCycle| |kind| |rightRecip| |partitions| |makeCrit| + |heap| |maxdeg| |retractIfCan| |removeZeroes| |argumentList!| + |resetVariableOrder| |graeffe| |exp| |c06fqf| |op| + |monicCompleteDecompose| |cyclotomicFactorization| |principal?| + |lambda| |stiffnessAndStabilityFactor| |graphs| |dim| |meatAxe| + |particularSolution| |extractClosed| |expenseOfEvaluation| + |scaleRoots| |dihedral| |lazyVariations| + |generalizedContinuumHypothesisAssumed| |shuffle| |OMreceive| + |upperCase?| |s13acf| |input| |oddInfiniteProduct| |characteristic| + |tan2cot| |decreasePrecision| |nextSubsetGray| |showSummary| + |critBonD| |f02aaf| |e01saf| |semiResultantReduitEuclidean| + |complexSolve| |library| |gcdprim| |twoFactor| |linearlyDependent?| + |ratDsolve| |cylindrical| |univcase| |f04asf| |deleteProperty!| + |horizConcat| |invertibleSet| |showAttributes| |polygamma| + |jordanAdmissible?| |indiceSubResultantEuclidean| + |generalizedEigenvectors| |possiblyNewVariety?| |more?| |derivative| + |coleman| |properties| |computeInt| |times!| |monic?| |countable?| + |ptree| |subResultantChain| |decompose| |vedf2vef| |leftGcd| + |translate| |merge| |systemSizeIF| |exprToXXP| |invertIfCan| + |associator| |set| |s17aff| |lp| |e01daf| + |degreeSubResultantEuclidean| |iiacsc| |leastPower| |infiniteProduct| + |map| |point| |setleft!| |bezoutResultant| |sup| |leadingBasisTerm| + |f04axf| |tableForDiscreteLogarithm| |decimal| |Is| |rightZero| + |OMencodingXML| |delay| |torsion?| |complete| |move| |imagI| + |karatsubaOnce| |radicalEigenvectors| |sort!| |subCase?| + |useSingleFactorBound?| |acosIfCan| |cExp| |sum| |coHeight| |scan| + |predicate| |update| |series| |oneDimensionalArray| |diagonals| + |maxrank| |second| |cap| |harmonic| |allRootsOf| |att2Result| + |viewWriteAvailable| |iicoth| |linearAssociatedExp| |prime| |third| + |cCsc| |factorSquareFreePolynomial| |leftRemainder| |karatsubaDivide| + |qqq| |convert| |createLowComplexityNormalBasis| |simplifyPower| + |part?| |solveLinearPolynomialEquationByFractions| |prologue| + |dmp2rfi| |recur| |middle| |oblateSpheroidal| |solveLinear| + |characteristicSerie| |getIdentifier| |putColorInfo| |gcdcofact| + |interpret| |internalIntegrate| |symmetricTensors| |min| |distance| + |constantKernel| |term?| |ellipticCylindrical| + |branchPointAtInfinity?| |goodnessOfFit| |overbar| |null?| |arguments| + |Hausdorff| |invertibleElseSplit?| |hasoln| |pushNewContour| |reify| + |newReduc| |univariatePolynomialsGcds| |hypergeometric0F1| |rombergo| + |lllip| |position| |rightTraceMatrix| |show| |ReduceOrder| |compose| + |magnitude| |genericLeftTraceForm| |showAll?| |empty?| |rootPower| + |logical?| |absolutelyIrreducible?| |triangSolve| + |ScanFloatIgnoreSpacesIfCan| |acotIfCan| |cyclicGroup| |maxPoints| + |getStream| |gradient| |rCoord| |void| |parameters| + |basisOfLeftNucloid| |trace| |fortranCarriageReturn| |sechIfCan| + |iiacsch| |element?| |solveInField| |torsionIfCan| |atanIfCan| + |SFunction| |basisOfCentroid| |cyclicCopy| + |tryFunctionalDecomposition?| |numFunEvals| |d01alf| |limit| + |trapezoidalo| |pdf2df| |remainder| |antisymmetricTensors| + |removeRoughlyRedundantFactorsInPol| |setref| |create| |numberOfHues| + |tanIfCan| |realZeros| |differentialVariables| |pointData| |solid| + |f04qaf| |combineFeatureCompatibility| |optional?| |tanh2trigh| + |iiacos| |iidprod| |functionIsFracPolynomial?| |f01rdf| |odd?| + |expPot| |eigenvector| |s21bcf| |beauzamyBound| |internalIntegrate0| + |genericRightDiscriminant| |root?| |writable?| |rroot| |rotatez| + |maxPoints3D| |resultantnaif| |OMputObject| |parabolic| |flagFactor| + |quasiComponent| |numberOfComputedEntries| |expandPower| + |factorsOfCyclicGroupSize| |iidsum| |iisqrt3| |rotatey| + |stosePrepareSubResAlgo| |create3Space| |categoryFrame| |mirror| + |bfKeys| |possiblyInfinite?| |showAllElements| |rk4qc| |c02aff| + |e01sef| |removeDuplicates!| |hermiteH| |expr| |powerSum| + |leftTraceMatrix| |dihedralGroup| |kovacic| |getGoodPrime| + |inconsistent?| |fixPredicate| |LowTriBddDenomInv| |drawComplex| + |optAttributes| |recoverAfterFail| |parts| |pastel| + |symmetricDifference| |pointSizeDefault| |palgLODE| |entries| + |gramschmidt| |minimize| |c06ebf| |printingInfo?| |s19adf| |rk4| + |generalizedContinuumHypothesisAssumed?| |denominator| + |halfExtendedResultant2| |splitConstant| |fortranLinkerArgs| + |palginfieldint| |topPredicate| |BumInSepFFE| |fortranComplex| + |leadingCoefficientRicDE| |variable| |tensorProduct| |multiset| + |collectUnder| |subst| |e02dcf| |outputMeasure| |hMonic| |ramified?| + |dAndcExp| |loadNativeModule| |iterators| |hostPlatform| |makeResult| + |univariate?| |integralAtInfinity?| |Vectorise| + |countRealRootsMultiple| |expintfldpoly| |nextPartition| |mainKernel| + |forLoop| |copy!| |argument| |nextPrimitiveNormalPoly| |c06gbf| + |algintegrate| |s18aff| |nextPrimitivePoly| |alphanumeric| + |flexibleArray| |error| |bezoutMatrix| |expenseOfEvaluationIF| |pow| + |next| |makeViewport3D| |rightOne| |plusInfinity| |curryRight| + |reverse!| |adjoint| |assert| |raisePolynomial| |lifting1| + |unitNormal| |e02dff| |minusInfinity| |listYoungTableaus| + |OMencodingBinary| |init| |reorder| |rightExactQuotient| |reverse| + |gcdPrimitive| |janko2| |removeSquaresIfCan| |clipBoolean| + |returnTypeOf| |enterPointData| |powers| |initiallyReduce| + |setProperty!| |copies| |nextSublist| |ipow| |aCubic| + |setVariableOrder| |partialQuotients| |tanh2coth| |datalist| + |seriesSolve| |splitDenominator| |drawStyle| |primitive?| |vectorise| + |sh| |parametric?| |quasiRegular| |basisOfCommutingElements| |lepol| + |rquo| |makeSin| |palglimint0| |simplify| |changeMeasure| |laurentRep| + |permutation| |matrixDimensions| |lowerCase| |sumOfDivisors| + |minimumDegree| |exp1| |e01baf| |fixedPointExquo| |tanQ| |type| + |derivationCoordinates| |tanNa| |OMputEndApp| |check| |badNum| + |accuracyIF| |colorDef| |basisOfRightNucloid| |pmComplexintegrate| + |resultantEuclidean| |inHallBasis?| |initiallyReduced?| |setFormula!| + |rootSplit| |limitedIntegrate| |rank| |complexRoots| |updatF| + |compBound| |maxRowIndex| |clearTheFTable| |OMencodingUnknown| + |segment| |iitan| |positiveRemainder| |point?| |credPol| |belong?| + |cubic| |pmintegrate| |elRow1!| |integralRepresents| |primextendedint| + |universe| |setImagSteps| |youngGroup| |setleaves!| |build| + |component| |changeVar| |rectangularMatrix| |firstSubsetGray| |f02wef| + |complexExpand| |merge!| |shallowCopy| |definingInequation| |bitCoef| + |cAsec| |lastSubResultantElseSplit| |pushuconst| |rubiksGroup| + |OMgetString| |dfRange| |cAcsch| |romberg| |color| + |subQuasiComponent?| |c06gsf| |norm| |simpson| |linearDependenceOverZ| + |reducedForm| |nextsousResultant2| |ramifiedAtInfinity?| |cons| + |getButtonValue| |linearAssociatedOrder| |divergence| |lazyPrem| + |bernoulli| |var2StepsDefault| |pascalTriangle| |OMgetSymbol| + |baseRDE| |lists| |tanSum| |setButtonValue| |imagk| |ref| |tan2trig| + |identity| |leftFactor| |rangePascalTriangle| |sort| + |indicialEquations| |stopTable!| |halfExtendedResultant1| + |cyclePartition| |numericalIntegration| |groebner| |cyclicParents| + |mainMonomials| |e01sff| |degreeSubResultant| |nil?| |slex| + |rational?| |unvectorise| |setlast!| |multiplyCoefficients| |e02akf| + |nodes| |balancedFactorisation| |d03edf| |bernoulliB| + |standardBasisOfCyclicSubmodule| |numberOfIrreduciblePoly| + |numberOfComponents| |pomopo!| |showFortranOutputStack| + |padicallyExpand| |localIntegralBasis| |karatsuba| |source| + |loopPoints| |noKaratsuba| |nativeModuleExtension| + |selectOrPolynomials| |coordinates| |imports| |Ei| |OMsupportsSymbol?| + |halfExtendedSubResultantGcd2| |changeName| |c05nbf| |checkForZero| + |precision| |f02abf| |closedCurve?| |extractProperty| |random| + |bitTruth| |lifting| |localUnquote| |iteratedInitials| |insertRoot!| + |mr| |selectPolynomials| |blue| |monomRDE| |prod| |Beta| |algDsolve| + |padecf| |elementary| |totalDifferential| |physicalLength!| |null| + |extendedSubResultantGcd| |e04fdf| |interpretString| |rootPoly| + |palgintegrate| |innerSolve| |selectFiniteRoutines| |s17dgf| |case| + |acscIfCan| |evenlambert| |quickSort| |associatedEquations| + |var1Steps| |arrayStack| |symbolTable| |iiatanh| |bright| |external?| + |Zero| |parent| |antiCommutative?| |besselJ| |setValue!| + |commutative?| |order| |binaryTree| |subNode?| |normalizeAtInfinity| + |semiDiscriminantEuclidean| |badValues| |One| |e02ahf| + |setScreenResolution| |alternating| |unitNormalize| |subResultantGcd| + |pushFortranOutputStack| |s21baf| |partialNumerators| |f01qcf| + |showTypeInOutput| |setClipValue| |alphanumeric?| |character?| + |generalSqFr| |diag| |varList| |popFortranOutputStack| |squareFree| + |irreducibleRepresentation| |s17adf| |df2st| |singular?| + |partialDenominators| |exprHasAlgebraicWeight| |mathieu11| + |stoseLastSubResultant| |supDimElseRittWu?| |outputAsFortran| + |chiSquare| |outputAsScript| |explimitedint| |pack!| |printStats!| + |pseudoRemainder| |nullity| |clipSurface| |Nul| |getPickedPoints| + |useSingleFactorBound| |categories| |exponent| |prepareSubResAlgo| + |UpTriBddDenomInv| |basisOfRightNucleus| |toScale| |extensionDegree| + |bumptab1| |push!| |sncndn| |key| |curve| |mathieu12| |elt| + |setProperties| |ode1| |qPot| |mvar| |contractSolve| |mapUp!| + |trace2PowMod| |makeViewport2D| |palgint| |palglimint| |zeroMatrix| + |iibinom| |spherical| |filename| |polygon| |primitivePart| + |viewport3D| |perspective| |orbit| |f07adf| |readIfCan!| GE + |sumOfSquares| |zerosOf| |fibonacci| |explicitlyEmpty?| + |nonSingularModel| |not?| |unary?| |outlineRender| |domainOf| + |logpart| GT |any| |operation| |showIntensityFunctions| |OMconnectTCP| + |semiLastSubResultantEuclidean| |singRicDE| |list?| |parse| + |numberOfMonomials| |gethi| |twist| |f07fdf| LE |extractIndex| + |knownInfBasis| |selectIntegrationRoutines| |basisOfNucleus| |iiexp| + |OMgetBind| |rightPower| |space| |perfectSquare?| LT |tubeRadius| + |label| |outputList| |getSyntaxFormsFromFile| |fixedDivisor| + |setAttributeButtonStep| |withPredicates| |log2| |extractIfCan| + |getMultiplicationTable| |traceMatrix| |complex| + |stoseIntegralLastSubResultant| |conjugate| |seed| |fortranInteger| + |e02bcf| |makeMulti| |bipolar| |eisensteinIrreducible?| |sinIfCan| + |realSolve| |createIrreduciblePoly| |viewPosDefault| |f02aff| + |OMserve| |meshFun2Var| |iCompose| |radPoly| |pureLex| |digit?| + |green| |FormatRoman| |showTheRoutinesTable| |linGenPos| + |solveLinearPolynomialEquationByRecursion| |rightDivide| + |SturmHabicht| |realEigenvalues| |subNodeOf?| |linkToFortran| |plus| + |e02ajf| |oddintegers| |getVariableOrder| |front| |vector| + |asechIfCan| |cycleElt| |normalDenom| |keys| |graphState| + |symbolIfCan| |gderiv| |pseudoDivide| |OMsupportsCD?| |clearTable!| + |differentiate| |lexico| |radix| |singularAtInfinity?| |pushdown| + |has?| |rationalPoint?| |var2Steps| |leadingTerm| |currentEnv| + |printTypes| |powmod| |setright!| |collectUpper| |lazyResidueClass| + |algebraicVariables| |semiIndiceSubResultantEuclidean| + |purelyAlgebraicLeadingMonomial?| |nary?| |finiteBasis| |solve| + |drawComplexVectorField| |increasePrecision| |tanAn| |ocf2ocdf| + |OMputBVar| |infinityNorm| |times| |integralMatrix| |nextItem| |dn| + |trailingCoefficient| |iicsch| + |removeRoughlyRedundantFactorsInContents| |search| |edf2ef| + |writeBytes!| |readable?| |omError| |index| |overset?| |setchildren!| + |d01anf| |pointColor| |lfunc| |iicosh| |rootRadius| |useNagFunctions| + |brillhartTrials| |cschIfCan| |meshPar1Var| |minrank| |setMinPoints3D| + |pointPlot| |intermediateResultsIF| |option| |intcompBasis| |call| + |d01apf| |idealiserMatrix| |OMopenFile| |randnum| |maxint| + |reciprocalPolynomial| |linearlyDependentOverZ?| |mapGen| |e04ycf| + |simpsono| |or?| |list| |monom| |conjug| |pair| |patternMatch| + |leviCivitaSymbol| |numberOfFactors| |controlPanel| |btwFact| |super| + |primitiveElement| |car| |normalForm| |primitivePart!| + |clipParametric| |createNormalElement| |rischNormalize| + |nthFractionalTerm| |declare| |s17aef| |semiResultantEuclidean2| |cdr| + |returnType!| |removeSuperfluousCases| |oddlambert| |listLoops| + |rightCharacteristicPolynomial| |heapSort| |laguerreL| |arg1| + |convergents| |common| |atanhIfCan| |setDifference| |removeCoshSq| + |constantOperator| |normalise| |checkPrecision| |aQuartic| |trueEqual| + |distFact| |cot2trig| |arg2| |function| |multiEuclidean| + |mergeFactors| |jacobi| |setIntersection| |regularRepresentation| + |irreducibleFactor| |max| |denomLODE| |leftRankPolynomial| |binary| + |unitCanonical| |setUnion| |lazyIrreducibleFactors| |overlabel| + |makingStats?| |critB| |associates?| |lllp| |backOldPos| |rightTrim| + |isList| |inverse| |leaves| |conditions| |rootKerSimp| + |fortranDoubleComplex| |apply| |blankSeparate| |iiacot| |paren| + |genericLeftNorm| |associative?| |f02bjf| |intersect| |leftTrim| + |and?| |exprHasLogarithmicWeights| |commonDenominator| + |LazardQuotient| |setTex!| |groebner?| |nthExpon| |nilFactor| + |chineseRemainder| |rootSimp| |push| |c06ecf| |size| |phiCoord| + |KrullNumber| |besselI| |minRowIndex| |univariatePolynomials| + |taylorRep| |getRef| |extendedIntegrate| |continuedFraction| + |startPolynomial| |collect| |structuralConstants| + |sumOfKthPowerDivisors| |infix| |OMReadError?| |log| |iiasinh| + |doubleDisc| |monomialIntPoly| |minColIndex| |rules| |trim| + |crushedSet| |fill!| |ridHack1| |numberOfImproperPartitions| + |basisOfLeftNucleus| |euclideanGroebner| |strongGenerators| |first| + |inrootof| |quote| |basisOfCenter| |rk4a| |shellSort| |s14baf| + |extension| |d01asf| |ScanArabic| |pattern| |rest| |find| |makeFR| + |rightTrace| |iilog| |explogs2trigs| |rowEch| |rule| |substitute| + |binomial| |round| |exactQuotient!| |lieAlgebra?| |rightScalarTimes!| + |isPlus| |e04ucf| |elColumn2!| |drawCurves| |factorGroebnerBasis| + |removeDuplicates| |lowerPolynomial| |bracket| |limitPlus| + |subtractIfCan| |scalarTypeOf| |lflimitedint| |deleteRoutine!| + |basisOfLeftAnnihilator| |padicFraction| |aspFilename| |multisect| + |vark| |d02kef| |fractionPart| |llprop| |cSin| + |rightMinimalPolynomial| |appendPoint| |vertConcat| |/\\| |lcm| + |message| |diagonal?| |newTypeLists| |viewPhiDefault| |integrate| + RF2UTS |processTemplate| |f02ajf| |usingTable?| |largest| |\\/| + |powern| |c06fpf| |subPolSet?| |OMputEndError| |degree| + |primextintfrac| |id| |extend| |lambert| |append| |pushdterm| |OMsend| + |unrankImproperPartitions0| |light| |getMeasure| |constantLeft| + |quasiMonic?| |extractSplittingLeaf| |gcd| |ceiling| |ListOfTerms| + |exponential| |minus!| |initTable!| |f04maf| |table| |slash| + |setEpilogue!| |false| |mathieu23| |matrixGcd| |cLog| + |computeCycleLength| |jacobian| |new| |completeSmith| |abelianGroup| + |pair?| |readByteIfCan!| |lyndonIfCan| |infieldIntegrate| + |boundOfCauchy| |leftRank| |factorList| |mpsode| |innerSolve1| + |getDatabase| |countRealRoots| |presuper| |getBadValues| |f01ref| + |createGenericMatrix| |constDsolve| |printInfo| |test| |fortranTypeOf| + |arity| |mainVariable?| |minPoints| |indiceSubResultant| |zero| + |distdfact| |showClipRegion| |comp| |sequences| |algebraicDecompose| + |#| |constantOpIfCan| |asinIfCan| |mainCoefficients| |approximants| + |complexForm| |inc| |OMclose| |stopTableGcd!| |cAtanh| |dflist| + |associatorDependence| |lineColorDefault| |submod| |And| |Lazard2| + |minGbasis| |setStatus!| |rightRank| |minimalPolynomial| + |integralBasisAtInfinity| |pointLists| |s17dcf| + |semiSubResultantGcdEuclidean1| |Or| |OMgetObject| |droot| |concat!| + |jordanAlgebra?| |mkPrim| |byte| |zeroDimPrime?| + |nextLatticePermutation| |f04mcf| |Not| |d01gbf| |remove| |stack| + |rewriteSetWithReduction| |less?| |cyclicEntries| |s13aaf| + |numericIfCan| |variable?| |cAsinh| |monicRightDivide| |nthFlag| + |fortranLiteralLine| |subresultantSequence| |module| |algebraicOf| + |iomode| |back| |last| |modifyPointData| |unitsColorDefault| + |createPrimitiveElement| |generalInfiniteProduct| |unit| ~= + |acschIfCan| |explicitEntries?| |assoc| |left| |fTable| + |resultantEuclideannaif| |quotientByP| |lazyPseudoRemainder| + |totalLex| |minordet| |ode| |coerce| |weights| |right| |normal?| + |divisors| |monicDecomposeIfCan| |mkIntegral| |central?| |construct| + |curryLeft| |iifact| |bitLength| |connect| |leftPower| + |multiplyExponents| |extendedEuclidean| |clearTheIFTable| |recip| + |LyndonWordsList1| |setPredicates| |hasSolution?| |showTheSymbolTable| + |lagrange| |nullSpace| |radicalRoots| |readLine!| |e02bdf| + |fractRagits| |ravel| |exists?| |weakBiRank| |nthRoot| + |moreAlgebraic?| |indicialEquationAtInfinity| |generalTwoFactor| + |reshape| |even?| |polynomialZeros| |addBadValue| + |basisOfMiddleNucleus| |cycle| ** |addPoint| |testModulus| + |leadingExponent| |freeOf?| |iiasin| |e02bbf| |primintegrate| + |deepCopy| |multinomial| |elem?| |transpose| |ScanFloatIgnoreSpaces| + |jacobiIdentity?| |scalarMatrix| |cCsch| |stFunc2| |iipow| |lex| + |open?| |size?| EQ |f02aef| |fmecg| |laplace| |simplifyExp| + |lazyGintegrate| |conditionsForIdempotents| |clikeUniv| + |triangularSystems| |groebgen| |symmetricProduct| |realEigenvectors| + |leftAlternative?| |externalList| |genericLeftMinimalPolynomial| + |unit?| |radicalEigenvector| |stFunc1| |OMunhandledSymbol| + |triangulate| |poisson| |OMgetError| |OMlistCDs| |modifyPoint| + |permutations| |tubeRadiusDefault| |thenBranch| |tubePointsDefault| + |cyclotomicDecomposition| |in?| |bat| |truncate| |extractTop!| + |flatten| |setMinPoints| |rotate!| |symbol| |f04atf| |matrix| |kmax| + |perfectNthRoot| |duplicates| |subSet| |trigs| |outputFixed| + |rightFactorCandidate| |RemainderList| |expression| |argumentListOf| + |isExpt| |callForm?| |hessian| |rootsOf| |charClass| |tubePoints| + |factorsOfDegree| |expandLog| |integer| |useEisensteinCriterion?| + |OMgetEndBind| |normalizedDivide| |firstDenom| |HenselLift| + |OMgetInteger| |univariatePolynomial| |fracPart| |unaryFunction| + |fixedPoints| |zeroDimensional?| |coerceImages| |dimension| |Aleph| + |rdHack1| |insertBottom!| |lexGroebner| |cSinh| |isQuotient| + |signature| |errorKind| |hash| |updateStatus!| |complexElementary| + |lquo| |localReal?| |lazy?| |approxSqrt| |chiSquare1| |argscript| + |mesh?| |cn| |makeCos| |reducedDiscriminant| |count| |hspace| |d02gbf| + |maxrow| |clearDenominator| |nor| |fi2df| |decrease| |not| + |systemCommand| |rischDEsys| |tValues| |secIfCan| |leftNorm| + |generators| |cotIfCan| |cPower| |bivariateSLPEBR| |alphabetic?| + |pointColorPalette| |checkRur| |sin2csc| |f04jgf| |tab| |geometric| + |rewriteIdealWithRemainder| |subspace| |stoseInvertible?reg| |double| + |complexEigenvalues| |mapExpon| |FormatArabic| + |useEisensteinCriterion| |sec2cos| |cAtan| |computePowers| |vspace| + |height| |divide| |computeBasis| |normal| |stoseInvertibleSet| + |OMgetApp| |subresultantVector| |rightRankPolynomial| |lyndon| + |expandTrigProducts| |listRepresentation| |expIfCan| |tab1| + |outerProduct| |lighting| |leader| |mix| |OMParseError?| + |rationalFunction| |conical| |f04arf| |coshIfCan| |iiasec| + |hyperelliptic| |linearMatrix| |npcoef| |brillhartIrreducible?| + |discriminant| |logGamma| |setAdaptive3D| |hexDigit| |writeByteIfCan!| + |squareFreeFactors| |leftDiscriminant| |directory| |coth2tanh| + |associatedSystem| |binaryTournament| |sizeMultiplication| + |unprotectedRemoveRedundantFactors| |f07fef| |figureUnits| + |factorPolynomial| |integer?| |key?| |coerceP| |postfix| |cosh2sech| + |henselFact| |splitLinear| |ratDenom| |product| |pToHdmp| |leftRecip| + |LyndonCoordinates| |c06eaf| |midpoint| |setfirst!| |ldf2vmf| + |nothing| |fullPartialFraction| |identityMatrix| |lprop| |declare!| + |subResultantsChain| |innerEigenvectors| |makeSUP| |iisech| + |monomials| |setMaxPoints3D| |term| |mainContent| |cond| + |roughBasicSet| |chebyshevT| |patternMatchTimes| + |stoseInvertibleSetreg| |rightUnits| |approxNthRoot| + |certainlySubVariety?| |primPartElseUnitCanonical!| + |internalInfRittWu?| |clipWithRanges| |brace| |midpoints| + |getProperties| |LiePolyIfCan| |equiv| |dot| |replace| |nextColeman| + |solid?| |s17dhf| |OMgetBVar| |diagonalMatrix| |factorSFBRlcUnit| + |implies?| |updatD| |OMgetVariable| |sayLength| |box| + |rightAlternative?| |yCoord| |rootProduct| |OMgetEndApp| + |PollardSmallFactor| |LyndonBasis| |polyPart| |createRandomElement| + |mainVariables| |solveLinearPolynomialEquation| |selectsecond| |stop| + |besselK| |failed| |mathieu22| |c05adf| |e02zaf| |semicolonSeparate| + |contours| |exponential1| |antiAssociative?| |stronglyReduced?| + |kroneckerDelta| |value| |companionBlocks| |choosemon| + |screenResolution3D| |ranges| |definingEquations| |varselect| + |outputFloating| |genericRightTrace| |makeTerm| |internalDecompose| + |ptFunc| |areEquivalent?| |mkcomm| |sts2stst| |mainExpression| + |s19abf| |numerator| |leftZero| |printHeader| |moebius| |asimpson| + |e02agf| |weierstrass| |anticoord| |s15adf| |notOperand| + |completeEchelonBasis| |completeHermite| |mapExponents| + |tryFunctionalDecomposition| |divideIfCan!| |operator| + |complexEigenvectors| |subTriSet?| |composite| + |transcendentalDecompose| |medialSet| |numberOfDivisors| |consnewpol| + |selectMultiDimensionalRoutines| |split| |quasiMonicPolynomials| + |edf2df| |completeHensel| |minPoints3D| |or| |adaptive| + |showScalarValues| |length| |principalIdeal| |makeEq| |laurentIfCan| + |scanOneDimSubspaces| |cSec| |quoByVar| |leftFactorIfCan| |e01bef| + |replaceKthElement| |s13adf| |scripts| |nand| |lfextendedint| + |enumerate| |exponents| |iiasech| |OMputError| + |squareFreeLexTriangular| |isMult| |pquo| |objectOf| |taylorIfCan| + |rootOfIrreduciblePoly| |algSplitSimple| |d03eef| |eigenvalues| + |dominantTerm| |roughSubIdeal?| |removeIrreducibleRedundantFactors| + |range| |typeLists| |high| |diophantineSystem| |numberOfChildren| + |superscript| |generator| |complexNormalize| |s21bdf| |redpps| |iicsc| + |currentSubProgram| |crest| |tablePow| |real?| |OMconnInDevice| + |branchIfCan| |indicialEquation| |generic?| + |createMultiplicationTable| |endOfFile?| |superHeight| + |modularGcdPrimitive| |d01akf| |diff| |OMputBind| + |stripCommentsAndBlanks| |setScreenResolution3D| |toseInvertible?| + |setProperty| |SturmHabichtSequence| |findBinding| |resetBadValues| + |rationalIfCan| |inspect| |tube| |topFortranOutputStack| + |semiResultantEuclidean1| |positive?| |mapUnivariate| |printInfo!| + |inf| |fortranLogical| |dimensionOfIrreducibleRepresentation| + |option?| |integral| |birth| |shiftLeft| |e04mbf| |constant?| + |copyInto!| |interval| |deepestInitial| |select!| |applyRules| + |selectODEIVPRoutines| |Si| |unitVector| |rspace| |rangeIsFinite| + |hex| |digit| |composites| |nonLinearPart| |linSolve| |style| |prem| + |cAcoth| |d01amf| |leftExactQuotient| |coerceS| |moduleSum| + |exprHasWeightCosWXorSinWX| |bringDown| |upperCase| |goto| + |complementaryBasis| |neglist| |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) ((-503 |#2| |#2|) -12 (|has| |#2| (-300 |#2|)) (|has| |#2| (-1063))) ((-622 |#2|) -1530 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-622 $) -1530 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-615 (-547)) -12 (|has| |#2| (-615 (-547))) (|has| |#2| (-1016))) ((-615 |#2|) |has| |#2| (-1016)) ((-692 |#2|) -1530 (|has| |#2| (-354)) (|has| |#2| (-169))) ((-701) -1530 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-701)) (|has| |#2| (-169))) ((-765) |has| |#2| (-819)) ((-766) -1530 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-767) |has| |#2| (-767)) ((-768) -1530 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-769) -1530 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-819) |has| |#2| (-819)) ((-821) -1530 (|has| |#2| (-819)) (|has| |#2| (-767))) ((-869 (-1136)) -12 (|has| |#2| (-869 (-1136))) (|has| |#2| (-1016))) ((-1007 (-398 (-547))) -12 (|has| |#2| (-1007 (-398 (-547)))) (|has| |#2| (-1063))) ((-1007 (-547)) -12 (|has| |#2| (-1007 (-547))) (|has| |#2| (-1063))) ((-1007 |#2|) |has| |#2| (-1063)) ((-1022 |#2|) -1530 (|has| |#2| (-1016)) (|has| |#2| (-354)) (|has| |#2| (-169))) ((-1022 $) |has| |#2| (-169)) ((-1016) -1530 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-1023) -1530 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-169))) ((-1075) -1530 (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-701)) (|has| |#2| (-169))) ((-1063) -1530 (|has| |#2| (-1063)) (|has| |#2| (-1016)) (|has| |#2| (-819)) (|has| |#2| (-767)) (|has| |#2| (-701)) (|has| |#2| (-359)) (|has| |#2| (-354)) (|has| |#2| (-169)) (|has| |#2| (-130)) (|has| |#2| (-25))) ((-1173) . 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T) ((-539) |has| |#1| (-539)) ((-622 #0#) |has| |#1| (-539)) ((-622 |#1|) |has| |#1| (-169)) ((-622 $) -1525 (|has| |#1| (-1016)) (|has| |#1| (-539)) (|has| |#1| (-169)) (|has| |#1| (-145)) (|has| |#1| (-143))) ((-615 (-547)) -12 (|has| |#1| (-615 (-547))) (|has| |#1| (-1016))) ((-615 |#1|) |has| |#1| (-1016)) ((-692 #0#) |has| |#1| (-539)) ((-692 |#1|) |has| |#1| (-169)) ((-692 $) |has| |#1| (-539)) ((-701) -1525 (|has| |#1| (-1075)) (|has| |#1| (-1016)) (|has| |#1| (-539)) (|has| |#1| (-463)) (|has| |#1| (-169)) (|has| |#1| (-145)) (|has| |#1| (-143))) ((-821) . T) ((-869 (-1135)) |has| |#1| (-1016)) ((-855 (-370)) |has| |#1| (-855 (-370))) ((-855 (-547)) |has| |#1| (-855 (-547))) ((-853 |#1|) . T) ((-889) |has| |#1| (-539)) ((-1007 (-398 (-547))) -1525 (|has| |#1| (-1007 (-398 (-547)))) (-12 (|has| |#1| (-539)) (|has| |#1| (-1007 (-547))))) ((-1007 (-398 (-921 |#1|))) |has| |#1| (-539)) ((-1007 (-547)) |has| |#1| (-1007 (-547))) ((-1007 (-590 $)) . 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T) ((-23) . T) ((-47 |#1| #0=(-547)) . T) ((-25) . T) ((-38 #1=(-398 (-547))) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-38 |#1|) |has| |#1| (-169)) ((-38 |#2|) |has| |#1| (-354)) ((-38 $) -1525 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-35) |has| |#1| (-38 (-398 (-547)))) ((-94) |has| |#1| (-38 (-398 (-547)))) ((-101) . T) ((-111 #1# #1#) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-354)) ((-111 $ $) -1525 (|has| |#1| (-539)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-130) . T) ((-143) -1525 (-12 (|has| |#1| (-354)) (|has| |#2| (-143))) (|has| |#1| (-143))) ((-145) -1525 (-12 (|has| |#1| (-354)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-591 (-832)) . T) ((-169) -1525 (|has| |#1| (-539)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-592 (-217)) -12 (|has| |#1| (-354)) (|has| |#2| (-991))) ((-592 (-370)) -12 (|has| |#1| (-354)) (|has| |#2| (-991))) ((-592 (-523)) -12 (|has| |#1| (-354)) (|has| |#2| (-592 (-523)))) ((-592 (-861 (-370))) -12 (|has| |#1| (-354)) (|has| |#2| (-592 (-861 (-370))))) ((-592 (-861 (-547))) -12 (|has| |#1| (-354)) (|has| |#2| (-592 (-861 (-547))))) ((-223 |#2|) |has| |#1| (-354)) ((-225) -1525 (-12 (|has| |#1| (-354)) (|has| |#2| (-225))) (|has| |#1| (-15 * (|#1| (-547) |#1|)))) ((-235) |has| |#1| (-354)) ((-275) |has| |#1| (-38 (-398 (-547)))) ((-277 |#2| $) -12 (|has| |#1| (-354)) (|has| |#2| (-277 |#2| |#2|))) ((-277 $ $) |has| (-547) (-1075)) ((-281) -1525 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-298) |has| |#1| (-354)) ((-300 |#2|) -12 (|has| |#1| (-354)) (|has| |#2| (-300 |#2|))) ((-354) |has| |#1| (-354)) ((-329 |#2|) |has| |#1| (-354)) ((-368 |#2|) |has| |#1| (-354)) ((-391 |#2|) |has| |#1| (-354)) ((-442) |has| |#1| (-354)) ((-482) |has| |#1| (-38 (-398 (-547)))) ((-503 (-1135) |#2|) -12 (|has| |#1| (-354)) (|has| |#2| (-503 (-1135) |#2|))) ((-503 |#2| |#2|) -12 (|has| |#1| (-354)) (|has| |#2| (-300 |#2|))) ((-539) -1525 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-622 #1#) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-622 |#1|) . T) ((-622 |#2|) |has| |#1| (-354)) ((-622 $) . T) ((-615 (-547)) -12 (|has| |#1| (-354)) (|has| |#2| (-615 (-547)))) ((-615 |#2|) |has| |#1| (-354)) ((-692 #1#) -1525 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-692 |#1|) |has| |#1| (-169)) ((-692 |#2|) |has| |#1| (-354)) ((-692 $) -1525 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-701) . 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T) ((-23) . T) ((-47 |#1| #0=(-547)) . T) ((-25) . T) ((-38 #1=(-398 (-547))) -1530 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-38 |#1|) |has| |#1| (-169)) ((-38 |#2|) |has| |#1| (-354)) ((-38 $) -1530 (|has| |#1| (-539)) (|has| |#1| (-354))) ((-35) |has| |#1| (-38 (-398 (-547)))) ((-94) |has| |#1| (-38 (-398 (-547)))) ((-101) . T) ((-111 #1# #1#) -1530 (|has| |#1| (-354)) (|has| |#1| (-38 (-398 (-547))))) ((-111 |#1| |#1|) . T) ((-111 |#2| |#2|) |has| |#1| (-354)) ((-111 $ $) -1530 (|has| |#1| (-539)) (|has| |#1| (-354)) (|has| |#1| (-169))) ((-130) . T) ((-143) -1530 (-12 (|has| |#1| (-354)) (|has| |#2| (-143))) (|has| |#1| (-143))) ((-145) -1530 (-12 (|has| |#1| (-354)) (|has| |#2| (-145))) (|has| |#1| (-145))) ((-591 (-832)) . 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"TSETCAT" 2875906 NIL TSETCAT (NIL T T T T) -9 NIL 2877437) (-1164 2861182 2862780 2864671 "TSETCAT-" 2864676 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1163 2855445 2856291 2857233 "TRMANIP" 2860318 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1162 2854886 2854949 2855112 "TRIMAT" 2855377 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1161 2852682 2852919 2853283 "TRIGMNIP" 2854635 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1160 2852202 2852315 2852345 "TRIGCAT" 2852558 T TRIGCAT (NIL) -9 NIL NIL) (-1159 2851871 2851950 2852091 "TRIGCAT-" 2852096 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1158 2848770 2850731 2851011 "TREE" 2851626 NIL TREE (NIL T) -8 NIL NIL) (-1157 2848044 2848572 2848602 "TRANFUN" 2848637 T TRANFUN (NIL) -9 NIL 2848703) (-1156 2847323 2847514 2847794 "TRANFUN-" 2847799 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1155 2847127 2847159 2847220 "TOPSP" 2847284 T TOPSP (NIL) -7 NIL NIL) (-1154 2846475 2846590 2846744 "TOOLSIGN" 2847008 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1153 2845136 2845652 2845891 "TEXTFILE" 2846258 T TEXTFILE (NIL) -8 NIL NIL) (-1152 2843001 2843515 2843953 "TEX" 2844720 T TEX (NIL) -8 NIL NIL) (-1151 2842782 2842813 2842885 "TEX1" 2842964 NIL TEX1 (NIL T) -7 NIL NIL) (-1150 2842430 2842493 2842583 "TEMUTL" 2842714 T TEMUTL (NIL) -7 NIL NIL) (-1149 2840584 2840864 2841189 "TBCMPPK" 2842153 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1148 2832472 2838744 2838800 "TBAGG" 2839200 NIL TBAGG (NIL T T) -9 NIL 2839411) (-1147 2827542 2829030 2830784 "TBAGG-" 2830789 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1146 2826926 2827033 2827178 "TANEXP" 2827431 NIL TANEXP (NIL T) -7 NIL NIL) (-1145 2820427 2826783 2826876 "TABLE" 2826881 NIL TABLE (NIL T T) -8 NIL NIL) (-1144 2819839 2819938 2820076 "TABLEAU" 2820324 NIL TABLEAU (NIL T) -8 NIL NIL) (-1143 2814447 2815667 2816915 "TABLBUMP" 2818625 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1142 2813875 2813975 2814103 "SYSTEM" 2814341 T SYSTEM (NIL) -7 NIL NIL) (-1141 2810338 2811033 2811816 "SYSSOLP" 2813126 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1140 2806629 2807337 2808071 "SYNTAX" 2809626 T SYNTAX (NIL) -8 NIL NIL) (-1139 2803787 2804389 2805021 "SYMTAB" 2806019 T SYMTAB (NIL) -8 NIL NIL) (-1138 2799036 2799938 2800921 "SYMS" 2802826 T SYMS (NIL) -8 NIL NIL) (-1137 2796308 2798494 2798724 "SYMPOLY" 2798841 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1136 2795825 2795900 2796023 "SYMFUNC" 2796220 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1135 2791802 2793062 2793884 "SYMBOL" 2795025 T SYMBOL (NIL) -8 NIL NIL) (-1134 2785341 2787030 2788750 "SWITCH" 2790104 T SWITCH (NIL) -8 NIL NIL) (-1133 2778611 2784162 2784465 "SUTS" 2785096 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1132 2770580 2777726 2778008 "SUPXS" 2778387 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1131 2762109 2770198 2770324 "SUP" 2770489 NIL SUP (NIL T) -8 NIL NIL) (-1130 2761268 2761395 2761612 "SUPFRACF" 2761977 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1129 2760889 2760948 2761061 "SUP2" 2761203 NIL SUP2 (NIL T T) -7 NIL NIL) (-1128 2759302 2759576 2759939 "SUMRF" 2760588 NIL SUMRF (NIL T) -7 NIL NIL) (-1127 2758616 2758682 2758881 "SUMFS" 2759223 NIL SUMFS (NIL T T) -7 NIL NIL) (-1126 2742625 2757793 2758044 "SULS" 2758423 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1125 2741947 2742150 2742290 "SUCH" 2742533 NIL SUCH (NIL T T) -8 NIL NIL) (-1124 2735841 2736853 2737812 "SUBSPACE" 2741035 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1123 2735271 2735361 2735525 "SUBRESP" 2735729 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1122 2728640 2729936 2731247 "STTF" 2734007 NIL STTF (NIL T) -7 NIL NIL) (-1121 2722813 2723933 2725080 "STTFNC" 2727540 NIL STTFNC (NIL T) -7 NIL NIL) (-1120 2714128 2715995 2717789 "STTAYLOR" 2721054 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1119 2707372 2713992 2714075 "STRTBL" 2714080 NIL STRTBL (NIL T) -8 NIL NIL) (-1118 2702763 2707327 2707358 "STRING" 2707363 T STRING (NIL) -8 NIL NIL) (-1117 2697651 2702136 2702166 "STRICAT" 2702225 T STRICAT (NIL) -9 NIL 2702287) (-1116 2690364 2695174 2695794 "STREAM" 2697066 NIL STREAM (NIL T) -8 NIL NIL) (-1115 2689874 2689951 2690095 "STREAM3" 2690281 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1114 2688856 2689039 2689274 "STREAM2" 2689687 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1113 2688544 2688596 2688689 "STREAM1" 2688798 NIL STREAM1 (NIL T) -7 NIL NIL) (-1112 2687560 2687741 2687972 "STINPROD" 2688360 NIL STINPROD (NIL T) -7 NIL NIL) (-1111 2687138 2687322 2687352 "STEP" 2687432 T STEP (NIL) -9 NIL 2687510) (-1110 2680681 2687037 2687114 "STBL" 2687119 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1109 2675856 2679903 2679946 "STAGG" 2680099 NIL STAGG (NIL T) -9 NIL 2680188) (-1108 2673558 2674160 2675032 "STAGG-" 2675037 NIL STAGG- (NIL T T) -8 NIL NIL) (-1107 2671753 2673328 2673420 "STACK" 2673501 NIL STACK (NIL T) -8 NIL NIL) (-1106 2664478 2669894 2670350 "SREGSET" 2671383 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1105 2656904 2658272 2659785 "SRDCMPK" 2663084 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1104 2649871 2654344 2654374 "SRAGG" 2655677 T SRAGG (NIL) -9 NIL 2656285) (-1103 2648888 2649143 2649522 "SRAGG-" 2649527 NIL SRAGG- (NIL T) -8 NIL NIL) (-1102 2643374 2647803 2648231 "SQMATRIX" 2648507 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1101 2637126 2640094 2640820 "SPLTREE" 2642720 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1100 2633116 2633782 2634428 "SPLNODE" 2636552 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1099 2632163 2632396 2632426 "SPFCAT" 2632870 T SPFCAT (NIL) -9 NIL NIL) (-1098 2630900 2631110 2631374 "SPECOUT" 2631921 T SPECOUT (NIL) -7 NIL NIL) (-1097 2630661 2630701 2630770 "SPADPRSR" 2630853 T SPADPRSR (NIL) -7 NIL NIL) (-1096 2622632 2624379 2624422 "SPACEC" 2628795 NIL SPACEC (NIL T) -9 NIL 2630611) (-1095 2620803 2622564 2622613 "SPACE3" 2622618 NIL SPACE3 (NIL T) -8 NIL NIL) (-1094 2619555 2619726 2620017 "SORTPAK" 2620608 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1093 2617605 2617908 2618327 "SOLVETRA" 2619219 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1092 2616616 2616838 2617112 "SOLVESER" 2617378 NIL SOLVESER (NIL T) -7 NIL NIL) (-1091 2611836 2612717 2613719 "SOLVERAD" 2615668 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1090 2607651 2608260 2608989 "SOLVEFOR" 2611203 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1089 2601948 2607000 2607097 "SNTSCAT" 2607102 NIL SNTSCAT (NIL T T T T) -9 NIL 2607172) (-1088 2596091 2600271 2600662 "SMTS" 2601638 NIL SMTS (NIL T T T) -8 NIL NIL) (-1087 2590541 2595979 2596056 "SMP" 2596061 NIL SMP (NIL T T) -8 NIL NIL) (-1086 2588700 2589001 2589399 "SMITH" 2590238 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1085 2581683 2585838 2585941 "SMATCAT" 2587292 NIL SMATCAT (NIL NIL T T T) -9 NIL 2587842) (-1084 2578623 2579446 2580624 "SMATCAT-" 2580629 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1083 2576336 2577859 2577902 "SKAGG" 2578163 NIL SKAGG (NIL T) -9 NIL 2578298) (-1082 2572452 2575440 2575718 "SINT" 2576080 T SINT (NIL) -8 NIL NIL) (-1081 2572224 2572262 2572328 "SIMPAN" 2572408 T SIMPAN (NIL) -7 NIL NIL) (-1080 2571531 2571759 2571899 "SIG" 2572106 T SIG (NIL) -8 NIL NIL) (-1079 2570369 2570590 2570865 "SIGNRF" 2571290 NIL SIGNRF (NIL T) -7 NIL NIL) (-1078 2569174 2569325 2569616 "SIGNEF" 2570198 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1077 2566864 2567318 2567824 "SHP" 2568715 NIL SHP (NIL T NIL) -7 NIL NIL) (-1076 2560770 2566765 2566841 "SHDP" 2566846 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1075 2560369 2560535 2560565 "SGROUP" 2560658 T SGROUP (NIL) -9 NIL 2560720) (-1074 2560227 2560253 2560326 "SGROUP-" 2560331 NIL SGROUP- (NIL T) -8 NIL NIL) (-1073 2557063 2557760 2558483 "SGCF" 2559526 T SGCF (NIL) -7 NIL NIL) (-1072 2551458 2556510 2556607 "SFRTCAT" 2556612 NIL SFRTCAT (NIL T T T T) -9 NIL 2556651) (-1071 2544882 2545897 2547033 "SFRGCD" 2550441 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1070 2538010 2539081 2540267 "SFQCMPK" 2543815 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1069 2537632 2537721 2537831 "SFORT" 2537951 NIL SFORT (NIL T T) -8 NIL NIL) (-1068 2536777 2537472 2537593 "SEXOF" 2537598 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1067 2535911 2536658 2536726 "SEX" 2536731 T SEX (NIL) -8 NIL NIL) (-1066 2530687 2531376 2531471 "SEXCAT" 2535242 NIL SEXCAT (NIL T T T T T) -9 NIL 2535861) (-1065 2527867 2530621 2530669 "SET" 2530674 NIL SET (NIL T) -8 NIL NIL) (-1064 2526118 2526580 2526885 "SETMN" 2527608 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1063 2525724 2525850 2525880 "SETCAT" 2525997 T SETCAT (NIL) -9 NIL 2526082) (-1062 2525504 2525556 2525655 "SETCAT-" 2525660 NIL SETCAT- (NIL T) -8 NIL NIL) (-1061 2521891 2523965 2524008 "SETAGG" 2524878 NIL SETAGG (NIL T) -9 NIL 2525218) (-1060 2521349 2521465 2521702 "SETAGG-" 2521707 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1059 2520553 2520846 2520907 "SEGXCAT" 2521193 NIL SEGXCAT (NIL T T) -9 NIL 2521313) (-1058 2519609 2520219 2520401 "SEG" 2520406 NIL SEG (NIL T) -8 NIL NIL) (-1057 2518516 2518729 2518772 "SEGCAT" 2519354 NIL SEGCAT (NIL T) -9 NIL 2519592) (-1056 2517565 2517895 2518095 "SEGBIND" 2518351 NIL SEGBIND (NIL T) -8 NIL NIL) (-1055 2517186 2517245 2517358 "SEGBIND2" 2517500 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1054 2516804 2516987 2517064 "SEGAST" 2517131 T SEGAST (NIL) -8 NIL NIL) (-1053 2516023 2516149 2516353 "SEG2" 2516648 NIL SEG2 (NIL T T) -7 NIL NIL) (-1052 2515460 2515958 2516005 "SDVAR" 2516010 NIL SDVAR (NIL T) -8 NIL NIL) (-1051 2507750 2515230 2515360 "SDPOL" 2515365 NIL SDPOL (NIL T) -8 NIL NIL) (-1050 2506343 2506609 2506928 "SCPKG" 2507465 NIL SCPKG (NIL T) -7 NIL NIL) (-1049 2505479 2505659 2505859 "SCOPE" 2506165 T SCOPE (NIL) -8 NIL NIL) (-1048 2504700 2504833 2505012 "SCACHE" 2505334 NIL SCACHE (NIL T) -7 NIL NIL) (-1047 2504426 2504569 2504599 "SASTCAT" 2504604 T SASTCAT (NIL) -9 NIL 2504617) (-1046 2504215 2504260 2504358 "SASTCAT-" 2504363 NIL SASTCAT- (NIL T) -8 NIL NIL) (-1045 2503654 2503975 2504060 "SAOS" 2504152 T SAOS (NIL) -8 NIL NIL) (-1044 2503219 2503254 2503427 "SAERFFC" 2503613 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1043 2497193 2503116 2503196 "SAE" 2503201 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1042 2496786 2496821 2496980 "SAEFACT" 2497152 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1041 2495107 2495421 2495822 "RURPK" 2496452 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1040 2493743 2494022 2494334 "RULESET" 2494941 NIL RULESET (NIL T T T) -8 NIL NIL) (-1039 2490930 2491433 2491898 "RULE" 2493424 NIL RULE (NIL T T T) -8 NIL NIL) (-1038 2490569 2490724 2490807 "RULECOLD" 2490882 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1037 2485418 2486212 2487132 "RSETGCD" 2489768 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1036 2474675 2479727 2479824 "RSETCAT" 2483943 NIL RSETCAT (NIL T T T T) -9 NIL 2485040) (-1035 2472602 2473141 2473965 "RSETCAT-" 2473970 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1034 2464989 2466364 2467884 "RSDCMPK" 2471201 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2462994 2463435 2463509 "RRCC" 2464595 NIL RRCC (NIL T T) -9 NIL 2464939) (-1032 2462345 2462519 2462798 "RRCC-" 2462803 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1031 2461832 2462041 2462142 "RPTAST" 2462266 T RPTAST (NIL) -8 NIL NIL) (-1030 2436060 2445645 2445712 "RPOLCAT" 2456376 NIL RPOLCAT (NIL T T T) -9 NIL 2459535) (-1029 2427560 2429898 2433020 "RPOLCAT-" 2433025 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1028 2418607 2425771 2426253 "ROUTINE" 2427100 T ROUTINE (NIL) -8 NIL NIL) (-1027 2415365 2418158 2418307 "ROMAN" 2418480 T ROMAN (NIL) -8 NIL NIL) (-1026 2413640 2414225 2414485 "ROIRC" 2415170 NIL ROIRC (NIL T T) -8 NIL NIL) (-1025 2410091 2412330 2412360 "RNS" 2412664 T RNS (NIL) -9 NIL 2412936) (-1024 2408600 2408983 2409517 "RNS-" 2409592 NIL RNS- (NIL T) -8 NIL NIL) (-1023 2408049 2408431 2408461 "RNG" 2408466 T RNG (NIL) -9 NIL 2408487) (-1022 2407441 2407803 2407846 "RMODULE" 2407908 NIL RMODULE (NIL T) -9 NIL 2407950) (-1021 2406277 2406371 2406707 "RMCAT2" 2407342 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1020 2402982 2405451 2405776 "RMATRIX" 2406011 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1019 2395924 2398158 2398273 "RMATCAT" 2401632 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2402614) (-1018 2395299 2395446 2395753 "RMATCAT-" 2395758 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1017 2394866 2394941 2395069 "RINTERP" 2395218 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1016 2393954 2394474 2394504 "RING" 2394616 T RING (NIL) -9 NIL 2394711) (-1015 2393746 2393790 2393887 "RING-" 2393892 NIL RING- (NIL T) -8 NIL NIL) (-1014 2392587 2392824 2393082 "RIDIST" 2393510 T RIDIST (NIL) -7 NIL NIL) (-1013 2383903 2392055 2392261 "RGCHAIN" 2392435 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1012 2380897 2381511 2382181 "RF" 2383267 NIL RF (NIL T) -7 NIL NIL) (-1011 2380543 2380606 2380709 "RFFACTOR" 2380828 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1010 2380268 2380303 2380400 "RFFACT" 2380502 NIL RFFACT (NIL T) -7 NIL NIL) (-1009 2378385 2378749 2379131 "RFDIST" 2379908 T RFDIST (NIL) -7 NIL NIL) (-1008 2377838 2377930 2378093 "RETSOL" 2378287 NIL RETSOL (NIL T T) -7 NIL NIL) (-1007 2377426 2377506 2377549 "RETRACT" 2377742 NIL RETRACT (NIL T) -9 NIL NIL) (-1006 2377275 2377300 2377387 "RETRACT-" 2377392 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1005 2376921 2377097 2377167 "RETAST" 2377227 T RETAST (NIL) -8 NIL NIL) (-1004 2369775 2376574 2376701 "RESULT" 2376816 T RESULT (NIL) -8 NIL NIL) (-1003 2368401 2369044 2369243 "RESRING" 2369678 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1002 2368037 2368086 2368184 "RESLATC" 2368338 NIL RESLATC (NIL T) -7 NIL NIL) (-1001 2367743 2367777 2367884 "REPSQ" 2367996 NIL REPSQ (NIL T) -7 NIL NIL) (-1000 2365165 2365745 2366347 "REP" 2367163 T REP (NIL) -7 NIL NIL) (-999 2364866 2364900 2365009 "REPDB" 2365124 NIL REPDB (NIL T) -7 NIL NIL) (-998 2358794 2360173 2361394 "REP2" 2363678 NIL REP2 (NIL T) -7 NIL NIL) (-997 2355186 2355867 2356673 "REP1" 2358021 NIL REP1 (NIL T) -7 NIL NIL) (-996 2347924 2353339 2353793 "REGSET" 2354816 NIL REGSET (NIL T T T T) -8 NIL NIL) (-995 2346745 2347080 2347328 "REF" 2347709 NIL REF (NIL T) -8 NIL NIL) (-994 2346126 2346229 2346394 "REDORDER" 2346629 NIL REDORDER (NIL T T) -7 NIL NIL) (-993 2342146 2345354 2345577 "RECLOS" 2345955 NIL RECLOS (NIL T) -8 NIL NIL) (-992 2341203 2341384 2341597 "REALSOLV" 2341953 T REALSOLV (NIL) -7 NIL NIL) (-991 2341051 2341092 2341120 "REAL" 2341125 T REAL (NIL) -9 NIL 2341160) (-990 2337542 2338344 2339226 "REAL0Q" 2340216 NIL REAL0Q (NIL T) -7 NIL NIL) (-989 2333153 2334141 2335200 "REAL0" 2336523 NIL REAL0 (NIL T) -7 NIL NIL) (-988 2332673 2332874 2332966 "RDUCEAST" 2333081 T RDUCEAST (NIL) -8 NIL NIL) (-987 2332081 2332153 2332358 "RDIV" 2332595 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-986 2331154 2331328 2331539 "RDIST" 2331903 NIL RDIST (NIL T) -7 NIL NIL) (-985 2329755 2330042 2330412 "RDETRS" 2330862 NIL RDETRS (NIL T T) -7 NIL NIL) (-984 2327572 2328026 2328562 "RDETR" 2329297 NIL RDETR (NIL T T) -7 NIL NIL) (-983 2326186 2326464 2326866 "RDEEFS" 2327288 NIL RDEEFS (NIL T T) -7 NIL NIL) (-982 2324684 2324990 2325420 "RDEEF" 2325874 NIL RDEEF (NIL T T) -7 NIL NIL) (-981 2319021 2321892 2321920 "RCFIELD" 2323197 T RCFIELD (NIL) -9 NIL 2323927) (-980 2317090 2317594 2318287 "RCFIELD-" 2318360 NIL RCFIELD- (NIL T) -8 NIL NIL) (-979 2313421 2315206 2315247 "RCAGG" 2316318 NIL RCAGG (NIL T) -9 NIL 2316783) (-978 2313052 2313146 2313306 "RCAGG-" 2313311 NIL RCAGG- (NIL T T) -8 NIL NIL) (-977 2312392 2312504 2312667 "RATRET" 2312936 NIL RATRET (NIL T) -7 NIL NIL) (-976 2311949 2312016 2312135 "RATFACT" 2312320 NIL RATFACT (NIL T) -7 NIL NIL) (-975 2311264 2311384 2311534 "RANDSRC" 2311819 T RANDSRC (NIL) -7 NIL NIL) (-974 2311001 2311045 2311116 "RADUTIL" 2311213 T RADUTIL (NIL) -7 NIL NIL) (-973 2304066 2309744 2310061 "RADIX" 2310716 NIL RADIX (NIL NIL) -8 NIL NIL) (-972 2295722 2303910 2304038 "RADFF" 2304043 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-971 2295374 2295449 2295477 "RADCAT" 2295634 T RADCAT (NIL) -9 NIL NIL) (-970 2295159 2295207 2295304 "RADCAT-" 2295309 NIL RADCAT- (NIL T) -8 NIL NIL) (-969 2293310 2294934 2295023 "QUEUE" 2295103 NIL QUEUE (NIL T) -8 NIL NIL) (-968 2289886 2293247 2293292 "QUAT" 2293297 NIL QUAT (NIL T) -8 NIL NIL) (-967 2289524 2289567 2289694 "QUATCT2" 2289837 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-966 2283384 2286685 2286725 "QUATCAT" 2287505 NIL QUATCAT (NIL T) -9 NIL 2288271) (-965 2279528 2280565 2281952 "QUATCAT-" 2282046 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-964 2277048 2278612 2278653 "QUAGG" 2279028 NIL QUAGG (NIL T) -9 NIL 2279203) (-963 2276697 2276873 2276941 "QQUTAST" 2277000 T QQUTAST (NIL) -8 NIL NIL) (-962 2275622 2276095 2276267 "QFORM" 2276569 NIL QFORM (NIL NIL T) -8 NIL NIL) (-961 2266955 2272158 2272198 "QFCAT" 2272856 NIL QFCAT (NIL T) -9 NIL 2273855) (-960 2262527 2263728 2265319 "QFCAT-" 2265413 NIL QFCAT- (NIL T T) -8 NIL NIL) (-959 2262165 2262208 2262335 "QFCAT2" 2262478 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-958 2261625 2261735 2261865 "QEQUAT" 2262055 T QEQUAT (NIL) -8 NIL NIL) (-957 2254773 2255844 2257028 "QCMPACK" 2260558 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-956 2252349 2252770 2253198 "QALGSET" 2254428 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-955 2251594 2251768 2252000 "QALGSET2" 2252169 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-954 2250285 2250508 2250825 "PWFFINTB" 2251367 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-953 2248467 2248635 2248989 "PUSHVAR" 2250099 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-952 2244385 2245439 2245480 "PTRANFN" 2247364 NIL PTRANFN (NIL T) -9 NIL NIL) (-951 2242787 2243078 2243400 "PTPACK" 2244096 NIL PTPACK (NIL T) -7 NIL NIL) (-950 2242419 2242476 2242585 "PTFUNC2" 2242724 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-949 2236885 2241230 2241271 "PTCAT" 2241644 NIL PTCAT (NIL T) -9 NIL 2241806) (-948 2236543 2236578 2236702 "PSQFR" 2236844 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-947 2235138 2235436 2235770 "PSEUDLIN" 2236241 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-946 2221907 2224272 2226596 "PSETPK" 2232898 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-945 2214951 2217665 2217761 "PSETCAT" 2220782 NIL PSETCAT (NIL T T T T) -9 NIL 2221596) (-944 2212787 2213421 2214242 "PSETCAT-" 2214247 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-943 2212136 2212301 2212329 "PSCURVE" 2212597 T PSCURVE (NIL) -9 NIL 2212764) (-942 2208617 2210099 2210164 "PSCAT" 2211008 NIL PSCAT (NIL T T T) -9 NIL 2211248) (-941 2207680 2207896 2208296 "PSCAT-" 2208301 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-940 2206332 2206965 2207179 "PRTITION" 2207486 T PRTITION (NIL) -8 NIL NIL) (-939 2205852 2206053 2206145 "PRTDAST" 2206260 T PRTDAST (NIL) -8 NIL NIL) (-938 2194950 2197156 2199344 "PRS" 2203714 NIL PRS (NIL T T) -7 NIL NIL) (-937 2192808 2194300 2194340 "PRQAGG" 2194523 NIL PRQAGG (NIL T) -9 NIL 2194625) (-936 2192194 2192423 2192451 "PROPLOG" 2192636 T PROPLOG (NIL) -9 NIL 2192758) (-935 2189364 2190008 2190472 "PROPFRML" 2191762 NIL PROPFRML (NIL T) -8 NIL NIL) (-934 2188824 2188934 2189064 "PROPERTY" 2189254 T PROPERTY (NIL) -8 NIL NIL) (-933 2182909 2186990 2187810 "PRODUCT" 2188050 NIL PRODUCT (NIL T T) -8 NIL NIL) (-932 2180222 2182367 2182601 "PR" 2182720 NIL PR (NIL T T) -8 NIL NIL) (-931 2180018 2180050 2180109 "PRINT" 2180183 T PRINT (NIL) -7 NIL NIL) (-930 2179358 2179475 2179627 "PRIMES" 2179898 NIL PRIMES (NIL T) -7 NIL NIL) (-929 2177423 2177824 2178290 "PRIMELT" 2178937 NIL PRIMELT (NIL T) -7 NIL NIL) (-928 2177152 2177201 2177229 "PRIMCAT" 2177353 T PRIMCAT (NIL) -9 NIL NIL) (-927 2173313 2177090 2177135 "PRIMARR" 2177140 NIL PRIMARR (NIL T) -8 NIL NIL) (-926 2172320 2172498 2172726 "PRIMARR2" 2173131 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-925 2171963 2172019 2172130 "PREASSOC" 2172258 NIL PREASSOC (NIL T T) -7 NIL NIL) (-924 2171438 2171571 2171599 "PPCURVE" 2171804 T PPCURVE (NIL) -9 NIL 2171940) (-923 2171060 2171233 2171316 "PORTNUM" 2171375 T PORTNUM (NIL) -8 NIL NIL) (-922 2168419 2168818 2169410 "POLYROOT" 2170641 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-921 2162364 2168023 2168183 "POLY" 2168292 NIL POLY (NIL T) -8 NIL NIL) (-920 2161747 2161805 2162039 "POLYLIFT" 2162300 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-919 2158022 2158471 2159100 "POLYCATQ" 2161292 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-918 2145061 2150417 2150482 "POLYCAT" 2153996 NIL POLYCAT (NIL T T T) -9 NIL 2155924) (-917 2138511 2140372 2142756 "POLYCAT-" 2142761 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-916 2138098 2138166 2138286 "POLY2UP" 2138437 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-915 2137730 2137787 2137896 "POLY2" 2138035 NIL POLY2 (NIL T T) -7 NIL NIL) (-914 2136415 2136654 2136930 "POLUTIL" 2137504 NIL POLUTIL (NIL T T) -7 NIL NIL) (-913 2134770 2135047 2135378 "POLTOPOL" 2136137 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-912 2130288 2134706 2134752 "POINT" 2134757 NIL POINT (NIL T) -8 NIL NIL) (-911 2128475 2128832 2129207 "PNTHEORY" 2129933 T PNTHEORY (NIL) -7 NIL NIL) (-910 2126894 2127191 2127603 "PMTOOLS" 2128173 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-909 2126487 2126565 2126682 "PMSYM" 2126810 NIL PMSYM (NIL T) -7 NIL NIL) (-908 2125997 2126066 2126240 "PMQFCAT" 2126412 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-907 2125352 2125462 2125618 "PMPRED" 2125874 NIL PMPRED (NIL T) -7 NIL NIL) (-906 2124748 2124834 2124995 "PMPREDFS" 2125253 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-905 2123391 2123599 2123984 "PMPLCAT" 2124510 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-904 2122923 2123002 2123154 "PMLSAGG" 2123306 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-903 2122398 2122474 2122655 "PMKERNEL" 2122841 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-902 2122015 2122090 2122203 "PMINS" 2122317 NIL PMINS (NIL T) -7 NIL NIL) (-901 2121443 2121512 2121728 "PMFS" 2121940 NIL PMFS (NIL T T T) -7 NIL NIL) (-900 2120671 2120789 2120994 "PMDOWN" 2121320 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-899 2119834 2119993 2120175 "PMASS" 2120509 T PMASS (NIL) -7 NIL NIL) (-898 2119108 2119219 2119382 "PMASSFS" 2119720 NIL PMASSFS (NIL T T) -7 NIL NIL) (-897 2118763 2118831 2118925 "PLOTTOOL" 2119034 T PLOTTOOL (NIL) -7 NIL NIL) (-896 2113385 2114574 2115722 "PLOT" 2117635 T PLOT (NIL) -8 NIL NIL) (-895 2109199 2110233 2111154 "PLOT3D" 2112484 T PLOT3D (NIL) -8 NIL NIL) (-894 2108111 2108288 2108523 "PLOT1" 2109003 NIL PLOT1 (NIL T) -7 NIL NIL) (-893 2083505 2088177 2093028 "PLEQN" 2103377 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-892 2082823 2082945 2083125 "PINTERP" 2083370 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-891 2082516 2082563 2082666 "PINTERPA" 2082770 NIL PINTERPA (NIL T T) -7 NIL NIL) (-890 2081801 2082322 2082409 "PI" 2082449 T PI (NIL) -8 NIL NIL) (-889 2080233 2081174 2081202 "PID" 2081384 T PID (NIL) -9 NIL 2081518) (-888 2079958 2079995 2080083 "PICOERCE" 2080190 NIL PICOERCE (NIL T) -7 NIL NIL) (-887 2079278 2079417 2079593 "PGROEB" 2079814 NIL PGROEB (NIL T) -7 NIL NIL) (-886 2074865 2075679 2076584 "PGE" 2078393 T PGE (NIL) -7 NIL NIL) (-885 2072989 2073235 2073601 "PGCD" 2074582 NIL PGCD (NIL T T T T) -7 NIL NIL) (-884 2072327 2072430 2072591 "PFRPAC" 2072873 NIL PFRPAC (NIL T) -7 NIL NIL) (-883 2069007 2070875 2071228 "PFR" 2072006 NIL PFR (NIL T) -8 NIL NIL) (-882 2067396 2067640 2067965 "PFOTOOLS" 2068754 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-881 2065929 2066168 2066519 "PFOQ" 2067153 NIL PFOQ (NIL T T T) -7 NIL NIL) (-880 2064402 2064614 2064977 "PFO" 2065713 NIL PFO (NIL T T T T T) -7 NIL NIL) (-879 2060990 2064291 2064360 "PF" 2064365 NIL PF (NIL NIL) -8 NIL NIL) (-878 2058459 2059696 2059724 "PFECAT" 2060309 T PFECAT (NIL) -9 NIL 2060693) (-877 2057904 2058058 2058272 "PFECAT-" 2058277 NIL PFECAT- (NIL T) -8 NIL NIL) (-876 2056508 2056759 2057060 "PFBRU" 2057653 NIL PFBRU (NIL T T) -7 NIL NIL) (-875 2054375 2054726 2055158 "PFBR" 2056159 NIL PFBR (NIL T T T T) -7 NIL NIL) (-874 2050291 2051751 2052427 "PERM" 2053732 NIL PERM (NIL T) -8 NIL NIL) (-873 2045557 2046498 2047368 "PERMGRP" 2049454 NIL PERMGRP (NIL T) -8 NIL NIL) (-872 2043689 2044620 2044661 "PERMCAT" 2045107 NIL PERMCAT (NIL T) -9 NIL 2045412) (-871 2043342 2043383 2043507 "PERMAN" 2043642 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-870 2040782 2042911 2043042 "PENDTREE" 2043244 NIL PENDTREE (NIL T) -8 NIL NIL) (-869 2038895 2039629 2039670 "PDRING" 2040327 NIL PDRING (NIL T) -9 NIL 2040613) (-868 2037998 2038216 2038578 "PDRING-" 2038583 NIL PDRING- (NIL T T) -8 NIL NIL) (-867 2035139 2035890 2036581 "PDEPROB" 2037327 T PDEPROB (NIL) -8 NIL NIL) (-866 2032686 2033188 2033743 "PDEPACK" 2034604 T PDEPACK (NIL) -7 NIL NIL) (-865 2031598 2031788 2032039 "PDECOMP" 2032485 NIL PDECOMP (NIL T T) -7 NIL NIL) (-864 2029203 2030020 2030048 "PDECAT" 2030835 T PDECAT (NIL) -9 NIL 2031548) (-863 2028954 2028987 2029077 "PCOMP" 2029164 NIL PCOMP (NIL T T) -7 NIL NIL) (-862 2027159 2027755 2028052 "PBWLB" 2028683 NIL PBWLB (NIL T) -8 NIL NIL) (-861 2019663 2021232 2022570 "PATTERN" 2025842 NIL PATTERN (NIL T) -8 NIL NIL) (-860 2019295 2019352 2019461 "PATTERN2" 2019600 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-859 2017052 2017440 2017897 "PATTERN1" 2018884 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-858 2014447 2015001 2015482 "PATRES" 2016617 NIL PATRES (NIL T T) -8 NIL NIL) (-857 2014011 2014078 2014210 "PATRES2" 2014374 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-856 2011894 2012299 2012706 "PATMATCH" 2013678 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-855 2011430 2011613 2011654 "PATMAB" 2011761 NIL PATMAB (NIL T) -9 NIL 2011844) (-854 2009975 2010284 2010542 "PATLRES" 2011235 NIL PATLRES (NIL T T T) -8 NIL NIL) (-853 2009521 2009644 2009685 "PATAB" 2009690 NIL PATAB (NIL T) -9 NIL 2009862) (-852 2007002 2007534 2008107 "PARTPERM" 2008968 T PARTPERM (NIL) -7 NIL NIL) (-851 2006623 2006686 2006788 "PARSURF" 2006933 NIL PARSURF (NIL T) -8 NIL NIL) (-850 2006255 2006312 2006421 "PARSU2" 2006560 NIL PARSU2 (NIL T T) -7 NIL NIL) (-849 2006019 2006059 2006126 "PARSER" 2006208 T PARSER (NIL) -7 NIL NIL) (-848 2005640 2005703 2005805 "PARSCURV" 2005950 NIL PARSCURV (NIL T) -8 NIL NIL) (-847 2005272 2005329 2005438 "PARSC2" 2005577 NIL PARSC2 (NIL T T) -7 NIL NIL) (-846 2004911 2004969 2005066 "PARPCURV" 2005208 NIL PARPCURV (NIL T) -8 NIL NIL) (-845 2004543 2004600 2004709 "PARPC2" 2004848 NIL PARPC2 (NIL T T) -7 NIL NIL) (-844 2004063 2004149 2004268 "PAN2EXPR" 2004444 T PAN2EXPR (NIL) -7 NIL NIL) (-843 2002869 2003184 2003412 "PALETTE" 2003855 T PALETTE (NIL) -8 NIL NIL) (-842 2001337 2001874 2002234 "PAIR" 2002555 NIL PAIR (NIL T T) -8 NIL NIL) (-841 1995245 2000596 2000790 "PADICRC" 2001192 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-840 1988511 1994591 1994775 "PADICRAT" 1995093 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-839 1986861 1988448 1988493 "PADIC" 1988498 NIL PADIC (NIL NIL) -8 NIL NIL) (-838 1984106 1985636 1985676 "PADICCT" 1986257 NIL PADICCT (NIL NIL) -9 NIL 1986539) (-837 1983063 1983263 1983531 "PADEPAC" 1983893 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-836 1982275 1982408 1982614 "PADE" 1982925 NIL PADE (NIL T T T) -7 NIL NIL) (-835 1980325 1981111 1981428 "OWP" 1982042 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-834 1979434 1979930 1980102 "OVAR" 1980193 NIL OVAR (NIL NIL) -8 NIL NIL) (-833 1978698 1978819 1978980 "OUT" 1979293 T OUT (NIL) -7 NIL NIL) (-832 1967752 1969923 1972093 "OUTFORM" 1976548 T OUTFORM (NIL) -8 NIL NIL) (-831 1967389 1967472 1967500 "OUTBCON" 1967651 T OUTBCON (NIL) -9 NIL 1967736) (-830 1967229 1967264 1967340 "OUTBCON-" 1967345 NIL OUTBCON- (NIL T) -8 NIL NIL) (-829 1966637 1966958 1967047 "OSI" 1967160 T OSI (NIL) -8 NIL NIL) (-828 1966193 1966505 1966533 "OSGROUP" 1966538 T OSGROUP (NIL) -9 NIL 1966560) (-827 1964938 1965165 1965450 "ORTHPOL" 1965940 NIL ORTHPOL (NIL T) -7 NIL NIL) (-826 1962348 1964597 1964736 "OREUP" 1964881 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-825 1959786 1962039 1962166 "ORESUP" 1962290 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-824 1957314 1957814 1958375 "OREPCTO" 1959275 NIL OREPCTO (NIL T T) -7 NIL NIL) (-823 1951225 1953392 1953433 "OREPCAT" 1955781 NIL OREPCAT (NIL T) -9 NIL 1956885) (-822 1948372 1949154 1950212 "OREPCAT-" 1950217 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-821 1947549 1947821 1947849 "ORDSET" 1948158 T ORDSET (NIL) -9 NIL 1948322) (-820 1947068 1947190 1947383 "ORDSET-" 1947388 NIL ORDSET- (NIL T) -8 NIL NIL) (-819 1945722 1946479 1946507 "ORDRING" 1946709 T ORDRING (NIL) -9 NIL 1946834) (-818 1945367 1945461 1945605 "ORDRING-" 1945610 NIL ORDRING- (NIL T) -8 NIL NIL) (-817 1944773 1945210 1945238 "ORDMON" 1945243 T ORDMON (NIL) -9 NIL 1945264) (-816 1943935 1944082 1944277 "ORDFUNS" 1944622 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-815 1943446 1943805 1943833 "ORDFIN" 1943838 T ORDFIN (NIL) -9 NIL 1943859) (-814 1940038 1942032 1942441 "ORDCOMP" 1943070 NIL ORDCOMP (NIL T) -8 NIL NIL) (-813 1939304 1939431 1939617 "ORDCOMP2" 1939898 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-812 1935811 1936694 1937531 "OPTPROB" 1938487 T OPTPROB (NIL) -8 NIL NIL) (-811 1932613 1933252 1933956 "OPTPACK" 1935127 T OPTPACK (NIL) -7 NIL NIL) (-810 1930326 1931066 1931094 "OPTCAT" 1931913 T OPTCAT (NIL) -9 NIL 1932563) (-809 1930094 1930133 1930199 "OPQUERY" 1930280 T OPQUERY (NIL) -7 NIL NIL) (-808 1927260 1928405 1928909 "OP" 1929623 NIL OP (NIL T) -8 NIL NIL) (-807 1924105 1926057 1926426 "ONECOMP" 1926924 NIL ONECOMP (NIL T) -8 NIL NIL) (-806 1923410 1923525 1923699 "ONECOMP2" 1923977 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-805 1922829 1922935 1923065 "OMSERVER" 1923300 T OMSERVER (NIL) -7 NIL NIL) (-804 1919717 1922269 1922309 "OMSAGG" 1922370 NIL OMSAGG (NIL T) -9 NIL 1922434) (-803 1918340 1918603 1918885 "OMPKG" 1919455 T OMPKG (NIL) -7 NIL NIL) (-802 1917770 1917873 1917901 "OM" 1918200 T OM (NIL) -9 NIL NIL) (-801 1916352 1917319 1917488 "OMLO" 1917651 NIL OMLO (NIL T T) -8 NIL NIL) (-800 1915277 1915424 1915651 "OMEXPR" 1916178 NIL OMEXPR (NIL T) -7 NIL NIL) (-799 1914595 1914823 1914959 "OMERR" 1915161 T OMERR (NIL) -8 NIL NIL) (-798 1913773 1914016 1914176 "OMERRK" 1914455 T OMERRK (NIL) -8 NIL NIL) (-797 1913251 1913450 1913558 "OMENC" 1913685 T OMENC (NIL) -8 NIL NIL) (-796 1907146 1908331 1909502 "OMDEV" 1912100 T OMDEV (NIL) -8 NIL NIL) (-795 1906215 1906386 1906580 "OMCONN" 1906972 T OMCONN (NIL) -8 NIL NIL) (-794 1904871 1905813 1905841 "OINTDOM" 1905846 T OINTDOM (NIL) -9 NIL 1905867) (-793 1900677 1901861 1902577 "OFMONOID" 1904187 NIL OFMONOID (NIL T) -8 NIL NIL) (-792 1900115 1900614 1900659 "ODVAR" 1900664 NIL ODVAR (NIL T) -8 NIL NIL) (-791 1897325 1899612 1899797 "ODR" 1899990 NIL ODR (NIL T T NIL) -8 NIL NIL) (-790 1889669 1897101 1897227 "ODPOL" 1897232 NIL ODPOL (NIL T) -8 NIL NIL) (-789 1883545 1889541 1889646 "ODP" 1889651 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-788 1882311 1882526 1882801 "ODETOOLS" 1883319 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-787 1879280 1879936 1880652 "ODESYS" 1881644 NIL ODESYS (NIL T T) -7 NIL NIL) (-786 1874162 1875070 1876095 "ODERTRIC" 1878355 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-785 1873588 1873670 1873864 "ODERED" 1874074 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-784 1870476 1871024 1871701 "ODERAT" 1873011 NIL ODERAT (NIL T T) -7 NIL NIL) (-783 1867436 1867900 1868497 "ODEPRRIC" 1870005 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-782 1865305 1865874 1866383 "ODEPROB" 1866947 T ODEPROB (NIL) -8 NIL NIL) (-781 1861827 1862310 1862957 "ODEPRIM" 1864784 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-780 1861076 1861178 1861438 "ODEPAL" 1861719 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-779 1857238 1858029 1858893 "ODEPACK" 1860232 T ODEPACK (NIL) -7 NIL NIL) (-778 1856271 1856378 1856607 "ODEINT" 1857127 NIL ODEINT (NIL T T) -7 NIL NIL) (-777 1850372 1851797 1853244 "ODEIFTBL" 1854844 T ODEIFTBL (NIL) -8 NIL NIL) (-776 1845707 1846493 1847452 "ODEEF" 1849531 NIL ODEEF (NIL T T) -7 NIL NIL) (-775 1845042 1845131 1845361 "ODECONST" 1845612 NIL ODECONST (NIL T T T) -7 NIL NIL) (-774 1843193 1843828 1843856 "ODECAT" 1844461 T ODECAT (NIL) -9 NIL 1844992) (-773 1840100 1842905 1843024 "OCT" 1843106 NIL OCT (NIL T) -8 NIL NIL) (-772 1839738 1839781 1839908 "OCTCT2" 1840051 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-771 1834599 1836999 1837039 "OC" 1838136 NIL OC (NIL T) -9 NIL 1838994) (-770 1831826 1832574 1833564 "OC-" 1833658 NIL OC- (NIL T T) -8 NIL NIL) (-769 1831204 1831646 1831674 "OCAMON" 1831679 T OCAMON (NIL) -9 NIL 1831700) (-768 1830761 1831076 1831104 "OASGP" 1831109 T OASGP (NIL) -9 NIL 1831129) (-767 1830048 1830511 1830539 "OAMONS" 1830579 T OAMONS (NIL) -9 NIL 1830622) (-766 1829488 1829895 1829923 "OAMON" 1829928 T OAMON (NIL) -9 NIL 1829948) (-765 1828792 1829284 1829312 "OAGROUP" 1829317 T OAGROUP (NIL) -9 NIL 1829337) (-764 1828482 1828532 1828620 "NUMTUBE" 1828736 NIL NUMTUBE (NIL T) -7 NIL NIL) (-763 1822055 1823573 1825109 "NUMQUAD" 1826966 T NUMQUAD (NIL) -7 NIL NIL) (-762 1817811 1818799 1819824 "NUMODE" 1821050 T NUMODE (NIL) -7 NIL NIL) (-761 1815192 1816046 1816074 "NUMINT" 1816997 T NUMINT (NIL) -9 NIL 1817761) (-760 1814140 1814337 1814555 "NUMFMT" 1814994 T NUMFMT (NIL) -7 NIL NIL) (-759 1800499 1803444 1805976 "NUMERIC" 1811647 NIL NUMERIC (NIL T) -7 NIL NIL) (-758 1794896 1799948 1800043 "NTSCAT" 1800048 NIL NTSCAT (NIL T T T T) -9 NIL 1800087) (-757 1794090 1794255 1794448 "NTPOLFN" 1794735 NIL NTPOLFN (NIL T) -7 NIL NIL) (-756 1781930 1790915 1791727 "NSUP" 1793311 NIL NSUP (NIL T) -8 NIL NIL) (-755 1781562 1781619 1781728 "NSUP2" 1781867 NIL NSUP2 (NIL T T) -7 NIL NIL) (-754 1771559 1781336 1781469 "NSMP" 1781474 NIL NSMP (NIL T T) -8 NIL NIL) (-753 1769991 1770292 1770649 "NREP" 1771247 NIL NREP (NIL T) -7 NIL NIL) (-752 1768582 1768834 1769192 "NPCOEF" 1769734 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-751 1767648 1767763 1767979 "NORMRETR" 1768463 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-750 1765689 1765979 1766388 "NORMPK" 1767356 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-749 1765374 1765402 1765526 "NORMMA" 1765655 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-748 1765201 1765331 1765360 "NONE" 1765365 T NONE (NIL) -8 NIL NIL) (-747 1764990 1765019 1765088 "NONE1" 1765165 NIL NONE1 (NIL T) -7 NIL NIL) (-746 1764473 1764535 1764721 "NODE1" 1764922 NIL NODE1 (NIL T T) -7 NIL NIL) (-745 1762813 1763636 1763891 "NNI" 1764238 T NNI (NIL) -8 NIL NIL) (-744 1761233 1761546 1761910 "NLINSOL" 1762481 NIL NLINSOL (NIL T) -7 NIL NIL) (-743 1757400 1758368 1759290 "NIPROB" 1760331 T NIPROB (NIL) -8 NIL NIL) (-742 1756157 1756391 1756693 "NFINTBAS" 1757162 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-741 1754865 1755096 1755377 "NCODIV" 1755925 NIL NCODIV (NIL T T) -7 NIL NIL) (-740 1754627 1754664 1754739 "NCNTFRAC" 1754822 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-739 1752807 1753171 1753591 "NCEP" 1754252 NIL NCEP (NIL T) -7 NIL NIL) (-738 1751718 1752457 1752485 "NASRING" 1752595 T NASRING (NIL) -9 NIL 1752669) (-737 1751513 1751557 1751651 "NASRING-" 1751656 NIL NASRING- (NIL T) -8 NIL NIL) (-736 1750666 1751165 1751193 "NARNG" 1751310 T NARNG (NIL) -9 NIL 1751401) (-735 1750358 1750425 1750559 "NARNG-" 1750564 NIL NARNG- (NIL T) -8 NIL NIL) (-734 1749237 1749444 1749679 "NAGSP" 1750143 T NAGSP (NIL) -7 NIL NIL) (-733 1740509 1742193 1743866 "NAGS" 1747584 T NAGS (NIL) -7 NIL NIL) (-732 1739057 1739365 1739696 "NAGF07" 1740198 T NAGF07 (NIL) -7 NIL NIL) (-731 1733595 1734886 1736193 "NAGF04" 1737770 T NAGF04 (NIL) -7 NIL NIL) (-730 1726563 1728177 1729810 "NAGF02" 1731982 T NAGF02 (NIL) -7 NIL NIL) (-729 1721787 1722887 1724004 "NAGF01" 1725466 T NAGF01 (NIL) -7 NIL NIL) (-728 1715415 1716981 1718566 "NAGE04" 1720222 T NAGE04 (NIL) -7 NIL NIL) (-727 1706584 1708705 1710835 "NAGE02" 1713305 T NAGE02 (NIL) -7 NIL NIL) (-726 1702537 1703484 1704448 "NAGE01" 1705640 T NAGE01 (NIL) -7 NIL NIL) (-725 1700332 1700866 1701424 "NAGD03" 1701999 T NAGD03 (NIL) -7 NIL NIL) (-724 1692082 1694010 1695964 "NAGD02" 1698398 T NAGD02 (NIL) -7 NIL NIL) (-723 1685893 1687318 1688758 "NAGD01" 1690662 T NAGD01 (NIL) -7 NIL NIL) (-722 1682102 1682924 1683761 "NAGC06" 1685076 T NAGC06 (NIL) -7 NIL NIL) (-721 1680567 1680899 1681255 "NAGC05" 1681766 T NAGC05 (NIL) -7 NIL NIL) (-720 1679943 1680062 1680206 "NAGC02" 1680443 T NAGC02 (NIL) -7 NIL NIL) (-719 1679003 1679560 1679600 "NAALG" 1679679 NIL NAALG (NIL T) -9 NIL 1679740) (-718 1678838 1678867 1678957 "NAALG-" 1678962 NIL NAALG- (NIL T T) -8 NIL NIL) (-717 1672788 1673896 1675083 "MULTSQFR" 1677734 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-716 1672107 1672182 1672366 "MULTFACT" 1672700 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-715 1665330 1669195 1669248 "MTSCAT" 1670318 NIL MTSCAT (NIL T T) -9 NIL 1670832) (-714 1665042 1665096 1665188 "MTHING" 1665270 NIL MTHING (NIL T) -7 NIL NIL) (-713 1664834 1664867 1664927 "MSYSCMD" 1665002 T MSYSCMD (NIL) -7 NIL NIL) (-712 1660946 1663589 1663909 "MSET" 1664547 NIL MSET (NIL T) -8 NIL NIL) (-711 1658041 1660507 1660548 "MSETAGG" 1660553 NIL MSETAGG (NIL T) -9 NIL 1660587) (-710 1653924 1655420 1656165 "MRING" 1657341 NIL MRING (NIL T T) -8 NIL NIL) (-709 1653490 1653557 1653688 "MRF2" 1653851 NIL MRF2 (NIL T T T) -7 NIL NIL) (-708 1653108 1653143 1653287 "MRATFAC" 1653449 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-707 1650720 1651015 1651446 "MPRFF" 1652813 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-706 1644780 1650574 1650671 "MPOLY" 1650676 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-705 1644270 1644305 1644513 "MPCPF" 1644739 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-704 1643784 1643827 1644011 "MPC3" 1644221 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-703 1642979 1643060 1643281 "MPC2" 1643699 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-702 1641280 1641617 1642007 "MONOTOOL" 1642639 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-701 1640531 1640822 1640850 "MONOID" 1641069 T MONOID (NIL) -9 NIL 1641216) (-700 1640077 1640196 1640377 "MONOID-" 1640382 NIL MONOID- (NIL T) -8 NIL NIL) (-699 1631127 1637033 1637092 "MONOGEN" 1637766 NIL MONOGEN (NIL T T) -9 NIL 1638222) (-698 1628345 1629080 1630080 "MONOGEN-" 1630199 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-697 1627204 1627624 1627652 "MONADWU" 1628044 T MONADWU (NIL) -9 NIL 1628282) (-696 1626576 1626735 1626983 "MONADWU-" 1626988 NIL MONADWU- (NIL T) -8 NIL NIL) (-695 1625961 1626179 1626207 "MONAD" 1626414 T MONAD (NIL) -9 NIL 1626526) (-694 1625646 1625724 1625856 "MONAD-" 1625861 NIL MONAD- (NIL T) -8 NIL NIL) (-693 1623962 1624559 1624838 "MOEBIUS" 1625399 NIL MOEBIUS (NIL T) -8 NIL NIL) (-692 1623354 1623732 1623772 "MODULE" 1623777 NIL MODULE (NIL T) -9 NIL 1623803) (-691 1622922 1623018 1623208 "MODULE-" 1623213 NIL MODULE- (NIL T T) -8 NIL NIL) (-690 1620637 1621286 1621613 "MODRING" 1622746 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1617623 1618742 1619263 "MODOP" 1620166 NIL MODOP (NIL T T) -8 NIL NIL) (-688 1615810 1616262 1616603 "MODMONOM" 1617422 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-687 1605518 1614002 1614425 "MODMON" 1615438 NIL MODMON (NIL T T) -8 NIL NIL) (-686 1602709 1604362 1604638 "MODFIELD" 1605393 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-685 1601713 1601990 1602180 "MMLFORM" 1602539 T MMLFORM (NIL) -8 NIL NIL) (-684 1601239 1601282 1601461 "MMAP" 1601664 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-683 1599508 1600241 1600282 "MLO" 1600705 NIL MLO (NIL T) -9 NIL 1600947) (-682 1596875 1597390 1597992 "MLIFT" 1598989 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-681 1596266 1596350 1596504 "MKUCFUNC" 1596786 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-680 1595865 1595935 1596058 "MKRECORD" 1596189 NIL MKRECORD (NIL T T) -7 NIL NIL) (-679 1594913 1595074 1595302 "MKFUNC" 1595676 NIL MKFUNC (NIL T) -7 NIL NIL) (-678 1594301 1594405 1594561 "MKFLCFN" 1594796 NIL MKFLCFN (NIL T) -7 NIL NIL) (-677 1593727 1594094 1594183 "MKCHSET" 1594245 NIL MKCHSET (NIL T) -8 NIL NIL) (-676 1593004 1593106 1593291 "MKBCFUNC" 1593620 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-675 1589746 1592558 1592694 "MINT" 1592888 T MINT (NIL) -8 NIL NIL) (-674 1588558 1588801 1589078 "MHROWRED" 1589501 NIL MHROWRED (NIL T) -7 NIL NIL) (-673 1583890 1586999 1587425 "MFLOAT" 1588152 T MFLOAT (NIL) -8 NIL NIL) (-672 1583247 1583323 1583494 "MFINFACT" 1583802 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-671 1579562 1580410 1581294 "MESH" 1582383 T MESH (NIL) -7 NIL NIL) (-670 1577952 1578264 1578617 "MDDFACT" 1579249 NIL MDDFACT (NIL T) -7 NIL NIL) (-669 1574794 1577111 1577152 "MDAGG" 1577407 NIL MDAGG (NIL T) -9 NIL 1577550) (-668 1564574 1574087 1574294 "MCMPLX" 1574607 T MCMPLX (NIL) -8 NIL NIL) (-667 1563715 1563861 1564061 "MCDEN" 1564423 NIL MCDEN (NIL T T) -7 NIL NIL) (-666 1561605 1561875 1562255 "MCALCFN" 1563445 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-665 1560516 1560689 1560930 "MAYBE" 1561403 NIL MAYBE (NIL T) -8 NIL NIL) (-664 1558128 1558651 1559213 "MATSTOR" 1559987 NIL MATSTOR (NIL T) -7 NIL NIL) (-663 1554134 1557500 1557748 "MATRIX" 1557913 NIL MATRIX (NIL T) -8 NIL NIL) (-662 1549903 1550607 1551343 "MATLIN" 1553491 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-661 1540057 1543195 1543272 "MATCAT" 1548152 NIL MATCAT (NIL T T T) -9 NIL 1549569) (-660 1536421 1537434 1538790 "MATCAT-" 1538795 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-659 1535015 1535168 1535501 "MATCAT2" 1536256 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-658 1533127 1533451 1533835 "MAPPKG3" 1534690 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-657 1532108 1532281 1532503 "MAPPKG2" 1532951 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-656 1530607 1530891 1531218 "MAPPKG1" 1531814 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-655 1529730 1530013 1530190 "MAPPAST" 1530450 T MAPPAST (NIL) -8 NIL NIL) (-654 1529341 1529399 1529522 "MAPHACK3" 1529666 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-653 1528933 1528994 1529108 "MAPHACK2" 1529273 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-652 1528371 1528474 1528616 "MAPHACK1" 1528824 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-651 1526477 1527071 1527375 "MAGMA" 1528099 NIL MAGMA (NIL T) -8 NIL NIL) (-650 1525972 1526180 1526278 "MACROAST" 1526399 T MACROAST (NIL) -8 NIL NIL) (-649 1522439 1524211 1524672 "M3D" 1525544 NIL M3D (NIL T) -8 NIL NIL) (-648 1516594 1520809 1520850 "LZSTAGG" 1521632 NIL LZSTAGG (NIL T) -9 NIL 1521927) (-647 1512567 1513725 1515182 "LZSTAGG-" 1515187 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-646 1509681 1510458 1510945 "LWORD" 1512112 NIL LWORD (NIL T) -8 NIL NIL) (-645 1509301 1509485 1509560 "LSTAST" 1509626 T LSTAST (NIL) -8 NIL NIL) (-644 1502502 1509072 1509206 "LSQM" 1509211 NIL LSQM (NIL NIL T) -8 NIL NIL) (-643 1501726 1501865 1502093 "LSPP" 1502357 NIL LSPP (NIL T T T T) -7 NIL NIL) (-642 1499538 1499839 1500295 "LSMP" 1501415 NIL LSMP (NIL T T T T) -7 NIL NIL) (-641 1496317 1496991 1497721 "LSMP1" 1498840 NIL LSMP1 (NIL T) -7 NIL NIL) (-640 1490243 1495485 1495526 "LSAGG" 1495588 NIL LSAGG (NIL T) -9 NIL 1495666) (-639 1486938 1487862 1489075 "LSAGG-" 1489080 NIL LSAGG- (NIL T T) -8 NIL NIL) (-638 1484564 1486082 1486331 "LPOLY" 1486733 NIL LPOLY (NIL T T) -8 NIL NIL) (-637 1484146 1484231 1484354 "LPEFRAC" 1484473 NIL LPEFRAC (NIL T) -7 NIL NIL) (-636 1482493 1483240 1483493 "LO" 1483978 NIL LO (NIL T T T) -8 NIL NIL) (-635 1482145 1482257 1482285 "LOGIC" 1482396 T LOGIC (NIL) -9 NIL 1482477) (-634 1482007 1482030 1482101 "LOGIC-" 1482106 NIL LOGIC- (NIL T) -8 NIL NIL) (-633 1481200 1481340 1481533 "LODOOPS" 1481863 NIL LODOOPS (NIL T T) -7 NIL NIL) (-632 1478658 1481116 1481182 "LODO" 1481187 NIL LODO (NIL T NIL) -8 NIL NIL) (-631 1477196 1477431 1477784 "LODOF" 1478405 NIL LODOF (NIL T T) -7 NIL NIL) (-630 1473639 1476036 1476077 "LODOCAT" 1476515 NIL LODOCAT (NIL T) -9 NIL 1476726) (-629 1473372 1473430 1473557 "LODOCAT-" 1473562 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-628 1470727 1473213 1473331 "LODO2" 1473336 NIL LODO2 (NIL T T) -8 NIL NIL) (-627 1468197 1470664 1470709 "LODO1" 1470714 NIL LODO1 (NIL T) -8 NIL NIL) (-626 1467057 1467222 1467534 "LODEEF" 1468020 NIL LODEEF (NIL T T T) -7 NIL NIL) (-625 1462343 1465187 1465228 "LNAGG" 1466175 NIL LNAGG (NIL T) -9 NIL 1466619) (-624 1461490 1461704 1462046 "LNAGG-" 1462051 NIL LNAGG- (NIL T T) -8 NIL NIL) (-623 1457653 1458415 1459054 "LMOPS" 1460905 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-622 1457048 1457410 1457451 "LMODULE" 1457512 NIL LMODULE (NIL T) -9 NIL 1457554) (-621 1454294 1456693 1456816 "LMDICT" 1456958 NIL LMDICT (NIL T) -8 NIL NIL) (-620 1454038 1454202 1454262 "LITERAL" 1454267 NIL LITERAL (NIL T) -8 NIL NIL) (-619 1447265 1452984 1453282 "LIST" 1453773 NIL LIST (NIL T) -8 NIL NIL) (-618 1446790 1446864 1447003 "LIST3" 1447185 NIL LIST3 (NIL T T T) -7 NIL NIL) (-617 1445797 1445975 1446203 "LIST2" 1446608 NIL LIST2 (NIL T T) -7 NIL NIL) (-616 1443931 1444243 1444642 "LIST2MAP" 1445444 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-615 1442681 1443317 1443358 "LINEXP" 1443613 NIL LINEXP (NIL T) -9 NIL 1443762) (-614 1441328 1441588 1441885 "LINDEP" 1442433 NIL LINDEP (NIL T T) -7 NIL NIL) (-613 1438095 1438814 1439591 "LIMITRF" 1440583 NIL LIMITRF (NIL T) -7 NIL NIL) (-612 1436371 1436666 1437082 "LIMITPS" 1437790 NIL LIMITPS (NIL T T) -7 NIL NIL) (-611 1430826 1435882 1436110 "LIE" 1436192 NIL LIE (NIL T T) -8 NIL NIL) (-610 1429875 1430318 1430358 "LIECAT" 1430498 NIL LIECAT (NIL T) -9 NIL 1430649) (-609 1429716 1429743 1429831 "LIECAT-" 1429836 NIL LIECAT- (NIL T T) -8 NIL NIL) (-608 1422328 1429165 1429330 "LIB" 1429571 T LIB (NIL) -8 NIL NIL) (-607 1417965 1418846 1419781 "LGROBP" 1421445 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-606 1415831 1416105 1416467 "LF" 1417686 NIL LF (NIL T T) -7 NIL NIL) (-605 1414671 1415363 1415391 "LFCAT" 1415598 T LFCAT (NIL) -9 NIL 1415737) (-604 1411575 1412203 1412891 "LEXTRIPK" 1414035 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-603 1408346 1409145 1409648 "LEXP" 1411155 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-602 1407866 1408067 1408159 "LETAST" 1408274 T LETAST (NIL) -8 NIL NIL) (-601 1406264 1406577 1406978 "LEADCDET" 1407548 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-600 1405454 1405528 1405757 "LAZM3PK" 1406185 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-599 1400410 1403531 1404069 "LAUPOL" 1404966 NIL LAUPOL (NIL T T) -8 NIL NIL) (-598 1399975 1400019 1400187 "LAPLACE" 1400360 NIL LAPLACE (NIL T T) -7 NIL NIL) (-597 1397949 1399076 1399327 "LA" 1399808 NIL LA (NIL T T T) -8 NIL NIL) (-596 1397050 1397600 1397641 "LALG" 1397703 NIL LALG (NIL T) -9 NIL 1397762) (-595 1396764 1396823 1396959 "LALG-" 1396964 NIL LALG- (NIL T T) -8 NIL NIL) (-594 1395564 1395981 1396210 "KTVLOGIC" 1396555 T KTVLOGIC (NIL) -8 NIL NIL) (-593 1394468 1394655 1394954 "KOVACIC" 1395364 NIL KOVACIC (NIL T T) -7 NIL NIL) (-592 1394303 1394327 1394368 "KONVERT" 1394430 NIL KONVERT (NIL T) -9 NIL NIL) (-591 1394138 1394162 1394203 "KOERCE" 1394265 NIL KOERCE (NIL T) -9 NIL NIL) (-590 1391872 1392632 1393025 "KERNEL" 1393777 NIL KERNEL (NIL T) -8 NIL NIL) (-589 1391374 1391455 1391585 "KERNEL2" 1391786 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-588 1385225 1389913 1389967 "KDAGG" 1390344 NIL KDAGG (NIL T T) -9 NIL 1390550) (-587 1384754 1384878 1385083 "KDAGG-" 1385088 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-586 1377929 1384415 1384570 "KAFILE" 1384632 NIL KAFILE (NIL T) -8 NIL NIL) (-585 1372384 1377440 1377668 "JORDAN" 1377750 NIL JORDAN (NIL T T) -8 NIL NIL) (-584 1371808 1372033 1372154 "JOINAST" 1372283 T JOINAST (NIL) -8 NIL NIL) (-583 1371537 1371596 1371683 "JAVACODE" 1371741 T JAVACODE (NIL) -8 NIL NIL) (-582 1367836 1369742 1369796 "IXAGG" 1370725 NIL IXAGG (NIL T T) -9 NIL 1371184) (-581 1366755 1367061 1367480 "IXAGG-" 1367485 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-580 1362335 1366677 1366736 "IVECTOR" 1366741 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-579 1361101 1361338 1361604 "ITUPLE" 1362102 NIL ITUPLE (NIL T) -8 NIL NIL) (-578 1359537 1359714 1360020 "ITRIGMNP" 1360923 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-577 1358282 1358486 1358769 "ITFUN3" 1359313 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-576 1357914 1357971 1358080 "ITFUN2" 1358219 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-575 1355751 1356776 1357075 "ITAYLOR" 1357648 NIL ITAYLOR (NIL T) -8 NIL NIL) (-574 1344745 1349897 1351057 "ISUPS" 1354624 NIL ISUPS (NIL T) -8 NIL NIL) (-573 1343849 1343989 1344225 "ISUMP" 1344592 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-572 1339113 1343650 1343729 "ISTRING" 1343802 NIL ISTRING (NIL NIL) -8 NIL NIL) (-571 1338633 1338834 1338926 "ISAST" 1339041 T ISAST (NIL) -8 NIL NIL) (-570 1337843 1337924 1338140 "IRURPK" 1338547 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-569 1336779 1336980 1337220 "IRSN" 1337623 T IRSN (NIL) -7 NIL NIL) (-568 1334808 1335163 1335599 "IRRF2F" 1336417 NIL IRRF2F (NIL T) -7 NIL NIL) (-567 1334555 1334593 1334669 "IRREDFFX" 1334764 NIL IRREDFFX (NIL T) -7 NIL NIL) (-566 1333170 1333429 1333728 "IROOT" 1334288 NIL IROOT (NIL T) -7 NIL NIL) (-565 1329802 1330854 1331546 "IR" 1332510 NIL IR (NIL T) -8 NIL NIL) (-564 1327415 1327910 1328476 "IR2" 1329280 NIL IR2 (NIL T T) -7 NIL NIL) (-563 1326487 1326600 1326821 "IR2F" 1327298 NIL IR2F (NIL T T) -7 NIL NIL) (-562 1326278 1326312 1326372 "IPRNTPK" 1326447 T IPRNTPK (NIL) -7 NIL NIL) (-561 1322897 1326167 1326236 "IPF" 1326241 NIL IPF (NIL NIL) -8 NIL NIL) (-560 1321260 1322822 1322879 "IPADIC" 1322884 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-559 1321024 1321164 1321192 "IOBCON" 1321197 T IOBCON (NIL) -9 NIL 1321218) (-558 1320521 1320579 1320769 "INVLAPLA" 1320960 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-557 1310170 1312523 1314909 "INTTR" 1318185 NIL INTTR (NIL T T) -7 NIL NIL) (-556 1306514 1307256 1308120 "INTTOOLS" 1309355 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-555 1306100 1306191 1306308 "INTSLPE" 1306417 T INTSLPE (NIL) -7 NIL NIL) (-554 1304095 1306023 1306082 "INTRVL" 1306087 NIL INTRVL (NIL T) -8 NIL NIL) (-553 1301697 1302209 1302784 "INTRF" 1303580 NIL INTRF (NIL T) -7 NIL NIL) (-552 1301108 1301205 1301347 "INTRET" 1301595 NIL INTRET (NIL T) -7 NIL NIL) (-551 1299105 1299494 1299964 "INTRAT" 1300716 NIL INTRAT (NIL T T) -7 NIL NIL) (-550 1296333 1296916 1297542 "INTPM" 1298590 NIL INTPM (NIL T T) -7 NIL NIL) (-549 1293036 1293635 1294380 "INTPAF" 1295719 NIL INTPAF (NIL T T T) -7 NIL NIL) (-548 1288215 1289177 1290228 "INTPACK" 1292005 T INTPACK (NIL) -7 NIL NIL) (-547 1285127 1287944 1288071 "INT" 1288108 T INT (NIL) -8 NIL NIL) (-546 1284379 1284531 1284739 "INTHERTR" 1284969 NIL INTHERTR (NIL T T) -7 NIL NIL) (-545 1283818 1283898 1284086 "INTHERAL" 1284293 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-544 1281664 1282107 1282564 "INTHEORY" 1283381 T INTHEORY (NIL) -7 NIL NIL) (-543 1272972 1274593 1276372 "INTG0" 1280016 NIL INTG0 (NIL T T T) -7 NIL NIL) (-542 1253545 1258335 1263145 "INTFTBL" 1268182 T INTFTBL (NIL) -8 NIL NIL) (-541 1252794 1252932 1253105 "INTFACT" 1253404 NIL INTFACT (NIL T) -7 NIL NIL) (-540 1250179 1250625 1251189 "INTEF" 1252348 NIL INTEF (NIL T T) -7 NIL NIL) (-539 1248681 1249386 1249414 "INTDOM" 1249715 T INTDOM (NIL) -9 NIL 1249922) (-538 1248050 1248224 1248466 "INTDOM-" 1248471 NIL INTDOM- (NIL T) -8 NIL NIL) (-537 1244583 1246469 1246523 "INTCAT" 1247322 NIL INTCAT (NIL T) -9 NIL 1247642) (-536 1244056 1244158 1244286 "INTBIT" 1244475 T INTBIT (NIL) -7 NIL NIL) (-535 1242727 1242881 1243195 "INTALG" 1243901 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-534 1242184 1242274 1242444 "INTAF" 1242631 NIL INTAF (NIL T T) -7 NIL NIL) (-533 1235638 1241994 1242134 "INTABL" 1242139 NIL INTABL (NIL T T T) -8 NIL NIL) (-532 1230693 1233364 1233392 "INS" 1234326 T INS (NIL) -9 NIL 1234990) (-531 1227933 1228704 1229678 "INS-" 1229751 NIL INS- (NIL T) -8 NIL NIL) (-530 1226708 1226935 1227233 "INPSIGN" 1227686 NIL INPSIGN (NIL T T) -7 NIL NIL) (-529 1225826 1225943 1226140 "INPRODPF" 1226588 NIL INPRODPF (NIL T T) -7 NIL NIL) (-528 1224720 1224837 1225074 "INPRODFF" 1225706 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-527 1223720 1223872 1224132 "INNMFACT" 1224556 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-526 1222917 1223014 1223202 "INMODGCD" 1223619 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-525 1221426 1221670 1221994 "INFSP" 1222662 NIL INFSP (NIL T T T) -7 NIL NIL) (-524 1220610 1220727 1220910 "INFPROD0" 1221306 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-523 1217492 1218675 1219190 "INFORM" 1220103 T INFORM (NIL) -8 NIL NIL) (-522 1217102 1217162 1217260 "INFORM1" 1217427 NIL INFORM1 (NIL T) -7 NIL NIL) (-521 1216625 1216714 1216828 "INFINITY" 1217008 T INFINITY (NIL) -7 NIL NIL) (-520 1215242 1215491 1215812 "INEP" 1216373 NIL INEP (NIL T T T) -7 NIL NIL) (-519 1214518 1215139 1215204 "INDE" 1215209 NIL INDE (NIL T) -8 NIL NIL) (-518 1214082 1214150 1214267 "INCRMAPS" 1214445 NIL INCRMAPS (NIL T) -7 NIL NIL) (-517 1209393 1210318 1211262 "INBFF" 1213170 NIL INBFF (NIL T) -7 NIL NIL) (-516 1209062 1209138 1209166 "INBCON" 1209299 T INBCON (NIL) -9 NIL 1209377) (-515 1208902 1208937 1209013 "INBCON-" 1209018 NIL INBCON- (NIL T) -8 NIL NIL) (-514 1208421 1208623 1208715 "INAST" 1208830 T INAST (NIL) -8 NIL NIL) (-513 1207892 1208100 1208206 "IMPTAST" 1208335 T IMPTAST (NIL) -8 NIL NIL) (-512 1204386 1207736 1207840 "IMATRIX" 1207845 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-511 1203098 1203221 1203536 "IMATQF" 1204242 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-510 1201318 1201545 1201882 "IMATLIN" 1202854 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-509 1195944 1201242 1201300 "ILIST" 1201305 NIL ILIST (NIL T NIL) -8 NIL NIL) (-508 1193897 1195804 1195917 "IIARRAY2" 1195922 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-507 1189330 1193808 1193872 "IFF" 1193877 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-506 1188721 1188947 1189063 "IFAST" 1189234 T IFAST (NIL) -8 NIL NIL) (-505 1183764 1188013 1188201 "IFARRAY" 1188578 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-504 1182971 1183668 1183741 "IFAMON" 1183746 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-503 1182555 1182620 1182674 "IEVALAB" 1182881 NIL IEVALAB (NIL T T) -9 NIL NIL) (-502 1182230 1182298 1182458 "IEVALAB-" 1182463 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-501 1181888 1182144 1182207 "IDPO" 1182212 NIL IDPO (NIL T T) -8 NIL NIL) (-500 1181165 1181777 1181852 "IDPOAMS" 1181857 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-499 1180499 1181054 1181129 "IDPOAM" 1181134 NIL IDPOAM (NIL T T) -8 NIL NIL) (-498 1179584 1179834 1179887 "IDPC" 1180300 NIL IDPC (NIL T T) -9 NIL 1180449) (-497 1179080 1179476 1179549 "IDPAM" 1179554 NIL IDPAM (NIL T T) -8 NIL NIL) (-496 1178483 1178972 1179045 "IDPAG" 1179050 NIL IDPAG (NIL T T) -8 NIL NIL) (-495 1178231 1178398 1178448 "IDENT" 1178453 T IDENT (NIL) -8 NIL NIL) (-494 1174486 1175334 1176229 "IDECOMP" 1177388 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-493 1167359 1168409 1169456 "IDEAL" 1173522 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-492 1166523 1166635 1166834 "ICDEN" 1167243 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-491 1165622 1166003 1166150 "ICARD" 1166396 T ICARD (NIL) -8 NIL NIL) (-490 1163682 1163995 1164400 "IBPTOOLS" 1165299 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-489 1159316 1163302 1163415 "IBITS" 1163601 NIL IBITS (NIL NIL) -8 NIL NIL) (-488 1156039 1156615 1157310 "IBATOOL" 1158733 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-487 1153819 1154280 1154813 "IBACHIN" 1155574 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-486 1151696 1153665 1153768 "IARRAY2" 1153773 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-485 1147849 1151622 1151679 "IARRAY1" 1151684 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-484 1141844 1146263 1146743 "IAN" 1147389 T IAN (NIL) -8 NIL NIL) (-483 1141355 1141412 1141585 "IALGFACT" 1141781 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-482 1140883 1140996 1141024 "HYPCAT" 1141231 T HYPCAT (NIL) -9 NIL NIL) (-481 1140421 1140538 1140724 "HYPCAT-" 1140729 NIL HYPCAT- (NIL T) -8 NIL NIL) (-480 1140043 1140216 1140299 "HOSTNAME" 1140358 T HOSTNAME (NIL) -8 NIL NIL) (-479 1136722 1138053 1138094 "HOAGG" 1139075 NIL HOAGG (NIL T) -9 NIL 1139754) (-478 1135316 1135715 1136241 "HOAGG-" 1136246 NIL HOAGG- (NIL T T) -8 NIL NIL) (-477 1129204 1134757 1134923 "HEXADEC" 1135170 T HEXADEC (NIL) -8 NIL NIL) (-476 1127952 1128174 1128437 "HEUGCD" 1128981 NIL HEUGCD (NIL T) -7 NIL NIL) (-475 1127055 1127789 1127919 "HELLFDIV" 1127924 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-474 1125283 1126832 1126920 "HEAP" 1126999 NIL HEAP (NIL T) -8 NIL NIL) (-473 1124591 1124835 1124969 "HEADAST" 1125169 T HEADAST (NIL) -8 NIL NIL) (-472 1118511 1124506 1124568 "HDP" 1124573 NIL HDP (NIL NIL T) -8 NIL NIL) (-471 1112262 1118146 1118298 "HDMP" 1118412 NIL HDMP (NIL NIL T) -8 NIL NIL) (-470 1111587 1111726 1111890 "HB" 1112118 T HB (NIL) -7 NIL NIL) (-469 1105084 1111433 1111537 "HASHTBL" 1111542 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-468 1104604 1104805 1104897 "HASAST" 1105012 T HASAST (NIL) -8 NIL NIL) (-467 1102418 1104228 1104409 "HACKPI" 1104443 T HACKPI (NIL) -8 NIL NIL) (-466 1098113 1102271 1102384 "GTSET" 1102389 NIL GTSET (NIL T T T T) -8 NIL NIL) (-465 1091639 1097991 1098089 "GSTBL" 1098094 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-464 1083952 1090670 1090935 "GSERIES" 1091430 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-463 1083119 1083510 1083538 "GROUP" 1083741 T GROUP (NIL) -9 NIL 1083875) (-462 1082485 1082644 1082895 "GROUP-" 1082900 NIL GROUP- (NIL T) -8 NIL NIL) (-461 1080854 1081173 1081560 "GROEBSOL" 1082162 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-460 1079794 1080056 1080107 "GRMOD" 1080636 NIL GRMOD (NIL T T) -9 NIL 1080804) (-459 1079562 1079598 1079726 "GRMOD-" 1079731 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-458 1074887 1075916 1076916 "GRIMAGE" 1078582 T GRIMAGE (NIL) -8 NIL NIL) (-457 1073354 1073614 1073938 "GRDEF" 1074583 T GRDEF (NIL) -7 NIL NIL) (-456 1072798 1072914 1073055 "GRAY" 1073233 T GRAY (NIL) -7 NIL NIL) (-455 1072029 1072409 1072460 "GRALG" 1072613 NIL GRALG (NIL T T) -9 NIL 1072706) (-454 1071690 1071763 1071926 "GRALG-" 1071931 NIL GRALG- (NIL T T T) -8 NIL NIL) (-453 1068494 1071275 1071453 "GPOLSET" 1071597 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-452 1067848 1067905 1068163 "GOSPER" 1068431 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-451 1063607 1064286 1064812 "GMODPOL" 1067547 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-450 1062612 1062796 1063034 "GHENSEL" 1063419 NIL GHENSEL (NIL T T) -7 NIL NIL) (-449 1056663 1057506 1058533 "GENUPS" 1061696 NIL GENUPS (NIL T T) -7 NIL NIL) (-448 1056360 1056411 1056500 "GENUFACT" 1056606 NIL GENUFACT (NIL T) -7 NIL NIL) (-447 1055772 1055849 1056014 "GENPGCD" 1056278 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-446 1055246 1055281 1055494 "GENMFACT" 1055731 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-445 1053814 1054069 1054376 "GENEEZ" 1054989 NIL GENEEZ (NIL T T) -7 NIL NIL) (-444 1047727 1053425 1053587 "GDMP" 1053737 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-443 1037104 1041498 1042604 "GCNAALG" 1046710 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-442 1035566 1036394 1036422 "GCDDOM" 1036677 T GCDDOM (NIL) -9 NIL 1036834) (-441 1035036 1035163 1035378 "GCDDOM-" 1035383 NIL GCDDOM- (NIL T) -8 NIL NIL) (-440 1033708 1033893 1034197 "GB" 1034815 NIL GB (NIL T T T T) -7 NIL NIL) (-439 1022328 1024654 1027046 "GBINTERN" 1031399 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-438 1020165 1020457 1020878 "GBF" 1022003 NIL GBF (NIL T T T T) -7 NIL NIL) (-437 1018946 1019111 1019378 "GBEUCLID" 1019981 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-436 1018295 1018420 1018569 "GAUSSFAC" 1018817 T GAUSSFAC (NIL) -7 NIL NIL) (-435 1016662 1016964 1017278 "GALUTIL" 1018014 NIL GALUTIL (NIL T) -7 NIL NIL) (-434 1014970 1015244 1015568 "GALPOLYU" 1016389 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-433 1012335 1012625 1013032 "GALFACTU" 1014667 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-432 1004141 1005640 1007248 "GALFACT" 1010767 NIL GALFACT (NIL T) -7 NIL NIL) (-431 1001529 1002187 1002215 "FVFUN" 1003371 T FVFUN (NIL) -9 NIL 1004091) (-430 1000795 1000977 1001005 "FVC" 1001296 T FVC (NIL) -9 NIL 1001479) (-429 1000437 1000592 1000673 "FUNCTION" 1000747 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-428 998107 998658 999147 "FT" 999968 T FT (NIL) -8 NIL NIL) (-427 996925 997408 997611 "FTEM" 997924 T FTEM (NIL) -8 NIL NIL) (-426 995181 995470 995874 "FSUPFACT" 996616 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-425 993578 993867 994199 "FST" 994869 T FST (NIL) -8 NIL NIL) (-424 992749 992855 993050 "FSRED" 993460 NIL FSRED (NIL T T) -7 NIL NIL) (-423 991428 991683 992037 "FSPRMELT" 992464 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-422 988513 988951 989450 "FSPECF" 990991 NIL FSPECF (NIL T T) -7 NIL NIL) (-421 970955 979397 979437 "FS" 983285 NIL FS (NIL T) -9 NIL 985574) (-420 959605 962595 966651 "FS-" 966948 NIL FS- (NIL T T) -8 NIL NIL) (-419 959119 959173 959350 "FSINT" 959546 NIL FSINT (NIL T T) -7 NIL NIL) (-418 957446 958112 958415 "FSERIES" 958898 NIL FSERIES (NIL T T) -8 NIL NIL) (-417 956460 956576 956807 "FSCINT" 957326 NIL FSCINT (NIL T T) -7 NIL NIL) (-416 952694 955404 955445 "FSAGG" 955815 NIL FSAGG (NIL T) -9 NIL 956074) (-415 950456 951057 951853 "FSAGG-" 951948 NIL FSAGG- (NIL T T) -8 NIL NIL) (-414 949498 949641 949868 "FSAGG2" 950309 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-413 947153 947432 947986 "FS2UPS" 949216 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-412 946735 946778 946933 "FS2" 947104 NIL FS2 (NIL T T T T) -7 NIL NIL) (-411 945592 945763 946072 "FS2EXPXP" 946560 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-410 945018 945133 945285 "FRUTIL" 945472 NIL FRUTIL (NIL T) -7 NIL NIL) (-409 936479 940517 941873 "FR" 943694 NIL FR (NIL T) -8 NIL NIL) (-408 931554 934197 934237 "FRNAALG" 935633 NIL FRNAALG (NIL T) -9 NIL 936240) (-407 927232 928303 929578 "FRNAALG-" 930328 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-406 926870 926913 927040 "FRNAAF2" 927183 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-405 925277 925724 926019 "FRMOD" 926682 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-404 923056 923660 923977 "FRIDEAL" 925068 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-403 922251 922338 922627 "FRIDEAL2" 922963 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-402 921493 921907 921948 "FRETRCT" 921953 NIL FRETRCT (NIL T) -9 NIL 922129) (-401 920605 920836 921187 "FRETRCT-" 921192 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-400 917855 919031 919090 "FRAMALG" 919972 NIL FRAMALG (NIL T T) -9 NIL 920264) (-399 915989 916444 917074 "FRAMALG-" 917297 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-398 909949 915464 915740 "FRAC" 915745 NIL FRAC (NIL T) -8 NIL NIL) (-397 909585 909642 909749 "FRAC2" 909886 NIL FRAC2 (NIL T T) -7 NIL NIL) (-396 909221 909278 909385 "FR2" 909522 NIL FR2 (NIL T T) -7 NIL NIL) (-395 903951 906799 906827 "FPS" 907946 T FPS (NIL) -9 NIL 908503) (-394 903400 903509 903673 "FPS-" 903819 NIL FPS- (NIL T) -8 NIL NIL) (-393 900906 902541 902569 "FPC" 902794 T FPC (NIL) -9 NIL 902936) (-392 900699 900739 900836 "FPC-" 900841 NIL FPC- (NIL T) -8 NIL NIL) (-391 899577 900187 900228 "FPATMAB" 900233 NIL FPATMAB (NIL T) -9 NIL 900385) (-390 897277 897753 898179 "FPARFRAC" 899214 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-389 892670 893169 893851 "FORTRAN" 896709 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-388 890386 890886 891425 "FORT" 892151 T FORT (NIL) -7 NIL NIL) (-387 888062 888624 888652 "FORTFN" 889712 T FORTFN (NIL) -9 NIL 890336) (-386 887826 887876 887904 "FORTCAT" 887963 T FORTCAT (NIL) -9 NIL 888025) (-385 885886 886369 886768 "FORMULA" 887447 T FORMULA (NIL) -8 NIL NIL) (-384 885674 885704 885773 "FORMULA1" 885850 NIL FORMULA1 (NIL T) -7 NIL NIL) (-383 885197 885249 885422 "FORDER" 885616 NIL FORDER (NIL T T T T) -7 NIL NIL) (-382 884293 884457 884650 "FOP" 885024 T FOP (NIL) -7 NIL NIL) (-381 882901 883573 883747 "FNLA" 884175 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-380 881569 881958 881986 "FNCAT" 882558 T FNCAT (NIL) -9 NIL 882851) (-379 881135 881528 881556 "FNAME" 881561 T FNAME (NIL) -8 NIL NIL) (-378 879833 880762 880790 "FMTC" 880795 T FMTC (NIL) -9 NIL 880831) (-377 876195 877356 877985 "FMONOID" 879237 NIL FMONOID (NIL T) -8 NIL NIL) (-376 875414 875937 876086 "FM" 876091 NIL FM (NIL T T) -8 NIL NIL) (-375 872838 873484 873512 "FMFUN" 874656 T FMFUN (NIL) -9 NIL 875364) (-374 872107 872288 872316 "FMC" 872606 T FMC (NIL) -9 NIL 872788) (-373 869319 870153 870207 "FMCAT" 871402 NIL FMCAT (NIL T T) -9 NIL 871897) (-372 868212 869085 869185 "FM1" 869264 NIL FM1 (NIL T T) -8 NIL NIL) (-371 865986 866402 866896 "FLOATRP" 867763 NIL FLOATRP (NIL T) -7 NIL NIL) (-370 859537 863642 864272 "FLOAT" 865376 T FLOAT (NIL) -8 NIL NIL) (-369 856975 857475 858053 "FLOATCP" 859004 NIL FLOATCP (NIL T) -7 NIL NIL) (-368 855804 856608 856649 "FLINEXP" 856654 NIL FLINEXP (NIL T) -9 NIL 856747) (-367 854958 855193 855521 "FLINEXP-" 855526 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-366 854034 854178 854402 "FLASORT" 854810 NIL FLASORT (NIL T T) -7 NIL NIL) (-365 851251 852093 852145 "FLALG" 853372 NIL FLALG (NIL T T) -9 NIL 853839) (-364 845035 848737 848778 "FLAGG" 850040 NIL FLAGG (NIL T) -9 NIL 850692) (-363 843761 844100 844590 "FLAGG-" 844595 NIL FLAGG- (NIL T T) -8 NIL NIL) (-362 842803 842946 843173 "FLAGG2" 843614 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-361 839816 840790 840849 "FINRALG" 841977 NIL FINRALG (NIL T T) -9 NIL 842485) (-360 838976 839205 839544 "FINRALG-" 839549 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-359 838382 838595 838623 "FINITE" 838819 T FINITE (NIL) -9 NIL 838926) (-358 830840 833001 833041 "FINAALG" 836708 NIL FINAALG (NIL T) -9 NIL 838161) (-357 826181 827222 828366 "FINAALG-" 829745 NIL FINAALG- (NIL T T) -8 NIL NIL) (-356 825576 825936 826039 "FILE" 826111 NIL FILE (NIL T) -8 NIL NIL) (-355 824260 824572 824626 "FILECAT" 825310 NIL FILECAT (NIL T T) -9 NIL 825526) (-354 822180 823674 823702 "FIELD" 823742 T FIELD (NIL) -9 NIL 823822) (-353 820800 821185 821696 "FIELD-" 821701 NIL FIELD- (NIL T) -8 NIL NIL) (-352 818678 819435 819782 "FGROUP" 820486 NIL FGROUP (NIL T) -8 NIL NIL) (-351 817768 817932 818152 "FGLMICPK" 818510 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-350 813635 817693 817750 "FFX" 817755 NIL FFX (NIL T NIL) -8 NIL NIL) (-349 813236 813297 813432 "FFSLPE" 813568 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-348 809229 810008 810804 "FFPOLY" 812472 NIL FFPOLY (NIL T) -7 NIL NIL) (-347 808733 808769 808978 "FFPOLY2" 809187 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-346 804619 808652 808715 "FFP" 808720 NIL FFP (NIL T NIL) -8 NIL NIL) (-345 800052 804530 804594 "FF" 804599 NIL FF (NIL NIL NIL) -8 NIL NIL) (-344 795213 799395 799585 "FFNBX" 799906 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-343 790187 794348 794606 "FFNBP" 795067 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-342 784855 789471 789682 "FFNB" 790020 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-341 783687 783885 784200 "FFINTBAS" 784652 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-340 779971 782146 782174 "FFIELDC" 782794 T FFIELDC (NIL) -9 NIL 783170) (-339 778634 779004 779501 "FFIELDC-" 779506 NIL FFIELDC- (NIL T) -8 NIL NIL) (-338 778204 778249 778373 "FFHOM" 778576 NIL FFHOM (NIL T T T) -7 NIL NIL) (-337 775902 776386 776903 "FFF" 777719 NIL FFF (NIL T) -7 NIL NIL) (-336 771555 775644 775745 "FFCGX" 775845 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-335 767222 771287 771394 "FFCGP" 771498 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-334 762440 766949 767057 "FFCG" 767158 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-333 744498 753534 753620 "FFCAT" 758785 NIL FFCAT (NIL T T T) -9 NIL 760236) (-332 739696 740743 742057 "FFCAT-" 743287 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-331 739107 739150 739385 "FFCAT2" 739647 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-330 728319 732079 733299 "FEXPR" 737959 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-329 727319 727754 727795 "FEVALAB" 727879 NIL FEVALAB (NIL T) -9 NIL 728140) (-328 726478 726688 727026 "FEVALAB-" 727031 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-327 725071 725861 726064 "FDIV" 726377 NIL FDIV (NIL T T T T) -8 NIL NIL) (-326 722137 722852 722967 "FDIVCAT" 724535 NIL FDIVCAT (NIL T T T T) -9 NIL 724972) (-325 721899 721926 722096 "FDIVCAT-" 722101 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-324 721119 721206 721483 "FDIV2" 721806 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-323 719805 720064 720353 "FCPAK1" 720850 T FCPAK1 (NIL) -7 NIL NIL) (-322 718933 719305 719446 "FCOMP" 719696 NIL FCOMP (NIL T) -8 NIL NIL) (-321 702568 705982 709543 "FC" 715392 T FC (NIL) -8 NIL NIL) (-320 695221 699202 699242 "FAXF" 701044 NIL FAXF (NIL T) -9 NIL 701736) (-319 692500 693155 693980 "FAXF-" 694445 NIL FAXF- (NIL T T) -8 NIL NIL) (-318 687600 691876 692052 "FARRAY" 692357 NIL FARRAY (NIL T) -8 NIL NIL) (-317 683007 685039 685092 "FAMR" 686115 NIL FAMR (NIL T T) -9 NIL 686575) (-316 681897 682199 682634 "FAMR-" 682639 NIL FAMR- (NIL T T T) -8 NIL NIL) (-315 681093 681819 681872 "FAMONOID" 681877 NIL FAMONOID (NIL T) -8 NIL NIL) (-314 678923 679607 679660 "FAMONC" 680601 NIL FAMONC (NIL T T) -9 NIL 680987) (-313 677615 678677 678814 "FAGROUP" 678819 NIL FAGROUP (NIL T) -8 NIL NIL) (-312 675410 675729 676132 "FACUTIL" 677296 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-311 674509 674694 674916 "FACTFUNC" 675220 NIL FACTFUNC (NIL T) -7 NIL NIL) (-310 666914 673760 673972 "EXPUPXS" 674365 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-309 664397 664937 665523 "EXPRTUBE" 666348 T EXPRTUBE (NIL) -7 NIL NIL) (-308 660591 661183 661920 "EXPRODE" 663736 NIL EXPRODE (NIL T T) -7 NIL NIL) (-307 645965 659246 659674 "EXPR" 660195 NIL EXPR (NIL T) -8 NIL NIL) (-306 640372 640959 641772 "EXPR2UPS" 645263 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-305 640008 640065 640172 "EXPR2" 640309 NIL EXPR2 (NIL T T) -7 NIL NIL) (-304 631415 639140 639437 "EXPEXPAN" 639845 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-303 631242 631372 631401 "EXIT" 631406 T EXIT (NIL) -8 NIL NIL) (-302 630766 630966 631057 "EXITAST" 631171 T EXITAST (NIL) -8 NIL NIL) (-301 630393 630455 630568 "EVALCYC" 630698 NIL EVALCYC (NIL T) -7 NIL NIL) (-300 629934 630052 630093 "EVALAB" 630263 NIL EVALAB (NIL T) -9 NIL 630367) (-299 629415 629537 629758 "EVALAB-" 629763 NIL EVALAB- (NIL T T) -8 NIL NIL) (-298 626918 628186 628214 "EUCDOM" 628769 T EUCDOM (NIL) -9 NIL 629119) (-297 625323 625765 626355 "EUCDOM-" 626360 NIL EUCDOM- (NIL T) -8 NIL NIL) (-296 612863 615621 618371 "ESTOOLS" 622593 T ESTOOLS (NIL) -7 NIL NIL) (-295 612495 612552 612661 "ESTOOLS2" 612800 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-294 612246 612288 612368 "ESTOOLS1" 612447 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-293 606171 607899 607927 "ES" 610695 T ES (NIL) -9 NIL 612104) (-292 601118 602405 604222 "ES-" 604386 NIL ES- (NIL T) -8 NIL NIL) (-291 597493 598253 599033 "ESCONT" 600358 T ESCONT (NIL) -7 NIL NIL) (-290 597238 597270 597352 "ESCONT1" 597455 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-289 596913 596963 597063 "ES2" 597182 NIL ES2 (NIL T T) -7 NIL NIL) (-288 596543 596601 596710 "ES1" 596849 NIL ES1 (NIL T T) -7 NIL NIL) (-287 595759 595888 596064 "ERROR" 596387 T ERROR (NIL) -7 NIL NIL) (-286 589262 595618 595709 "EQTBL" 595714 NIL EQTBL (NIL T T) -8 NIL NIL) (-285 581819 584576 586025 "EQ" 587846 NIL -3897 (NIL T) -8 NIL NIL) (-284 581451 581508 581617 "EQ2" 581756 NIL EQ2 (NIL T T) -7 NIL NIL) (-283 576743 577789 578882 "EP" 580390 NIL EP (NIL T) -7 NIL NIL) (-282 575325 575626 575943 "ENV" 576446 T ENV (NIL) -8 NIL NIL) (-281 574524 575044 575072 "ENTIRER" 575077 T ENTIRER (NIL) -9 NIL 575123) (-280 571026 572479 572849 "EMR" 574323 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-279 570170 570355 570409 "ELTAGG" 570789 NIL ELTAGG (NIL T T) -9 NIL 571000) (-278 569889 569951 570092 "ELTAGG-" 570097 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-277 569678 569707 569761 "ELTAB" 569845 NIL ELTAB (NIL T T) -9 NIL NIL) (-276 568804 568950 569149 "ELFUTS" 569529 NIL ELFUTS (NIL T T) -7 NIL NIL) (-275 568546 568602 568630 "ELEMFUN" 568735 T ELEMFUN (NIL) -9 NIL NIL) (-274 568416 568437 568505 "ELEMFUN-" 568510 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-273 563307 566516 566557 "ELAGG" 567497 NIL ELAGG (NIL T) -9 NIL 567960) (-272 561592 562026 562689 "ELAGG-" 562694 NIL ELAGG- (NIL T T) -8 NIL NIL) (-271 560249 560529 560824 "ELABEXPR" 561317 T ELABEXPR (NIL) -8 NIL NIL) (-270 553115 554916 555743 "EFUPXS" 559525 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-269 546565 548366 549176 "EFULS" 552391 NIL EFULS (NIL T T T) -8 NIL NIL) (-268 543987 544345 544824 "EFSTRUC" 546197 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-267 533059 534624 536184 "EF" 542502 NIL EF (NIL T T) -7 NIL NIL) (-266 532160 532544 532693 "EAB" 532930 T EAB (NIL) -8 NIL NIL) (-265 531369 532119 532147 "E04UCFA" 532152 T E04UCFA (NIL) -8 NIL NIL) (-264 530578 531328 531356 "E04NAFA" 531361 T E04NAFA (NIL) -8 NIL NIL) (-263 529787 530537 530565 "E04MBFA" 530570 T E04MBFA (NIL) -8 NIL NIL) (-262 528996 529746 529774 "E04JAFA" 529779 T E04JAFA (NIL) -8 NIL NIL) (-261 528207 528955 528983 "E04GCFA" 528988 T E04GCFA (NIL) -8 NIL NIL) (-260 527418 528166 528194 "E04FDFA" 528199 T E04FDFA (NIL) -8 NIL NIL) (-259 526627 527377 527405 "E04DGFA" 527410 T E04DGFA (NIL) -8 NIL NIL) (-258 520805 522152 523516 "E04AGNT" 525283 T E04AGNT (NIL) -7 NIL NIL) (-257 519529 520009 520049 "DVARCAT" 520524 NIL DVARCAT (NIL T) -9 NIL 520723) (-256 518733 518945 519259 "DVARCAT-" 519264 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-255 511633 518532 518661 "DSMP" 518666 NIL DSMP (NIL T T T) -8 NIL NIL) (-254 506443 507578 508646 "DROPT" 510585 T DROPT (NIL) -8 NIL NIL) (-253 506108 506167 506265 "DROPT1" 506378 NIL DROPT1 (NIL T) -7 NIL NIL) (-252 501223 502349 503486 "DROPT0" 504991 T DROPT0 (NIL) -7 NIL NIL) (-251 499568 499893 500279 "DRAWPT" 500857 T DRAWPT (NIL) -7 NIL NIL) (-250 494155 495078 496157 "DRAW" 498542 NIL DRAW (NIL T) -7 NIL NIL) (-249 493788 493841 493959 "DRAWHACK" 494096 NIL DRAWHACK (NIL T) -7 NIL NIL) (-248 492519 492788 493079 "DRAWCX" 493517 T DRAWCX (NIL) -7 NIL NIL) (-247 492035 492103 492254 "DRAWCURV" 492445 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-246 482506 484465 486580 "DRAWCFUN" 489940 T DRAWCFUN (NIL) -7 NIL NIL) (-245 479319 481201 481242 "DQAGG" 481871 NIL DQAGG (NIL T) -9 NIL 482144) (-244 467838 474535 474618 "DPOLCAT" 476470 NIL DPOLCAT (NIL T T T T) -9 NIL 477015) (-243 462677 464023 465981 "DPOLCAT-" 465986 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-242 455832 462538 462636 "DPMO" 462641 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-241 448890 455612 455779 "DPMM" 455784 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-240 448310 448513 448627 "DOMAIN" 448796 T DOMAIN (NIL) -8 NIL NIL) (-239 442061 447945 448097 "DMP" 448211 NIL DMP (NIL NIL T) -8 NIL NIL) (-238 441661 441717 441861 "DLP" 441999 NIL DLP (NIL T) -7 NIL NIL) (-237 435305 440762 440989 "DLIST" 441466 NIL DLIST (NIL T) -8 NIL NIL) (-236 432151 434160 434201 "DLAGG" 434751 NIL DLAGG (NIL T) -9 NIL 434980) (-235 431001 431631 431659 "DIVRING" 431751 T DIVRING (NIL) -9 NIL 431834) (-234 430238 430428 430728 "DIVRING-" 430733 NIL DIVRING- (NIL T) -8 NIL NIL) (-233 428340 428697 429103 "DISPLAY" 429852 T DISPLAY (NIL) -7 NIL NIL) (-232 422282 428254 428317 "DIRPROD" 428322 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-231 421130 421333 421598 "DIRPROD2" 422075 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-230 410668 416620 416673 "DIRPCAT" 417083 NIL DIRPCAT (NIL NIL T) -9 NIL 417923) (-229 407994 408636 409517 "DIRPCAT-" 409854 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-228 407281 407441 407627 "DIOSP" 407828 T DIOSP (NIL) -7 NIL NIL) (-227 403983 406193 406234 "DIOPS" 406668 NIL DIOPS (NIL T) -9 NIL 406897) (-226 403532 403646 403837 "DIOPS-" 403842 NIL DIOPS- (NIL T T) -8 NIL NIL) (-225 402444 403038 403066 "DIFRING" 403253 T DIFRING (NIL) -9 NIL 403363) (-224 402090 402167 402319 "DIFRING-" 402324 NIL DIFRING- (NIL T) -8 NIL NIL) (-223 399915 401153 401194 "DIFEXT" 401557 NIL DIFEXT (NIL T) -9 NIL 401851) (-222 398200 398628 399294 "DIFEXT-" 399299 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-221 395522 397732 397773 "DIAGG" 397778 NIL DIAGG (NIL T) -9 NIL 397798) (-220 394906 395063 395315 "DIAGG-" 395320 NIL DIAGG- (NIL T T) -8 NIL NIL) (-219 390371 393865 394142 "DHMATRIX" 394675 NIL DHMATRIX (NIL T) -8 NIL NIL) (-218 385983 386892 387902 "DFSFUN" 389381 T DFSFUN (NIL) -7 NIL NIL) (-217 380951 384798 385140 "DFLOAT" 385661 T DFLOAT (NIL) -8 NIL NIL) (-216 379179 379460 379856 "DFINTTLS" 380659 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-215 376244 377200 377600 "DERHAM" 378845 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-214 374093 376019 376108 "DEQUEUE" 376188 NIL DEQUEUE (NIL T) -8 NIL NIL) (-213 373308 373441 373637 "DEGRED" 373955 NIL DEGRED (NIL T T) -7 NIL NIL) (-212 369703 370448 371301 "DEFINTRF" 372536 NIL DEFINTRF (NIL T) -7 NIL NIL) (-211 367230 367699 368298 "DEFINTEF" 369222 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-210 366596 366829 366951 "DEFAST" 367128 T DEFAST (NIL) -8 NIL NIL) (-209 360484 366037 366203 "DECIMAL" 366450 T DECIMAL (NIL) -8 NIL NIL) (-208 357996 358454 358960 "DDFACT" 360028 NIL DDFACT (NIL T T) -7 NIL NIL) (-207 357592 357635 357786 "DBLRESP" 357947 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-206 355302 355636 356005 "DBASE" 357350 NIL DBASE (NIL T) -8 NIL NIL) (-205 354571 354782 354928 "DATABUF" 355201 NIL DATABUF (NIL NIL T) -8 NIL NIL) (-204 353704 354530 354558 "D03FAFA" 354563 T D03FAFA (NIL) -8 NIL NIL) (-203 352838 353663 353691 "D03EEFA" 353696 T D03EEFA (NIL) -8 NIL NIL) (-202 350788 351254 351743 "D03AGNT" 352369 T D03AGNT (NIL) -7 NIL NIL) (-201 350104 350747 350775 "D02EJFA" 350780 T D02EJFA (NIL) -8 NIL NIL) (-200 349420 350063 350091 "D02CJFA" 350096 T D02CJFA (NIL) -8 NIL NIL) (-199 348736 349379 349407 "D02BHFA" 349412 T D02BHFA (NIL) -8 NIL NIL) (-198 348052 348695 348723 "D02BBFA" 348728 T D02BBFA (NIL) -8 NIL NIL) (-197 341250 342838 344444 "D02AGNT" 346466 T D02AGNT (NIL) -7 NIL NIL) (-196 339019 339541 340087 "D01WGTS" 340724 T D01WGTS (NIL) -7 NIL NIL) (-195 338114 338978 339006 "D01TRNS" 339011 T D01TRNS (NIL) -8 NIL NIL) (-194 337209 338073 338101 "D01GBFA" 338106 T D01GBFA (NIL) -8 NIL NIL) (-193 336304 337168 337196 "D01FCFA" 337201 T D01FCFA (NIL) -8 NIL NIL) (-192 335399 336263 336291 "D01ASFA" 336296 T D01ASFA (NIL) -8 NIL NIL) (-191 334494 335358 335386 "D01AQFA" 335391 T D01AQFA (NIL) -8 NIL NIL) (-190 333589 334453 334481 "D01APFA" 334486 T D01APFA (NIL) -8 NIL NIL) (-189 332684 333548 333576 "D01ANFA" 333581 T D01ANFA (NIL) -8 NIL NIL) (-188 331779 332643 332671 "D01AMFA" 332676 T D01AMFA (NIL) -8 NIL NIL) (-187 330874 331738 331766 "D01ALFA" 331771 T D01ALFA (NIL) -8 NIL NIL) (-186 329969 330833 330861 "D01AKFA" 330866 T D01AKFA (NIL) -8 NIL NIL) (-185 329064 329928 329956 "D01AJFA" 329961 T D01AJFA (NIL) -8 NIL NIL) (-184 322361 323912 325473 "D01AGNT" 327523 T D01AGNT (NIL) -7 NIL NIL) (-183 321698 321826 321978 "CYCLOTOM" 322229 T CYCLOTOM (NIL) -7 NIL NIL) (-182 318433 319146 319873 "CYCLES" 320991 T CYCLES (NIL) -7 NIL NIL) (-181 317745 317879 318050 "CVMP" 318294 NIL CVMP (NIL T) -7 NIL NIL) (-180 315516 315774 316150 "CTRIGMNP" 317473 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-179 315027 315216 315315 "CTORCALL" 315437 T CTORCALL (NIL) -8 NIL NIL) (-178 314401 314500 314653 "CSTTOOLS" 314924 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-177 310200 310857 311615 "CRFP" 313713 NIL CRFP (NIL T T) -7 NIL 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UPXSCONS (NIL T T) -8 NIL NIL) (-1202 3010301 3017046 3017108 "UPXSCCA" 3017764 NIL UPXSCCA (NIL T T) -9 NIL 3018006) (-1201 3009939 3010024 3010198 "UPXSCCA-" 3010203 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1200 3000223 3006741 3006784 "UPXSCAT" 3007432 NIL UPXSCAT (NIL T) -9 NIL 3008040) (-1199 2999653 2999732 2999911 "UPXS2" 3000138 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1198 2998307 2998560 2998911 "UPSQFREE" 2999396 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1197 2992225 2995234 2995289 "UPSCAT" 2996450 NIL UPSCAT (NIL T T) -9 NIL 2997224) (-1196 2991429 2991636 2991963 "UPSCAT-" 2991968 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1195 2977520 2985516 2985559 "UPOLYC" 2987660 NIL UPOLYC (NIL T) -9 NIL 2988881) (-1194 2968849 2971274 2974421 "UPOLYC-" 2974426 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1193 2968476 2968519 2968652 "UPOLYC2" 2968800 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1192 2959933 2968042 2968180 "UP" 2968386 NIL UP (NIL NIL T) -8 NIL NIL) (-1191 2959272 2959379 2959543 "UPMP" 2959822 NIL UPMP (NIL T T) -7 NIL NIL) (-1190 2958825 2958906 2959045 "UPDIVP" 2959185 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1189 2957393 2957642 2957958 "UPDECOMP" 2958574 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1188 2956628 2956740 2956925 "UPCDEN" 2957277 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1187 2956147 2956216 2956365 "UP2" 2956553 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1186 2954664 2955351 2955628 "UNISEG" 2955905 NIL UNISEG (NIL T) -8 NIL NIL) (-1185 2953879 2954006 2954211 "UNISEG2" 2954507 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1184 2952939 2953119 2953345 "UNIFACT" 2953695 NIL UNIFACT (NIL T) -7 NIL NIL) (-1183 2936908 2952116 2952367 "ULS" 2952746 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1182 2924950 2936812 2936884 "ULSCONS" 2936889 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1181 2907754 2919689 2919751 "ULSCCAT" 2920471 NIL ULSCCAT (NIL T T) -9 NIL 2920768) (-1180 2906804 2907049 2907437 "ULSCCAT-" 2907442 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1179 2896865 2903297 2903340 "ULSCAT" 2904203 NIL ULSCAT (NIL T) -9 NIL 2904933) (-1178 2896295 2896374 2896553 "ULS2" 2896780 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1177 2894733 2895656 2895686 "UFD" 2895898 T UFD (NIL) -9 NIL 2896012) (-1176 2894527 2894573 2894668 "UFD-" 2894673 NIL UFD- (NIL T) -8 NIL NIL) (-1175 2893609 2893792 2894008 "UDVO" 2894333 T UDVO (NIL) -7 NIL NIL) (-1174 2891425 2891834 2892305 "UDPO" 2893173 NIL UDPO (NIL T) -7 NIL NIL) (-1173 2891358 2891363 2891393 "TYPE" 2891398 T TYPE (NIL) -9 NIL NIL) (-1172 2891012 2891180 2891250 "TYPEAST" 2891310 T TYPEAST (NIL) -8 NIL NIL) (-1171 2889983 2890185 2890425 "TWOFACT" 2890806 NIL TWOFACT (NIL T) -7 NIL NIL) (-1170 2888921 2889258 2889521 "TUPLE" 2889755 NIL TUPLE (NIL T) -8 NIL NIL) (-1169 2886612 2887131 2887670 "TUBETOOL" 2888404 T TUBETOOL (NIL) -7 NIL NIL) (-1168 2885461 2885666 2885907 "TUBE" 2886405 NIL TUBE (NIL T) -8 NIL NIL) (-1167 2880225 2884433 2884716 "TS" 2885213 NIL TS (NIL T) -8 NIL NIL) (-1166 2868892 2872984 2873081 "TSETCAT" 2878350 NIL TSETCAT (NIL T T T T) -9 NIL 2879881) (-1165 2863626 2865224 2867115 "TSETCAT-" 2867120 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1164 2857889 2858735 2859677 "TRMANIP" 2862762 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1163 2857330 2857393 2857556 "TRIMAT" 2857821 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1162 2855126 2855363 2855727 "TRIGMNIP" 2857079 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1161 2854646 2854759 2854789 "TRIGCAT" 2855002 T TRIGCAT (NIL) -9 NIL NIL) (-1160 2854315 2854394 2854535 "TRIGCAT-" 2854540 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1159 2851214 2853175 2853455 "TREE" 2854070 NIL TREE (NIL T) -8 NIL NIL) (-1158 2850488 2851016 2851046 "TRANFUN" 2851081 T TRANFUN (NIL) -9 NIL 2851147) (-1157 2849767 2849958 2850238 "TRANFUN-" 2850243 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1156 2849571 2849603 2849664 "TOPSP" 2849728 T TOPSP (NIL) -7 NIL NIL) (-1155 2848919 2849034 2849188 "TOOLSIGN" 2849452 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1154 2847580 2848096 2848335 "TEXTFILE" 2848702 T TEXTFILE (NIL) -8 NIL NIL) (-1153 2845445 2845959 2846397 "TEX" 2847164 T TEX (NIL) -8 NIL NIL) (-1152 2845226 2845257 2845329 "TEX1" 2845408 NIL TEX1 (NIL T) -7 NIL NIL) (-1151 2844874 2844937 2845027 "TEMUTL" 2845158 T TEMUTL (NIL) -7 NIL NIL) (-1150 2843028 2843308 2843633 "TBCMPPK" 2844597 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1149 2834916 2841188 2841244 "TBAGG" 2841644 NIL TBAGG (NIL T T) -9 NIL 2841855) (-1148 2829986 2831474 2833228 "TBAGG-" 2833233 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1147 2829370 2829477 2829622 "TANEXP" 2829875 NIL TANEXP (NIL T) -7 NIL NIL) (-1146 2822871 2829227 2829320 "TABLE" 2829325 NIL TABLE (NIL T T) -8 NIL NIL) (-1145 2822283 2822382 2822520 "TABLEAU" 2822768 NIL TABLEAU (NIL T) -8 NIL NIL) (-1144 2816891 2818111 2819359 "TABLBUMP" 2821069 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1143 2816319 2816419 2816547 "SYSTEM" 2816785 T SYSTEM (NIL) -7 NIL NIL) (-1142 2812782 2813477 2814260 "SYSSOLP" 2815570 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1141 2809073 2809781 2810515 "SYNTAX" 2812070 T SYNTAX (NIL) -8 NIL NIL) (-1140 2806231 2806833 2807465 "SYMTAB" 2808463 T SYMTAB (NIL) -8 NIL NIL) (-1139 2801480 2802382 2803365 "SYMS" 2805270 T SYMS (NIL) -8 NIL NIL) (-1138 2798752 2800938 2801168 "SYMPOLY" 2801285 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1137 2798269 2798344 2798467 "SYMFUNC" 2798664 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1136 2794246 2795506 2796328 "SYMBOL" 2797469 T SYMBOL (NIL) -8 NIL NIL) (-1135 2787785 2789474 2791194 "SWITCH" 2792548 T SWITCH (NIL) -8 NIL NIL) (-1134 2781055 2786606 2786909 "SUTS" 2787540 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1133 2773024 2780170 2780452 "SUPXS" 2780831 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1132 2764553 2772642 2772768 "SUP" 2772933 NIL SUP (NIL T) -8 NIL NIL) (-1131 2763712 2763839 2764056 "SUPFRACF" 2764421 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1130 2763333 2763392 2763505 "SUP2" 2763647 NIL SUP2 (NIL T T) -7 NIL NIL) (-1129 2761746 2762020 2762383 "SUMRF" 2763032 NIL SUMRF (NIL T) -7 NIL NIL) (-1128 2761060 2761126 2761325 "SUMFS" 2761667 NIL SUMFS (NIL T T) -7 NIL NIL) (-1127 2745069 2760237 2760488 "SULS" 2760867 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1126 2744391 2744594 2744734 "SUCH" 2744977 NIL SUCH (NIL T T) -8 NIL NIL) (-1125 2738285 2739297 2740256 "SUBSPACE" 2743479 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1124 2737715 2737805 2737969 "SUBRESP" 2738173 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1123 2731084 2732380 2733691 "STTF" 2736451 NIL STTF (NIL T) -7 NIL NIL) (-1122 2725257 2726377 2727524 "STTFNC" 2729984 NIL STTFNC (NIL T) -7 NIL NIL) (-1121 2716572 2718439 2720233 "STTAYLOR" 2723498 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1120 2709816 2716436 2716519 "STRTBL" 2716524 NIL STRTBL (NIL T) -8 NIL NIL) (-1119 2705207 2709771 2709802 "STRING" 2709807 T STRING (NIL) -8 NIL NIL) (-1118 2700095 2704580 2704610 "STRICAT" 2704669 T STRICAT (NIL) -9 NIL 2704731) (-1117 2692808 2697618 2698238 "STREAM" 2699510 NIL STREAM (NIL T) -8 NIL NIL) (-1116 2692318 2692395 2692539 "STREAM3" 2692725 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1115 2691300 2691483 2691718 "STREAM2" 2692131 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1114 2690988 2691040 2691133 "STREAM1" 2691242 NIL STREAM1 (NIL T) -7 NIL NIL) (-1113 2690004 2690185 2690416 "STINPROD" 2690804 NIL STINPROD (NIL T) -7 NIL NIL) (-1112 2689582 2689766 2689796 "STEP" 2689876 T STEP (NIL) -9 NIL 2689954) (-1111 2683125 2689481 2689558 "STBL" 2689563 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1110 2678300 2682347 2682390 "STAGG" 2682543 NIL STAGG (NIL T) -9 NIL 2682632) (-1109 2676002 2676604 2677476 "STAGG-" 2677481 NIL STAGG- (NIL T T) -8 NIL NIL) (-1108 2674197 2675772 2675864 "STACK" 2675945 NIL STACK (NIL T) -8 NIL NIL) (-1107 2666922 2672338 2672794 "SREGSET" 2673827 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1106 2659348 2660716 2662229 "SRDCMPK" 2665528 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1105 2652315 2656788 2656818 "SRAGG" 2658121 T SRAGG (NIL) -9 NIL 2658729) (-1104 2651332 2651587 2651966 "SRAGG-" 2651971 NIL SRAGG- (NIL T) -8 NIL NIL) (-1103 2645818 2650247 2650675 "SQMATRIX" 2650951 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1102 2639570 2642538 2643264 "SPLTREE" 2645164 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1101 2635560 2636226 2636872 "SPLNODE" 2638996 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1100 2634607 2634840 2634870 "SPFCAT" 2635314 T SPFCAT (NIL) -9 NIL NIL) (-1099 2633344 2633554 2633818 "SPECOUT" 2634365 T SPECOUT (NIL) -7 NIL NIL) (-1098 2630900 2631728 2631758 "SPADXPT" 2632517 T SPADXPT (NIL) -9 NIL 2633233) (-1097 2630661 2630701 2630770 "SPADPRSR" 2630853 T SPADPRSR (NIL) -7 NIL NIL) (-1096 2622632 2624379 2624422 "SPACEC" 2628795 NIL SPACEC (NIL T) -9 NIL 2630611) (-1095 2620803 2622564 2622613 "SPACE3" 2622618 NIL SPACE3 (NIL T) -8 NIL NIL) (-1094 2619555 2619726 2620017 "SORTPAK" 2620608 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1093 2617605 2617908 2618327 "SOLVETRA" 2619219 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1092 2616616 2616838 2617112 "SOLVESER" 2617378 NIL SOLVESER (NIL T) -7 NIL NIL) (-1091 2611836 2612717 2613719 "SOLVERAD" 2615668 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1090 2607651 2608260 2608989 "SOLVEFOR" 2611203 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1089 2601948 2607000 2607097 "SNTSCAT" 2607102 NIL SNTSCAT (NIL T T T T) -9 NIL 2607172) (-1088 2596091 2600271 2600662 "SMTS" 2601638 NIL SMTS (NIL T T T) -8 NIL NIL) (-1087 2590541 2595979 2596056 "SMP" 2596061 NIL SMP (NIL T T) -8 NIL NIL) (-1086 2588700 2589001 2589399 "SMITH" 2590238 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1085 2581683 2585838 2585941 "SMATCAT" 2587292 NIL SMATCAT (NIL NIL T T T) -9 NIL 2587842) (-1084 2578623 2579446 2580624 "SMATCAT-" 2580629 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1083 2576336 2577859 2577902 "SKAGG" 2578163 NIL SKAGG (NIL T) -9 NIL 2578298) (-1082 2572452 2575440 2575718 "SINT" 2576080 T SINT (NIL) -8 NIL NIL) (-1081 2572224 2572262 2572328 "SIMPAN" 2572408 T SIMPAN (NIL) -7 NIL NIL) (-1080 2571531 2571759 2571899 "SIG" 2572106 T SIG (NIL) -8 NIL NIL) (-1079 2570369 2570590 2570865 "SIGNRF" 2571290 NIL SIGNRF (NIL T) -7 NIL NIL) (-1078 2569174 2569325 2569616 "SIGNEF" 2570198 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1077 2566864 2567318 2567824 "SHP" 2568715 NIL SHP (NIL T NIL) -7 NIL NIL) (-1076 2560770 2566765 2566841 "SHDP" 2566846 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1075 2560369 2560535 2560565 "SGROUP" 2560658 T SGROUP (NIL) -9 NIL 2560720) (-1074 2560227 2560253 2560326 "SGROUP-" 2560331 NIL SGROUP- (NIL T) -8 NIL NIL) (-1073 2557063 2557760 2558483 "SGCF" 2559526 T SGCF (NIL) -7 NIL NIL) (-1072 2551458 2556510 2556607 "SFRTCAT" 2556612 NIL SFRTCAT (NIL T T T T) -9 NIL 2556651) (-1071 2544882 2545897 2547033 "SFRGCD" 2550441 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1070 2538010 2539081 2540267 "SFQCMPK" 2543815 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1069 2537632 2537721 2537831 "SFORT" 2537951 NIL SFORT (NIL T T) -8 NIL NIL) (-1068 2536777 2537472 2537593 "SEXOF" 2537598 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1067 2535911 2536658 2536726 "SEX" 2536731 T SEX (NIL) -8 NIL NIL) (-1066 2530687 2531376 2531471 "SEXCAT" 2535242 NIL SEXCAT (NIL T T T T T) -9 NIL 2535861) (-1065 2527867 2530621 2530669 "SET" 2530674 NIL SET (NIL T) -8 NIL NIL) (-1064 2526118 2526580 2526885 "SETMN" 2527608 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1063 2525724 2525850 2525880 "SETCAT" 2525997 T SETCAT (NIL) -9 NIL 2526082) (-1062 2525504 2525556 2525655 "SETCAT-" 2525660 NIL SETCAT- (NIL T) -8 NIL NIL) (-1061 2521891 2523965 2524008 "SETAGG" 2524878 NIL SETAGG (NIL T) -9 NIL 2525218) (-1060 2521349 2521465 2521702 "SETAGG-" 2521707 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1059 2520553 2520846 2520907 "SEGXCAT" 2521193 NIL SEGXCAT (NIL T T) -9 NIL 2521313) (-1058 2519609 2520219 2520401 "SEG" 2520406 NIL SEG (NIL T) -8 NIL NIL) (-1057 2518516 2518729 2518772 "SEGCAT" 2519354 NIL SEGCAT (NIL T) -9 NIL 2519592) (-1056 2517565 2517895 2518095 "SEGBIND" 2518351 NIL SEGBIND (NIL T) -8 NIL NIL) (-1055 2517186 2517245 2517358 "SEGBIND2" 2517500 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1054 2516804 2516987 2517064 "SEGAST" 2517131 T SEGAST (NIL) -8 NIL NIL) (-1053 2516023 2516149 2516353 "SEG2" 2516648 NIL SEG2 (NIL T T) -7 NIL NIL) (-1052 2515460 2515958 2516005 "SDVAR" 2516010 NIL SDVAR (NIL T) -8 NIL NIL) (-1051 2507750 2515230 2515360 "SDPOL" 2515365 NIL SDPOL (NIL T) -8 NIL NIL) (-1050 2506343 2506609 2506928 "SCPKG" 2507465 NIL SCPKG (NIL T) -7 NIL NIL) (-1049 2505479 2505659 2505859 "SCOPE" 2506165 T SCOPE (NIL) -8 NIL NIL) (-1048 2504700 2504833 2505012 "SCACHE" 2505334 NIL SCACHE (NIL T) -7 NIL NIL) (-1047 2504426 2504569 2504599 "SASTCAT" 2504604 T SASTCAT (NIL) -9 NIL 2504617) (-1046 2504215 2504260 2504358 "SASTCAT-" 2504363 NIL SASTCAT- (NIL T) -8 NIL NIL) (-1045 2503654 2503975 2504060 "SAOS" 2504152 T SAOS (NIL) -8 NIL NIL) (-1044 2503219 2503254 2503427 "SAERFFC" 2503613 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-1043 2497193 2503116 2503196 "SAE" 2503201 NIL SAE (NIL T T NIL) -8 NIL NIL) (-1042 2496786 2496821 2496980 "SAEFACT" 2497152 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-1041 2495107 2495421 2495822 "RURPK" 2496452 NIL RURPK (NIL T NIL) -7 NIL NIL) (-1040 2493743 2494022 2494334 "RULESET" 2494941 NIL RULESET (NIL T T T) -8 NIL NIL) (-1039 2490930 2491433 2491898 "RULE" 2493424 NIL RULE (NIL T T T) -8 NIL NIL) (-1038 2490569 2490724 2490807 "RULECOLD" 2490882 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-1037 2485418 2486212 2487132 "RSETGCD" 2489768 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-1036 2474675 2479727 2479824 "RSETCAT" 2483943 NIL RSETCAT (NIL T T T T) -9 NIL 2485040) (-1035 2472602 2473141 2473965 "RSETCAT-" 2473970 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-1034 2464989 2466364 2467884 "RSDCMPK" 2471201 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-1033 2462994 2463435 2463509 "RRCC" 2464595 NIL RRCC (NIL T T) -9 NIL 2464939) (-1032 2462345 2462519 2462798 "RRCC-" 2462803 NIL RRCC- (NIL T T T) -8 NIL NIL) (-1031 2461832 2462041 2462142 "RPTAST" 2462266 T RPTAST (NIL) -8 NIL NIL) (-1030 2436060 2445645 2445712 "RPOLCAT" 2456376 NIL RPOLCAT (NIL T T T) -9 NIL 2459535) (-1029 2427560 2429898 2433020 "RPOLCAT-" 2433025 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-1028 2418607 2425771 2426253 "ROUTINE" 2427100 T ROUTINE (NIL) -8 NIL NIL) (-1027 2415365 2418158 2418307 "ROMAN" 2418480 T ROMAN (NIL) -8 NIL NIL) (-1026 2413640 2414225 2414485 "ROIRC" 2415170 NIL ROIRC (NIL T T) -8 NIL NIL) (-1025 2410091 2412330 2412360 "RNS" 2412664 T RNS (NIL) -9 NIL 2412936) (-1024 2408600 2408983 2409517 "RNS-" 2409592 NIL RNS- (NIL T) -8 NIL NIL) (-1023 2408049 2408431 2408461 "RNG" 2408466 T RNG (NIL) -9 NIL 2408487) (-1022 2407441 2407803 2407846 "RMODULE" 2407908 NIL RMODULE (NIL T) -9 NIL 2407950) (-1021 2406277 2406371 2406707 "RMCAT2" 2407342 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-1020 2402982 2405451 2405776 "RMATRIX" 2406011 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-1019 2395924 2398158 2398273 "RMATCAT" 2401632 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2402614) (-1018 2395299 2395446 2395753 "RMATCAT-" 2395758 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-1017 2394866 2394941 2395069 "RINTERP" 2395218 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-1016 2393954 2394474 2394504 "RING" 2394616 T RING (NIL) -9 NIL 2394711) (-1015 2393746 2393790 2393887 "RING-" 2393892 NIL RING- (NIL T) -8 NIL NIL) (-1014 2392587 2392824 2393082 "RIDIST" 2393510 T RIDIST (NIL) -7 NIL NIL) (-1013 2383903 2392055 2392261 "RGCHAIN" 2392435 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-1012 2380897 2381511 2382181 "RF" 2383267 NIL RF (NIL T) -7 NIL NIL) (-1011 2380543 2380606 2380709 "RFFACTOR" 2380828 NIL RFFACTOR (NIL T) -7 NIL NIL) (-1010 2380268 2380303 2380400 "RFFACT" 2380502 NIL RFFACT (NIL T) -7 NIL NIL) (-1009 2378385 2378749 2379131 "RFDIST" 2379908 T RFDIST (NIL) -7 NIL NIL) (-1008 2377838 2377930 2378093 "RETSOL" 2378287 NIL RETSOL (NIL T T) -7 NIL NIL) (-1007 2377426 2377506 2377549 "RETRACT" 2377742 NIL RETRACT (NIL T) -9 NIL NIL) (-1006 2377275 2377300 2377387 "RETRACT-" 2377392 NIL RETRACT- (NIL T T) -8 NIL NIL) (-1005 2376921 2377097 2377167 "RETAST" 2377227 T RETAST (NIL) -8 NIL NIL) (-1004 2369775 2376574 2376701 "RESULT" 2376816 T RESULT (NIL) -8 NIL NIL) (-1003 2368401 2369044 2369243 "RESRING" 2369678 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-1002 2368037 2368086 2368184 "RESLATC" 2368338 NIL RESLATC (NIL T) -7 NIL NIL) (-1001 2367743 2367777 2367884 "REPSQ" 2367996 NIL REPSQ (NIL T) -7 NIL NIL) (-1000 2365165 2365745 2366347 "REP" 2367163 T REP (NIL) -7 NIL NIL) (-999 2364866 2364900 2365009 "REPDB" 2365124 NIL REPDB (NIL T) -7 NIL NIL) (-998 2358794 2360173 2361394 "REP2" 2363678 NIL REP2 (NIL T) -7 NIL NIL) (-997 2355186 2355867 2356673 "REP1" 2358021 NIL REP1 (NIL T) -7 NIL NIL) (-996 2347924 2353339 2353793 "REGSET" 2354816 NIL REGSET (NIL T T T T) -8 NIL NIL) (-995 2346745 2347080 2347328 "REF" 2347709 NIL REF (NIL T) -8 NIL NIL) (-994 2346126 2346229 2346394 "REDORDER" 2346629 NIL REDORDER (NIL T T) -7 NIL NIL) (-993 2342146 2345354 2345577 "RECLOS" 2345955 NIL RECLOS (NIL T) -8 NIL NIL) (-992 2341203 2341384 2341597 "REALSOLV" 2341953 T REALSOLV (NIL) -7 NIL NIL) (-991 2341051 2341092 2341120 "REAL" 2341125 T REAL (NIL) -9 NIL 2341160) (-990 2337542 2338344 2339226 "REAL0Q" 2340216 NIL REAL0Q (NIL T) -7 NIL NIL) (-989 2333153 2334141 2335200 "REAL0" 2336523 NIL REAL0 (NIL T) -7 NIL NIL) (-988 2332673 2332874 2332966 "RDUCEAST" 2333081 T RDUCEAST (NIL) -8 NIL NIL) (-987 2332081 2332153 2332358 "RDIV" 2332595 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-986 2331154 2331328 2331539 "RDIST" 2331903 NIL RDIST (NIL T) -7 NIL NIL) (-985 2329755 2330042 2330412 "RDETRS" 2330862 NIL RDETRS (NIL T T) -7 NIL NIL) (-984 2327572 2328026 2328562 "RDETR" 2329297 NIL RDETR (NIL T T) -7 NIL NIL) (-983 2326186 2326464 2326866 "RDEEFS" 2327288 NIL RDEEFS (NIL T T) -7 NIL NIL) (-982 2324684 2324990 2325420 "RDEEF" 2325874 NIL RDEEF (NIL T T) -7 NIL NIL) (-981 2319021 2321892 2321920 "RCFIELD" 2323197 T RCFIELD (NIL) -9 NIL 2323927) (-980 2317090 2317594 2318287 "RCFIELD-" 2318360 NIL RCFIELD- (NIL T) -8 NIL NIL) (-979 2313421 2315206 2315247 "RCAGG" 2316318 NIL RCAGG (NIL T) -9 NIL 2316783) (-978 2313052 2313146 2313306 "RCAGG-" 2313311 NIL RCAGG- (NIL T T) -8 NIL NIL) (-977 2312392 2312504 2312667 "RATRET" 2312936 NIL RATRET (NIL T) -7 NIL NIL) (-976 2311949 2312016 2312135 "RATFACT" 2312320 NIL RATFACT (NIL T) -7 NIL NIL) (-975 2311264 2311384 2311534 "RANDSRC" 2311819 T RANDSRC (NIL) -7 NIL NIL) (-974 2311001 2311045 2311116 "RADUTIL" 2311213 T RADUTIL (NIL) -7 NIL NIL) (-973 2304066 2309744 2310061 "RADIX" 2310716 NIL RADIX (NIL NIL) -8 NIL NIL) (-972 2295722 2303910 2304038 "RADFF" 2304043 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-971 2295374 2295449 2295477 "RADCAT" 2295634 T RADCAT (NIL) -9 NIL NIL) (-970 2295159 2295207 2295304 "RADCAT-" 2295309 NIL RADCAT- (NIL T) -8 NIL NIL) (-969 2293310 2294934 2295023 "QUEUE" 2295103 NIL QUEUE (NIL T) -8 NIL NIL) (-968 2289886 2293247 2293292 "QUAT" 2293297 NIL QUAT (NIL T) -8 NIL NIL) (-967 2289524 2289567 2289694 "QUATCT2" 2289837 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-966 2283384 2286685 2286725 "QUATCAT" 2287505 NIL QUATCAT (NIL T) -9 NIL 2288271) (-965 2279528 2280565 2281952 "QUATCAT-" 2282046 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-964 2277048 2278612 2278653 "QUAGG" 2279028 NIL QUAGG (NIL T) -9 NIL 2279203) (-963 2276697 2276873 2276941 "QQUTAST" 2277000 T QQUTAST (NIL) -8 NIL NIL) (-962 2275622 2276095 2276267 "QFORM" 2276569 NIL QFORM (NIL NIL T) -8 NIL NIL) (-961 2266955 2272158 2272198 "QFCAT" 2272856 NIL QFCAT (NIL T) -9 NIL 2273855) (-960 2262527 2263728 2265319 "QFCAT-" 2265413 NIL QFCAT- (NIL T T) -8 NIL NIL) (-959 2262165 2262208 2262335 "QFCAT2" 2262478 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-958 2261625 2261735 2261865 "QEQUAT" 2262055 T QEQUAT (NIL) -8 NIL NIL) (-957 2254773 2255844 2257028 "QCMPACK" 2260558 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-956 2252349 2252770 2253198 "QALGSET" 2254428 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-955 2251594 2251768 2252000 "QALGSET2" 2252169 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-954 2250285 2250508 2250825 "PWFFINTB" 2251367 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-953 2248467 2248635 2248989 "PUSHVAR" 2250099 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-952 2244385 2245439 2245480 "PTRANFN" 2247364 NIL PTRANFN (NIL T) -9 NIL NIL) (-951 2242787 2243078 2243400 "PTPACK" 2244096 NIL PTPACK (NIL T) -7 NIL NIL) (-950 2242419 2242476 2242585 "PTFUNC2" 2242724 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-949 2236885 2241230 2241271 "PTCAT" 2241644 NIL PTCAT (NIL T) -9 NIL 2241806) (-948 2236543 2236578 2236702 "PSQFR" 2236844 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-947 2235138 2235436 2235770 "PSEUDLIN" 2236241 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-946 2221907 2224272 2226596 "PSETPK" 2232898 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-945 2214951 2217665 2217761 "PSETCAT" 2220782 NIL PSETCAT (NIL T T T T) -9 NIL 2221596) (-944 2212787 2213421 2214242 "PSETCAT-" 2214247 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-943 2212136 2212301 2212329 "PSCURVE" 2212597 T PSCURVE (NIL) -9 NIL 2212764) (-942 2208617 2210099 2210164 "PSCAT" 2211008 NIL PSCAT (NIL T T T) -9 NIL 2211248) (-941 2207680 2207896 2208296 "PSCAT-" 2208301 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-940 2206332 2206965 2207179 "PRTITION" 2207486 T PRTITION (NIL) -8 NIL NIL) (-939 2205852 2206053 2206145 "PRTDAST" 2206260 T PRTDAST (NIL) -8 NIL NIL) (-938 2194950 2197156 2199344 "PRS" 2203714 NIL PRS (NIL T T) -7 NIL NIL) (-937 2192808 2194300 2194340 "PRQAGG" 2194523 NIL PRQAGG (NIL T) -9 NIL 2194625) (-936 2192194 2192423 2192451 "PROPLOG" 2192636 T PROPLOG (NIL) -9 NIL 2192758) (-935 2189364 2190008 2190472 "PROPFRML" 2191762 NIL PROPFRML (NIL T) -8 NIL NIL) (-934 2188824 2188934 2189064 "PROPERTY" 2189254 T PROPERTY (NIL) -8 NIL NIL) (-933 2182909 2186990 2187810 "PRODUCT" 2188050 NIL PRODUCT (NIL T T) -8 NIL NIL) (-932 2180222 2182367 2182601 "PR" 2182720 NIL PR (NIL T T) -8 NIL NIL) (-931 2180018 2180050 2180109 "PRINT" 2180183 T PRINT (NIL) -7 NIL NIL) (-930 2179358 2179475 2179627 "PRIMES" 2179898 NIL PRIMES (NIL T) -7 NIL NIL) (-929 2177423 2177824 2178290 "PRIMELT" 2178937 NIL PRIMELT (NIL T) -7 NIL NIL) (-928 2177152 2177201 2177229 "PRIMCAT" 2177353 T PRIMCAT (NIL) -9 NIL NIL) (-927 2173313 2177090 2177135 "PRIMARR" 2177140 NIL PRIMARR (NIL T) -8 NIL NIL) (-926 2172320 2172498 2172726 "PRIMARR2" 2173131 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-925 2171963 2172019 2172130 "PREASSOC" 2172258 NIL PREASSOC (NIL T T) -7 NIL NIL) (-924 2171438 2171571 2171599 "PPCURVE" 2171804 T PPCURVE (NIL) -9 NIL 2171940) (-923 2171060 2171233 2171316 "PORTNUM" 2171375 T PORTNUM (NIL) -8 NIL NIL) (-922 2168419 2168818 2169410 "POLYROOT" 2170641 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-921 2162364 2168023 2168183 "POLY" 2168292 NIL POLY (NIL T) -8 NIL NIL) (-920 2161747 2161805 2162039 "POLYLIFT" 2162300 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-919 2158022 2158471 2159100 "POLYCATQ" 2161292 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-918 2145061 2150417 2150482 "POLYCAT" 2153996 NIL POLYCAT (NIL T T T) -9 NIL 2155924) (-917 2138511 2140372 2142756 "POLYCAT-" 2142761 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-916 2138098 2138166 2138286 "POLY2UP" 2138437 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-915 2137730 2137787 2137896 "POLY2" 2138035 NIL POLY2 (NIL T T) -7 NIL NIL) (-914 2136415 2136654 2136930 "POLUTIL" 2137504 NIL POLUTIL (NIL T T) -7 NIL NIL) (-913 2134770 2135047 2135378 "POLTOPOL" 2136137 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-912 2130288 2134706 2134752 "POINT" 2134757 NIL POINT (NIL T) -8 NIL NIL) (-911 2128475 2128832 2129207 "PNTHEORY" 2129933 T PNTHEORY (NIL) -7 NIL NIL) (-910 2126894 2127191 2127603 "PMTOOLS" 2128173 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-909 2126487 2126565 2126682 "PMSYM" 2126810 NIL PMSYM (NIL T) -7 NIL NIL) (-908 2125997 2126066 2126240 "PMQFCAT" 2126412 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-907 2125352 2125462 2125618 "PMPRED" 2125874 NIL PMPRED (NIL T) -7 NIL NIL) (-906 2124748 2124834 2124995 "PMPREDFS" 2125253 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-905 2123391 2123599 2123984 "PMPLCAT" 2124510 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-904 2122923 2123002 2123154 "PMLSAGG" 2123306 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-903 2122398 2122474 2122655 "PMKERNEL" 2122841 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-902 2122015 2122090 2122203 "PMINS" 2122317 NIL PMINS (NIL T) -7 NIL NIL) (-901 2121443 2121512 2121728 "PMFS" 2121940 NIL PMFS (NIL T T T) -7 NIL NIL) (-900 2120671 2120789 2120994 "PMDOWN" 2121320 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-899 2119834 2119993 2120175 "PMASS" 2120509 T PMASS (NIL) -7 NIL NIL) (-898 2119108 2119219 2119382 "PMASSFS" 2119720 NIL PMASSFS (NIL T T) -7 NIL NIL) (-897 2118763 2118831 2118925 "PLOTTOOL" 2119034 T PLOTTOOL (NIL) -7 NIL NIL) (-896 2113385 2114574 2115722 "PLOT" 2117635 T PLOT (NIL) -8 NIL NIL) (-895 2109199 2110233 2111154 "PLOT3D" 2112484 T PLOT3D (NIL) -8 NIL NIL) (-894 2108111 2108288 2108523 "PLOT1" 2109003 NIL PLOT1 (NIL T) -7 NIL NIL) (-893 2083505 2088177 2093028 "PLEQN" 2103377 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-892 2082823 2082945 2083125 "PINTERP" 2083370 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-891 2082516 2082563 2082666 "PINTERPA" 2082770 NIL PINTERPA (NIL T T) -7 NIL NIL) (-890 2081801 2082322 2082409 "PI" 2082449 T PI (NIL) -8 NIL NIL) (-889 2080233 2081174 2081202 "PID" 2081384 T PID (NIL) -9 NIL 2081518) (-888 2079958 2079995 2080083 "PICOERCE" 2080190 NIL PICOERCE (NIL T) -7 NIL NIL) (-887 2079278 2079417 2079593 "PGROEB" 2079814 NIL PGROEB (NIL T) -7 NIL NIL) (-886 2074865 2075679 2076584 "PGE" 2078393 T PGE (NIL) -7 NIL NIL) (-885 2072989 2073235 2073601 "PGCD" 2074582 NIL PGCD (NIL T T T T) -7 NIL NIL) (-884 2072327 2072430 2072591 "PFRPAC" 2072873 NIL PFRPAC (NIL T) -7 NIL NIL) (-883 2069007 2070875 2071228 "PFR" 2072006 NIL PFR (NIL T) -8 NIL NIL) (-882 2067396 2067640 2067965 "PFOTOOLS" 2068754 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-881 2065929 2066168 2066519 "PFOQ" 2067153 NIL PFOQ (NIL T T T) -7 NIL NIL) (-880 2064402 2064614 2064977 "PFO" 2065713 NIL PFO (NIL T T T T T) -7 NIL NIL) (-879 2060990 2064291 2064360 "PF" 2064365 NIL PF (NIL NIL) -8 NIL NIL) (-878 2058459 2059696 2059724 "PFECAT" 2060309 T PFECAT (NIL) -9 NIL 2060693) (-877 2057904 2058058 2058272 "PFECAT-" 2058277 NIL PFECAT- (NIL T) -8 NIL NIL) (-876 2056508 2056759 2057060 "PFBRU" 2057653 NIL PFBRU (NIL T T) -7 NIL NIL) (-875 2054375 2054726 2055158 "PFBR" 2056159 NIL PFBR (NIL T T T T) -7 NIL NIL) (-874 2050291 2051751 2052427 "PERM" 2053732 NIL PERM (NIL T) -8 NIL NIL) (-873 2045557 2046498 2047368 "PERMGRP" 2049454 NIL PERMGRP (NIL T) -8 NIL NIL) (-872 2043689 2044620 2044661 "PERMCAT" 2045107 NIL PERMCAT (NIL T) -9 NIL 2045412) (-871 2043342 2043383 2043507 "PERMAN" 2043642 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-870 2040782 2042911 2043042 "PENDTREE" 2043244 NIL PENDTREE (NIL T) -8 NIL NIL) (-869 2038895 2039629 2039670 "PDRING" 2040327 NIL PDRING (NIL T) -9 NIL 2040613) (-868 2037998 2038216 2038578 "PDRING-" 2038583 NIL PDRING- (NIL T T) -8 NIL NIL) (-867 2035139 2035890 2036581 "PDEPROB" 2037327 T PDEPROB (NIL) -8 NIL NIL) (-866 2032686 2033188 2033743 "PDEPACK" 2034604 T PDEPACK (NIL) -7 NIL NIL) (-865 2031598 2031788 2032039 "PDECOMP" 2032485 NIL PDECOMP (NIL T T) -7 NIL NIL) (-864 2029203 2030020 2030048 "PDECAT" 2030835 T PDECAT (NIL) -9 NIL 2031548) (-863 2028954 2028987 2029077 "PCOMP" 2029164 NIL PCOMP (NIL T T) -7 NIL NIL) (-862 2027159 2027755 2028052 "PBWLB" 2028683 NIL PBWLB (NIL T) -8 NIL NIL) (-861 2019663 2021232 2022570 "PATTERN" 2025842 NIL PATTERN (NIL T) -8 NIL NIL) (-860 2019295 2019352 2019461 "PATTERN2" 2019600 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-859 2017052 2017440 2017897 "PATTERN1" 2018884 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-858 2014447 2015001 2015482 "PATRES" 2016617 NIL PATRES (NIL T T) -8 NIL NIL) (-857 2014011 2014078 2014210 "PATRES2" 2014374 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-856 2011894 2012299 2012706 "PATMATCH" 2013678 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-855 2011430 2011613 2011654 "PATMAB" 2011761 NIL PATMAB (NIL T) -9 NIL 2011844) (-854 2009975 2010284 2010542 "PATLRES" 2011235 NIL PATLRES (NIL T T T) -8 NIL NIL) (-853 2009521 2009644 2009685 "PATAB" 2009690 NIL PATAB (NIL T) -9 NIL 2009862) (-852 2007002 2007534 2008107 "PARTPERM" 2008968 T PARTPERM (NIL) -7 NIL NIL) (-851 2006623 2006686 2006788 "PARSURF" 2006933 NIL PARSURF (NIL T) -8 NIL NIL) (-850 2006255 2006312 2006421 "PARSU2" 2006560 NIL PARSU2 (NIL T T) -7 NIL NIL) (-849 2006019 2006059 2006126 "PARSER" 2006208 T PARSER (NIL) -7 NIL NIL) (-848 2005640 2005703 2005805 "PARSCURV" 2005950 NIL PARSCURV (NIL T) -8 NIL NIL) (-847 2005272 2005329 2005438 "PARSC2" 2005577 NIL PARSC2 (NIL T T) -7 NIL NIL) (-846 2004911 2004969 2005066 "PARPCURV" 2005208 NIL PARPCURV (NIL T) -8 NIL NIL) (-845 2004543 2004600 2004709 "PARPC2" 2004848 NIL PARPC2 (NIL T T) -7 NIL NIL) (-844 2004063 2004149 2004268 "PAN2EXPR" 2004444 T PAN2EXPR (NIL) -7 NIL NIL) (-843 2002869 2003184 2003412 "PALETTE" 2003855 T PALETTE (NIL) -8 NIL NIL) (-842 2001337 2001874 2002234 "PAIR" 2002555 NIL PAIR (NIL T T) -8 NIL NIL) (-841 1995245 2000596 2000790 "PADICRC" 2001192 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-840 1988511 1994591 1994775 "PADICRAT" 1995093 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-839 1986861 1988448 1988493 "PADIC" 1988498 NIL PADIC (NIL NIL) -8 NIL NIL) (-838 1984106 1985636 1985676 "PADICCT" 1986257 NIL PADICCT (NIL NIL) -9 NIL 1986539) (-837 1983063 1983263 1983531 "PADEPAC" 1983893 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-836 1982275 1982408 1982614 "PADE" 1982925 NIL PADE (NIL T T T) -7 NIL NIL) (-835 1980325 1981111 1981428 "OWP" 1982042 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-834 1979434 1979930 1980102 "OVAR" 1980193 NIL OVAR (NIL NIL) -8 NIL NIL) (-833 1978698 1978819 1978980 "OUT" 1979293 T OUT (NIL) -7 NIL NIL) (-832 1967752 1969923 1972093 "OUTFORM" 1976548 T OUTFORM (NIL) -8 NIL NIL) (-831 1967389 1967472 1967500 "OUTBCON" 1967651 T OUTBCON (NIL) -9 NIL 1967736) (-830 1967229 1967264 1967340 "OUTBCON-" 1967345 NIL OUTBCON- (NIL T) -8 NIL NIL) (-829 1966637 1966958 1967047 "OSI" 1967160 T OSI (NIL) -8 NIL NIL) (-828 1966193 1966505 1966533 "OSGROUP" 1966538 T OSGROUP (NIL) -9 NIL 1966560) (-827 1964938 1965165 1965450 "ORTHPOL" 1965940 NIL ORTHPOL (NIL T) -7 NIL NIL) (-826 1962348 1964597 1964736 "OREUP" 1964881 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-825 1959786 1962039 1962166 "ORESUP" 1962290 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-824 1957314 1957814 1958375 "OREPCTO" 1959275 NIL OREPCTO (NIL T T) -7 NIL NIL) (-823 1951225 1953392 1953433 "OREPCAT" 1955781 NIL OREPCAT (NIL T) -9 NIL 1956885) (-822 1948372 1949154 1950212 "OREPCAT-" 1950217 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-821 1947549 1947821 1947849 "ORDSET" 1948158 T ORDSET (NIL) -9 NIL 1948322) (-820 1947068 1947190 1947383 "ORDSET-" 1947388 NIL ORDSET- (NIL T) -8 NIL NIL) (-819 1945722 1946479 1946507 "ORDRING" 1946709 T ORDRING (NIL) -9 NIL 1946834) (-818 1945367 1945461 1945605 "ORDRING-" 1945610 NIL ORDRING- (NIL T) -8 NIL NIL) (-817 1944773 1945210 1945238 "ORDMON" 1945243 T ORDMON (NIL) -9 NIL 1945264) (-816 1943935 1944082 1944277 "ORDFUNS" 1944622 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-815 1943446 1943805 1943833 "ORDFIN" 1943838 T ORDFIN (NIL) -9 NIL 1943859) (-814 1940038 1942032 1942441 "ORDCOMP" 1943070 NIL ORDCOMP (NIL T) -8 NIL NIL) (-813 1939304 1939431 1939617 "ORDCOMP2" 1939898 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-812 1935811 1936694 1937531 "OPTPROB" 1938487 T OPTPROB (NIL) -8 NIL NIL) (-811 1932613 1933252 1933956 "OPTPACK" 1935127 T OPTPACK (NIL) -7 NIL NIL) (-810 1930326 1931066 1931094 "OPTCAT" 1931913 T OPTCAT (NIL) -9 NIL 1932563) (-809 1930094 1930133 1930199 "OPQUERY" 1930280 T OPQUERY (NIL) -7 NIL NIL) (-808 1927260 1928405 1928909 "OP" 1929623 NIL OP (NIL T) -8 NIL NIL) (-807 1924105 1926057 1926426 "ONECOMP" 1926924 NIL ONECOMP (NIL T) -8 NIL NIL) (-806 1923410 1923525 1923699 "ONECOMP2" 1923977 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-805 1922829 1922935 1923065 "OMSERVER" 1923300 T OMSERVER (NIL) -7 NIL NIL) (-804 1919717 1922269 1922309 "OMSAGG" 1922370 NIL OMSAGG (NIL T) -9 NIL 1922434) (-803 1918340 1918603 1918885 "OMPKG" 1919455 T OMPKG (NIL) -7 NIL NIL) (-802 1917770 1917873 1917901 "OM" 1918200 T OM (NIL) -9 NIL NIL) (-801 1916352 1917319 1917488 "OMLO" 1917651 NIL OMLO (NIL T T) -8 NIL NIL) (-800 1915277 1915424 1915651 "OMEXPR" 1916178 NIL OMEXPR (NIL T) -7 NIL NIL) (-799 1914595 1914823 1914959 "OMERR" 1915161 T OMERR (NIL) -8 NIL NIL) (-798 1913773 1914016 1914176 "OMERRK" 1914455 T OMERRK (NIL) -8 NIL NIL) (-797 1913251 1913450 1913558 "OMENC" 1913685 T OMENC (NIL) -8 NIL NIL) (-796 1907146 1908331 1909502 "OMDEV" 1912100 T OMDEV (NIL) -8 NIL NIL) (-795 1906215 1906386 1906580 "OMCONN" 1906972 T OMCONN (NIL) -8 NIL NIL) (-794 1904871 1905813 1905841 "OINTDOM" 1905846 T OINTDOM (NIL) -9 NIL 1905867) (-793 1900677 1901861 1902577 "OFMONOID" 1904187 NIL OFMONOID (NIL T) -8 NIL NIL) (-792 1900115 1900614 1900659 "ODVAR" 1900664 NIL ODVAR (NIL T) -8 NIL NIL) (-791 1897325 1899612 1899797 "ODR" 1899990 NIL ODR (NIL T T NIL) -8 NIL NIL) (-790 1889669 1897101 1897227 "ODPOL" 1897232 NIL ODPOL (NIL T) -8 NIL NIL) (-789 1883545 1889541 1889646 "ODP" 1889651 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-788 1882311 1882526 1882801 "ODETOOLS" 1883319 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-787 1879280 1879936 1880652 "ODESYS" 1881644 NIL ODESYS (NIL T T) -7 NIL NIL) (-786 1874162 1875070 1876095 "ODERTRIC" 1878355 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-785 1873588 1873670 1873864 "ODERED" 1874074 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-784 1870476 1871024 1871701 "ODERAT" 1873011 NIL ODERAT (NIL T T) -7 NIL NIL) (-783 1867436 1867900 1868497 "ODEPRRIC" 1870005 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-782 1865305 1865874 1866383 "ODEPROB" 1866947 T ODEPROB (NIL) -8 NIL NIL) (-781 1861827 1862310 1862957 "ODEPRIM" 1864784 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-780 1861076 1861178 1861438 "ODEPAL" 1861719 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-779 1857238 1858029 1858893 "ODEPACK" 1860232 T ODEPACK (NIL) -7 NIL NIL) (-778 1856271 1856378 1856607 "ODEINT" 1857127 NIL ODEINT (NIL T T) -7 NIL NIL) (-777 1850372 1851797 1853244 "ODEIFTBL" 1854844 T ODEIFTBL (NIL) -8 NIL NIL) (-776 1845707 1846493 1847452 "ODEEF" 1849531 NIL ODEEF (NIL T T) -7 NIL NIL) (-775 1845042 1845131 1845361 "ODECONST" 1845612 NIL ODECONST (NIL T T T) -7 NIL NIL) (-774 1843193 1843828 1843856 "ODECAT" 1844461 T ODECAT (NIL) -9 NIL 1844992) (-773 1840100 1842905 1843024 "OCT" 1843106 NIL OCT (NIL T) -8 NIL NIL) (-772 1839738 1839781 1839908 "OCTCT2" 1840051 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-771 1834599 1836999 1837039 "OC" 1838136 NIL OC (NIL T) -9 NIL 1838994) (-770 1831826 1832574 1833564 "OC-" 1833658 NIL OC- (NIL T T) -8 NIL NIL) (-769 1831204 1831646 1831674 "OCAMON" 1831679 T OCAMON (NIL) -9 NIL 1831700) (-768 1830761 1831076 1831104 "OASGP" 1831109 T OASGP (NIL) -9 NIL 1831129) (-767 1830048 1830511 1830539 "OAMONS" 1830579 T OAMONS (NIL) -9 NIL 1830622) (-766 1829488 1829895 1829923 "OAMON" 1829928 T OAMON (NIL) -9 NIL 1829948) (-765 1828792 1829284 1829312 "OAGROUP" 1829317 T OAGROUP (NIL) -9 NIL 1829337) (-764 1828482 1828532 1828620 "NUMTUBE" 1828736 NIL NUMTUBE (NIL T) -7 NIL NIL) (-763 1822055 1823573 1825109 "NUMQUAD" 1826966 T NUMQUAD (NIL) -7 NIL NIL) (-762 1817811 1818799 1819824 "NUMODE" 1821050 T NUMODE (NIL) -7 NIL NIL) (-761 1815192 1816046 1816074 "NUMINT" 1816997 T NUMINT (NIL) -9 NIL 1817761) (-760 1814140 1814337 1814555 "NUMFMT" 1814994 T NUMFMT (NIL) -7 NIL NIL) (-759 1800499 1803444 1805976 "NUMERIC" 1811647 NIL NUMERIC (NIL T) -7 NIL NIL) (-758 1794896 1799948 1800043 "NTSCAT" 1800048 NIL NTSCAT (NIL T T T T) -9 NIL 1800087) (-757 1794090 1794255 1794448 "NTPOLFN" 1794735 NIL NTPOLFN (NIL T) -7 NIL NIL) (-756 1781930 1790915 1791727 "NSUP" 1793311 NIL NSUP (NIL T) -8 NIL NIL) (-755 1781562 1781619 1781728 "NSUP2" 1781867 NIL NSUP2 (NIL T T) -7 NIL NIL) (-754 1771559 1781336 1781469 "NSMP" 1781474 NIL NSMP (NIL T T) -8 NIL NIL) (-753 1769991 1770292 1770649 "NREP" 1771247 NIL NREP (NIL T) -7 NIL NIL) (-752 1768582 1768834 1769192 "NPCOEF" 1769734 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-751 1767648 1767763 1767979 "NORMRETR" 1768463 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-750 1765689 1765979 1766388 "NORMPK" 1767356 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-749 1765374 1765402 1765526 "NORMMA" 1765655 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-748 1765201 1765331 1765360 "NONE" 1765365 T NONE (NIL) -8 NIL NIL) (-747 1764990 1765019 1765088 "NONE1" 1765165 NIL NONE1 (NIL T) -7 NIL NIL) (-746 1764473 1764535 1764721 "NODE1" 1764922 NIL NODE1 (NIL T T) -7 NIL NIL) (-745 1762813 1763636 1763891 "NNI" 1764238 T NNI (NIL) -8 NIL NIL) (-744 1761233 1761546 1761910 "NLINSOL" 1762481 NIL NLINSOL (NIL T) -7 NIL NIL) (-743 1757400 1758368 1759290 "NIPROB" 1760331 T NIPROB (NIL) -8 NIL NIL) (-742 1756157 1756391 1756693 "NFINTBAS" 1757162 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-741 1754865 1755096 1755377 "NCODIV" 1755925 NIL NCODIV (NIL T T) -7 NIL NIL) (-740 1754627 1754664 1754739 "NCNTFRAC" 1754822 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-739 1752807 1753171 1753591 "NCEP" 1754252 NIL NCEP (NIL T) -7 NIL NIL) (-738 1751718 1752457 1752485 "NASRING" 1752595 T NASRING (NIL) -9 NIL 1752669) (-737 1751513 1751557 1751651 "NASRING-" 1751656 NIL NASRING- (NIL T) -8 NIL NIL) (-736 1750666 1751165 1751193 "NARNG" 1751310 T NARNG (NIL) -9 NIL 1751401) (-735 1750358 1750425 1750559 "NARNG-" 1750564 NIL NARNG- (NIL T) -8 NIL NIL) (-734 1749237 1749444 1749679 "NAGSP" 1750143 T NAGSP (NIL) -7 NIL NIL) (-733 1740509 1742193 1743866 "NAGS" 1747584 T NAGS (NIL) -7 NIL NIL) (-732 1739057 1739365 1739696 "NAGF07" 1740198 T NAGF07 (NIL) -7 NIL NIL) (-731 1733595 1734886 1736193 "NAGF04" 1737770 T NAGF04 (NIL) -7 NIL NIL) (-730 1726563 1728177 1729810 "NAGF02" 1731982 T NAGF02 (NIL) -7 NIL NIL) (-729 1721787 1722887 1724004 "NAGF01" 1725466 T NAGF01 (NIL) -7 NIL NIL) (-728 1715415 1716981 1718566 "NAGE04" 1720222 T NAGE04 (NIL) -7 NIL NIL) (-727 1706584 1708705 1710835 "NAGE02" 1713305 T NAGE02 (NIL) -7 NIL NIL) (-726 1702537 1703484 1704448 "NAGE01" 1705640 T NAGE01 (NIL) -7 NIL NIL) (-725 1700332 1700866 1701424 "NAGD03" 1701999 T NAGD03 (NIL) -7 NIL NIL) (-724 1692082 1694010 1695964 "NAGD02" 1698398 T NAGD02 (NIL) -7 NIL NIL) (-723 1685893 1687318 1688758 "NAGD01" 1690662 T NAGD01 (NIL) -7 NIL NIL) (-722 1682102 1682924 1683761 "NAGC06" 1685076 T NAGC06 (NIL) -7 NIL NIL) (-721 1680567 1680899 1681255 "NAGC05" 1681766 T NAGC05 (NIL) -7 NIL NIL) (-720 1679943 1680062 1680206 "NAGC02" 1680443 T NAGC02 (NIL) -7 NIL NIL) (-719 1679003 1679560 1679600 "NAALG" 1679679 NIL NAALG (NIL T) -9 NIL 1679740) (-718 1678838 1678867 1678957 "NAALG-" 1678962 NIL NAALG- (NIL T T) -8 NIL NIL) (-717 1672788 1673896 1675083 "MULTSQFR" 1677734 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-716 1672107 1672182 1672366 "MULTFACT" 1672700 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-715 1665330 1669195 1669248 "MTSCAT" 1670318 NIL MTSCAT (NIL T T) -9 NIL 1670832) (-714 1665042 1665096 1665188 "MTHING" 1665270 NIL MTHING (NIL T) -7 NIL NIL) (-713 1664834 1664867 1664927 "MSYSCMD" 1665002 T MSYSCMD (NIL) -7 NIL NIL) (-712 1660946 1663589 1663909 "MSET" 1664547 NIL MSET (NIL T) -8 NIL NIL) (-711 1658041 1660507 1660548 "MSETAGG" 1660553 NIL MSETAGG (NIL T) -9 NIL 1660587) (-710 1653924 1655420 1656165 "MRING" 1657341 NIL MRING (NIL T T) -8 NIL NIL) (-709 1653490 1653557 1653688 "MRF2" 1653851 NIL MRF2 (NIL T T T) -7 NIL NIL) (-708 1653108 1653143 1653287 "MRATFAC" 1653449 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-707 1650720 1651015 1651446 "MPRFF" 1652813 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-706 1644780 1650574 1650671 "MPOLY" 1650676 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-705 1644270 1644305 1644513 "MPCPF" 1644739 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-704 1643784 1643827 1644011 "MPC3" 1644221 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-703 1642979 1643060 1643281 "MPC2" 1643699 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-702 1641280 1641617 1642007 "MONOTOOL" 1642639 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-701 1640531 1640822 1640850 "MONOID" 1641069 T MONOID (NIL) -9 NIL 1641216) (-700 1640077 1640196 1640377 "MONOID-" 1640382 NIL MONOID- (NIL T) -8 NIL NIL) (-699 1631127 1637033 1637092 "MONOGEN" 1637766 NIL MONOGEN (NIL T T) -9 NIL 1638222) (-698 1628345 1629080 1630080 "MONOGEN-" 1630199 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-697 1627204 1627624 1627652 "MONADWU" 1628044 T MONADWU (NIL) -9 NIL 1628282) (-696 1626576 1626735 1626983 "MONADWU-" 1626988 NIL MONADWU- (NIL T) -8 NIL NIL) (-695 1625961 1626179 1626207 "MONAD" 1626414 T MONAD (NIL) -9 NIL 1626526) (-694 1625646 1625724 1625856 "MONAD-" 1625861 NIL MONAD- (NIL T) -8 NIL NIL) (-693 1623962 1624559 1624838 "MOEBIUS" 1625399 NIL MOEBIUS (NIL T) -8 NIL NIL) (-692 1623354 1623732 1623772 "MODULE" 1623777 NIL MODULE (NIL T) -9 NIL 1623803) (-691 1622922 1623018 1623208 "MODULE-" 1623213 NIL MODULE- (NIL T T) -8 NIL NIL) (-690 1620637 1621286 1621613 "MODRING" 1622746 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-689 1617623 1618742 1619263 "MODOP" 1620166 NIL MODOP (NIL T T) -8 NIL NIL) (-688 1615810 1616262 1616603 "MODMONOM" 1617422 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-687 1605518 1614002 1614425 "MODMON" 1615438 NIL MODMON (NIL T T) -8 NIL NIL) (-686 1602709 1604362 1604638 "MODFIELD" 1605393 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-685 1601713 1601990 1602180 "MMLFORM" 1602539 T MMLFORM (NIL) -8 NIL NIL) (-684 1601239 1601282 1601461 "MMAP" 1601664 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-683 1599508 1600241 1600282 "MLO" 1600705 NIL MLO (NIL T) -9 NIL 1600947) (-682 1596875 1597390 1597992 "MLIFT" 1598989 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-681 1596266 1596350 1596504 "MKUCFUNC" 1596786 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-680 1595865 1595935 1596058 "MKRECORD" 1596189 NIL MKRECORD (NIL T T) -7 NIL NIL) (-679 1594913 1595074 1595302 "MKFUNC" 1595676 NIL MKFUNC (NIL T) -7 NIL NIL) (-678 1594301 1594405 1594561 "MKFLCFN" 1594796 NIL MKFLCFN (NIL T) -7 NIL NIL) (-677 1593727 1594094 1594183 "MKCHSET" 1594245 NIL MKCHSET (NIL T) -8 NIL NIL) (-676 1593004 1593106 1593291 "MKBCFUNC" 1593620 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-675 1589746 1592558 1592694 "MINT" 1592888 T MINT (NIL) -8 NIL NIL) (-674 1588558 1588801 1589078 "MHROWRED" 1589501 NIL MHROWRED (NIL T) -7 NIL NIL) (-673 1583890 1586999 1587425 "MFLOAT" 1588152 T MFLOAT (NIL) -8 NIL NIL) (-672 1583247 1583323 1583494 "MFINFACT" 1583802 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-671 1579562 1580410 1581294 "MESH" 1582383 T MESH (NIL) -7 NIL NIL) (-670 1577952 1578264 1578617 "MDDFACT" 1579249 NIL MDDFACT (NIL T) -7 NIL NIL) (-669 1574794 1577111 1577152 "MDAGG" 1577407 NIL MDAGG (NIL T) -9 NIL 1577550) (-668 1564574 1574087 1574294 "MCMPLX" 1574607 T MCMPLX (NIL) -8 NIL NIL) (-667 1563715 1563861 1564061 "MCDEN" 1564423 NIL MCDEN (NIL T T) -7 NIL NIL) (-666 1561605 1561875 1562255 "MCALCFN" 1563445 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-665 1560516 1560689 1560930 "MAYBE" 1561403 NIL MAYBE (NIL T) -8 NIL NIL) (-664 1558128 1558651 1559213 "MATSTOR" 1559987 NIL MATSTOR (NIL T) -7 NIL NIL) (-663 1554134 1557500 1557748 "MATRIX" 1557913 NIL MATRIX (NIL T) -8 NIL NIL) (-662 1549903 1550607 1551343 "MATLIN" 1553491 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-661 1540057 1543195 1543272 "MATCAT" 1548152 NIL MATCAT (NIL T T T) -9 NIL 1549569) (-660 1536421 1537434 1538790 "MATCAT-" 1538795 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-659 1535015 1535168 1535501 "MATCAT2" 1536256 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-658 1533127 1533451 1533835 "MAPPKG3" 1534690 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-657 1532108 1532281 1532503 "MAPPKG2" 1532951 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-656 1530607 1530891 1531218 "MAPPKG1" 1531814 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-655 1529730 1530013 1530190 "MAPPAST" 1530450 T MAPPAST (NIL) -8 NIL NIL) (-654 1529341 1529399 1529522 "MAPHACK3" 1529666 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-653 1528933 1528994 1529108 "MAPHACK2" 1529273 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-652 1528371 1528474 1528616 "MAPHACK1" 1528824 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-651 1526477 1527071 1527375 "MAGMA" 1528099 NIL MAGMA (NIL T) -8 NIL NIL) (-650 1525972 1526180 1526278 "MACROAST" 1526399 T MACROAST (NIL) -8 NIL NIL) (-649 1522439 1524211 1524672 "M3D" 1525544 NIL M3D (NIL T) -8 NIL NIL) (-648 1516594 1520809 1520850 "LZSTAGG" 1521632 NIL LZSTAGG (NIL T) -9 NIL 1521927) (-647 1512567 1513725 1515182 "LZSTAGG-" 1515187 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-646 1509681 1510458 1510945 "LWORD" 1512112 NIL LWORD (NIL T) -8 NIL NIL) (-645 1509301 1509485 1509560 "LSTAST" 1509626 T LSTAST (NIL) -8 NIL NIL) (-644 1502502 1509072 1509206 "LSQM" 1509211 NIL LSQM (NIL NIL T) -8 NIL NIL) (-643 1501726 1501865 1502093 "LSPP" 1502357 NIL LSPP (NIL T T T T) -7 NIL NIL) (-642 1499538 1499839 1500295 "LSMP" 1501415 NIL LSMP (NIL T T T T) -7 NIL NIL) (-641 1496317 1496991 1497721 "LSMP1" 1498840 NIL LSMP1 (NIL T) -7 NIL NIL) (-640 1490243 1495485 1495526 "LSAGG" 1495588 NIL LSAGG (NIL T) -9 NIL 1495666) (-639 1486938 1487862 1489075 "LSAGG-" 1489080 NIL LSAGG- (NIL T T) -8 NIL NIL) (-638 1484564 1486082 1486331 "LPOLY" 1486733 NIL LPOLY (NIL T T) -8 NIL NIL) (-637 1484146 1484231 1484354 "LPEFRAC" 1484473 NIL LPEFRAC (NIL T) -7 NIL NIL) (-636 1482493 1483240 1483493 "LO" 1483978 NIL LO (NIL T T T) -8 NIL NIL) (-635 1482145 1482257 1482285 "LOGIC" 1482396 T LOGIC (NIL) -9 NIL 1482477) (-634 1482007 1482030 1482101 "LOGIC-" 1482106 NIL LOGIC- (NIL T) -8 NIL NIL) (-633 1481200 1481340 1481533 "LODOOPS" 1481863 NIL LODOOPS (NIL T T) -7 NIL NIL) (-632 1478658 1481116 1481182 "LODO" 1481187 NIL LODO (NIL T NIL) -8 NIL NIL) (-631 1477196 1477431 1477784 "LODOF" 1478405 NIL LODOF (NIL T T) -7 NIL NIL) (-630 1473639 1476036 1476077 "LODOCAT" 1476515 NIL LODOCAT (NIL T) -9 NIL 1476726) (-629 1473372 1473430 1473557 "LODOCAT-" 1473562 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-628 1470727 1473213 1473331 "LODO2" 1473336 NIL LODO2 (NIL T T) -8 NIL NIL) (-627 1468197 1470664 1470709 "LODO1" 1470714 NIL LODO1 (NIL T) -8 NIL NIL) (-626 1467057 1467222 1467534 "LODEEF" 1468020 NIL LODEEF (NIL T T T) -7 NIL NIL) (-625 1462343 1465187 1465228 "LNAGG" 1466175 NIL LNAGG (NIL T) -9 NIL 1466619) (-624 1461490 1461704 1462046 "LNAGG-" 1462051 NIL LNAGG- (NIL T T) -8 NIL NIL) (-623 1457653 1458415 1459054 "LMOPS" 1460905 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-622 1457048 1457410 1457451 "LMODULE" 1457512 NIL LMODULE (NIL T) -9 NIL 1457554) (-621 1454294 1456693 1456816 "LMDICT" 1456958 NIL LMDICT (NIL T) -8 NIL NIL) (-620 1454038 1454202 1454262 "LITERAL" 1454267 NIL LITERAL (NIL T) -8 NIL NIL) (-619 1447265 1452984 1453282 "LIST" 1453773 NIL LIST (NIL T) -8 NIL NIL) (-618 1446790 1446864 1447003 "LIST3" 1447185 NIL LIST3 (NIL T T T) -7 NIL NIL) (-617 1445797 1445975 1446203 "LIST2" 1446608 NIL LIST2 (NIL T T) -7 NIL NIL) (-616 1443931 1444243 1444642 "LIST2MAP" 1445444 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-615 1442681 1443317 1443358 "LINEXP" 1443613 NIL LINEXP (NIL T) -9 NIL 1443762) (-614 1441328 1441588 1441885 "LINDEP" 1442433 NIL LINDEP (NIL T T) -7 NIL NIL) (-613 1438095 1438814 1439591 "LIMITRF" 1440583 NIL LIMITRF (NIL T) -7 NIL NIL) (-612 1436371 1436666 1437082 "LIMITPS" 1437790 NIL LIMITPS (NIL T T) -7 NIL NIL) (-611 1430826 1435882 1436110 "LIE" 1436192 NIL LIE (NIL T T) -8 NIL NIL) (-610 1429875 1430318 1430358 "LIECAT" 1430498 NIL LIECAT (NIL T) -9 NIL 1430649) (-609 1429716 1429743 1429831 "LIECAT-" 1429836 NIL LIECAT- (NIL T T) -8 NIL NIL) (-608 1422328 1429165 1429330 "LIB" 1429571 T LIB (NIL) -8 NIL NIL) (-607 1417965 1418846 1419781 "LGROBP" 1421445 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-606 1415831 1416105 1416467 "LF" 1417686 NIL LF (NIL T T) -7 NIL NIL) (-605 1414671 1415363 1415391 "LFCAT" 1415598 T LFCAT (NIL) -9 NIL 1415737) (-604 1411575 1412203 1412891 "LEXTRIPK" 1414035 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-603 1408346 1409145 1409648 "LEXP" 1411155 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-602 1407866 1408067 1408159 "LETAST" 1408274 T LETAST (NIL) -8 NIL NIL) (-601 1406264 1406577 1406978 "LEADCDET" 1407548 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-600 1405454 1405528 1405757 "LAZM3PK" 1406185 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-599 1400410 1403531 1404069 "LAUPOL" 1404966 NIL LAUPOL (NIL T T) -8 NIL NIL) (-598 1399975 1400019 1400187 "LAPLACE" 1400360 NIL LAPLACE (NIL T T) -7 NIL NIL) (-597 1397949 1399076 1399327 "LA" 1399808 NIL LA (NIL T T T) -8 NIL NIL) (-596 1397050 1397600 1397641 "LALG" 1397703 NIL LALG (NIL T) -9 NIL 1397762) (-595 1396764 1396823 1396959 "LALG-" 1396964 NIL LALG- (NIL T T) -8 NIL NIL) (-594 1395564 1395981 1396210 "KTVLOGIC" 1396555 T KTVLOGIC (NIL) -8 NIL NIL) (-593 1394468 1394655 1394954 "KOVACIC" 1395364 NIL KOVACIC (NIL T T) -7 NIL NIL) (-592 1394303 1394327 1394368 "KONVERT" 1394430 NIL KONVERT (NIL T) -9 NIL NIL) (-591 1394138 1394162 1394203 "KOERCE" 1394265 NIL KOERCE (NIL T) -9 NIL NIL) (-590 1391872 1392632 1393025 "KERNEL" 1393777 NIL KERNEL (NIL T) -8 NIL NIL) (-589 1391374 1391455 1391585 "KERNEL2" 1391786 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-588 1385225 1389913 1389967 "KDAGG" 1390344 NIL KDAGG (NIL T T) -9 NIL 1390550) (-587 1384754 1384878 1385083 "KDAGG-" 1385088 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-586 1377929 1384415 1384570 "KAFILE" 1384632 NIL KAFILE (NIL T) -8 NIL NIL) (-585 1372384 1377440 1377668 "JORDAN" 1377750 NIL JORDAN (NIL T T) -8 NIL NIL) (-584 1371808 1372033 1372154 "JOINAST" 1372283 T JOINAST (NIL) -8 NIL NIL) (-583 1371537 1371596 1371683 "JAVACODE" 1371741 T JAVACODE (NIL) -8 NIL NIL) (-582 1367836 1369742 1369796 "IXAGG" 1370725 NIL IXAGG (NIL T T) -9 NIL 1371184) (-581 1366755 1367061 1367480 "IXAGG-" 1367485 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-580 1362335 1366677 1366736 "IVECTOR" 1366741 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-579 1361101 1361338 1361604 "ITUPLE" 1362102 NIL ITUPLE (NIL T) -8 NIL NIL) (-578 1359537 1359714 1360020 "ITRIGMNP" 1360923 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-577 1358282 1358486 1358769 "ITFUN3" 1359313 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-576 1357914 1357971 1358080 "ITFUN2" 1358219 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-575 1355751 1356776 1357075 "ITAYLOR" 1357648 NIL ITAYLOR (NIL T) -8 NIL NIL) (-574 1344745 1349897 1351057 "ISUPS" 1354624 NIL ISUPS (NIL T) -8 NIL NIL) (-573 1343849 1343989 1344225 "ISUMP" 1344592 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-572 1339113 1343650 1343729 "ISTRING" 1343802 NIL ISTRING (NIL NIL) -8 NIL NIL) (-571 1338633 1338834 1338926 "ISAST" 1339041 T ISAST (NIL) -8 NIL NIL) (-570 1337843 1337924 1338140 "IRURPK" 1338547 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-569 1336779 1336980 1337220 "IRSN" 1337623 T IRSN (NIL) -7 NIL NIL) (-568 1334808 1335163 1335599 "IRRF2F" 1336417 NIL IRRF2F (NIL T) -7 NIL NIL) (-567 1334555 1334593 1334669 "IRREDFFX" 1334764 NIL IRREDFFX (NIL T) -7 NIL NIL) (-566 1333170 1333429 1333728 "IROOT" 1334288 NIL IROOT (NIL T) -7 NIL NIL) (-565 1329802 1330854 1331546 "IR" 1332510 NIL IR (NIL T) -8 NIL NIL) (-564 1327415 1327910 1328476 "IR2" 1329280 NIL IR2 (NIL T T) -7 NIL NIL) (-563 1326487 1326600 1326821 "IR2F" 1327298 NIL IR2F (NIL T T) -7 NIL NIL) (-562 1326278 1326312 1326372 "IPRNTPK" 1326447 T IPRNTPK (NIL) -7 NIL NIL) (-561 1322897 1326167 1326236 "IPF" 1326241 NIL IPF (NIL NIL) -8 NIL NIL) (-560 1321260 1322822 1322879 "IPADIC" 1322884 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-559 1321024 1321164 1321192 "IOBCON" 1321197 T IOBCON (NIL) -9 NIL 1321218) (-558 1320521 1320579 1320769 "INVLAPLA" 1320960 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-557 1310170 1312523 1314909 "INTTR" 1318185 NIL INTTR (NIL T T) -7 NIL NIL) (-556 1306514 1307256 1308120 "INTTOOLS" 1309355 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-555 1306100 1306191 1306308 "INTSLPE" 1306417 T INTSLPE (NIL) -7 NIL NIL) (-554 1304095 1306023 1306082 "INTRVL" 1306087 NIL INTRVL (NIL T) -8 NIL NIL) (-553 1301697 1302209 1302784 "INTRF" 1303580 NIL INTRF (NIL T) -7 NIL NIL) (-552 1301108 1301205 1301347 "INTRET" 1301595 NIL INTRET (NIL T) -7 NIL NIL) (-551 1299105 1299494 1299964 "INTRAT" 1300716 NIL INTRAT (NIL T T) -7 NIL NIL) (-550 1296333 1296916 1297542 "INTPM" 1298590 NIL INTPM (NIL T T) -7 NIL NIL) (-549 1293036 1293635 1294380 "INTPAF" 1295719 NIL INTPAF (NIL T T T) -7 NIL NIL) (-548 1288215 1289177 1290228 "INTPACK" 1292005 T INTPACK (NIL) -7 NIL NIL) (-547 1285127 1287944 1288071 "INT" 1288108 T INT (NIL) -8 NIL NIL) (-546 1284379 1284531 1284739 "INTHERTR" 1284969 NIL INTHERTR (NIL T T) -7 NIL NIL) (-545 1283818 1283898 1284086 "INTHERAL" 1284293 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-544 1281664 1282107 1282564 "INTHEORY" 1283381 T INTHEORY (NIL) -7 NIL NIL) (-543 1272972 1274593 1276372 "INTG0" 1280016 NIL INTG0 (NIL T T T) -7 NIL NIL) (-542 1253545 1258335 1263145 "INTFTBL" 1268182 T INTFTBL (NIL) -8 NIL NIL) (-541 1252794 1252932 1253105 "INTFACT" 1253404 NIL INTFACT (NIL T) -7 NIL NIL) (-540 1250179 1250625 1251189 "INTEF" 1252348 NIL INTEF (NIL T T) -7 NIL NIL) (-539 1248681 1249386 1249414 "INTDOM" 1249715 T INTDOM (NIL) -9 NIL 1249922) (-538 1248050 1248224 1248466 "INTDOM-" 1248471 NIL INTDOM- (NIL T) -8 NIL NIL) (-537 1244583 1246469 1246523 "INTCAT" 1247322 NIL INTCAT (NIL T) -9 NIL 1247642) (-536 1244056 1244158 1244286 "INTBIT" 1244475 T INTBIT (NIL) -7 NIL NIL) (-535 1242727 1242881 1243195 "INTALG" 1243901 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-534 1242184 1242274 1242444 "INTAF" 1242631 NIL INTAF (NIL T T) -7 NIL NIL) (-533 1235638 1241994 1242134 "INTABL" 1242139 NIL INTABL (NIL T T T) -8 NIL NIL) (-532 1230693 1233364 1233392 "INS" 1234326 T INS (NIL) -9 NIL 1234990) (-531 1227933 1228704 1229678 "INS-" 1229751 NIL INS- (NIL T) -8 NIL NIL) (-530 1226708 1226935 1227233 "INPSIGN" 1227686 NIL INPSIGN (NIL T T) -7 NIL NIL) (-529 1225826 1225943 1226140 "INPRODPF" 1226588 NIL INPRODPF (NIL T T) -7 NIL NIL) (-528 1224720 1224837 1225074 "INPRODFF" 1225706 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-527 1223720 1223872 1224132 "INNMFACT" 1224556 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-526 1222917 1223014 1223202 "INMODGCD" 1223619 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-525 1221426 1221670 1221994 "INFSP" 1222662 NIL INFSP (NIL T T T) -7 NIL NIL) (-524 1220610 1220727 1220910 "INFPROD0" 1221306 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-523 1217492 1218675 1219190 "INFORM" 1220103 T INFORM (NIL) -8 NIL NIL) (-522 1217102 1217162 1217260 "INFORM1" 1217427 NIL INFORM1 (NIL T) -7 NIL NIL) (-521 1216625 1216714 1216828 "INFINITY" 1217008 T INFINITY (NIL) -7 NIL NIL) (-520 1215242 1215491 1215812 "INEP" 1216373 NIL INEP (NIL T T T) -7 NIL NIL) (-519 1214518 1215139 1215204 "INDE" 1215209 NIL INDE (NIL T) -8 NIL NIL) (-518 1214082 1214150 1214267 "INCRMAPS" 1214445 NIL INCRMAPS (NIL T) -7 NIL NIL) (-517 1209393 1210318 1211262 "INBFF" 1213170 NIL INBFF (NIL T) -7 NIL NIL) (-516 1209062 1209138 1209166 "INBCON" 1209299 T INBCON (NIL) -9 NIL 1209377) (-515 1208902 1208937 1209013 "INBCON-" 1209018 NIL INBCON- (NIL T) -8 NIL NIL) (-514 1208421 1208623 1208715 "INAST" 1208830 T INAST (NIL) -8 NIL NIL) (-513 1207892 1208100 1208206 "IMPTAST" 1208335 T IMPTAST (NIL) -8 NIL NIL) (-512 1204386 1207736 1207840 "IMATRIX" 1207845 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-511 1203098 1203221 1203536 "IMATQF" 1204242 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-510 1201318 1201545 1201882 "IMATLIN" 1202854 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-509 1195944 1201242 1201300 "ILIST" 1201305 NIL ILIST (NIL T NIL) -8 NIL NIL) (-508 1193897 1195804 1195917 "IIARRAY2" 1195922 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-507 1189330 1193808 1193872 "IFF" 1193877 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-506 1188721 1188947 1189063 "IFAST" 1189234 T IFAST (NIL) -8 NIL NIL) (-505 1183764 1188013 1188201 "IFARRAY" 1188578 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-504 1182971 1183668 1183741 "IFAMON" 1183746 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-503 1182555 1182620 1182674 "IEVALAB" 1182881 NIL IEVALAB (NIL T T) -9 NIL NIL) (-502 1182230 1182298 1182458 "IEVALAB-" 1182463 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-501 1181888 1182144 1182207 "IDPO" 1182212 NIL IDPO (NIL T T) -8 NIL NIL) (-500 1181165 1181777 1181852 "IDPOAMS" 1181857 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-499 1180499 1181054 1181129 "IDPOAM" 1181134 NIL IDPOAM (NIL T T) -8 NIL NIL) (-498 1179584 1179834 1179887 "IDPC" 1180300 NIL IDPC (NIL T T) -9 NIL 1180449) (-497 1179080 1179476 1179549 "IDPAM" 1179554 NIL IDPAM (NIL T T) -8 NIL NIL) (-496 1178483 1178972 1179045 "IDPAG" 1179050 NIL IDPAG (NIL T T) -8 NIL NIL) (-495 1178231 1178398 1178448 "IDENT" 1178453 T IDENT (NIL) -8 NIL NIL) (-494 1174486 1175334 1176229 "IDECOMP" 1177388 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-493 1167359 1168409 1169456 "IDEAL" 1173522 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-492 1166523 1166635 1166834 "ICDEN" 1167243 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-491 1165622 1166003 1166150 "ICARD" 1166396 T ICARD (NIL) -8 NIL NIL) (-490 1163682 1163995 1164400 "IBPTOOLS" 1165299 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-489 1159316 1163302 1163415 "IBITS" 1163601 NIL IBITS (NIL NIL) -8 NIL NIL) (-488 1156039 1156615 1157310 "IBATOOL" 1158733 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-487 1153819 1154280 1154813 "IBACHIN" 1155574 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-486 1151696 1153665 1153768 "IARRAY2" 1153773 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-485 1147849 1151622 1151679 "IARRAY1" 1151684 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-484 1141844 1146263 1146743 "IAN" 1147389 T IAN (NIL) -8 NIL NIL) (-483 1141355 1141412 1141585 "IALGFACT" 1141781 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-482 1140883 1140996 1141024 "HYPCAT" 1141231 T HYPCAT (NIL) -9 NIL NIL) (-481 1140421 1140538 1140724 "HYPCAT-" 1140729 NIL HYPCAT- (NIL T) -8 NIL NIL) (-480 1140043 1140216 1140299 "HOSTNAME" 1140358 T HOSTNAME (NIL) -8 NIL NIL) (-479 1136722 1138053 1138094 "HOAGG" 1139075 NIL HOAGG (NIL T) -9 NIL 1139754) (-478 1135316 1135715 1136241 "HOAGG-" 1136246 NIL HOAGG- (NIL T T) -8 NIL NIL) (-477 1129204 1134757 1134923 "HEXADEC" 1135170 T HEXADEC (NIL) -8 NIL NIL) (-476 1127952 1128174 1128437 "HEUGCD" 1128981 NIL HEUGCD (NIL T) -7 NIL NIL) (-475 1127055 1127789 1127919 "HELLFDIV" 1127924 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-474 1125283 1126832 1126920 "HEAP" 1126999 NIL HEAP (NIL T) -8 NIL NIL) (-473 1124591 1124835 1124969 "HEADAST" 1125169 T HEADAST (NIL) -8 NIL NIL) (-472 1118511 1124506 1124568 "HDP" 1124573 NIL HDP (NIL NIL T) -8 NIL NIL) (-471 1112262 1118146 1118298 "HDMP" 1118412 NIL HDMP (NIL NIL T) -8 NIL NIL) (-470 1111587 1111726 1111890 "HB" 1112118 T HB (NIL) -7 NIL NIL) (-469 1105084 1111433 1111537 "HASHTBL" 1111542 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-468 1104604 1104805 1104897 "HASAST" 1105012 T HASAST (NIL) -8 NIL NIL) (-467 1102418 1104228 1104409 "HACKPI" 1104443 T HACKPI (NIL) -8 NIL NIL) (-466 1098113 1102271 1102384 "GTSET" 1102389 NIL GTSET (NIL T T T T) -8 NIL NIL) (-465 1091639 1097991 1098089 "GSTBL" 1098094 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-464 1083952 1090670 1090935 "GSERIES" 1091430 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-463 1083119 1083510 1083538 "GROUP" 1083741 T GROUP (NIL) -9 NIL 1083875) (-462 1082485 1082644 1082895 "GROUP-" 1082900 NIL GROUP- (NIL T) -8 NIL NIL) (-461 1080854 1081173 1081560 "GROEBSOL" 1082162 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-460 1079794 1080056 1080107 "GRMOD" 1080636 NIL GRMOD (NIL T T) -9 NIL 1080804) (-459 1079562 1079598 1079726 "GRMOD-" 1079731 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-458 1074887 1075916 1076916 "GRIMAGE" 1078582 T GRIMAGE (NIL) -8 NIL NIL) (-457 1073354 1073614 1073938 "GRDEF" 1074583 T GRDEF (NIL) -7 NIL NIL) (-456 1072798 1072914 1073055 "GRAY" 1073233 T GRAY (NIL) -7 NIL NIL) (-455 1072029 1072409 1072460 "GRALG" 1072613 NIL GRALG (NIL T T) -9 NIL 1072706) (-454 1071690 1071763 1071926 "GRALG-" 1071931 NIL GRALG- (NIL T T T) -8 NIL NIL) (-453 1068494 1071275 1071453 "GPOLSET" 1071597 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-452 1067848 1067905 1068163 "GOSPER" 1068431 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-451 1063607 1064286 1064812 "GMODPOL" 1067547 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-450 1062612 1062796 1063034 "GHENSEL" 1063419 NIL GHENSEL (NIL T T) -7 NIL NIL) (-449 1056663 1057506 1058533 "GENUPS" 1061696 NIL GENUPS (NIL T T) -7 NIL NIL) (-448 1056360 1056411 1056500 "GENUFACT" 1056606 NIL GENUFACT (NIL T) -7 NIL NIL) (-447 1055772 1055849 1056014 "GENPGCD" 1056278 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-446 1055246 1055281 1055494 "GENMFACT" 1055731 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-445 1053814 1054069 1054376 "GENEEZ" 1054989 NIL GENEEZ (NIL T T) -7 NIL NIL) (-444 1047727 1053425 1053587 "GDMP" 1053737 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-443 1037104 1041498 1042604 "GCNAALG" 1046710 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-442 1035566 1036394 1036422 "GCDDOM" 1036677 T GCDDOM (NIL) -9 NIL 1036834) (-441 1035036 1035163 1035378 "GCDDOM-" 1035383 NIL GCDDOM- (NIL T) -8 NIL NIL) (-440 1033708 1033893 1034197 "GB" 1034815 NIL GB (NIL T T T T) -7 NIL NIL) (-439 1022328 1024654 1027046 "GBINTERN" 1031399 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-438 1020165 1020457 1020878 "GBF" 1022003 NIL GBF (NIL T T T T) -7 NIL NIL) (-437 1018946 1019111 1019378 "GBEUCLID" 1019981 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-436 1018295 1018420 1018569 "GAUSSFAC" 1018817 T GAUSSFAC (NIL) -7 NIL NIL) (-435 1016662 1016964 1017278 "GALUTIL" 1018014 NIL GALUTIL (NIL T) -7 NIL NIL) (-434 1014970 1015244 1015568 "GALPOLYU" 1016389 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-433 1012335 1012625 1013032 "GALFACTU" 1014667 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-432 1004141 1005640 1007248 "GALFACT" 1010767 NIL GALFACT (NIL T) -7 NIL NIL) (-431 1001529 1002187 1002215 "FVFUN" 1003371 T FVFUN (NIL) -9 NIL 1004091) (-430 1000795 1000977 1001005 "FVC" 1001296 T FVC (NIL) -9 NIL 1001479) (-429 1000437 1000592 1000673 "FUNCTION" 1000747 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-428 998107 998658 999147 "FT" 999968 T FT (NIL) -8 NIL NIL) (-427 996925 997408 997611 "FTEM" 997924 T FTEM (NIL) -8 NIL NIL) (-426 995181 995470 995874 "FSUPFACT" 996616 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-425 993578 993867 994199 "FST" 994869 T FST (NIL) -8 NIL NIL) (-424 992749 992855 993050 "FSRED" 993460 NIL FSRED (NIL T T) -7 NIL NIL) (-423 991428 991683 992037 "FSPRMELT" 992464 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-422 988513 988951 989450 "FSPECF" 990991 NIL FSPECF (NIL T T) -7 NIL NIL) (-421 970955 979397 979437 "FS" 983285 NIL FS (NIL T) -9 NIL 985574) (-420 959605 962595 966651 "FS-" 966948 NIL FS- (NIL T T) -8 NIL NIL) (-419 959119 959173 959350 "FSINT" 959546 NIL FSINT (NIL T T) -7 NIL NIL) (-418 957446 958112 958415 "FSERIES" 958898 NIL FSERIES (NIL T T) -8 NIL NIL) (-417 956460 956576 956807 "FSCINT" 957326 NIL FSCINT (NIL T T) -7 NIL NIL) (-416 952694 955404 955445 "FSAGG" 955815 NIL FSAGG (NIL T) -9 NIL 956074) (-415 950456 951057 951853 "FSAGG-" 951948 NIL FSAGG- (NIL T T) -8 NIL NIL) (-414 949498 949641 949868 "FSAGG2" 950309 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-413 947153 947432 947986 "FS2UPS" 949216 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-412 946735 946778 946933 "FS2" 947104 NIL FS2 (NIL T T T T) -7 NIL NIL) (-411 945592 945763 946072 "FS2EXPXP" 946560 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-410 945018 945133 945285 "FRUTIL" 945472 NIL FRUTIL (NIL T) -7 NIL NIL) (-409 936479 940517 941873 "FR" 943694 NIL FR (NIL T) -8 NIL NIL) (-408 931554 934197 934237 "FRNAALG" 935633 NIL FRNAALG (NIL T) -9 NIL 936240) (-407 927232 928303 929578 "FRNAALG-" 930328 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-406 926870 926913 927040 "FRNAAF2" 927183 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-405 925277 925724 926019 "FRMOD" 926682 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-404 923056 923660 923977 "FRIDEAL" 925068 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-403 922251 922338 922627 "FRIDEAL2" 922963 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-402 921493 921907 921948 "FRETRCT" 921953 NIL FRETRCT (NIL T) -9 NIL 922129) (-401 920605 920836 921187 "FRETRCT-" 921192 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-400 917855 919031 919090 "FRAMALG" 919972 NIL FRAMALG (NIL T T) -9 NIL 920264) (-399 915989 916444 917074 "FRAMALG-" 917297 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-398 909949 915464 915740 "FRAC" 915745 NIL FRAC (NIL T) -8 NIL NIL) (-397 909585 909642 909749 "FRAC2" 909886 NIL FRAC2 (NIL T T) -7 NIL NIL) (-396 909221 909278 909385 "FR2" 909522 NIL FR2 (NIL T T) -7 NIL NIL) (-395 903951 906799 906827 "FPS" 907946 T FPS (NIL) -9 NIL 908503) (-394 903400 903509 903673 "FPS-" 903819 NIL FPS- (NIL T) -8 NIL NIL) (-393 900906 902541 902569 "FPC" 902794 T FPC (NIL) -9 NIL 902936) (-392 900699 900739 900836 "FPC-" 900841 NIL FPC- (NIL T) -8 NIL NIL) (-391 899577 900187 900228 "FPATMAB" 900233 NIL FPATMAB (NIL T) -9 NIL 900385) (-390 897277 897753 898179 "FPARFRAC" 899214 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-389 892670 893169 893851 "FORTRAN" 896709 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-388 890386 890886 891425 "FORT" 892151 T FORT (NIL) -7 NIL NIL) (-387 888062 888624 888652 "FORTFN" 889712 T FORTFN (NIL) -9 NIL 890336) (-386 887826 887876 887904 "FORTCAT" 887963 T FORTCAT (NIL) -9 NIL 888025) (-385 885886 886369 886768 "FORMULA" 887447 T FORMULA (NIL) -8 NIL NIL) (-384 885674 885704 885773 "FORMULA1" 885850 NIL FORMULA1 (NIL T) -7 NIL NIL) (-383 885197 885249 885422 "FORDER" 885616 NIL FORDER (NIL T T T T) -7 NIL NIL) (-382 884293 884457 884650 "FOP" 885024 T FOP (NIL) -7 NIL NIL) (-381 882901 883573 883747 "FNLA" 884175 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-380 881569 881958 881986 "FNCAT" 882558 T FNCAT (NIL) -9 NIL 882851) (-379 881135 881528 881556 "FNAME" 881561 T FNAME (NIL) -8 NIL NIL) (-378 879833 880762 880790 "FMTC" 880795 T FMTC (NIL) -9 NIL 880831) (-377 876195 877356 877985 "FMONOID" 879237 NIL FMONOID (NIL T) -8 NIL NIL) (-376 875414 875937 876086 "FM" 876091 NIL FM (NIL T T) -8 NIL NIL) (-375 872838 873484 873512 "FMFUN" 874656 T FMFUN (NIL) -9 NIL 875364) (-374 872107 872288 872316 "FMC" 872606 T FMC (NIL) -9 NIL 872788) (-373 869319 870153 870207 "FMCAT" 871402 NIL FMCAT (NIL T T) -9 NIL 871897) (-372 868212 869085 869185 "FM1" 869264 NIL FM1 (NIL T T) -8 NIL NIL) (-371 865986 866402 866896 "FLOATRP" 867763 NIL FLOATRP (NIL T) -7 NIL NIL) (-370 859537 863642 864272 "FLOAT" 865376 T FLOAT (NIL) -8 NIL NIL) (-369 856975 857475 858053 "FLOATCP" 859004 NIL FLOATCP (NIL T) -7 NIL NIL) (-368 855804 856608 856649 "FLINEXP" 856654 NIL FLINEXP (NIL T) -9 NIL 856747) (-367 854958 855193 855521 "FLINEXP-" 855526 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-366 854034 854178 854402 "FLASORT" 854810 NIL FLASORT (NIL T T) -7 NIL NIL) (-365 851251 852093 852145 "FLALG" 853372 NIL FLALG (NIL T T) -9 NIL 853839) (-364 845035 848737 848778 "FLAGG" 850040 NIL FLAGG (NIL T) -9 NIL 850692) (-363 843761 844100 844590 "FLAGG-" 844595 NIL FLAGG- (NIL T T) -8 NIL NIL) (-362 842803 842946 843173 "FLAGG2" 843614 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-361 839816 840790 840849 "FINRALG" 841977 NIL FINRALG (NIL T T) -9 NIL 842485) (-360 838976 839205 839544 "FINRALG-" 839549 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-359 838382 838595 838623 "FINITE" 838819 T FINITE (NIL) -9 NIL 838926) (-358 830840 833001 833041 "FINAALG" 836708 NIL FINAALG (NIL T) -9 NIL 838161) (-357 826181 827222 828366 "FINAALG-" 829745 NIL FINAALG- (NIL T T) -8 NIL NIL) (-356 825576 825936 826039 "FILE" 826111 NIL FILE (NIL T) -8 NIL NIL) (-355 824260 824572 824626 "FILECAT" 825310 NIL FILECAT (NIL T T) -9 NIL 825526) (-354 822180 823674 823702 "FIELD" 823742 T FIELD (NIL) -9 NIL 823822) (-353 820800 821185 821696 "FIELD-" 821701 NIL FIELD- (NIL T) -8 NIL NIL) (-352 818678 819435 819782 "FGROUP" 820486 NIL FGROUP (NIL T) -8 NIL NIL) (-351 817768 817932 818152 "FGLMICPK" 818510 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-350 813635 817693 817750 "FFX" 817755 NIL FFX (NIL T NIL) -8 NIL NIL) (-349 813236 813297 813432 "FFSLPE" 813568 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-348 809229 810008 810804 "FFPOLY" 812472 NIL FFPOLY (NIL T) -7 NIL NIL) (-347 808733 808769 808978 "FFPOLY2" 809187 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-346 804619 808652 808715 "FFP" 808720 NIL FFP (NIL T NIL) -8 NIL NIL) (-345 800052 804530 804594 "FF" 804599 NIL FF (NIL NIL NIL) -8 NIL NIL) (-344 795213 799395 799585 "FFNBX" 799906 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-343 790187 794348 794606 "FFNBP" 795067 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-342 784855 789471 789682 "FFNB" 790020 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-341 783687 783885 784200 "FFINTBAS" 784652 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-340 779971 782146 782174 "FFIELDC" 782794 T FFIELDC (NIL) -9 NIL 783170) (-339 778634 779004 779501 "FFIELDC-" 779506 NIL FFIELDC- (NIL T) -8 NIL NIL) (-338 778204 778249 778373 "FFHOM" 778576 NIL FFHOM (NIL T T T) -7 NIL NIL) (-337 775902 776386 776903 "FFF" 777719 NIL FFF (NIL T) -7 NIL NIL) (-336 771555 775644 775745 "FFCGX" 775845 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-335 767222 771287 771394 "FFCGP" 771498 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-334 762440 766949 767057 "FFCG" 767158 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-333 744498 753534 753620 "FFCAT" 758785 NIL FFCAT (NIL T T T) -9 NIL 760236) (-332 739696 740743 742057 "FFCAT-" 743287 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-331 739107 739150 739385 "FFCAT2" 739647 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-330 728319 732079 733299 "FEXPR" 737959 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-329 727319 727754 727795 "FEVALAB" 727879 NIL FEVALAB (NIL T) -9 NIL 728140) (-328 726478 726688 727026 "FEVALAB-" 727031 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-327 725071 725861 726064 "FDIV" 726377 NIL FDIV (NIL T T T T) -8 NIL NIL) (-326 722137 722852 722967 "FDIVCAT" 724535 NIL FDIVCAT (NIL T T T T) -9 NIL 724972) (-325 721899 721926 722096 "FDIVCAT-" 722101 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-324 721119 721206 721483 "FDIV2" 721806 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-323 719805 720064 720353 "FCPAK1" 720850 T FCPAK1 (NIL) -7 NIL NIL) (-322 718933 719305 719446 "FCOMP" 719696 NIL FCOMP (NIL T) -8 NIL NIL) (-321 702568 705982 709543 "FC" 715392 T FC (NIL) -8 NIL NIL) (-320 695221 699202 699242 "FAXF" 701044 NIL FAXF (NIL T) -9 NIL 701736) (-319 692500 693155 693980 "FAXF-" 694445 NIL FAXF- (NIL T T) -8 NIL NIL) (-318 687600 691876 692052 "FARRAY" 692357 NIL FARRAY (NIL T) -8 NIL NIL) (-317 683007 685039 685092 "FAMR" 686115 NIL FAMR (NIL T T) -9 NIL 686575) (-316 681897 682199 682634 "FAMR-" 682639 NIL FAMR- (NIL T T T) -8 NIL NIL) (-315 681093 681819 681872 "FAMONOID" 681877 NIL FAMONOID (NIL T) -8 NIL NIL) (-314 678923 679607 679660 "FAMONC" 680601 NIL FAMONC (NIL T T) -9 NIL 680987) (-313 677615 678677 678814 "FAGROUP" 678819 NIL FAGROUP (NIL T) -8 NIL NIL) (-312 675410 675729 676132 "FACUTIL" 677296 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-311 674509 674694 674916 "FACTFUNC" 675220 NIL FACTFUNC (NIL T) -7 NIL NIL) (-310 666914 673760 673972 "EXPUPXS" 674365 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-309 664397 664937 665523 "EXPRTUBE" 666348 T EXPRTUBE (NIL) -7 NIL NIL) (-308 660591 661183 661920 "EXPRODE" 663736 NIL EXPRODE (NIL T T) -7 NIL NIL) (-307 645965 659246 659674 "EXPR" 660195 NIL EXPR (NIL T) -8 NIL NIL) (-306 640372 640959 641772 "EXPR2UPS" 645263 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-305 640008 640065 640172 "EXPR2" 640309 NIL EXPR2 (NIL T T) -7 NIL NIL) (-304 631415 639140 639437 "EXPEXPAN" 639845 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-303 631242 631372 631401 "EXIT" 631406 T EXIT (NIL) -8 NIL NIL) (-302 630766 630966 631057 "EXITAST" 631171 T EXITAST (NIL) -8 NIL NIL) (-301 630393 630455 630568 "EVALCYC" 630698 NIL EVALCYC (NIL T) -7 NIL NIL) (-300 629934 630052 630093 "EVALAB" 630263 NIL EVALAB (NIL T) -9 NIL 630367) (-299 629415 629537 629758 "EVALAB-" 629763 NIL EVALAB- (NIL T T) -8 NIL NIL) (-298 626918 628186 628214 "EUCDOM" 628769 T EUCDOM (NIL) -9 NIL 629119) (-297 625323 625765 626355 "EUCDOM-" 626360 NIL EUCDOM- (NIL T) -8 NIL NIL) (-296 612863 615621 618371 "ESTOOLS" 622593 T ESTOOLS (NIL) -7 NIL NIL) (-295 612495 612552 612661 "ESTOOLS2" 612800 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-294 612246 612288 612368 "ESTOOLS1" 612447 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-293 606171 607899 607927 "ES" 610695 T ES (NIL) -9 NIL 612104) (-292 601118 602405 604222 "ES-" 604386 NIL ES- (NIL T) -8 NIL NIL) (-291 597493 598253 599033 "ESCONT" 600358 T ESCONT (NIL) -7 NIL NIL) (-290 597238 597270 597352 "ESCONT1" 597455 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-289 596913 596963 597063 "ES2" 597182 NIL ES2 (NIL T T) -7 NIL NIL) (-288 596543 596601 596710 "ES1" 596849 NIL ES1 (NIL T T) -7 NIL NIL) (-287 595759 595888 596064 "ERROR" 596387 T ERROR (NIL) -7 NIL NIL) (-286 589262 595618 595709 "EQTBL" 595714 NIL EQTBL (NIL T T) -8 NIL NIL) (-285 581819 584576 586025 "EQ" 587846 NIL -3900 (NIL T) -8 NIL NIL) (-284 581451 581508 581617 "EQ2" 581756 NIL EQ2 (NIL T T) -7 NIL NIL) (-283 576743 577789 578882 "EP" 580390 NIL EP (NIL T) -7 NIL NIL) (-282 575325 575626 575943 "ENV" 576446 T ENV (NIL) -8 NIL NIL) (-281 574524 575044 575072 "ENTIRER" 575077 T ENTIRER (NIL) -9 NIL 575123) (-280 571026 572479 572849 "EMR" 574323 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-279 570170 570355 570409 "ELTAGG" 570789 NIL ELTAGG (NIL T T) -9 NIL 571000) (-278 569889 569951 570092 "ELTAGG-" 570097 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-277 569678 569707 569761 "ELTAB" 569845 NIL ELTAB (NIL T T) -9 NIL NIL) (-276 568804 568950 569149 "ELFUTS" 569529 NIL ELFUTS (NIL T T) -7 NIL NIL) (-275 568546 568602 568630 "ELEMFUN" 568735 T ELEMFUN (NIL) -9 NIL NIL) (-274 568416 568437 568505 "ELEMFUN-" 568510 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-273 563307 566516 566557 "ELAGG" 567497 NIL ELAGG (NIL T) -9 NIL 567960) (-272 561592 562026 562689 "ELAGG-" 562694 NIL ELAGG- (NIL T T) -8 NIL NIL) (-271 560249 560529 560824 "ELABEXPR" 561317 T ELABEXPR (NIL) -8 NIL NIL) (-270 553115 554916 555743 "EFUPXS" 559525 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-269 546565 548366 549176 "EFULS" 552391 NIL EFULS (NIL T T T) -8 NIL NIL) (-268 543987 544345 544824 "EFSTRUC" 546197 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-267 533059 534624 536184 "EF" 542502 NIL EF (NIL T T) -7 NIL NIL) (-266 532160 532544 532693 "EAB" 532930 T EAB (NIL) -8 NIL NIL) (-265 531369 532119 532147 "E04UCFA" 532152 T E04UCFA (NIL) -8 NIL NIL) (-264 530578 531328 531356 "E04NAFA" 531361 T E04NAFA (NIL) -8 NIL NIL) (-263 529787 530537 530565 "E04MBFA" 530570 T E04MBFA (NIL) -8 NIL NIL) (-262 528996 529746 529774 "E04JAFA" 529779 T E04JAFA (NIL) -8 NIL NIL) (-261 528207 528955 528983 "E04GCFA" 528988 T E04GCFA (NIL) -8 NIL NIL) (-260 527418 528166 528194 "E04FDFA" 528199 T E04FDFA (NIL) -8 NIL NIL) (-259 526627 527377 527405 "E04DGFA" 527410 T E04DGFA (NIL) -8 NIL NIL) (-258 520805 522152 523516 "E04AGNT" 525283 T E04AGNT (NIL) -7 NIL NIL) (-257 519529 520009 520049 "DVARCAT" 520524 NIL DVARCAT (NIL T) -9 NIL 520723) (-256 518733 518945 519259 "DVARCAT-" 519264 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-255 511633 518532 518661 "DSMP" 518666 NIL DSMP (NIL T T T) -8 NIL NIL) (-254 506443 507578 508646 "DROPT" 510585 T DROPT (NIL) -8 NIL NIL) (-253 506108 506167 506265 "DROPT1" 506378 NIL DROPT1 (NIL T) -7 NIL NIL) (-252 501223 502349 503486 "DROPT0" 504991 T DROPT0 (NIL) -7 NIL NIL) (-251 499568 499893 500279 "DRAWPT" 500857 T DRAWPT (NIL) -7 NIL NIL) (-250 494155 495078 496157 "DRAW" 498542 NIL DRAW (NIL T) -7 NIL NIL) (-249 493788 493841 493959 "DRAWHACK" 494096 NIL DRAWHACK (NIL T) -7 NIL NIL) (-248 492519 492788 493079 "DRAWCX" 493517 T DRAWCX (NIL) -7 NIL NIL) (-247 492035 492103 492254 "DRAWCURV" 492445 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-246 482506 484465 486580 "DRAWCFUN" 489940 T DRAWCFUN (NIL) -7 NIL NIL) (-245 479319 481201 481242 "DQAGG" 481871 NIL DQAGG (NIL T) -9 NIL 482144) (-244 467838 474535 474618 "DPOLCAT" 476470 NIL DPOLCAT (NIL T T T T) -9 NIL 477015) (-243 462677 464023 465981 "DPOLCAT-" 465986 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-242 455832 462538 462636 "DPMO" 462641 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-241 448890 455612 455779 "DPMM" 455784 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-240 448310 448513 448627 "DOMAIN" 448796 T DOMAIN (NIL) -8 NIL NIL) (-239 442061 447945 448097 "DMP" 448211 NIL DMP (NIL NIL T) -8 NIL NIL) (-238 441661 441717 441861 "DLP" 441999 NIL DLP (NIL T) -7 NIL NIL) (-237 435305 440762 440989 "DLIST" 441466 NIL DLIST (NIL T) -8 NIL NIL) (-236 432151 434160 434201 "DLAGG" 434751 NIL DLAGG (NIL T) -9 NIL 434980) (-235 431001 431631 431659 "DIVRING" 431751 T DIVRING (NIL) -9 NIL 431834) (-234 430238 430428 430728 "DIVRING-" 430733 NIL DIVRING- (NIL T) -8 NIL NIL) (-233 428340 428697 429103 "DISPLAY" 429852 T DISPLAY (NIL) -7 NIL NIL) (-232 422282 428254 428317 "DIRPROD" 428322 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-231 421130 421333 421598 "DIRPROD2" 422075 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-230 410668 416620 416673 "DIRPCAT" 417083 NIL DIRPCAT (NIL NIL T) -9 NIL 417923) (-229 407994 408636 409517 "DIRPCAT-" 409854 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-228 407281 407441 407627 "DIOSP" 407828 T DIOSP (NIL) -7 NIL NIL) (-227 403983 406193 406234 "DIOPS" 406668 NIL DIOPS (NIL T) -9 NIL 406897) (-226 403532 403646 403837 "DIOPS-" 403842 NIL DIOPS- (NIL T T) -8 NIL NIL) (-225 402444 403038 403066 "DIFRING" 403253 T DIFRING (NIL) -9 NIL 403363) (-224 402090 402167 402319 "DIFRING-" 402324 NIL DIFRING- (NIL T) -8 NIL NIL) (-223 399915 401153 401194 "DIFEXT" 401557 NIL DIFEXT (NIL T) -9 NIL 401851) (-222 398200 398628 399294 "DIFEXT-" 399299 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-221 395522 397732 397773 "DIAGG" 397778 NIL DIAGG (NIL T) -9 NIL 397798) (-220 394906 395063 395315 "DIAGG-" 395320 NIL DIAGG- (NIL T T) -8 NIL NIL) (-219 390371 393865 394142 "DHMATRIX" 394675 NIL DHMATRIX (NIL T) -8 NIL NIL) (-218 385983 386892 387902 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228323 228532 228631 "CATAST" 228753 T CATAST (NIL) -8 NIL NIL) (-136 227843 228044 228136 "CASEAST" 228251 T CASEAST (NIL) -8 NIL NIL) (-135 222895 223872 224625 "CARTEN" 227146 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-134 222003 222151 222372 "CARTEN2" 222742 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-133 220345 221153 221410 "CARD" 221766 T CARD (NIL) -8 NIL NIL) (-132 219965 220149 220224 "CAPSLAST" 220290 T CAPSLAST (NIL) -8 NIL NIL) (-131 219337 219665 219693 "CACHSET" 219825 T CACHSET (NIL) -9 NIL 219902) (-130 218833 219129 219157 "CABMON" 219207 T CABMON (NIL) -9 NIL 219263) (-129 218002 218380 218523 "BYTE" 218710 T BYTE (NIL) -8 NIL NIL) (-128 213950 217949 217983 "BYTEARY" 217988 T BYTEARY (NIL) -8 NIL NIL) (-127 211507 213642 213749 "BTREE" 213876 NIL BTREE (NIL T) -8 NIL NIL) (-126 209005 211155 211277 "BTOURN" 211417 NIL BTOURN (NIL T) -8 NIL NIL) (-125 206423 208476 208517 "BTCAT" 208585 NIL BTCAT (NIL T) -9 NIL 208662) (-124 206090 206170 206319 "BTCAT-" 206324 NIL BTCAT- (NIL T T) -8 NIL NIL) (-123 201382 205233 205261 "BTAGG" 205483 T BTAGG (NIL) -9 NIL 205644) (-122 200872 200997 201203 "BTAGG-" 201208 NIL BTAGG- (NIL T) -8 NIL NIL) (-121 197916 200150 200365 "BSTREE" 200689 NIL BSTREE (NIL T) -8 NIL NIL) (-120 197054 197180 197364 "BRILL" 197772 NIL BRILL (NIL T) -7 NIL NIL) (-119 193755 195782 195823 "BRAGG" 196472 NIL BRAGG (NIL T) -9 NIL 196729) (-118 192284 192690 193245 "BRAGG-" 193250 NIL BRAGG- (NIL T T) -8 NIL NIL) (-117 185550 191630 191814 "BPADICRT" 192132 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-116 183900 185487 185532 "BPADIC" 185537 NIL BPADIC (NIL NIL) -8 NIL NIL) (-115 183598 183628 183742 "BOUNDZRO" 183864 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-114 179113 180204 181071 "BOP" 182751 T BOP (NIL) -8 NIL NIL) (-113 176734 177178 177698 "BOP1" 178626 NIL BOP1 (NIL T) -7 NIL NIL) (-112 175472 176158 176351 "BOOLEAN" 176561 T BOOLEAN (NIL) -8 NIL NIL) (-111 174834 175212 175266 "BMODULE" 175271 NIL BMODULE (NIL T T) -9 NIL 175336) (-110 170664 174632 174705 "BITS" 174781 T BITS (NIL) -8 NIL NIL) (-109 169761 170196 170348 "BINFILE" 170532 T BINFILE (NIL) -8 NIL NIL) (-108 169173 169295 169437 "BINDING" 169639 T BINDING (NIL) -8 NIL NIL) (-107 163065 168617 168782 "BINARY" 169028 T BINARY (NIL) -8 NIL NIL) (-106 160892 162320 162361 "BGAGG" 162621 NIL BGAGG (NIL T) -9 NIL 162758) (-105 160723 160755 160846 "BGAGG-" 160851 NIL BGAGG- (NIL T T) -8 NIL NIL) (-104 159821 160107 160312 "BFUNCT" 160538 T BFUNCT (NIL) -8 NIL NIL) (-103 158511 158689 158977 "BEZOUT" 159645 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-102 155028 157363 157693 "BBTREE" 158214 NIL BBTREE (NIL T) -8 NIL NIL) (-101 154762 154815 154843 "BASTYPE" 154962 T BASTYPE (NIL) -9 NIL NIL) (-100 154614 154643 154716 "BASTYPE-" 154721 NIL BASTYPE- (NIL T) -8 NIL NIL) (-99 154052 154128 154278 "BALFACT" 154525 NIL BALFACT (NIL T T) -7 NIL NIL) (-98 152935 153467 153653 "AUTOMOR" 153897 NIL AUTOMOR (NIL T) -8 NIL NIL) (-97 152661 152666 152692 "ATTREG" 152697 T ATTREG (NIL) -9 NIL NIL) (-96 150940 151358 151710 "ATTRBUT" 152327 T ATTRBUT (NIL) -8 NIL NIL) (-95 150592 150768 150834 "ATTRAST" 150892 T ATTRAST (NIL) -8 NIL NIL) (-94 150128 150241 150267 "ATRIG" 150468 T ATRIG (NIL) -9 NIL NIL) (-93 149937 149978 150065 "ATRIG-" 150070 NIL ATRIG- (NIL T) -8 NIL NIL) (-92 149662 149805 149831 "ASTCAT" 149836 T ASTCAT (NIL) -9 NIL 149866) (-91 149459 149502 149594 "ASTCAT-" 149599 NIL ASTCAT- (NIL T) -8 NIL NIL) (-90 147656 149235 149323 "ASTACK" 149402 NIL ASTACK (NIL T) -8 NIL NIL) (-89 146161 146458 146823 "ASSOCEQ" 147338 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-88 145193 145820 145944 "ASP9" 146068 NIL ASP9 (NIL NIL) -8 NIL NIL) (-87 144957 145141 145180 "ASP8" 145185 NIL ASP8 (NIL NIL) -8 NIL NIL) (-86 143826 144562 144704 "ASP80" 144846 NIL ASP80 (NIL NIL) -8 NIL NIL) (-85 142725 143461 143593 "ASP7" 143725 NIL ASP7 (NIL NIL) -8 NIL NIL) (-84 141679 142402 142520 "ASP78" 142638 NIL ASP78 (NIL NIL) -8 NIL NIL) (-83 140648 141359 141476 "ASP77" 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67776 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-41 62906 63591 64246 "ALGMANIP" 66690 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-40 54312 62532 62682 "ALGFF" 62839 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-39 53508 53639 53818 "ALGFACT" 54170 NIL ALGFACT (NIL T) -7 NIL NIL) (-38 52538 53104 53142 "ALGEBRA" 53202 NIL ALGEBRA (NIL T) -9 NIL 53261) (-37 52256 52315 52447 "ALGEBRA-" 52452 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-36 34516 50259 50311 "ALAGG" 50447 NIL ALAGG (NIL T T) -9 NIL 50608) (-35 34052 34165 34191 "AHYP" 34392 T AHYP (NIL) -9 NIL NIL) (-34 32983 33231 33257 "AGG" 33756 T AGG (NIL) -9 NIL 34035) (-33 32417 32579 32793 "AGG-" 32798 NIL AGG- (NIL T) -8 NIL NIL) (-32 30094 30516 30934 "AF" 32059 NIL AF (NIL T T) -7 NIL NIL) (-31 29618 29819 29909 "ADDAST" 30022 T ADDAST (NIL) -8 NIL NIL) (-30 28887 29145 29301 "ACPLOT" 29480 T ACPLOT (NIL) -8 NIL NIL) (-29 18358 26279 26330 "ACFS" 27041 NIL ACFS (NIL T) -9 NIL 27280) (-28 16372 16862 17637 "ACFS-" 17642 NIL ACFS- (NIL T T) -8 NIL NIL) 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 322b855b..38334ce8 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,1931 +1,1846 @@ -(732944 . 3430962941) -(((*1 *2 *2) (-12 (-5 *2 (-1116 (-619 (-547)))) (-5 *1 (-852))))) +(733842 . 3431009357) +(((*1 *2 *2) (-12 (-5 *2 (-619 *3)) (-4 *3 (-819)) (-5 *1 (-294 *3))))) +(((*1 *2 *2) + (-12 (-5 *2 (-1219 *1)) (-4 *1 (-333 *3 *4 *5)) (-4 *3 (-1177)) + (-4 *4 (-1195 *3)) (-4 *5 (-1195 (-398 *4)))))) +(((*1 *1 *2) (-12 (-5 *2 (-1082)) (-5 *1 (-321))))) +(((*1 *1) (-5 *1 (-139))) ((*1 *1 *1) (-5 *1 (-142))) + ((*1 *1 *1) (-4 *1 (-1105)))) (((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |lcmfij| *5) (|:| |totdeg| (-745)) (|:| |poli| *2) - (|:| |polj| *2))) - (-4 *5 (-767)) (-4 *2 (-918 *4 *5 *6)) (-5 *1 (-439 *4 *5 *6 *2)) - (-4 *4 (-442)) (-4 *6 (-821))))) -(((*1 *1 *2) (-12 (-5 *2 (-179)) (-5 *1 (-240))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *5 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(-4 *2 (-1063)))) @@ -1953,7 +1868,7 @@ (-12 (-5 *2 (-745)) (-4 *3 (-354)) (-4 *4 (-767)) (-4 *5 (-821)) (-5 *1 (-493 *3 *4 *5 *6)) (-4 *6 (-918 *3 *4 *5)))) ((*1 *2 *2 *3) - (-12 (-5 *2 (-1218 *4)) (-5 *3 (-547)) (-4 *4 (-340)) + (-12 (-5 *2 (-1219 *4)) (-5 *3 (-547)) (-4 *4 (-340)) (-5 *1 (-517 *4)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-547)) (-5 *1 (-523)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-745)) (-5 *1 (-523)))) @@ -1991,38 +1906,28 @@ (-12 (-5 *2 (-547)) (-4 *1 (-1085 *3 *4 *5 *6)) (-4 *4 (-1016)) (-4 *5 (-230 *3 *4)) (-4 *6 (-230 *3 *4)) (-4 *4 (-354)))) ((*1 *2 *2 *2) - (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) - (-5 *1 (-1121 *3)))) - ((*1 *2 *2 *2) - (-12 (-5 *2 (-1116 *3)) (-4 *3 (-38 (-398 (-547)))) + (-12 (-5 *2 (-1117 *3)) (-4 *3 (-38 (-398 (-547)))) (-5 *1 (-1122 *3)))) + ((*1 *2 *2 *2) + (-12 (-5 *2 (-1117 *3)) (-4 *3 (-38 (-398 (-547)))) + (-5 *1 (-1123 *3)))) ((*1 *1 *1 *2) - (-12 (-4 *1 (-1209 *2)) (-4 *2 (-1016)) (-4 *2 (-354))))) -(((*1 *2 *3) - (-12 (-4 *1 (-864)) - 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(-4 *3 (-13 (-169) (-38 (-398 (-547))))))) @@ -2485,55 +2413,55 @@ (-12 (-5 *2 (-1087 *3 (-590 *1))) (-4 *3 (-1016)) (-4 *3 (-821)) (-4 *1 (-421 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-1067)) (-5 *1 (-425)))) - ((*1 *2 *1) (-12 (-5 *2 (-1135)) (-5 *1 (-425)))) - ((*1 *1 *2) (-12 (-5 *2 (-1135)) (-5 *1 (-425)))) - ((*1 *1 *2) (-12 (-5 *2 (-1118)) (-5 *1 (-425)))) + ((*1 *2 *1) (-12 (-5 *2 (-1136)) (-5 *1 (-425)))) + ((*1 *1 *2) (-12 (-5 *2 (-1136)) (-5 *1 (-425)))) + ((*1 *1 *2) (-12 (-5 *2 (-1119)) (-5 *1 (-425)))) ((*1 *1 *2) (-12 (-5 *2 (-425)) (-5 *1 (-428)))) ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-428)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2088 (-619 (-321))))) + (-5 *2 (-2 (|:| |localSymbols| (-1140)) (|:| -2096 (-619 (-321))))) (-4 *1 (-430)))) ((*1 *1 *2) (-12 (-5 *2 (-321)) (-4 *1 (-430)))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-321))) (-4 *1 (-430)))) - ((*1 *1 *2) (-12 (-5 *2 (-1218 (-673))) (-4 *1 (-430)))) + ((*1 *1 *2) (-12 (-5 *2 (-1219 (-673))) (-4 *1 (-430)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1139)) (|:| -2088 (-619 (-321))))) + (-5 *2 (-2 (|:| |localSymbols| (-1140)) (|:| -2096 (-619 (-321))))) (-4 *1 (-431)))) ((*1 *1 *2) (-12 (-5 *2 (-321)) (-4 *1 (-431)))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-321))) (-4 *1 (-431)))) ((*1 *1 *2) - (-12 (-5 *2 (-1218 (-398 (-921 *3)))) (-4 *3 (-169)) - (-14 *6 (-1218 (-663 *3))) (-5 *1 (-443 *3 *4 *5 *6)) - (-14 *4 (-890)) (-14 *5 (-619 (-1135))))) + (-12 (-5 *2 (-1219 (-398 (-921 *3)))) (-4 *3 (-169)) + (-14 *6 (-1219 (-663 *3))) (-5 *1 (-443 *3 *4 *5 *6)) + (-14 *4 (-890)) (-14 *5 (-619 (-1136))))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-619 (-912 (-217))))) (-5 *1 (-458)))) ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-458)))) ((*1 *1 *2) - (-12 (-5 *2 (-1203 *3 *4 *5)) (-4 *3 (-1016)) (-14 *4 (-1135)) + (-12 (-5 *2 (-1204 *3 *4 *5)) (-4 *3 (-1016)) (-14 *4 (-1136)) (-14 *5 *3) (-5 *1 (-464 *3 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-1214 *4)) (-14 *4 (-1135)) (-5 *1 (-464 *3 *4 *5)) + (-12 (-5 *2 (-1215 *4)) (-14 *4 (-1136)) (-5 *1 (-464 *3 *4 *5)) (-4 *3 (-1016)) (-14 *5 *3))) ((*1 *2 *1) (-12 (-5 *2 (-973 16)) (-5 *1 (-477)))) ((*1 *2 *1) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-477)))) ((*1 *1 *2) (-12 (-5 *2 (-1087 (-547) (-590 (-484)))) (-5 *1 (-484)))) - ((*1 *1 *2) (-12 (-5 *2 (-1118)) (-5 *1 (-491)))) + ((*1 *1 *2) (-12 (-5 *2 (-1119)) (-5 *1 (-491)))) ((*1 *1 *2) (-12 (-5 *2 (-619 *6)) (-4 *6 (-918 *3 *4 *5)) (-4 *3 (-354)) (-4 *4 (-767)) (-4 *5 (-821)) (-5 *1 (-493 *3 *4 *5 *6)))) - ((*1 *1 *2) (-12 (-5 *2 (-619 (-1171))) (-5 *1 (-513)))) + ((*1 *1 *2) (-12 (-5 *2 (-619 (-1172))) (-5 *1 (-513)))) ((*1 *1 *2) (-12 (-5 *2 (-129)) (-5 *1 (-583)))) - ((*1 *1 *2) (-12 (-5 *2 (-619 (-1171))) (-5 *1 (-584)))) + ((*1 *1 *2) (-12 (-5 *2 (-619 (-1172))) (-5 *1 (-584)))) ((*1 *1 *2) (-12 (-4 *3 (-169)) (-5 *1 (-585 *3 *2)) (-4 *2 (-719 *3)))) - ((*1 *2 *1) (-12 (-4 *1 (-591 *2)) (-4 *2 (-1172)))) + ((*1 *2 *1) (-12 (-4 *1 (-591 *2)) (-4 *2 (-1173)))) ((*1 *1 *2) (-12 (-4 *1 (-596 *2)) (-4 *2 (-1016)))) ((*1 *2 *1) - (-12 (-5 *2 (-1238 *3 *4)) (-5 *1 (-603 *3 *4 *5)) (-4 *3 (-821)) + (-12 (-5 *2 (-1239 *3 *4)) (-5 *1 (-603 *3 *4 *5)) (-4 *3 (-821)) (-4 *4 (-13 (-169) (-692 (-398 (-547))))) (-14 *5 (-890)))) ((*1 *2 *1) - (-12 (-5 *2 (-1233 *3 *4)) (-5 *1 (-603 *3 *4 *5)) (-4 *3 (-821)) + (-12 (-5 *2 (-1234 *3 *4)) (-5 *1 (-603 *3 *4 *5)) (-4 *3 (-821)) (-4 *4 (-13 (-169) (-692 (-398 (-547))))) (-14 *5 (-890)))) ((*1 *1 *2) (-12 (-4 *3 (-169)) (-5 *1 (-611 *3 *2)) (-4 *2 (-719 *3)))) @@ -2563,26 +2491,26 @@ ((*1 *2 *3) (-12 (-5 *3 (-307 (-547))) (-5 *2 (-307 (-675))) (-5 *1 (-675)))) ((*1 *1 *2) (-12 (-5 *1 (-677 *2)) (-4 *2 (-1063)))) - ((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-1118)) (-5 *1 (-685)))) + ((*1 *2 *3) (-12 (-5 *3 (-832)) (-5 *2 (-1119)) (-5 *1 (-685)))) ((*1 *2 *1) (-12 (-4 *2 (-169)) (-5 *1 (-686 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-4 *3 (-1016)) (-5 *1 (-687 *3 *2)) (-4 *2 (-1194 *3)))) + (-12 (-4 *3 (-1016)) (-5 *1 (-687 *3 *2)) (-4 *2 (-1195 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -3481 *3) (|:| -1973 *4))) + (-12 (-5 *2 (-2 (|:| -3487 *3) (|:| -3322 *4))) (-5 *1 (-688 *3 *4 *5)) (-4 *3 (-821)) (-4 *4 (-1063)) (-14 *5 (-1 (-112) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -3481 *3) (|:| -1973 *4))) (-4 *3 (-821)) + (-12 (-5 *2 (-2 (|:| -3487 *3) (|:| -3322 *4))) (-4 *3 (-821)) (-4 *4 (-1063)) (-5 *1 (-688 *3 *4 *5)) (-14 *5 (-1 (-112) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-169)) (-5 *1 (-690 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-619 (-2 (|:| -1558 *3) (|:| -3514 *4)))) + (-12 (-5 *2 (-619 (-2 (|:| -1563 *3) (|:| -3518 *4)))) (-4 *3 (-1016)) (-4 *4 (-701)) (-5 *1 (-710 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-547)) (-4 *1 (-738)))) ((*1 *1 *2) @@ -2590,35 +2518,35 @@ (-5 *2 (-3 (|:| |nia| - (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (-2 (|:| |var| (-1136)) (|:| |fn| (-307 (-217))) + (|:| -4232 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (|:| |mdnia| (-2 (|:| |fn| (-307 (-217))) - (|:| -2905 (-619 (-1058 (-814 (-217))))) + (|:| -4232 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))))) (-5 *1 (-743)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-307 (-217))) - (|:| -2905 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) + (|:| -4232 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *1 (-743)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (-2 (|:| |var| (-1136)) (|:| |fn| (-307 (-217))) + (|:| -4232 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *1 (-743)))) ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-743)))) - ((*1 *2 *3) (-12 (-5 *2 (-748)) (-5 *1 (-747 *3)) (-4 *3 (-1172)))) + ((*1 *2 *3) (-12 (-5 *2 (-748)) (-5 *1 (-747 *3)) (-4 *3 (-1173)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |xinit| (-217)) (|:| |xend| (-217)) - (|:| |fn| (-1218 (-307 (-217)))) (|:| |yinit| (-619 (-217))) + (|:| |fn| (-1219 (-307 (-217)))) (|:| |yinit| (-619 (-217))) (|:| |intvals| (-619 (-217))) (|:| |g| (-307 (-217))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *1 (-782)))) @@ -2629,43 +2557,43 @@ ((*1 *1 *2) (-12 (-4 *3 (-1063)) (-14 *4 *3) (-5 *1 (-791 *3 *2 *4)) (-4 *2 (-869 *3)))) - ((*1 *1 *2) (-12 (-5 *2 (-1135)) (-5 *1 (-798)))) + ((*1 *1 *2) (-12 (-5 *2 (-1136)) (-5 *1 (-798)))) ((*1 *1 *2) (-12 (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-307 (-217))) (|:| -3046 (-619 (-217))) + (-2 (|:| |fn| (-307 (-217))) (|:| -3054 (-619 (-217))) (|:| |lb| (-619 (-814 (-217)))) (|:| |cf| (-619 (-307 (-217)))) (|:| |ub| (-619 (-814 (-217)))))) (|:| |lsa| (-2 (|:| |lfn| (-619 (-307 (-217)))) - (|:| -3046 (-619 (-217))))))) + (|:| -3054 (-619 (-217))))))) (-5 *1 (-812)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3046 (-619 (-217))))) + (-2 (|:| |lfn| (-619 (-307 (-217)))) (|:| -3054 (-619 (-217))))) (-5 *1 (-812)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-307 (-217))) (|:| -3046 (-619 (-217))) + (-2 (|:| |fn| (-307 (-217))) (|:| -3054 (-619 (-217))) (|:| |lb| (-619 (-814 (-217)))) (|:| |cf| (-619 (-307 (-217)))) (|:| |ub| (-619 (-814 (-217)))))) (-5 *1 (-812)))) ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-812)))) ((*1 *1 *2) - (-12 (-5 *2 (-1214 *3)) (-14 *3 (-1135)) (-5 *1 (-826 *3 *4 *5 *6)) + (-12 (-5 *2 (-1215 *3)) (-14 *3 (-1136)) (-5 *1 (-826 *3 *4 *5 *6)) (-4 *4 (-1016)) (-14 *5 (-98 *4)) (-14 *6 (-1 *4 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-547)) (-5 *1 (-829)))) ((*1 *1 *2) (-12 (-5 *2 (-921 *3)) (-4 *3 (-1016)) (-5 *1 (-835 *3 *4 *5 *6)) - (-14 *4 (-619 (-1135))) (-14 *5 (-619 (-745))) (-14 *6 (-745)))) + (-14 *4 (-619 (-1136))) (-14 *5 (-619 (-745))) (-14 *6 (-745)))) ((*1 *2 *1) (-12 (-5 *2 (-921 *3)) (-5 *1 (-835 *3 *4 *5 *6)) (-4 *3 (-1016)) - (-14 *4 (-619 (-1135))) (-14 *5 (-619 (-745))) (-14 *6 (-745)))) + (-14 *4 (-619 (-1136))) (-14 *5 (-619 (-745))) (-14 *6 (-745)))) ((*1 *1 *2) (-12 (-5 *2 (-154)) (-5 *1 (-843)))) ((*1 *2 *3) (-12 (-5 *3 (-921 (-48))) (-5 *2 (-307 (-547))) (-5 *1 (-844)))) @@ -2683,12 +2611,12 @@ (-2 (|:| |start| (-217)) (|:| |finish| (-217)) (|:| |grid| (-745)) (|:| |boundaryType| (-547)) (|:| |dStart| (-663 (-217))) (|:| |dFinish| (-663 (-217)))))) - (|:| |f| (-619 (-619 (-307 (-217))))) (|:| |st| (-1118)) + (|:| |f| (-619 (-619 (-307 (-217))))) (|:| |st| (-1119)) (|:| |tol| (-217)))) (-5 *1 (-867)))) ((*1 *2 *1) (-12 (-5 *2 (-832)) (-5 *1 (-867)))) ((*1 *2 *1) - (-12 (-5 *2 (-1158 *3)) (-5 *1 (-870 *3)) (-4 *3 (-1063)))) + (-12 (-5 *2 (-1159 *3)) (-5 *1 (-870 *3)) (-4 *3 (-1063)))) ((*1 *1 *2) (-12 (-5 *2 (-619 (-874 *3))) (-4 *3 (-1063)) (-5 *1 (-873 *3)))) ((*1 *2 *1) @@ -2702,18 +2630,18 @@ ((*1 *2 *3) (-12 (-5 *3 (-467)) (-5 *2 (-307 *4)) (-5 *1 (-888 *4)) (-4 *4 (-13 (-821) (-539))))) - ((*1 *1 *2) (-12 (-5 *2 (-1135)) (-5 *1 (-935 *3)) (-4 *3 (-936)))) + ((*1 *1 *2) (-12 (-5 *2 (-1136)) (-5 *1 (-935 *3)) (-4 *3 (-936)))) ((*1 *1 *2) (-12 (-5 *1 (-935 *2)) (-4 *2 (-936)))) ((*1 *2 *1) (-12 (-5 *2 (-619 (-547))) (-5 *1 (-940)))) ((*1 *2 *1) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-973 *3)) (-14 *3 (-547)))) - ((*1 *2 *3) (-12 (-5 *2 (-1223)) (-5 *1 (-1002 *3)) (-4 *3 (-1172)))) - ((*1 *2 *3) (-12 (-5 *3 (-303)) (-5 *1 (-1002 *2)) (-4 *2 (-1172)))) + ((*1 *2 *3) (-12 (-5 *2 (-1224)) (-5 *1 (-1002 *3)) (-4 *3 (-1173)))) + ((*1 *2 *3) (-12 (-5 *3 (-303)) (-5 *1 (-1002 *2)) (-4 *2 (-1173)))) ((*1 *1 *2) (-12 (-4 *3 (-354)) (-4 *4 (-767)) (-4 *5 (-821)) (-5 *1 (-1003 *3 *4 *5 *2 *6)) (-4 *2 (-918 *3 *4 *5)) (-14 *6 (-619 *2)))) - ((*1 *1 *2) (-12 (-4 *1 (-1007 *2)) (-4 *2 (-1172)))) + ((*1 *1 *2) (-12 (-4 *1 (-1007 *2)) (-4 *2 (-1173)))) ((*1 *2 *3) (-12 (-5 *2 (-398 (-921 *3))) (-5 *1 (-1012 *3)) (-4 *3 (-539)))) ((*1 *1 *2) (-12 (-5 *2 (-547)) (-4 *1 (-1016)))) @@ -2728,553 +2656,491 @@ (-4 *4 (-918 *3 (-519 *2) *2)))) ((*1 *2 *1) (-12 (-4 *1 (-1096 *3)) (-4 *3 (-1016)) (-5 *2 (-832)))) ((*1 *2 *1) - (-12 (-5 *2 (-663 *4)) (-5 *1 (-1102 *3 *4)) (-14 *3 (-745)) + (-12 (-5 *2 (-663 *4)) (-5 *1 (-1103 *3 *4)) (-14 *3 (-745)) (-4 *4 (-1016)))) - ((*1 *1 *2) (-12 (-5 *2 (-142)) (-4 *1 (-1104)))) + ((*1 *1 *2) (-12 (-5 *2 (-142)) (-4 *1 (-1105)))) ((*1 *1 *2) - (-12 (-5 *2 (-619 *3)) (-4 *3 (-1172)) (-5 *1 (-1116 *3)))) + (-12 (-5 *2 (-619 *3)) (-4 *3 (-1173)) (-5 *1 (-1117 *3)))) ((*1 *2 *3) - (-12 (-5 *2 (-1116 *3)) (-5 *1 (-1120 *3)) (-4 *3 (-1016)))) + (-12 (-5 *2 (-1117 *3)) (-5 *1 (-1121 *3)) (-4 *3 (-1016)))) ((*1 *1 *2) - (-12 (-5 *2 (-1214 *4)) (-14 *4 (-1135)) (-5 *1 (-1126 *3 *4 *5)) + (-12 (-5 *2 (-1215 *4)) (-14 *4 (-1136)) (-5 *1 (-1127 *3 *4 *5)) (-4 *3 (-1016)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1214 *4)) (-14 *4 (-1135)) (-5 *1 (-1132 *3 *4 *5)) + (-12 (-5 *2 (-1215 *4)) (-14 *4 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- (-4 *4 (-1194 *3)))) + (-4 *4 (-1195 *3)))) ((*1 *1 *1) (-12 (-4 *2 (-13 (-354) (-145))) (-5 *1 (-390 *2 *3)) - (-4 *3 (-1194 *2)))) + (-4 *3 (-1195 *2)))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-1214 *4)) (-14 *4 (-1135)) (-5 *1 (-464 *3 *4 *5)) + (-12 (-5 *2 (-1215 *4)) (-14 *4 (-1136)) (-5 *1 (-464 *3 *4 *5)) (-4 *3 (-1016)) (-14 *5 *3))) ((*1 *2 *1 *3) (-12 (-4 *2 (-354)) (-4 *2 (-869 *3)) (-5 *1 (-565 *2)) - (-5 *3 (-1135)))) + (-5 *3 (-1136)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-1 *2 *2)) (-5 *1 (-565 *2)) (-4 *2 (-354)))) ((*1 *1 *1 *2) (-12 (-5 *2 (-745)) (-5 *1 (-832)))) @@ -4596,60 +4974,54 @@ (-12 (-5 *2 (-619 *3)) (-4 *1 (-869 *3)) (-4 *3 (-1063)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-869 *2)) (-4 *2 (-1063)))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-1214 *4)) (-14 *4 (-1135)) (-5 *1 (-1126 *3 *4 *5)) + (-12 (-5 *2 (-1215 *4)) (-14 *4 (-1136)) (-5 *1 (-1127 *3 *4 *5)) (-4 *3 (-1016)) (-14 *5 *3))) ((*1 *1 *1 *2) - (-12 (-5 *2 (-1214 *4)) (-14 *4 (-1135)) (-5 *1 (-1132 *3 *4 *5)) + (-12 (-5 *2 (-1215 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(-821))))) +(((*1 *2 *1 *3 *4 *4 *4 *4 *5 *5 *5 *5 *6 *5 *6 *5) + (-12 (-5 *3 (-890)) (-5 *4 (-217)) (-5 *5 (-547)) (-5 *6 (-843)) + (-5 *2 (-1224)) (-5 *1 (-1220))))) (((*1 *2 *1) (-12 (-5 *2 (-619 - (-2 (|:| |var| (-1135)) (|:| |fn| (-307 (-217))) - (|:| -2905 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) + (-2 (|:| |var| (-1136)) (|:| |fn| (-307 (-217))) + (|:| -4232 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217))))) (-5 *1 (-542)))) ((*1 *2 *1) @@ -4660,84 +5032,30 @@ (-5 *2 (-619 (-2 (|:| |xinit| (-217)) (|:| |xend| (-217)) - (|:| |fn| (-1218 (-307 (-217)))) (|:| |yinit| (-619 (-217))) + (|:| |fn| (-1219 (-307 (-217)))) (|:| |yinit| (-619 (-217))) (|:| |intvals| (-619 (-217))) (|:| |g| (-307 (-217))) (|:| |abserr| (-217)) (|:| |relerr| (-217))))) (-5 *1 (-777))))) -(((*1 *2 *1) (-12 (-4 *1 (-537 *2)) (-4 *2 (-13 (-395) (-1157))))) - ((*1 *1 *1 *1) (-4 *1 (-767)))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-217)) (-5 *4 (-547)) (-5 *2 (-1004)) (-5 *1 (-733))))) + (-12 (-5 *3 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point continuity not yet evaluated"))) + (|:| |singularitiesStream| + (-3 (|:| |str| (-1117 (-217))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4232 + (-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 (-1004)) (-5 *1 (-296))))) (((*1 *2 *3) - (-12 (-4 *4 (-539)) (-5 *2 (-1131 *3)) (-5 *1 (-41 *4 *3)) - (-4 *3 - (-13 (-354) (-293) - (-10 -8 (-15 -1384 ((-1087 *4 (-590 $)) $)) - (-15 -1394 ((-1087 *4 (-590 $)) $)) - (-15 -3835 ($ (-1087 *4 (-590 $)))))))))) + (-12 (-5 *3 (-921 (-547))) (-5 *2 (-619 *1)) (-4 *1 (-981)))) + ((*1 *2 *3) + (-12 (-5 *3 (-921 (-398 (-547)))) (-5 *2 (-619 *1)) (-4 *1 (-981)))) + ((*1 *2 *3) (-12 (-5 *3 (-921 *1)) (-4 *1 (-981)) (-5 *2 (-619 *1)))) + ((*1 *2 *3) + (-12 (-5 *3 (-1132 (-547))) (-5 *2 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(-5 *2 (-858 *5 *3)) (-5 *1 (-856 *5 *3 *4)) + (-4000 (-4 *3 (-1007 (-1136)))) (-4000 (-4 *3 (-1016))) + (-4 *3 (-855 *5)) (-4 *4 (-592 (-861 *5)))))) +(((*1 *1 *2) (-12 (-5 *2 (-398 (-547))) (-5 *1 (-209))))) +(((*1 *2 *3) + (-12 (-4 *1 (-340)) (-5 *3 (-547)) (-5 *2 (-1146 (-890) (-745)))))) +(((*1 *2 *3 *4 *3 *5 *5 *3 *5 *4) + (-12 (-5 *4 (-663 (-217))) (-5 *5 (-663 (-547))) (-5 *3 (-547)) + (-5 *2 (-1004)) (-5 *1 (-731))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4329)) (-4 *1 (-1206 *2)) (-4 *2 (-1172))))) -(((*1 *2 *3 *4) - (-12 (-5 *4 (-745)) (-5 *2 (-112)) (-5 *1 (-566 *3)) (-4 *3 (-532))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-821) (-442))) (-5 *1 (-1163 *3 *2)) - (-4 *2 (-13 (-421 *3) (-1157)))))) -(((*1 *1 *2 *3) (-12 (-5 *2 (-1118)) (-5 *3 (-797)) (-5 *1 (-796))))) -(((*1 *2 *1) - (-12 (-5 *2 (-912 *4)) (-5 *1 (-1124 *3 *4)) (-14 *3 (-890)) - (-4 *4 (-1016))))) + (-12 (-5 *1 (-50 *2 *3)) (-4 *2 (-1016)) (-14 *3 (-619 (-1136))))) + ((*1 *1 *1) + (-12 (-5 *1 (-215 *2 *3)) (-4 *2 (-13 (-1016) (-821))) + (-14 *3 (-619 (-1136)))))) +(((*1 *2 *1) (-12 (-4 *1 (-537 *2)) (-4 *2 (-13 (-395) (-1158))))) + ((*1 *1 *1 *1) (-4 *1 (-767)))) +(((*1 *2 *3 *3) + (-12 (|has| *2 (-6 (-4331 "*"))) (-4 *5 (-364 *2)) (-4 *6 (-364 *2)) + (-4 *2 (-1016)) (-5 *1 (-103 *2 *3 *4 *5 *6)) (-4 *3 (-1195 *2)) + (-4 *4 (-661 *2 *5 *6))))) +(((*1 *1 *1 *1) + (-12 (|has| *1 (-6 -4330)) (-4 *1 (-119 *2)) (-4 *2 (-1173))))) (((*1 *2 *1 *3 *4) - (-12 (-5 *3 (-912 (-217))) (-5 *4 (-843)) (-5 *2 (-1223)) + (-12 (-5 *3 (-912 (-217))) (-5 *4 (-843)) (-5 *2 (-1224)) (-5 *1 (-458)))) ((*1 *1 *2) (-12 (-5 *2 (-619 *3)) (-4 *3 (-1016)) (-4 *1 (-949 *3)))) ((*1 *2 *1) @@ -8093,25 +8357,25 @@ ((*1 *1 *1 *2) (-12 (-5 *2 (-912 *3)) (-4 *1 (-1096 *3)) (-4 *3 (-1016)))) ((*1 *2 *3 *3 *3 *3) - (-12 (-5 *2 (-912 (-217))) (-5 *1 (-1168)) (-5 *3 (-217))))) + (-12 (-5 *2 (-912 (-217))) (-5 *1 (-1169)) (-5 *3 (-217))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-47 *3 *4)) (-4 *3 (-1016)) (-4 *4 (-766)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1016)) (-5 *1 (-50 *3 *4)) - (-14 *4 (-619 (-1135))))) + (-14 *4 (-619 (-1136))))) ((*1 *1 *2 *1 *1 *3) - (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1172)) + (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1173)) (-4 *4 (-364 *3)) (-4 *5 (-364 *3)))) ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1172)) + (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1173)) (-4 *4 (-364 *3)) (-4 *5 (-364 *3)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1172)) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-56 *3 *4 *5)) (-4 *3 (-1173)) (-4 *4 (-364 *3)) (-4 *5 (-364 *3)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-58 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-58 *6)) (-5 *1 (-57 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-58 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-58 *6)) (-5 *1 (-57 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *7)) (-5 *4 (-135 *5 *6 *7)) (-14 *5 (-547)) (-14 *6 (-745)) (-4 *7 (-169)) (-4 *8 (-169)) @@ -8121,19 +8385,19 @@ (-4 *6 (-169)) (-5 *2 (-166 *6)) (-5 *1 (-165 *5 *6)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-307 *3) (-307 *3))) (-4 *3 (-13 (-1016) (-821))) - (-5 *1 (-215 *3 *4)) (-14 *4 (-619 (-1135))))) + (-5 *1 (-215 *3 *4)) (-14 *4 (-619 (-1136))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-232 *5 *6)) (-14 *5 (-745)) - (-4 *6 (-1172)) (-4 *7 (-1172)) (-5 *2 (-232 *5 *7)) + (-4 *6 (-1173)) (-4 *7 (-1173)) (-5 *2 (-232 *5 *7)) (-5 *1 (-231 *5 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-285 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-285 *6)) (-5 *1 (-284 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-285 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-285 *6)) (-5 *1 (-284 *5 *6)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1172)) (-5 *1 (-285 *3)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1173)) (-5 *1 (-285 *3)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1118)) (-5 *5 (-590 *6)) - (-4 *6 (-293)) (-4 *2 (-1172)) (-5 *1 (-288 *6 *2)))) + (-12 (-5 *3 (-1 *2 *6)) (-5 *4 (-1119)) (-5 *5 (-590 *6)) + (-4 *6 (-293)) (-4 *2 (-1173)) (-5 *1 (-288 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *2 *5)) (-5 *4 (-590 *5)) (-4 *5 (-293)) (-4 *2 (-293)) (-5 *1 (-289 *5 *2)))) @@ -8147,20 +8411,20 @@ (-4 *6 (-821)) (-5 *2 (-307 *6)) (-5 *1 (-305 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-327 *5 *6 *7 *8)) (-4 *5 (-354)) - (-4 *6 (-1194 *5)) (-4 *7 (-1194 (-398 *6))) (-4 *8 (-333 *5 *6 *7)) - (-4 *9 (-354)) (-4 *10 (-1194 *9)) (-4 *11 (-1194 (-398 *10))) + (-4 *6 (-1195 *5)) (-4 *7 (-1195 (-398 *6))) (-4 *8 (-333 *5 *6 *7)) + (-4 *9 (-354)) (-4 *10 (-1195 *9)) (-4 *11 (-1195 (-398 *10))) (-5 *2 (-327 *9 *10 *11 *12)) (-5 *1 (-324 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-333 *9 *10 *11)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-329 *3)) (-4 *3 (-1063)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1176)) (-4 *8 (-1176)) - (-4 *6 (-1194 *5)) (-4 *7 (-1194 (-398 *6))) (-4 *9 (-1194 *8)) + (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1177)) (-4 *8 (-1177)) + (-4 *6 (-1195 *5)) (-4 *7 (-1195 (-398 *6))) (-4 *9 (-1195 *8)) (-4 *2 (-333 *8 *9 *10)) (-5 *1 (-331 *5 *6 *7 *4 *8 *9 *10 *2)) - (-4 *4 (-333 *5 *6 *7)) (-4 *10 (-1194 (-398 *9))))) + (-4 *4 (-333 *5 *6 *7)) (-4 *10 (-1195 (-398 *9))))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1172)) (-4 *6 (-1172)) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1173)) (-4 *6 (-1173)) (-4 *2 (-364 *6)) (-5 *1 (-362 *5 *4 *6 *2)) (-4 *4 (-364 *5)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-373 *3 *4)) (-4 *3 (-1016)) @@ -8173,9 +8437,9 @@ (-4 *6 (-539)) (-5 *2 (-398 *6)) (-5 *1 (-397 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-404 *5 *6 *7 *8)) (-4 *5 (-298)) - (-4 *6 (-961 *5)) (-4 *7 (-1194 *6)) + (-4 *6 (-961 *5)) (-4 *7 (-1195 *6)) (-4 *8 (-13 (-400 *6 *7) (-1007 *6))) (-4 *9 (-298)) - (-4 *10 (-961 *9)) (-4 *11 (-1194 *10)) + (-4 *10 (-961 *9)) (-4 *11 (-1195 *10)) (-5 *2 (-404 *9 *10 *11 *12)) (-5 *1 (-403 *5 *6 *7 *8 *9 *10 *11 *12)) (-4 *12 (-13 (-400 *10 *11) (-1007 *10))))) @@ -8192,7 +8456,7 @@ (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1063)) (-4 *6 (-1063)) (-4 *2 (-416 *6)) (-5 *1 (-414 *5 *4 *6 *2)) (-4 *4 (-416 *5)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-479 *3)) (-4 *3 (-1172)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-479 *3)) (-4 *3 (-1173)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-498 *3 *4)) (-4 *3 (-1063)) (-4 *4 (-821)))) @@ -8201,9 +8465,9 @@ (-4 *6 (-354)) (-5 *2 (-565 *6)) (-5 *1 (-564 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -1823 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -2510 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-354)) (-4 *6 (-354)) - (-5 *2 (-2 (|:| -1823 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -2510 *6) (|:| |coeff| *6))) (-5 *1 (-564 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -8223,31 +8487,31 @@ (-619 (-2 (|:| |coeff| *6) (|:| |logand| *6)))))) (-5 *1 (-564 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-579 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-579 *6)) (-5 *1 (-576 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-579 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-579 *6)) (-5 *1 (-576 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-579 *6)) (-5 *5 (-579 *7)) - (-4 *6 (-1172)) (-4 *7 (-1172)) (-4 *8 (-1172)) (-5 *2 (-579 *8)) + (-4 *6 (-1173)) (-4 *7 (-1173)) (-4 *8 (-1173)) (-5 *2 (-579 *8)) (-5 *1 (-577 *6 *7 *8)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1116 *6)) (-5 *5 (-579 *7)) - (-4 *6 (-1172)) (-4 *7 (-1172)) (-4 *8 (-1172)) (-5 *2 (-1116 *8)) + (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-1117 *6)) (-5 *5 (-579 *7)) + (-4 *6 (-1173)) (-4 *7 (-1173)) (-4 *8 (-1173)) (-5 *2 (-1117 *8)) (-5 *1 (-577 *6 *7 *8)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-579 *6)) (-5 *5 (-1116 *7)) - (-4 *6 (-1172)) (-4 *7 (-1172)) (-4 *8 (-1172)) (-5 *2 (-1116 *8)) + (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-579 *6)) (-5 *5 (-1117 *7)) + (-4 *6 (-1173)) (-4 *7 (-1173)) (-4 *8 (-1173)) (-5 *2 (-1117 *8)) (-5 *1 (-577 *6 *7 *8)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1172)) (-5 *1 (-579 *3)))) + (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-1173)) (-5 *1 (-579 *3)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-619 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-619 *6)) (-5 *1 (-617 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-619 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-619 *6)) (-5 *1 (-617 *5 *6)))) ((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *8 *6 *7)) (-5 *4 (-619 *6)) (-5 *5 (-619 *7)) - (-4 *6 (-1172)) (-4 *7 (-1172)) (-4 *8 (-1172)) (-5 *2 (-619 *8)) + (-4 *6 (-1173)) (-4 *7 (-1173)) (-4 *8 (-1173)) (-5 *2 (-619 *8)) (-5 *1 (-618 *6 *7 *8)))) ((*1 *1 *2 *1 *1) - (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-625 *3)) (-4 *3 (-1172)))) + (-12 (-5 *2 (-1 *3 *3 *3)) (-4 *1 (-625 *3)) (-4 *3 (-1173)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *8 *5)) (-4 *5 (-1016)) (-4 *8 (-1016)) (-4 *6 (-364 *5)) (-4 *7 (-364 *5)) (-4 *2 (-661 *8 *9 *10)) @@ -8260,9 +8524,9 @@ (-4 *4 (-661 *5 *6 *7)) (-4 *9 (-364 *8)) (-4 *10 (-364 *8)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *5)) (-4 *5 (-539)) (-4 *7 (-539)) - (-4 *6 (-1194 *5)) (-4 *2 (-1194 (-398 *8))) - (-5 *1 (-684 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1194 (-398 *6))) - (-4 *8 (-1194 *7)))) + (-4 *6 (-1195 *5)) (-4 *2 (-1195 (-398 *8))) + (-5 *1 (-684 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1195 (-398 *6))) + (-4 *8 (-1195 *7)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-1016)) (-4 *9 (-1016)) (-4 *5 (-821)) (-4 *6 (-767)) (-4 *2 (-918 *9 *7 *5)) @@ -8299,14 +8563,14 @@ (-12 (-5 *2 (-814 *6)) (-5 *3 (-1 *6 *5)) (-5 *4 (-814 *5)) (-4 *5 (-1063)) (-4 *6 (-1063)) (-5 *1 (-813 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-846 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-846 *6)) (-5 *1 (-845 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-846 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-846 *6)) (-5 *1 (-845 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-848 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-848 *6)) (-5 *1 (-847 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-848 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-848 *6)) (-5 *1 (-847 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-851 *5)) (-4 *5 (-1172)) - (-4 *6 (-1172)) (-5 *2 (-851 *6)) (-5 *1 (-850 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-851 *5)) (-4 *5 (-1173)) + (-4 *6 (-1173)) (-5 *2 (-851 *6)) (-5 *1 (-850 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-858 *5 *6)) (-4 *5 (-1063)) (-4 *6 (-1063)) (-4 *7 (-1063)) (-5 *2 (-858 *5 *7)) @@ -8322,11 +8586,11 @@ (-4 *8 (-1016)) (-4 *6 (-767)) (-4 *2 (-13 (-1063) - (-10 -8 (-15 -2471 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-745)))))) + (-10 -8 (-15 -2479 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-745)))))) (-5 *1 (-920 *6 *7 *8 *5 *2)) (-4 *5 (-918 *8 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-927 *5)) (-4 *5 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|abserr| (-217)) + (|:| |relerr| (-217)))) + (|:| -1786 + (-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| (-1117 (-217))) + (|:| |notEvaluated| + "Internal singularities not yet evaluated"))) + (|:| -4232 + (-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 (-542)))) + ((*1 *1 *2 *1 *3) + (-12 (-5 *3 (-745)) (-4 *1 (-669 *2)) (-4 *2 (-1063)))) + ((*1 *1 *2) + (-12 + (-5 *2 + (-2 + (|:| 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(((*1 *2 *1 *3 *3) (-12 (-5 *3 (-890)) (-5 *2 (-745)) (-5 *1 (-1064 *4 *5)) (-14 *4 *3) (-14 *5 *3)))) @@ -9448,43 +9622,43 @@ ((*1 *2 *1 *1) (-12 (-4 *1 (-981)) (-5 *2 (-398 (-547))))) ((*1 *2 *3 *1 *2) (-12 (-4 *1 (-1033 *2 *3)) (-4 *2 (-13 (-819) (-354))) - (-4 *3 (-1194 *2)))) + (-4 *3 (-1195 *2)))) ((*1 *2 *1 *3) - (-12 (-4 *1 (-1196 *2 *3)) (-4 *3 (-766)) - (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3835 (*2 (-1135)))) + (-12 (-4 *1 (-1197 *2 *3)) (-4 *3 (-766)) + (|has| *2 (-15 ** (*2 *2 *3))) (|has| *2 (-15 -3838 (*2 (-1136)))) (-4 *2 (-1016))))) -(((*1 *1 *1) (-12 (-5 *1 (-883 *2)) (-4 *2 (-298))))) -(((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1172)))) +(((*1 *2 *1) (-12 (-5 *2 (-1224)) (-5 *1 (-796))))) +(((*1 *2 *3) (-12 (-5 *3 (-52)) (-5 *1 (-51 *2)) (-4 *2 (-1173)))) ((*1 *1 *2) (-12 (-5 *2 (-921 (-370))) (-5 *1 (-330 *3 *4 *5)) - (-4 *5 (-1007 (-370))) (-14 *3 (-619 (-1135))) - (-14 *4 (-619 (-1135))) (-4 *5 (-378)))) + (-4 *5 (-1007 (-370))) (-14 *3 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(-814 (-217)))) (|:| |abserr| (-217)) + (-2 (|:| |var| (-1136)) (|:| |fn| (-307 (-217))) + (|:| -4232 (-1058 (-814 (-217)))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (|:| |mdnia| (-2 (|:| |fn| (-307 (-217))) - (|:| -2905 (-619 (-1058 (-814 (-217))))) + (|:| -4232 (-619 (-1058 (-814 (-217))))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))))) (-5 *1 (-743)))) ((*1 *2 *1) (-12 (-5 *2 (-2 (|:| |xinit| (-217)) (|:| |xend| (-217)) - (|:| |fn| (-1218 (-307 (-217)))) (|:| |yinit| (-619 (-217))) + (|:| |fn| (-1219 (-307 (-217)))) (|:| |yinit| (-619 (-217))) (|:| |intvals| (-619 (-217))) (|:| |g| (-307 (-217))) (|:| |abserr| (-217)) (|:| |relerr| (-217)))) (-5 *1 (-782)))) @@ -9529,13 +9703,13 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-307 (-217))) (|:| -3046 (-619 (-217))) + (-2 (|:| |fn| (-307 (-217))) (|:| -3054 (-619 (-217))) (|:| |lb| (-619 (-814 (-217)))) (|:| |cf| (-619 (-307 (-217)))) (|:| |ub| (-619 (-814 (-217)))))) (|:| |lsa| (-2 (|:| |lfn| (-619 (-307 (-217)))) - (|:| -3046 (-619 (-217))))))) + (|:| -3054 (-619 (-217))))))) (-5 *1 (-812)))) ((*1 *2 *1) (-12 @@ -9546,542 +9720,576 @@ (-2 (|:| |start| (-217)) (|:| |finish| (-217)) (|:| |grid| (-745)) (|:| |boundaryType| (-547)) (|:| |dStart| (-663 (-217))) (|:| |dFinish| (-663 (-217)))))) - (|:| |f| (-619 (-619 (-307 (-217))))) (|:| |st| (-1118)) + (|:| |f| (-619 (-619 (-307 (-217))))) (|:| |st| (-1119)) (|:| |tol| (-217)))) (-5 *1 (-867)))) ((*1 *1 *2) (-12 (-5 *2 (-619 *6)) (-4 *6 (-1030 *3 *4 *5)) (-4 *3 (-1016)) (-4 *4 (-767)) (-4 *5 (-821)) (-4 *1 (-945 *3 *4 *5 *6)))) - ((*1 *2 *1) (-12 (-4 *1 (-1007 *2)) (-4 *2 (-1172)))) + ((*1 *2 *1) (-12 (-4 *1 (-1007 *2)) (-4 *2 (-1173)))) ((*1 *1 *2) - (-1525 + (-1530 (-12 (-5 *2 (-921 *3)) - (-12 (-3998 (-4 *3 (-38 (-398 (-547))))) - (-3998 (-4 *3 (-38 (-547)))) (-4 *5 (-592 (-1135)))) + (-12 (-4000 (-4 *3 (-38 (-398 (-547))))) + (-4000 (-4 *3 (-38 (-547)))) (-4 *5 (-592 (-1136)))) (-4 *3 (-1016)) (-4 *1 (-1030 *3 *4 *5)) (-4 *4 (-767)) (-4 *5 (-821))) (-12 (-5 *2 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(-370))) (-5 *1 (-759 *3)) (-4 *3 (-592 (-370))))) ((*1 *2 *3 *4) @@ -12936,27 +13347,24 @@ (-12 (-5 *3 (-307 (-166 *5))) (-5 *4 (-890)) (-4 *5 (-539)) (-4 *5 (-821)) (-4 *5 (-592 (-370))) (-5 *2 (-166 (-370))) (-5 *1 (-759 *5))))) -(((*1 *2 *3) - (-12 (-4 *4 (-13 (-539) (-145))) (-5 *2 (-619 *3)) - (-5 *1 (-1188 *4 *3)) (-4 *3 (-1194 *4))))) (((*1 *2 *1) (-12 (-4 *1 (-47 *2 *3)) (-4 *3 (-766)) (-4 *2 (-1016)))) ((*1 *2 *1) - (-12 (-4 *2 (-1016)) (-5 *1 (-50 *2 *3)) (-14 *3 (-619 (-1135))))) + (-12 (-4 *2 (-1016)) (-5 *1 (-50 *2 *3)) (-14 *3 (-619 (-1136))))) ((*1 *2 *1) (-12 (-5 *2 (-307 *3)) (-5 *1 (-215 *3 *4)) - (-4 *3 (-13 (-1016) (-821))) (-14 *4 (-619 (-1135))))) + (-4 *3 (-13 (-1016) (-821))) (-14 *4 (-619 (-1136))))) ((*1 *2 *1) (-12 (-4 *1 (-373 *2 *3)) (-4 *3 (-1063)) (-4 *2 (-1016)))) ((*1 *2 *1) - (-12 (-14 *3 (-619 (-1135))) (-4 *5 (-230 (-3764 *3) (-745))) + (-12 (-14 *3 (-619 (-1136))) (-4 *5 (-230 (-3767 *3) (-745))) (-14 *6 - (-1 (-112) (-2 (|:| -3481 *4) (|:| -1973 *5)) - (-2 (|:| -3481 *4) (|:| -1973 *5)))) + (-1 (-112) (-2 (|:| -3487 *4) (|:| -3322 *5)) + (-2 (|:| -3487 *4) (|:| -3322 *5)))) (-4 *2 (-169)) (-5 *1 (-451 *3 *2 *4 *5 *6 *7)) (-4 *4 (-821)) (-4 *7 (-918 *2 *5 (-834 *3))))) ((*1 *2 *1) (-12 (-4 *1 (-498 *2 *3)) (-4 *3 (-821)) (-4 *2 (-1063)))) ((*1 *2 *1) - (-12 (-4 *2 (-539)) (-5 *1 (-599 *2 *3)) (-4 *3 (-1194 *2)))) + (-12 (-4 *2 (-539)) (-5 *1 (-599 *2 *3)) (-4 *3 (-1195 *2)))) ((*1 *2 *1) (-12 (-4 *1 (-683 *2)) (-4 *2 (-1016)))) ((*1 *2 *1) (-12 (-4 *2 (-1016)) (-5 *1 (-710 *2 *3)) (-4 *3 (-821)) @@ -12968,6 +13376,19 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-1030 *3 *4 *2)) (-4 *3 (-1016)) (-4 *4 (-767)) (-4 *2 (-821))))) +(((*1 *2 *1) (-12 (-5 *2 (-112)) (-5 *1 (-861 *3)) (-4 *3 (-1063))))) +(((*1 *2 *3 *3 *3 *4 *5) + (-12 (-5 *5 (-1 *3 *3)) (-4 *3 (-1195 *6)) + (-4 *6 (-13 (-354) (-145) (-1007 *4))) (-5 *4 (-547)) + (-5 *2 + (-3 (|:| |ans| (-2 (|:| |ans| *3) (|:| |nosol| (-112)))) + (|:| -2644 + (-2 (|:| |b| *3) (|:| |c| *3) (|:| |m| *4) (|:| |alpha| *3) + (|:| |beta| *3))))) + (-5 *1 (-984 *6 *3))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1136)) (-5 *2 (-1224)) (-5 *1 (-796))))) +(((*1 *1 *2) + (-12 (-5 *2 (-619 *3)) (-4 *3 (-1173)) (-5 *1 (-1117 *3))))) (((*1 *1 *1 *2) (|partial| -12 (-4 *1 (-163 *2)) (-4 *2 (-169)) (-4 *2 (-539)))) ((*1 *1 *1 *2) @@ -12982,64 +13403,71 @@ (|partial| -12 (-4 *1 (-823 *2)) (-4 *2 (-1016)) (-4 *2 (-539)))) ((*1 *1 *1 *1) (-5 *1 (-832))) ((*1 *2 *2 *3) - (-12 (-5 *2 (-1218 *4)) (-4 *4 (-1194 *3)) (-4 *3 (-539)) + (-12 (-5 *2 (-1219 *4)) (-4 *4 (-1195 *3)) (-4 *3 (-539)) (-5 *1 (-938 *3 *4)))) ((*1 *1 *1 *2) (|partial| -12 (-4 *1 (-1019 *3 *4 *2 *5 *6)) (-4 *2 (-1016)) (-4 *5 (-230 *4 *2)) (-4 *6 (-230 *3 *2)) (-4 *2 (-539)))) ((*1 *2 *2 *2) - (|partial| -12 (-5 *2 (-1116 *3)) (-4 *3 (-1016)) (-5 *1 (-1120 *3))))) -(((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-2 (|:| |totdeg| (-745)) (|:| -3528 *4))) (-5 *5 (-745)) - (-4 *4 (-918 *6 *7 *8)) (-4 *6 (-442)) (-4 *7 (-767)) (-4 *8 (-821)) - (-5 *2 - (-2 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*5) (|:| -1973 *6)) - (-2 (|:| -3481 *5) (|:| -1973 *6)))) + (-1 (-112) (-2 (|:| -3487 *5) (|:| -3322 *6)) + (-2 (|:| -3487 *5) (|:| -3322 *6)))) (-5 *2 (-688 *5 *6 *7)) (-5 *1 (-451 *3 *4 *5 *6 *7 *8)) (-4 *5 (-821)) (-4 *8 (-918 *4 *6 (-834 *3))))) ((*1 *2 *1) @@ -13048,979 +13476,1093 @@ ((*1 *1 *1) (-12 (-4 *1 (-942 *2 *3 *4)) (-4 *2 (-1016)) (-4 *3 (-766)) (-4 *4 (-821))))) -(((*1 *2 *3 *4 *3) - (|partial| -12 (-5 *4 (-1 *6 *6)) (-4 *6 (-1194 *5)) (-4 *5 (-354)) - (-5 *2 (-2 (|:| -1823 (-398 *6)) (|:| |coeff| (-398 *6)))) - (-5 *1 (-557 *5 *6)) (-5 *3 (-398 *6))))) -(((*1 *2) - (-12 (-5 *2 (-112)) (-5 *1 (-1149 *3 *4)) (-4 *3 (-1063)) - (-4 *4 (-1063))))) -(((*1 *2 *1) - (-12 (-4 *1 (-358 *3)) (-4 *3 (-169)) (-4 *3 (-539)) - (-5 *2 (-1131 *3))))) -(((*1 *1 *1 *2) (-12 (-5 *2 (-1135)) (-5 *1 (-1028))))) -(((*1 *2 *3 *3 *3 *3 *3 *3 *4 *4 *4 *3 *3 *5 *6 *3 *6 *6 *5 *6 *6 *6 *6 - *5 *3 *3 *3 *3 *3 *6 *6 *6 *3 *3 *3 *3 *3 *7 *4 *4 *4 *4 *3 *8 - *9) - (-12 (-5 *4 (-663 (-217))) (-5 *5 (-112)) (-5 *6 (-217)) - (-5 *7 (-663 (-547))) - (-5 *8 (-3 (|:| |fn| (-379)) (|:| |fp| (-79 CONFUN)))) - (-5 *9 (-3 (|:| |fn| (-379)) (|:| |fp| (-76 OBJFUN)))) - (-5 *3 (-547)) (-5 *2 (-1004)) (-5 *1 (-728))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-582 *3 *4)) (-4 *3 (-1063)) (-4 *4 (-1173)) + (-5 *2 (-112))))) +(((*1 *2 *3) + (-12 (-4 *4 (-539)) (-5 *2 (-745)) (-5 *1 (-43 *4 *3)) + (-4 *3 (-408 *4))))) +(((*1 *1 *1) (-12 (-4 *1 (-1207 *2)) (-4 *2 (-1173))))) +(((*1 *2 *3) + (|partial| -12 (-5 *2 (-547)) (-5 *1 (-1155 *3)) (-4 *3 (-1016))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-821) (-539))) (-5 *1 (-267 *3 *2)) - (-4 *2 (-13 (-421 *3) (-971)))))) -(((*1 *2 *3 *4 *5 *5 *5 *5 *4 *6) - (-12 (-5 *4 (-547)) (-5 *6 (-1 (-1223) (-1218 *5) (-1218 *5) (-370))) - (-5 *3 (-1218 (-370))) (-5 *5 (-370)) (-5 *2 (-1223)) - (-5 *1 (-762))))) -(((*1 *1 *1 *2) - (-12 (-4 *1 (-56 *2 *3 *4)) (-4 *2 (-1172)) (-4 *3 (-364 *2)) - (-4 *4 (-364 *2)))) - ((*1 *1 *1 *2) - (-12 (|has| *1 (-6 -4329)) (-4 *1 (-582 *3 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*6)))) (-5 *1 (-451 *3 *4 *5 *6 *7 *2)) (-4 *5 (-821)) (-4 *2 (-918 *4 *6 (-834 *3))))) ((*1 *1 *1 *2) @@ -14932,7 +15285,7 @@ (-12 (-4 *2 (-354)) (-4 *3 (-767)) (-4 *4 (-821)) (-5 *1 (-493 *2 *3 *4 *5)) (-4 *5 (-918 *2 *3 *4)))) ((*1 *2 *2 *2) - (-12 (-5 *2 (-1218 *3)) (-4 *3 (-340)) (-5 *1 (-517 *3)))) + (-12 (-5 *2 (-1219 *3)) (-4 *3 (-340)) (-5 *1 (-517 *3)))) ((*1 *1 *1 *1) (-5 *1 (-523))) ((*1 *1 *1 *2) (-12 (-5 *2 (-547)) (-5 *1 (-575 *3)) (-4 *3 (-1016)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-575 *2)) (-4 *2 (-1016)))) @@ -14967,7 +15320,7 @@ ((*1 *1 *1 *1) (-5 *1 (-832))) ((*1 *1 *1 *1) (-12 (-5 *1 (-861 *2)) (-4 *2 (-1063)))) ((*1 *2 *3 *2) - (-12 (-5 *2 (-1218 *4)) (-4 *4 (-1194 *3)) (-4 *3 (-539)) + (-12 (-5 *2 (-1219 *4)) (-4 *4 (-1195 *3)) (-4 *3 (-539)) (-5 *1 (-938 *3 *4)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1022 *2)) (-4 *2 (-1023)))) ((*1 *1 *1 *1) (-4 *1 (-1075))) @@ -14981,330 +15334,232 @@ (-12 (-4 *3 (-1016)) (-4 *4 (-821)) (-5 *1 (-1088 *3 *4 *2)) (-4 *2 (-918 *3 (-519 *4) 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\ No newline at end of file |