diff options
Diffstat (limited to 'src')
| -rw-r--r-- | src/ChangeLog | 9 | ||||
| -rw-r--r-- | src/algebra/Makefile.in | 6 | ||||
| -rw-r--r-- | src/algebra/Makefile.pamphlet | 6 | ||||
| -rw-r--r-- | src/algebra/any.spad.pamphlet | 24 | ||||
| -rw-r--r-- | src/algebra/exposed.lsp.pamphlet | 2 | ||||
| -rw-r--r-- | src/algebra/syntax.spad.pamphlet | 64 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 890 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1994 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1294 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8810 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 26922 |
11 files changed, 20045 insertions, 19976 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 64d98b6c..4b90f072 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,3 +1,12 @@ +2008-01-20 Gabriel Dos Reis <gdr@cs.tamu.edu> + + * algebra/syntax.spad.pamphlet (ElaboratedExpression): New. + * algebra/any.spad.pamphlet: Rename ObjectProperty to Property. + * algebra/exposed.lsp.pamphlet: Likewise. + * algebra/Makefile.pamphlet (axiom_algebra_layer_5): Include + ELABEXPR.o + * share/algebra: Update databases. + 2008-01-19 Gabriel Dos Reis <gdr@cs.tamu.edu> * algebra/syntax.spad.pamphlet: Rename from algebra/syntax.spad. diff --git a/src/algebra/Makefile.in b/src/algebra/Makefile.in index 1812268d..baf81660 100644 --- a/src/algebra/Makefile.in +++ b/src/algebra/Makefile.in @@ -377,7 +377,7 @@ axiom_algebra_layer_0 = \ KOERCE.o KONVERT.o MSYSCMD.o ODEIFTBL.o \ OM.o OMCONN.o OMDEV.o OUT.o \ PRIMCAT.o PRINT.o PTRANFN.o SPFCAT.o \ - TYPE.o UTYPE.o PROPLOG.o OBJPROP.o \ + TYPE.o UTYPE.o PROPLOG.o PROPERTY.o \ SYNTAX.o axiom_algebra_layer_0_nrlibs = \ @@ -434,7 +434,7 @@ axiom_algebra_layer_4 = \ REPDB.o RFDIST.o RIDIST.o RMODULE.o \ SEXCAT.o SGROUP.o SGROUP-.o SPACEC.o \ SPLNODE.o STEP.o SUCH.o TEX1.o \ - UDVO.o YSTREAM.o PAIR.o ENV.o + UDVO.o YSTREAM.o PAIR.o ENV.o axiom_algebra_layer_4_nrlibs = \ $(axiom_algebra_layer_4:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -454,7 +454,7 @@ axiom_algebra_layer_5 = \ ODVAR.o OPQUERY.o ORDFIN.o ORDMON.o \ PATMATCH.o PERMCAT.o PDRING.o PDRING-.o \ SDVAR.o SUP2.o TRIGCAT.o TRIGCAT-.o \ - ULS2.o UP2.o + ULS2.o UP2.o ELABEXPR.o axiom_algebra_layer_5_nrlibs = \ $(axiom_algebra_layer_5:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index 53ee408b..114935b0 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -205,7 +205,7 @@ axiom_algebra_layer_0 = \ KOERCE.o KONVERT.o MSYSCMD.o ODEIFTBL.o \ OM.o OMCONN.o OMDEV.o OUT.o \ PRIMCAT.o PRINT.o PTRANFN.o SPFCAT.o \ - TYPE.o UTYPE.o PROPLOG.o OBJPROP.o \ + TYPE.o UTYPE.o PROPLOG.o PROPERTY.o \ SYNTAX.o axiom_algebra_layer_0_nrlibs = \ @@ -309,7 +309,7 @@ axiom_algebra_layer_4 = \ REPDB.o RFDIST.o RIDIST.o RMODULE.o \ SEXCAT.o SGROUP.o SGROUP-.o SPACEC.o \ SPLNODE.o STEP.o SUCH.o TEX1.o \ - UDVO.o YSTREAM.o PAIR.o ENV.o + UDVO.o YSTREAM.o PAIR.o ENV.o axiom_algebra_layer_4_nrlibs = \ $(axiom_algebra_layer_4:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) @@ -340,7 +340,7 @@ axiom_algebra_layer_5 = \ ODVAR.o OPQUERY.o ORDFIN.o ORDMON.o \ PATMATCH.o PERMCAT.o PDRING.o PDRING-.o \ SDVAR.o SUP2.o TRIGCAT.o TRIGCAT-.o \ - ULS2.o UP2.o + ULS2.o UP2.o ELABEXPR.o axiom_algebra_layer_5_nrlibs = \ $(axiom_algebra_layer_5:.$(OBJEXT)=.NRLIB/code.$(OBJEXT)) diff --git a/src/algebra/any.spad.pamphlet b/src/algebra/any.spad.pamphlet index d86a0cd4..56da387a 100644 --- a/src/algebra/any.spad.pamphlet +++ b/src/algebra/any.spad.pamphlet @@ -189,14 +189,14 @@ AnyFunctions1(S:Type): with @ -\section{domain OBJPROP ObjectProperty} -<<domain OBJPROP ObjectProperty>>= -)abbrev domain OBJPROP ObjectProperty +\section{domain PROPERTY Property} +<<domain PROPERTY Property>>= +)abbrev domain PROPERTY Property ++ Author: Gabriel Dos Reis ++ Date Created: October 24, 2007 ++ Date Last Modified: January 18, 2008. -++ An `ObjectProperty' is a pair of name and value. -ObjectProperty(): Public == Private where +++ An `Property' is a pair of name and value. +Property(): Public == Private where Public ==> CoercibleTo(OutputForm) with name: % -> Symbol ++ name(p) returns the name of property p @@ -249,9 +249,9 @@ Binding(): Public == Private where Public ==> CoercibleTo(OutputForm) with name: % -> Symbol ++ name(b) returns the name of binding b - properties: % -> List ObjectProperty + properties: % -> List Property ++ properties(b) returns the properties associated with binding b. - binding: (Symbol, List ObjectProperty) -> % + binding: (Symbol, List Property) -> % ++ binding(n,props) constructs a binding with name `n' and ++ property list `props'. @@ -268,7 +268,7 @@ Binding(): Public == Private where symbol car rep b properties b == - (cdr rep b) pretend List(ObjectProperty) + (cdr rep b) pretend List(Property) binding(n,props) == per CONS(n,props)$Lisp @@ -382,10 +382,10 @@ Environment(): Public == Private where setProperty!: (Symbol, Symbol, SExpression, %) -> % ++ setProperty!(n,p,v,e) binds the property `(p,v)' to `n' ++ in the topmost scope of `e'. - getProperties: (Symbol, %) -> Union(List ObjectProperty, "failed") + getProperties: (Symbol, %) -> Union(List Property, "failed") ++ getBinding(n,e) returns the list of properties of `n' in ++ e; otherwise `failed'. - setProperties!: (Symbol, List ObjectProperty, %) -> % + setProperties!: (Symbol, List Property, %) -> % ++ setBinding!(n,props,e) set the list of properties of `n' ++ to `props' in `e'. currentEnv: () -> % @@ -411,7 +411,7 @@ Environment(): Public == Private where getProperties(n,e) == b: SExpression := getProplist(n,e)$Lisp null? b => "failed" - b pretend List(ObjectProperty) + b pretend List(Property) setProperties!(n,b,e) == addBinding(n,b,e)$Lisp @ % @@ -475,7 +475,7 @@ Environment(): Public == Private where <<domain ANY Any>> <<package ANY1 AnyFunctions1>> -<<domain OBJPROP ObjectProperty>> +<<domain PROPERTY Property>> <<domain BINDING Binding>> <<domain CONTOUR Contour>> <<domain SCOPE Scope>> diff --git a/src/algebra/exposed.lsp.pamphlet b/src/algebra/exposed.lsp.pamphlet index 2b0aab86..810b8ea7 100644 --- a/src/algebra/exposed.lsp.pamphlet +++ b/src/algebra/exposed.lsp.pamphlet @@ -236,7 +236,7 @@ (|NumericComplexEigenPackage| . NCEP) (|NumericRealEigenPackage| . NREP) (|NumericContinuedFraction| . NCNTFRAC) - (|ObjectProperty| . OBJPROP) + (|Property| . PROPERTY) (|Octonion| . OCT) (|OctonionCategoryFunctions2| . OCTCT2) (|OneDimensionalArray| . ARRAY1) diff --git a/src/algebra/syntax.spad.pamphlet b/src/algebra/syntax.spad.pamphlet index e7c2b50b..4b3ce07f 100644 --- a/src/algebra/syntax.spad.pamphlet +++ b/src/algebra/syntax.spad.pamphlet @@ -241,6 +241,69 @@ ConstructorCall(): Public == Private where outputDomainConstructor(x)$Lisp @ +\section{domain ElaboratedExpression} +<<domain ELABEXPR ElaboratedExpression>>= +)abbrev domain ELABEXPR ElaboratedExpression +++ Author: Gabriel Dos Reis +++ Date Created: January 19, 2008 +++ Date Last Updated: January 20, 2008 +++ Description: This domains an expresion as elaborated by the interpreter. +++ See Also: +ElaboratedExpression(): Public == Private where + Public ==> CoercibleTo OutputForm with + type: % -> ConstructorCall + ++ type(e) returns the type of the expression as computed by + ++ the interpreter. + constant?: % -> Boolean + ++ constant?(e) returns true if `e' is a constant. + getConstant: % -> Union(SExpression,"failed") + ++ getConstant(e) retrieves the constant value of `e'e. + variable?: % -> Boolean + ++ variable?(e) returns true if `e' is a variable. + getVariable: % -> Union(Symbol,"failed") + ++ getVariable(e) retrieves the name of the variable `e'. + callForm?: % -> Boolean + ++ callForm?(e) is true when `e' is a call expression. + getOperator: % -> Union(Symbol, "failed") + ++ getOperator(e) retrieves the operator being invoked in `e', + ++ when `e' is an expression. + getOperands: % -> Union(List %, "failed") + ++ getOperands(e) returns the of operands in `e'e, assuming it + ++ is a call form. + + Private ==> add + immediateDataTag := INTERN("--immediateData--")$Lisp + + isAtomic(x: %): Boolean == + ATOM(x)$Lisp @ Boolean + + type x == + getMode(x)$Lisp @ ConstructorCall + + callForm? x == + CONSP(x)$Lisp @ Boolean + + getOperator x == + op: SExpression := getUnnameIfCan(x)$Lisp + null? op => "failed" + op pretend Symbol + + constant? x == + isAtomic x and + EQ(getUnnameIfCan(x)$Lisp, immediateDataTag)$Lisp : Boolean + + getConstant x == + constant? x => getValue(x)$Lisp @ SExpression + "failed" + + variable? x == + isAtomic x and not constant? x + + getVariable x == + variable? x => symbol (getUnname(x)$Lisp@SExpression) + "failed" +@ + \section{License} <<license>>= @@ -280,6 +343,7 @@ ConstructorCall(): Public == Private where <<license>> <<domain SYNTAX Syntax>> <<domain CTORCALL ConstructorCall>> +<<domain ELABEXPR ElaboratedExpression>> @ \end{document} diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index cc7661dd..14ce0e7c 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2233102 . 3409778141) +(2233072 . 3409817877) (-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."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . 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}."))) @@ -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}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4230 . T) (-4228 . T) (-4227 . T) ((-4235 "*") . T) (-4226 . T) (-4231 . T) (-4225 . T) (-2046 . T)) +((-4230 . T) (-4228 . T) (-4227 . T) ((-4235 "*") . T) (-4226 . T) (-4231 . T) (-4225 . T) (-2092 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|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."))) @@ -62,7 +62,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4233))) (-33) ((|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|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-2046 . T)) +((-2092 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |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| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -84,14 +84,14 @@ NIL ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-39 -4049 UP UPUP -2704) +(-39 -4049 UP UPUP -3967) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) ((-4226 |has| (-381 |#2|) (-337)) (-4231 |has| (-381 |#2|) (-337)) (-4225 |has| (-381 |#2|) (-337)) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-381 |#2|) (QUOTE (-133))) (|HasCategory| (-381 |#2|) (QUOTE (-135))) (|HasCategory| (-381 |#2|) (QUOTE (-323))) (|HasCategory| (-381 |#2|) (QUOTE (-337))) (-3703 (|HasCategory| (-381 |#2|) (QUOTE (-337))) (|HasCategory| (-381 |#2|) (QUOTE (-323)))) (|HasCategory| (-381 |#2|) (QUOTE (-342))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-342))) (-3703 (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) +((|HasCategory| (-381 |#2|) (QUOTE (-133))) (|HasCategory| (-381 |#2|) (QUOTE (-135))) (|HasCategory| (-381 |#2|) (QUOTE (-323))) (|HasCategory| (-381 |#2|) (QUOTE (-337))) (-3703 (|HasCategory| (-381 |#2|) (QUOTE (-337))) (|HasCategory| (-381 |#2|) (QUOTE (-323)))) (|HasCategory| (-381 |#2|) (QUOTE (-342))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-342))) (-3703 (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) (-40 R -4049) ((|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 (-425))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -404) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -404) (|devaluate| |#1|))))) (-41 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{}lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -107,7 +107,7 @@ NIL (-44 |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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|)))))) (-3703 (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-783))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|)))))) (-3703 (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-783))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|))))))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-783))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))))) (-45 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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|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"))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-56 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),{}...]}."))) @@ -159,64 +159,64 @@ NIL (-57 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}"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-58 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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) -(-59 -2884) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) +(-59 -2890) ((|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 -(-60 -2884) +(-60 -2890) ((|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 -(-61 -2884) +(-61 -2890) ((|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 -(-62 -2884) +(-62 -2890) ((|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 -(-63 -2884) +(-63 -2890) ((|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 -(-64 -2884) +(-64 -2890) ((|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 -(-65 -2884) +(-65 -2890) ((|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 -(-66 -2884) +(-66 -2890) ((|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 -(-67 -2884) +(-67 -2890) ((|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 -(-68 -2884) +(-68 -2890) ((|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 -(-69 -2884) +(-69 -2890) ((|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 -(-70 -2884) +(-70 -2890) ((|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 -(-71 -2884) +(-71 -2890) ((|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 -(-72 -2884) +(-72 -2890) ((|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 @@ -228,55 +228,55 @@ 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 -(-75 -2884) +(-75 -2890) ((|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 -(-76 -2884) +(-76 -2890) ((|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 -(-77 -2884) +(-77 -2890) ((|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 -(-78 -2884) +(-78 -2890) ((|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 -(-79 -2884) +(-79 -2890) ((|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 -(-80 -2884) +(-80 -2890) ((|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 -(-81 -2884) +(-81 -2890) ((|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 -(-82 -2884) +(-82 -2890) ((|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 -(-83 -2884) +(-83 -2890) ((|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 -(-84 -2884) +(-84 -2890) ((|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 -(-85 -2884) +(-85 -2890) ((|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 -(-86 -2884) +(-86 -2890) ((|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 -(-87 -2884) +(-87 -2890) ((|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 @@ -287,7 +287,7 @@ NIL (-89 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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-90 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL @@ -323,7 +323,7 @@ NIL (-98 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-99 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 @@ -338,14 +338,14 @@ NIL NIL (-102 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."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-103) ((|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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-521) (QUOTE (-838))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-521) (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-135))) (|HasCategory| (-521) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-946))) (|HasCategory| (-521) (QUOTE (-757))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-1060))) (|HasCategory| (-521) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-521) (QUOTE (-210))) (|HasCategory| (-521) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-521) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -284) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -261) (QUOTE (-521)) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-282))) (|HasCategory| (-521) (QUOTE (-506))) (|HasCategory| (-521) (QUOTE (-784))) (-3703 (|HasCategory| (-521) (QUOTE (-757))) (|HasCategory| (-521) (QUOTE (-784)))) (|HasCategory| (-521) (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-838)))) (|HasCategory| (-521) (QUOTE (-133))))) +((|HasCategory| (-521) (QUOTE (-837))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-521) (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-135))) (|HasCategory| (-521) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-946))) (|HasCategory| (-521) (QUOTE (-756))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-1060))) (|HasCategory| (-521) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| (-521) (QUOTE (-210))) (|HasCategory| (-521) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-521) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -284) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -261) (QUOTE (-521)) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-282))) (|HasCategory| (-521) (QUOTE (-506))) (|HasCategory| (-521) (QUOTE (-783))) (-3703 (|HasCategory| (-521) (QUOTE (-756))) (|HasCategory| (-521) (QUOTE (-783)))) (|HasCategory| (-521) (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-837)))) (|HasCategory| (-521) (QUOTE (-133))))) (-104) -((|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| (|ObjectProperty|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|ObjectProperty|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) +((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|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|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL NIL (-105) @@ -355,7 +355,7 @@ NIL (-106) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| (-108) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-108) (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| (-108) (QUOTE (-1013))) (-12 (|HasCategory| (-108) (QUOTE (-1013))) (|HasCategory| (-108) (LIST (QUOTE -284) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| (-108) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-108) (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| (-108) (QUOTE (-1013))) (-12 (|HasCategory| (-108) (QUOTE (-1013))) (|HasCategory| (-108) (LIST (QUOTE -284) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -561) (QUOTE (-791))))) (-107 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}"))) ((-4228 . T) (-4227 . T)) @@ -367,7 +367,7 @@ NIL (-109 A) ((|constructor| (NIL "This package exports functions to set some commonly used properties of operators,{} including properties which contain functions.")) (|constantOpIfCan| (((|Union| |#1| "failed") (|BasicOperator|)) "\\spad{constantOpIfCan(op)} returns \\spad{a} if \\spad{op} is the constant nullary operator always returning \\spad{a},{} \"failed\" otherwise.")) (|constantOperator| (((|BasicOperator|) |#1|) "\\spad{constantOperator(a)} returns a nullary operator op such that \\spad{op()} always evaluate to \\spad{a}.")) (|derivative| (((|Union| (|List| (|Mapping| |#1| (|List| |#1|))) "failed") (|BasicOperator|)) "\\spad{derivative(op)} returns the value of the \"\\%diff\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{derivative(op,{} foo)} attaches foo as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{f},{} then applying a derivation \\spad{D} to \\spad{op}(a) returns \\spad{f(a) * D(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|List| (|Mapping| |#1| (|List| |#1|)))) "\\spad{derivative(op,{} [foo1,{}...,{}foon])} attaches [foo1,{}...,{}foon] as the \"\\%diff\" property of \\spad{op}. If \\spad{op} has an \"\\%diff\" property \\spad{[f1,{}...,{}fn]} then applying a derivation \\spad{D} to \\spad{op(a1,{}...,{}an)} returns \\spad{f1(a1,{}...,{}an) * D(a1) + ... + fn(a1,{}...,{}an) * D(an)}.")) (|evaluate| (((|Union| (|Mapping| |#1| (|List| |#1|)) "failed") (|BasicOperator|)) "\\spad{evaluate(op)} returns the value of the \"\\%eval\" property of \\spad{op} if it has one,{} and \"failed\" otherwise.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| |#1|)) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to a returns the result of \\spad{f(a)}. Argument \\spad{op} must be unary.") (((|BasicOperator|) (|BasicOperator|) (|Mapping| |#1| (|List| |#1|))) "\\spad{evaluate(op,{} foo)} attaches foo as the \"\\%eval\" property of \\spad{op}. If \\spad{op} has an \"\\%eval\" property \\spad{f},{} then applying \\spad{op} to \\spad{(a1,{}...,{}an)} returns the result of \\spad{f(a1,{}...,{}an)}.") (((|Union| |#1| "failed") (|BasicOperator|) (|List| |#1|)) "\\spad{evaluate(op,{} [a1,{}...,{}an])} checks if \\spad{op} has an \"\\%eval\" property \\spad{f}. If it has,{} then \\spad{f(a1,{}...,{}an)} is returned,{} and \"failed\" otherwise."))) NIL -((|HasCategory| |#1| (QUOTE (-784)))) +((|HasCategory| |#1| (QUOTE (-783)))) (-110) ((|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 @@ -383,14 +383,14 @@ NIL (-113 |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}."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-838))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-135))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-112 |#1|) (QUOTE (-946))) (|HasCategory| (-112 |#1|) (QUOTE (-757))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-112 |#1|) (QUOTE (-1060))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-112 |#1|) (QUOTE (-210))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -482) (QUOTE (-1084)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -284) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -261) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-282))) (|HasCategory| (-112 |#1|) (QUOTE (-506))) (|HasCategory| (-112 |#1|) (QUOTE (-784))) (-3703 (|HasCategory| (-112 |#1|) (QUOTE (-757))) (|HasCategory| (-112 |#1|) (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-838)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))))) +((|HasCategory| (-112 |#1|) (QUOTE (-837))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-135))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-112 |#1|) (QUOTE (-946))) (|HasCategory| (-112 |#1|) (QUOTE (-756))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-112 |#1|) (QUOTE (-1060))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-112 |#1|) (QUOTE (-210))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -482) (QUOTE (-1084)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -284) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -261) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-282))) (|HasCategory| (-112 |#1|) (QUOTE (-506))) (|HasCategory| (-112 |#1|) (QUOTE (-783))) (-3703 (|HasCategory| (-112 |#1|) (QUOTE (-756))) (|HasCategory| (-112 |#1|) (QUOTE (-783)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-112 |#1|) (QUOTE (-837)))) (|HasCategory| (-112 |#1|) (QUOTE (-133))))) (-114 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| (($ $) "\\spad{left(u)} returns the left child."))) NIL ((|HasAttribute| |#1| (QUOTE -4234))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "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."))) -((-2046 . T)) +((-2092 . T)) NIL (-116 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."))) @@ -399,14 +399,14 @@ NIL (-117 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"))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,16 +414,16 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-123 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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-124) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -436,18 +436,18 @@ NIL ((|constructor| (NIL "Members of the domain CardinalNumber are values indicating the cardinality of sets,{} both finite and infinite. Arithmetic operations are defined on cardinal numbers as follows. \\blankline If \\spad{x = \\#X} and \\spad{y = \\#Y} then \\indented{2}{\\spad{x+y\\space{2}= \\#(X+Y)}\\space{3}\\tab{30}disjoint union} \\indented{2}{\\spad{x-y\\space{2}= \\#(X-Y)}\\space{3}\\tab{30}relative complement} \\indented{2}{\\spad{x*y\\space{2}= \\#(X*Y)}\\space{3}\\tab{30}cartesian product} \\indented{2}{\\spad{x**y = \\#(X**Y)}\\space{2}\\tab{30}\\spad{X**Y = \\{g| g:Y->X\\}}} \\blankline The non-negative integers have a natural construction as cardinals \\indented{2}{\\spad{0 = \\#\\{\\}},{} \\spad{1 = \\{0\\}},{} \\spad{2 = \\{0,{} 1\\}},{} ...,{} \\spad{n = \\{i| 0 <= i < n\\}}.} \\blankline That \\spad{0} acts as a zero for the multiplication of cardinals is equivalent to the axiom of choice. \\blankline The generalized continuum hypothesis asserts \\center{\\spad{2**Aleph i = Aleph(i+1)}} and is independent of the axioms of set theory [Goedel 1940]. \\blankline Three commonly encountered cardinal numbers are \\indented{3}{\\spad{a = \\#Z}\\space{7}\\tab{30}countable infinity} \\indented{3}{\\spad{c = \\#R}\\space{7}\\tab{30}the continuum} \\indented{3}{\\spad{f = \\#\\{g| g:[0,{}1]->R\\}}} \\blankline In this domain,{} these values are obtained using \\indented{3}{\\spad{a := Aleph 0},{} \\spad{c := 2**a},{} \\spad{f := 2**c}.} \\blankline")) (|generalizedContinuumHypothesisAssumed| (((|Boolean|) (|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed(bool)} is used to dictate whether the hypothesis is to be assumed.")) (|generalizedContinuumHypothesisAssumed?| (((|Boolean|)) "\\spad{generalizedContinuumHypothesisAssumed?()} tests if the hypothesis is currently assumed.")) (|countable?| (((|Boolean|) $) "\\spad{countable?(\\spad{a})} determines whether \\spad{a} is a countable cardinal,{} \\spadignore{i.e.} an integer or \\spad{Aleph 0}.")) (|finite?| (((|Boolean|) $) "\\spad{finite?(\\spad{a})} determines whether \\spad{a} is a finite cardinal,{} \\spadignore{i.e.} an integer.")) (|Aleph| (($ (|NonNegativeInteger|)) "\\spad{Aleph(n)} provides the named (infinite) cardinal number.")) (** (($ $ $) "\\spad{x**y} returns \\spad{\\#(X**Y)} where \\spad{X**Y} is defined \\indented{1}{as \\spad{\\{g| g:Y->X\\}}.}")) (- (((|Union| $ "failed") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) (((-4235 "*") . T)) NIL -(-127 |minix| -2617 S T$) +(-127 |minix| -2623 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-128 |minix| -2617 R) +(-128 |minix| -2623 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\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 (-129) ((|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}."))) ((-4233 . T) (-4223 . T) (-4234 . T)) -((|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-132) (QUOTE (-342))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1013))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-3703 (-12 (|HasCategory| (-132) (QUOTE (-342))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-132) (QUOTE (-342))) (|HasCategory| (-132) (QUOTE (-783))) (|HasCategory| (-132) (QUOTE (-1013))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-3703 (-12 (|HasCategory| (-132) (QUOTE (-342))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-791))))) (-130 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 @@ -486,7 +486,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -4233))) (-139 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."))) -((-2046 . T)) +((-2092 . T)) NIL (-140 |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."))) @@ -531,10 +531,10 @@ NIL (-150 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 (-838))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-946))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-337))) (|HasAttribute| |#2| (QUOTE -4229)) (|HasAttribute| |#2| (QUOTE -4232)) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-784)))) +((|HasCategory| |#2| (QUOTE (-837))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-946))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-337))) (|HasAttribute| |#2| (QUOTE -4229)) (|HasAttribute| |#2| (QUOTE -4232)) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-783)))) (-151 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})"))) -((-4226 -3703 (|has| |#1| (-513)) (-12 (|has| |#1| (-282)) (|has| |#1| (-838)))) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4229 |has| |#1| (-6 -4229)) (-4232 |has| |#1| (-6 -4232)) (-3905 . T) (-2046 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-4226 -3703 (|has| |#1| (-513)) (-12 (|has| |#1| (-282)) (|has| |#1| (-837)))) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4229 |has| |#1| (-6 -4229)) (-4232 |has| |#1| (-6 -4232)) (-3905 . T) (-2092 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-152 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."))) @@ -546,8 +546,8 @@ NIL NIL (-154 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}."))) -((-4226 -3703 (|has| |#1| (-513)) (-12 (|has| |#1| (-282)) (|has| |#1| (-838)))) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4229 |has| |#1| (-6 -4229)) (-4232 |has| |#1| (-6 -4232)) (-3905 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-1105))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-1105)))) (|HasCategory| |#1| (QUOTE (-946))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE 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(|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337)))) (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084))))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-323))))) (-155 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 @@ -579,7 +579,7 @@ NIL (-162 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr,{} pat,{} res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-881 |#2|) (LIST (QUOTE -815) (|devaluate| |#1|)))) +((|HasCategory| (-880 |#2|) (LIST (QUOTE -814) (|devaluate| |#1|)))) (-163 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,{}r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,{}lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,{}lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)\\spad{*lm}(2)*...\\spad{*lm}(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,{}l)} \\undocumented{}"))) NIL @@ -711,7 +711,7 @@ NIL (-195) ((|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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-521) (QUOTE (-838))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-521) (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-135))) (|HasCategory| (-521) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-946))) (|HasCategory| (-521) (QUOTE (-757))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-1060))) (|HasCategory| (-521) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-521) (QUOTE (-210))) (|HasCategory| (-521) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-521) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -284) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -261) (QUOTE (-521)) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-282))) (|HasCategory| (-521) (QUOTE (-506))) (|HasCategory| (-521) (QUOTE (-784))) (-3703 (|HasCategory| (-521) (QUOTE (-757))) (|HasCategory| (-521) (QUOTE (-784)))) (|HasCategory| (-521) (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-838)))) (|HasCategory| (-521) (QUOTE (-133))))) +((|HasCategory| (-521) (QUOTE (-837))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-521) (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-135))) (|HasCategory| (-521) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-946))) (|HasCategory| (-521) (QUOTE (-756))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-1060))) (|HasCategory| (-521) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| (-521) (QUOTE (-210))) (|HasCategory| (-521) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-521) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -284) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -261) (QUOTE (-521)) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-282))) (|HasCategory| (-521) (QUOTE (-506))) (|HasCategory| (-521) (QUOTE (-783))) (-3703 (|HasCategory| (-521) (QUOTE (-756))) (|HasCategory| (-521) (QUOTE (-783)))) (|HasCategory| (-521) (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-837)))) (|HasCategory| (-521) (QUOTE (-133))))) (-196 R -4049) ((|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 @@ -727,7 +727,7 @@ NIL (-199 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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-200 |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}."))) ((-4230 . T)) @@ -738,7 +738,7 @@ NIL NIL (-202) ((|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}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\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}."))) -((-3894 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-3893 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-203) ((|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)}.}"))) @@ -747,19 +747,19 @@ NIL (-204 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}"))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-513))) (|HasAttribute| |#1| (QUOTE (-4235 "*"))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-513))) (|HasAttribute| |#1| (QUOTE (-4235 "*"))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-205 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 (-206 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."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-207 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 -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210)))) +((|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210)))) (-208 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}."))) ((-4230 . T)) @@ -778,28 +778,28 @@ NIL ((|HasAttribute| |#1| (QUOTE -4233))) (-212 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}."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-213) ((|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 -(-214 S -2617 R) +(-214 S -2623 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 (-337))) (|HasCategory| |#3| (QUOTE (-729))) (|HasCategory| |#3| (QUOTE (-782))) (|HasAttribute| |#3| (QUOTE -4230)) (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-970))) (|HasCategory| |#3| (QUOTE (-1013)))) -(-215 -2617 R) +((|HasCategory| |#3| (QUOTE (-337))) (|HasCategory| |#3| (QUOTE (-729))) (|HasCategory| |#3| (QUOTE (-781))) (|HasAttribute| |#3| (QUOTE -4230)) (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-970))) (|HasCategory| |#3| (QUOTE (-1013)))) +(-215 -2623 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"))) -((-4227 |has| |#2| (-970)) (-4228 |has| |#2| (-970)) (-4230 |has| |#2| (-6 -4230)) ((-4235 "*") |has| |#2| (-157)) (-4233 . T) (-2046 . T)) +((-4227 |has| |#2| (-970)) (-4228 |has| |#2| (-970)) (-4230 |has| |#2| (-6 -4230)) ((-4235 "*") |has| |#2| (-157)) (-4233 . T) (-2092 . T)) NIL -(-216 -2617 A B) +(-216 -2623 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 -(-217 -2617 R) +(-217 -2623 R) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying component type. This contrasts with simple vectors in that the members can be viewed as having constant length. Thus many categorical properties can by lifted from the underlying component type. Component extraction operations are provided but no updating operations. Thus new direct product elements can either be created by converting vector elements using the \\spadfun{directProduct} function or by taking appropriate linear combinations of basis vectors provided by the \\spad{unitVector} operation."))) ((-4227 |has| |#2| (-970)) (-4228 |has| |#2| (-970)) (-4230 |has| |#2| (-6 -4230)) ((-4235 "*") |has| |#2| (-157)) (-4233 . T)) -((|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-782))) (-3703 (|HasCategory| |#2| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-782)))) (|HasCategory| |#2| (QUOTE (-157))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-970)))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-337)))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-970)))) (|HasCategory| |#2| (QUOTE (-342))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (-3703 (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-970)))) (-3703 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((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -814,12 +814,12 @@ NIL NIL (-221 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."))) -((-2046 . T)) +((-2092 . T)) NIL (-222 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}"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-223 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 @@ -827,19 +827,19 @@ NIL (-224 |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|) $) "\\spad{reify(d)} returns the abstract syntax for the domain \\spad{`x'}."))) 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In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\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 @@ -850,7 +850,7 @@ NIL NIL (-230 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}."))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-231) ((|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."))) @@ -891,7 +891,7 @@ NIL (-240 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"))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#3| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#3| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#3| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#3| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#3| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#3| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#3| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#3| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#3| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#3| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) (-241 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 @@ -955,10 +955,10 @@ NIL (-256 A S) ((|constructor| (NIL "An extensible aggregate is one which allows insertion and deletion of entries. These aggregates are models of lists and streams which are represented by linked structures so as to make insertion,{} deletion,{} and concatenation efficient. However,{} access to elements of these extensible aggregates is generally slow since access is made from the end. See \\spadtype{FlexibleArray} for an exception.")) (|removeDuplicates!| (($ $) "\\spad{removeDuplicates!(u)} destructively removes duplicates from \\spad{u}.")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,{}u)} destructively changes \\spad{u} by keeping only values \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})}.")) (|merge!| (($ $ $) "\\spad{merge!(u,{}v)} destructively merges \\spad{u} and \\spad{v} in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge!(p,{}u,{}v)} destructively merges \\spad{u} and \\spad{v} using predicate \\spad{p}.")) (|insert!| (($ $ $ (|Integer|)) "\\spad{insert!(v,{}u,{}i)} destructively inserts aggregate \\spad{v} into \\spad{u} at position \\spad{i}.") (($ |#2| $ (|Integer|)) "\\spad{insert!(x,{}u,{}i)} destructively inserts \\spad{x} into \\spad{u} at position \\spad{i}.")) (|remove!| (($ |#2| $) "\\spad{remove!(x,{}u)} destructively removes all values \\spad{x} from \\spad{u}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,{}u)} destructively removes all elements \\spad{x} of \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.")) (|delete!| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete!(u,{}i..j)} destructively deletes elements \\spad{u}.\\spad{i} through \\spad{u}.\\spad{j}.") (($ $ (|Integer|)) "\\spad{delete!(u,{}i)} destructively deletes the \\axiom{\\spad{i}}th element of \\spad{u}.")) (|concat!| (($ $ $) "\\spad{concat!(u,{}v)} destructively appends \\spad{v} to the end of \\spad{u}. \\spad{v} is unchanged") (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}."))) NIL -((|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1013)))) +((|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-1013)))) (-257 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}."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-258 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}."))) @@ -984,7 +984,7 @@ NIL ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,{}x,{}y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,{}x,{}y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u,{} x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u,{} x,{} y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-264 S R |Mod| -2633 -1318 |exactQuo|) +(-264 S R |Mod| -1664 -3389 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL @@ -993,7 +993,7 @@ NIL ((-4226 . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-266) -((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|ObjectProperty|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|ObjectProperty|)) "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"))) +((|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"))) NIL NIL (-267 R) @@ -1007,11 +1007,11 @@ NIL (-269 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) (= (($ |#1| |#1|) "\\spad{a=b} creates an equation."))) 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Thus keys are considered equal only if they are the same instance of a structure."))) ((-4233 . T) (-4234 . 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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 @@ -1079,7 +1079,7 @@ NIL (-287 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))}."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-135))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-946))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-1060))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-210))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -482) (QUOTE (-1084)) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -284) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -261) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-282))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-506))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-784))) (-3703 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-784)))) (-12 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| $ (QUOTE (-133)))) (-3703 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (-12 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-838))) (|HasCategory| $ (QUOTE (-133)))))) +((|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-837))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-135))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-946))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-1060))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-210))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -482) (QUOTE (-1084)) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -284) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (LIST (QUOTE -261) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (LIST (QUOTE -1151) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-282))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-506))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-783))) (-3703 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-783)))) (-12 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-837))) (|HasCategory| $ (QUOTE (-133)))) (-3703 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-133))) (-12 (|HasCategory| (-1151 |#1| |#2| |#3| |#4|) (QUOTE (-837))) (|HasCategory| $ (QUOTE (-133)))))) (-288 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 @@ -1091,7 +1091,7 @@ NIL (-290 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} \\undocumented{}")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} \\undocumented{}")) (|simplifyPower| (($ $ (|Integer|)) "simplifyPower?(\\spad{f},{}\\spad{n}) \\undocumented{}")) (|number?| (((|Boolean|) $) "\\spad{number?(f)} tests if \\spad{f} is rational")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic quantities present in \\spad{f} by applying their defining relations."))) 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(-3703 (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-970)))) (-3703 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))))) (|HasCategory| |#1| (QUOTE (-1025))) (-3703 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#1| (QUOTE (-1025)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-1025)))) (-3703 (|HasCategory| |#1| (QUOTE (-25))) (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))))) (|HasCategory| $ (QUOTE (-970))) (|HasCategory| $ (LIST (QUOTE -961) (QUOTE (-521))))) (-291 R -4049) ((|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 @@ -1103,7 +1103,7 @@ NIL (-293 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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|))))) (|HasCategory| (-381 (-521)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasSignature| |#1| (LIST (QUOTE -2189) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2184) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4084) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|))))) (|HasCategory| (-381 (-521)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasSignature| |#1| (LIST (QUOTE -2223) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -1749) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4085) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) (-294 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1115,7 +1115,7 @@ NIL (-296 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."))) ((-4228 . T) (-4227 . T)) -((|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-728)))) +((|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-728)))) (-297 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}."))) NIL @@ -1135,7 +1135,7 @@ NIL (-301 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."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-302 S -4049) ((|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 @@ -1199,7 +1199,7 @@ NIL (-317 |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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-342))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3703 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-342))))) +((|HasCategory| (-838 |#1|) (QUOTE (-135))) (|HasCategory| (-838 |#1|) (QUOTE (-342))) (|HasCategory| (-838 |#1|) (QUOTE (-133))) (-3703 (|HasCategory| (-838 |#1|) (QUOTE (-133))) (|HasCategory| (-838 |#1|) (QUOTE (-342))))) (-318 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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -1231,7 +1231,7 @@ NIL (-325 |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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-342))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3703 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-342))))) +((|HasCategory| (-838 |#1|) (QUOTE (-135))) (|HasCategory| (-838 |#1|) (QUOTE (-342))) (|HasCategory| (-838 |#1|) (QUOTE (-133))) (-3703 (|HasCategory| (-838 |#1|) (QUOTE (-133))) (|HasCategory| (-838 |#1|) (QUOTE (-342))))) (-326 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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -1243,7 +1243,7 @@ NIL (-328 |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}."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-839 |#1|) (QUOTE (-135))) (|HasCategory| (-839 |#1|) (QUOTE (-342))) (|HasCategory| (-839 |#1|) (QUOTE (-133))) (-3703 (|HasCategory| (-839 |#1|) (QUOTE (-133))) (|HasCategory| (-839 |#1|) (QUOTE (-342))))) +((|HasCategory| (-838 |#1|) (QUOTE (-135))) (|HasCategory| (-838 |#1|) (QUOTE (-342))) (|HasCategory| (-838 |#1|) (QUOTE (-133))) (-3703 (|HasCategory| (-838 |#1|) (QUOTE (-133))) (|HasCategory| (-838 |#1|) (QUOTE (-342))))) (-329 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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -1315,10 +1315,10 @@ NIL (-346 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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4234)) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1013)))) +((|HasAttribute| |#1| (QUOTE -4234)) (|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-1013)))) (-347 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4233 . T) (-2046 . T)) +((-4233 . T) (-2092 . T)) NIL (-348 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|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."))) @@ -1342,7 +1342,7 @@ NIL NIL (-353) ((|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}."))) -((-4216 . T) (-4224 . T) (-3894 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-4216 . T) (-4224 . T) (-3893 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-354 |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}."))) @@ -1358,11 +1358,11 @@ NIL NIL (-357) ((|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}."))) -((-2046 . T)) +((-2092 . T)) NIL (-358) ((|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.}"))) -((-2046 . T)) +((-2092 . T)) NIL (-359 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."))) @@ -1371,7 +1371,7 @@ NIL (-360 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."))) NIL -((|HasCategory| |#1| (QUOTE (-784)))) +((|HasCategory| |#1| (QUOTE (-783)))) (-361) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -1406,17 +1406,17 @@ NIL NIL (-369) ((|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."))) -((-2046 . T)) +((-2092 . T)) NIL (-370) ((|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.}"))) -((-2046 . T)) +((-2092 . T)) NIL (-371) ((|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 -(-372 -2884 |returnType| -3885 |symbols|) +(-372 -2890 |returnType| -3886 |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 @@ -1426,7 +1426,7 @@ NIL NIL (-374 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)."))) -((-2046 . T)) +((-2092 . T)) NIL (-375 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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1442,7 +1442,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4216)) (|HasAttribute| |#1| (QUOTE -4224))) (-378) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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\"."))) -((-3894 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-3893 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-379 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."))) @@ -1455,7 +1455,7 @@ NIL (-381 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."))) ((-4220 -12 (|has| |#1| (-6 -4231)) (|has| |#1| (-425)) (|has| |#1| (-6 -4220))) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-946))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-506))) (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-765)))) (-12 (|HasAttribute| |#1| (QUOTE -4231)) (|HasAttribute| |#1| (QUOTE -4220)) (|HasCategory| |#1| (QUOTE (-425)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (-3703 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-765)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-765))))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-765))))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-946))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-506))) (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-764)))) (-12 (|HasAttribute| |#1| (QUOTE -4231)) (|HasAttribute| |#1| (QUOTE -4220)) (|HasCategory| |#1| (QUOTE (-425)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-764)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (-3703 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-783)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-764)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-764)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-764))))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-764))))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) (-382 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 @@ -1499,7 +1499,7 @@ NIL (-392 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."))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -284) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -261) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-946))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-1123))))) +((|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -284) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -261) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-1123))) (|HasCategory| |#1| (QUOTE (-946))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-1123))))) (-393 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 @@ -1523,10 +1523,10 @@ NIL (-398 A 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| ((|#2| $) "\\spad{min(u)} returns the smallest element of aggregate \\spad{u}.")) (|max| ((|#2| $) "\\spad{max(u)} returns the largest element of aggregate \\spad{u}.")) (|universe| (($) "\\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}."))) NIL -((|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-342)))) +((|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-342)))) (-399 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}."))) -((-4233 . T) (-4223 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4223 . T) (-4234 . T) (-2092 . T)) NIL (-400 R -4049) ((|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."))) @@ -1546,7 +1546,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (-404 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}."))) -((-4230 -3703 (|has| |#1| (-970)) (|has| |#1| (-446))) (-4228 |has| |#1| (-157)) (-4227 |has| |#1| (-157)) ((-4235 "*") |has| |#1| (-513)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-513)) (-4225 |has| |#1| (-513)) (-2046 . T)) +((-4230 -3703 (|has| |#1| (-970)) (|has| |#1| (-446))) (-4228 |has| |#1| (-157)) (-4227 |has| |#1| (-157)) ((-4235 "*") |has| |#1| (-513)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-513)) (-4225 |has| |#1| (-513)) (-2092 . T)) NIL (-405 R -4049) ((|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."))) @@ -1582,11 +1582,11 @@ NIL NIL (-413) ((|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}."))) -((-2046 . T)) +((-2092 . T)) NIL (-414) ((|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.}"))) -((-2046 . T)) +((-2092 . T)) NIL (-415 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."))) @@ -1634,12 +1634,12 @@ NIL NIL (-426 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"))) -((-4230 |has| (-381 (-881 |#1|)) (-513)) (-4228 . T) (-4227 . T)) -((|HasCategory| (-381 (-881 |#1|)) (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| (-381 (-881 |#1|)) (QUOTE (-513)))) +((-4230 |has| (-381 (-880 |#1|)) (-513)) (-4228 . T) (-4227 . T)) +((|HasCategory| (-381 (-880 |#1|)) (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| (-381 (-880 |#1|)) (QUOTE (-513)))) (-427 |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"))) (((-4235 "*") |has| |#2| (-157)) (-4226 |has| |#2| (-513)) (-4231 |has| |#2| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . 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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 @@ -1675,7 +1675,7 @@ NIL (-436 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}}."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-791))))) (-437 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) NIL @@ -1719,15 +1719,15 @@ NIL (-447 |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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4227 . T) (-4228 . T) (-4230 . 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T)) -((|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|)))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|)))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))))) (-449 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)}"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-791))))) (-450) ((|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| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) 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Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL @@ -1743,15 +1743,15 @@ NIL (-453 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) ((-4233 . T) (-4234 . 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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 -4233)) (|HasAttribute| |#1| (QUOTE -4234)) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasAttribute| |#1| (QUOTE -4233)) (|HasAttribute| |#1| (QUOTE -4234)) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-460 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-2046 . T)) +((-2092 . T)) NIL (-461 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1791,11 +1791,11 @@ NIL (-465 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-466 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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-467 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 @@ -1807,7 +1807,7 @@ NIL (-469 |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}."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| (-108) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-108) (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| (-108) (QUOTE (-1013))) (-12 (|HasCategory| (-108) (QUOTE (-1013))) (|HasCategory| (-108) (LIST (QUOTE -284) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| (-108) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-108) (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| (-108) (QUOTE (-1013))) (-12 (|HasCategory| (-108) (QUOTE (-1013))) (|HasCategory| (-108) (LIST (QUOTE -284) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -561) (QUOTE (-791))))) (-470 K R UP L) ((|constructor| (NIL "IntegralBasisPolynomialTools provides functions for \\indented{1}{mapping functions on the coefficients of univariate and bivariate} \\indented{1}{polynomials.}")) (|mapBivariate| (((|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#4|)) (|Mapping| |#4| |#1|) |#3|) "\\spad{mapBivariate(f,{}p(x,{}y))} applies the function \\spad{f} to the coefficients of \\spad{p(x,{}y)}.")) (|mapMatrixIfCan| (((|Union| (|Matrix| |#2|) "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|Matrix| (|SparseUnivariatePolynomial| |#4|))) "\\spad{mapMatrixIfCan(f,{}mat)} applies the function \\spad{f} to the coefficients of the entries of \\spad{mat} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariateIfCan| (((|Union| |#2| "failed") (|Mapping| (|Union| |#1| "failed") |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariateIfCan(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)},{} if possible,{} and returns \\spad{\"failed\"} otherwise.")) (|mapUnivariate| (((|SparseUnivariatePolynomial| |#4|) (|Mapping| |#4| |#1|) |#2|) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}.") ((|#2| (|Mapping| |#1| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{mapUnivariate(f,{}p(x))} applies the function \\spad{f} to the coefficients of \\spad{p(x)}."))) NIL @@ -1867,7 +1867,7 @@ NIL (-484 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}"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-485 |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}."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -1875,11 +1875,11 @@ NIL (-486 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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-487 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."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-488 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 @@ -1891,7 +1891,7 @@ NIL (-490 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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-513))) (|HasAttribute| |#1| (QUOTE (-4235 "*"))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-513))) (|HasAttribute| |#1| (QUOTE (-4235 "*"))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-491 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1959,7 +1959,7 @@ NIL (-507 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))))) (-508 R -4049) ((|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 @@ -1974,7 +1974,7 @@ NIL NIL (-511 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."))) -((-3894 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-3893 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-512 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."))) @@ -2027,7 +2027,7 @@ NIL (-524 R -4049) ((|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 -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-1048)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-573))))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-1048)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-573))))) (-525 -4049 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 @@ -2042,7 +2042,7 @@ NIL NIL (-528 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."))) -((-3894 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-3893 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-529) ((|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."))) @@ -2051,7 +2051,7 @@ NIL (-530 R -4049) ((|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 -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-259))) (|HasCategory| |#2| (QUOTE (-573))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084))))) (-12 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-259)))) (|HasCategory| |#1| (QUOTE (-513)))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-259))) (|HasCategory| |#2| (QUOTE (-573))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084))))) (-12 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-259)))) (|HasCategory| |#1| (QUOTE (-513)))) (-531 -4049 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 @@ -2083,7 +2083,7 @@ NIL (-538 -4049) ((|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}."))) ((-4228 . T) (-4227 . T)) -((|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-1084))))) +((|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-1084))))) (-539 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 @@ -2107,7 +2107,7 @@ NIL (-544 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1013))) (-3703 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1013)))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-3703 (-12 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-792)))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))))) +((|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-132) (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| (-132) (QUOTE (-1013))) (-3703 (|HasCategory| (-132) (QUOTE (-783))) (|HasCategory| (-132) (QUOTE (-1013)))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-3703 (-12 (|HasCategory| (-132) (QUOTE (-783))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-791)))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))))) (-545 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 @@ -2115,7 +2115,7 @@ NIL (-546 |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}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-521)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-521)) (|devaluate| |#1|))))) (|HasCategory| (-521) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-521))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2189) (LIST (|devaluate| |#1|) (QUOTE (-1084))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-521)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-521)) (|devaluate| |#1|))))) (|HasCategory| (-521) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-521))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2223) (LIST (|devaluate| |#1|) (QUOTE (-1084))))))) (-547 |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.}"))) ((-4228 |has| |#1| (-513)) (-4227 |has| |#1| (-513)) ((-4235 "*") |has| |#1| (-513)) (-4226 |has| |#1| (-513)) (-4230 . T)) @@ -2139,14 +2139,14 @@ NIL (-552 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-970)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-970)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-553 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 -4234)) (|HasCategory| |#2| (QUOTE (-784))) (|HasAttribute| |#1| (QUOTE -4233)) (|HasCategory| |#3| (QUOTE (-1013)))) +((|HasAttribute| |#1| (QUOTE -4234)) (|HasCategory| |#2| (QUOTE (-783))) (|HasAttribute| |#1| (QUOTE -4233)) (|HasCategory| |#3| (QUOTE (-1013)))) (-554 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-2046 . T)) +((-2092 . T)) NIL (-555 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) @@ -2155,14 +2155,14 @@ NIL (-556 |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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| (-1067) (QUOTE (-784))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (QUOTE (-1067))) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| (-1067) (QUOTE (-783))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (QUOTE (-1067))) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -561) (QUOTE (-791))))) (-557 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 (-558 |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}."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-559 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"))) @@ -2171,7 +2171,7 @@ NIL (-560 S) ((|constructor| (NIL "A kernel over a set \\spad{S} is an operator applied to a given list of arguments from \\spad{S}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op(a1,{}...,{}an),{} s)} tests if the name of op is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(op(a1,{}...,{}an),{} f)} tests if op = \\spad{f}.")) (|symbolIfCan| (((|Union| (|Symbol|) "failed") $) "\\spad{symbolIfCan(k)} returns \\spad{k} viewed as a symbol if \\spad{k} is a symbol,{} and \"failed\" otherwise.")) (|kernel| (($ (|Symbol|)) "\\spad{kernel(x)} returns \\spad{x} viewed as a kernel.") (($ (|BasicOperator|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{kernel(op,{} [a1,{}...,{}an],{} m)} returns the kernel \\spad{op(a1,{}...,{}an)} of nesting level \\spad{m}. Error: if \\spad{op} is \\spad{k}-ary for some \\spad{k} not equal to \\spad{m}.")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(k)} returns the nesting level of \\spad{k}.")) (|argument| (((|List| |#1|) $) "\\spad{argument(op(a1,{}...,{}an))} returns \\spad{[a1,{}...,{}an]}.")) (|operator| (((|BasicOperator|) $) "\\spad{operator(op(a1,{}...,{}an))} returns the operator op.")) (|name| (((|Symbol|) $) "\\spad{name(op(a1,{}...,{}an))} returns the name of op."))) NIL -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-561 S) ((|constructor| (NIL "A is coercible to \\spad{B} means any element of A can automatically be converted into an element of \\spad{B} by the interpreter.")) (|coerce| ((|#1| $) "\\spad{coerce(a)} transforms a into an element of \\spad{S}."))) NIL @@ -2195,7 +2195,7 @@ NIL (-566 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}."))) ((-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-782)))) +((|HasCategory| |#1| (QUOTE (-781)))) (-567 R -4049) ((|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 @@ -2203,7 +2203,7 @@ NIL (-568 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"))) ((-4228 . T) (-4227 . T) ((-4235 "*") . T) (-4226 . T) (-4230 . T)) -((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) +((|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (-569 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 @@ -2235,7 +2235,7 @@ NIL (-576) ((|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."))) ((-4234 . T)) -((|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-1067) (QUOTE (-784))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1013))) (-12 (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -284) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (QUOTE (-1067))) (LIST (QUOTE |:|) (QUOTE -3045) (QUOTE (-51))))))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-1067) (QUOTE (-783))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (QUOTE (-1013))) (-12 (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -284) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (QUOTE (-1067))) (LIST (QUOTE |:|) (QUOTE -3050) (QUOTE (-51))))))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791)))))) (-577 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 @@ -2259,7 +2259,7 @@ NIL (-582 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 -((|HasCategory| |#1| (QUOTE (-337))) (-2400 (|HasCategory| |#1| (QUOTE (-337))))) +((|HasCategory| |#1| (QUOTE (-337))) (-2416 (|HasCategory| |#1| (QUOTE (-337))))) (-583 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| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) ((-4230 . T)) @@ -2279,11 +2279,11 @@ NIL (-587 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#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."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-765))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-764))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-588 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|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-589 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2298,7 +2298,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4234))) (-592 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})}."))) -((-2046 . T)) +((-2092 . T)) NIL (-593 R -4049 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."))) @@ -2324,7 +2324,7 @@ NIL ((|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)))) -(-599 A -3838) +(-599 A -3274) ((|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}}"))) ((-4227 . T) (-4228 . T) (-4230 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-337)))) @@ -2358,7 +2358,7 @@ NIL NIL (-607 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}."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-608 -4049) ((|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}."))) @@ -2375,7 +2375,7 @@ NIL (-611 |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."))) ((-4230 . T) (-4233 . T) (-4227 . T) (-4228 . T)) -((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-513))) (-3703 (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-3703 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-157)))) +((|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-513))) (-3703 (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-3703 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-157)))) (-612 |VarSet|) ((|constructor| (NIL "Lyndon words over arbitrary (ordered) symbols: see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). A Lyndon word is a word which is smaller than any of its right factors \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering. If \\axiom{a} and \\axiom{\\spad{b}} are two Lyndon words such that \\axiom{a < \\spad{b}} holds \\spad{w}.\\spad{r}.\\spad{t} lexicographical ordering then \\axiom{a*b} is a Lyndon word. Parenthesized Lyndon words can be generated from symbols by using the following rule: \\axiom{[[a,{}\\spad{b}],{}\\spad{c}]} is a Lyndon word iff \\axiom{a*b < \\spad{c} \\spad{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2386,12 +2386,12 @@ NIL NIL (-614 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|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)]}."))) -((-2046 . T)) +((-2092 . T)) NIL (-615 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 -((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-616 |VarSet|) ((|constructor| (NIL "This type is the basic representation of parenthesized words (binary trees over arbitrary symbols) useful in \\spadtype{LiePolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2430,7 +2430,7 @@ NIL ((|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-513)))) (-625 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"))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-626 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."))) @@ -2439,7 +2439,7 @@ NIL (-627 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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-513))) (|HasAttribute| |#1| (QUOTE (-4235 "*"))) (|HasCategory| |#1| (QUOTE (-337))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-282))) (|HasCategory| |#1| (QUOTE (-513))) (|HasAttribute| |#1| (QUOTE (-4235 "*"))) (|HasCategory| |#1| (QUOTE (-337))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-628 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 @@ -2455,10 +2455,10 @@ NIL (-631) ((|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"))) ((-4226 . T) (-4231 |has| (-636) (-337)) (-4225 |has| (-636) (-337)) (-3905 . T) (-4232 |has| (-636) (-6 -4232)) (-4229 |has| (-636) (-6 -4229)) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-636) (QUOTE (-135))) (|HasCategory| (-636) (QUOTE (-133))) (|HasCategory| (-636) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-636) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-636) (QUOTE (-342))) (|HasCategory| (-636) (QUOTE (-337))) (|HasCategory| (-636) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-636) (QUOTE (-210))) (|HasCategory| (-636) (QUOTE (-323))) (-3703 (|HasCategory| (-636) (QUOTE (-337))) (|HasCategory| (-636) (QUOTE (-323)))) (|HasCategory| (-636) (LIST (QUOTE -261) (QUOTE (-636)) (QUOTE (-636)))) (|HasCategory| (-636) (LIST (QUOTE -284) (QUOTE (-636)))) (|HasCategory| (-636) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-636)))) (|HasCategory| (-636) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-636) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-636) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-636) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) 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(|HasCategory| (-636) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-636) (QUOTE (-337)))) (|HasCategory| (-636) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-636) (QUOTE (-783))) (|HasCategory| (-636) (QUOTE (-513))) (|HasAttribute| (-636) (QUOTE -4232)) (|HasAttribute| (-636) (QUOTE -4229)) (-12 (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (-3703 (-12 (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (|HasCategory| (-636) (QUOTE (-337))) (-12 (|HasCategory| (-636) (QUOTE (-323))) (|HasCategory| (-636) (QUOTE (-837))))) (-3703 (-12 (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (-12 (|HasCategory| (-636) (QUOTE (-337))) (|HasCategory| (-636) (QUOTE (-837)))) (-12 (|HasCategory| (-636) (QUOTE (-323))) (|HasCategory| (-636) (QUOTE (-837))))) (-3703 (-12 (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (|HasCategory| (-636) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (|HasCategory| (-636) (QUOTE (-513)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (|HasCategory| (-636) (QUOTE (-133)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-636) (QUOTE (-282))) (|HasCategory| (-636) (QUOTE (-837)))) (|HasCategory| (-636) (QUOTE (-323))))) (-632 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}."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-633 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}."))) @@ -2474,7 +2474,7 @@ NIL NIL (-636) ((|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}"))) -((-3894 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-3893 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-637 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."))) @@ -2504,7 +2504,7 @@ 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 -(-644 S -2212 I) +(-644 S -2244 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 @@ -2520,14 +2520,14 @@ NIL ((|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}."))) NIL NIL -(-648 R |Mod| -2633 -1318 |exactQuo|) +(-648 R |Mod| -1664 -3389 |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| $) "\\spad{modulus(x)} \\undocumented"))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-649 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\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"))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4229 |has| |#1| (-337)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-998) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-323))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-998) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-323))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) (-650 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| $) "\\spad{exponent(x)} \\undocumented"))) NIL @@ -2536,7 +2536,7 @@ NIL ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) ((-4228 |has| |#1| (-157)) (-4227 |has| |#1| (-157)) (-4230 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135)))) -(-652 R |Mod| -2633 -1318 |exactQuo|) +(-652 R |Mod| -1664 -3389 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) ((-4230 . T)) NIL @@ -2603,7 +2603,7 @@ NIL (-668 |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."))) (((-4235 "*") |has| |#2| (-157)) (-4226 |has| |#2| (-513)) (-4231 |has| |#2| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-157))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-513)))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| (-794 |#1|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (QUOTE (-337))) (-3703 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#2| (QUOTE -4231)) (|HasCategory| |#2| (QUOTE (-425))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) +((|HasCategory| |#2| (QUOTE (-837))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-157))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-513)))) (-12 (|HasCategory| (-793 |#1|) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| (-793 |#1|) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| (-793 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| (-793 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| (-793 |#1|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (QUOTE (-337))) (-3703 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#2| (QUOTE -4231)) (|HasCategory| |#2| (QUOTE (-425))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-133))))) (-669 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2619,15 +2619,15 @@ NIL (-672 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) ((-4228 |has| |#1| (-157)) (-4227 |has| |#1| (-157)) (-4230 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#2| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-784)))) +((-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#2| (QUOTE (-342)))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-783)))) (-673 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4223 . T) (-4234 . T) (-2046 . T)) +((-4223 . T) (-4234 . T) (-2092 . T)) NIL (-674 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}."))) ((-4233 . T) (-4223 . T) (-4234 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791))))) (-675) ((|constructor| (NIL "\\spadtype{MoreSystemCommands} implements an interface with the system command facility. These are the commands that are issued from source files or the system interpreter and they start with a close parenthesis,{} \\spadignore{e.g.} \\spadsyscom{what} commands.")) (|systemCommand| (((|Void|) (|String|)) "\\spad{systemCommand(cmd)} takes the string \\spadvar{\\spad{cmd}} and passes it to the runtime environment for execution as a system command. Although various things may be printed,{} no usable value is returned."))) NIL @@ -2795,7 +2795,7 @@ NIL (-716 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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . 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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 @@ -2803,19 +2803,19 @@ NIL (-718 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)}"))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4229 |has| |#1| (-337)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-998) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-998) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-1060))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) (-719 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 -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-720 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.}"))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-721 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x,{} n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,{}n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x,{} n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-513))) (-12 (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-157)))) +((|HasCategory| |#1| (QUOTE (-513))) (-12 (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-783)))) (|HasCategory| |#1| (QUOTE (-970))) (|HasCategory| |#1| (QUOTE (-157)))) (-722) ((|constructor| (NIL "NumberFormats provides function to format and read arabic and roman numbers,{} to convert numbers to strings and to read floating-point numbers.")) (|ScanFloatIgnoreSpacesIfCan| (((|Union| (|Float|) "failed") (|String|)) "\\spad{ScanFloatIgnoreSpacesIfCan(s)} tries to form a floating point number from the string \\spad{s} ignoring any spaces.")) (|ScanFloatIgnoreSpaces| (((|Float|) (|String|)) "\\spad{ScanFloatIgnoreSpaces(s)} forms a floating point number from the string \\spad{s} ignoring any spaces. Error is generated if the string is not recognised as a floating point number.")) (|ScanRoman| (((|PositiveInteger|) (|String|)) "\\spad{ScanRoman(s)} forms an integer from a Roman numeral string \\spad{s}.")) (|FormatRoman| (((|String|) (|PositiveInteger|)) "\\spad{FormatRoman(n)} forms a Roman numeral string from an integer \\spad{n}.")) (|ScanArabic| (((|PositiveInteger|) (|String|)) "\\spad{ScanArabic(s)} forms an integer from an Arabic numeral string \\spad{s}.")) (|FormatArabic| (((|String|) (|PositiveInteger|)) "\\spad{FormatArabic(n)} forms an Arabic numeral string from an integer \\spad{n}."))) NIL @@ -2853,664 +2853,664 @@ NIL NIL NIL (-731) -((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `ObjectProperty' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) -NIL -NIL -(-732) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-733 S R) +(-732 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-342)))) -(-734 R) +((|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-342)))) +(-733 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\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| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) ((-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-735 -3703 R OS S) +(-734 -3703 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL -(-736 R) +(-735 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) ((-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (-3703 (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-3703 (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))))) -(-737) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-506))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (-3703 (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-3703 (|HasCategory| (-924 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))))) +(-736) ((|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 -(-738 R -4049 L) +(-737 R -4049 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 -(-739 R -4049) +(-738 R -4049) ((|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 -(-740) +(-739) ((|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 -(-741 R -4049) +(-740 R -4049) ((|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 -(-742) +(-741) ((|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 -(-743 -4049 UP UPUP R) +(-742 -4049 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 -(-744 -4049 UP L LQ) +(-743 -4049 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 -(-745) +(-744) ((|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 -(-746 -4049 UP L LQ) +(-745 -4049 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 -(-747 -4049 UP) +(-746 -4049 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 -(-748 -4049 L UP A LO) +(-747 -4049 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 -(-749 -4049 UP) +(-748 -4049 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)))) -(-750 -4049 LO) +(-749 -4049 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 -(-751 -4049 LODO) +(-750 -4049 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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((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. 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(|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."))) (((-4235 "*") |has| |#2| (-337)) (-4226 |has| |#2| (-337)) (-4231 |has| |#2| (-337)) (-4225 |has| |#2| (-337)) (-4230 . T) (-4228 . T) (-4227 . T)) ((|HasCategory| |#2| (QUOTE (-337)))) -(-755 S) +(-754 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}))."))) NIL NIL -(-756 S) +(-755 S) ((|constructor| (NIL "\\indented{3}{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 non-negative integers. The multiplication is not commutative. For two elements \\spad{x} and \\spad{y} the relation \\spad{x < y} holds if either \\spad{length(x) < length(y)} holds or if these lengths are equal and if \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\spad{S}. This domain inherits implementation from \\spadtype{FreeMonoid}.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables of \\spad{x}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the length of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the \\spad{n-th} monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the \\spad{n-th} monomial of \\spad{x}.")) (|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} and \\spad{y = m * r} hold and such that \\spad{l} and \\spad{r} have no overlap,{} that is \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|div| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{x div y} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} that is \\spad{[l,{} r]} such that \\spad{x = l * y * r}. \"failed\" is returned iff \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x,{} s)} returns the exact right quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} that is \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x,{} s)} returns the exact left quotient of \\spad{x} by \\spad{s}.") (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} \\indented{1}{by \\spad{y} that is \\spad{q} such that \\spad{x = y * q},{}} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} that is the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (|lexico| (((|Boolean|) $ $) "\\spad{lexico(x,{}y)} returns \\spad{true} iff \\spad{x} is smaller than \\spad{y} \\spad{w}.\\spad{r}.\\spad{t}. the pure lexicographical ordering induced by \\spad{S}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns the reversed word of \\spad{x}.")) (|rest| (($ $) "\\spad{rest(x)} returns \\spad{x} except the first letter.")) (|first| ((|#1| $) "\\spad{first(x)} returns the first letter of \\spad{x}.")) (** (($ |#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."))) NIL NIL -(-757) +(-756) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-758) +(-757) ((|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}"))) NIL NIL -(-759) +(-758) ((|constructor| (NIL "\\spadtype{OpenMathDevice} provides support for reading and writing openMath objects to files,{} strings etc. It also provides access to low-level operations from within the interpreter.")) (|OMgetType| (((|Symbol|) $) "\\spad{OMgetType(dev)} returns the type of the next object on \\axiom{\\spad{dev}}.")) (|OMgetSymbol| (((|Record| (|:| |cd| (|String|)) (|:| |name| (|String|))) $) "\\spad{OMgetSymbol(dev)} reads a symbol from \\axiom{\\spad{dev}}.")) (|OMgetString| (((|String|) $) "\\spad{OMgetString(dev)} reads a string from \\axiom{\\spad{dev}}.")) (|OMgetVariable| (((|Symbol|) $) "\\spad{OMgetVariable(dev)} reads a variable from \\axiom{\\spad{dev}}.")) (|OMgetFloat| (((|DoubleFloat|) $) "\\spad{OMgetFloat(dev)} reads a float from \\axiom{\\spad{dev}}.")) (|OMgetInteger| (((|Integer|) $) "\\spad{OMgetInteger(dev)} reads an integer from \\axiom{\\spad{dev}}.")) (|OMgetEndObject| (((|Void|) $) "\\spad{OMgetEndObject(dev)} reads an end object token from \\axiom{\\spad{dev}}.")) (|OMgetEndError| (((|Void|) $) "\\spad{OMgetEndError(dev)} reads an end error token from \\axiom{\\spad{dev}}.")) (|OMgetEndBVar| (((|Void|) $) "\\spad{OMgetEndBVar(dev)} reads an end bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetEndBind| (((|Void|) $) "\\spad{OMgetEndBind(dev)} reads an end binder token from \\axiom{\\spad{dev}}.")) (|OMgetEndAttr| (((|Void|) $) "\\spad{OMgetEndAttr(dev)} reads an end attribute token from \\axiom{\\spad{dev}}.")) (|OMgetEndAtp| (((|Void|) $) "\\spad{OMgetEndAtp(dev)} reads an end attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetEndApp| (((|Void|) $) "\\spad{OMgetEndApp(dev)} reads an end application token from \\axiom{\\spad{dev}}.")) (|OMgetObject| (((|Void|) $) "\\spad{OMgetObject(dev)} reads a begin object token from \\axiom{\\spad{dev}}.")) (|OMgetError| (((|Void|) $) "\\spad{OMgetError(dev)} reads a begin error token from \\axiom{\\spad{dev}}.")) (|OMgetBVar| (((|Void|) $) "\\spad{OMgetBVar(dev)} reads a begin bound variable list token from \\axiom{\\spad{dev}}.")) (|OMgetBind| (((|Void|) $) "\\spad{OMgetBind(dev)} reads a begin binder token from \\axiom{\\spad{dev}}.")) (|OMgetAttr| (((|Void|) $) "\\spad{OMgetAttr(dev)} reads a begin attribute token from \\axiom{\\spad{dev}}.")) (|OMgetAtp| (((|Void|) $) "\\spad{OMgetAtp(dev)} reads a begin attribute pair token from \\axiom{\\spad{dev}}.")) (|OMgetApp| (((|Void|) $) "\\spad{OMgetApp(dev)} reads a begin application token from \\axiom{\\spad{dev}}.")) (|OMputSymbol| (((|Void|) $ (|String|) (|String|)) "\\spad{OMputSymbol(dev,{}cd,{}s)} writes the symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}} to \\axiom{\\spad{dev}}.")) (|OMputString| (((|Void|) $ (|String|)) "\\spad{OMputString(dev,{}i)} writes the string \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputVariable| (((|Void|) $ (|Symbol|)) "\\spad{OMputVariable(dev,{}i)} writes the variable \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputFloat| (((|Void|) $ (|DoubleFloat|)) "\\spad{OMputFloat(dev,{}i)} writes the float \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputInteger| (((|Void|) $ (|Integer|)) "\\spad{OMputInteger(dev,{}i)} writes the integer \\axiom{\\spad{i}} to \\axiom{\\spad{dev}}.")) (|OMputEndObject| (((|Void|) $) "\\spad{OMputEndObject(dev)} writes an end object token to \\axiom{\\spad{dev}}.")) (|OMputEndError| (((|Void|) $) "\\spad{OMputEndError(dev)} writes an end error token to \\axiom{\\spad{dev}}.")) (|OMputEndBVar| (((|Void|) $) "\\spad{OMputEndBVar(dev)} writes an end bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputEndBind| (((|Void|) $) "\\spad{OMputEndBind(dev)} writes an end binder token to \\axiom{\\spad{dev}}.")) (|OMputEndAttr| (((|Void|) $) "\\spad{OMputEndAttr(dev)} writes an end attribute token to \\axiom{\\spad{dev}}.")) (|OMputEndAtp| (((|Void|) $) "\\spad{OMputEndAtp(dev)} writes an end attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputEndApp| (((|Void|) $) "\\spad{OMputEndApp(dev)} writes an end application token to \\axiom{\\spad{dev}}.")) (|OMputObject| (((|Void|) $) "\\spad{OMputObject(dev)} writes a begin object token to \\axiom{\\spad{dev}}.")) (|OMputError| (((|Void|) $) "\\spad{OMputError(dev)} writes a begin error token to \\axiom{\\spad{dev}}.")) (|OMputBVar| (((|Void|) $) "\\spad{OMputBVar(dev)} writes a begin bound variable list token to \\axiom{\\spad{dev}}.")) (|OMputBind| (((|Void|) $) "\\spad{OMputBind(dev)} writes a begin binder token to \\axiom{\\spad{dev}}.")) (|OMputAttr| (((|Void|) $) "\\spad{OMputAttr(dev)} writes a begin attribute token to \\axiom{\\spad{dev}}.")) (|OMputAtp| (((|Void|) $) "\\spad{OMputAtp(dev)} writes a begin attribute pair token to \\axiom{\\spad{dev}}.")) (|OMputApp| (((|Void|) $) "\\spad{OMputApp(dev)} writes a begin application token to \\axiom{\\spad{dev}}.")) (|OMsetEncoding| (((|Void|) $ (|OpenMathEncoding|)) "\\spad{OMsetEncoding(dev,{}enc)} sets the encoding used for reading or writing OpenMath objects to or from \\axiom{\\spad{dev}} to \\axiom{\\spad{enc}}.")) (|OMclose| (((|Void|) $) "\\spad{OMclose(dev)} closes \\axiom{\\spad{dev}},{} flushing output if necessary.")) (|OMopenString| (($ (|String|) (|OpenMathEncoding|)) "\\spad{OMopenString(s,{}mode)} opens the string \\axiom{\\spad{s}} for reading or writing OpenMath objects in encoding \\axiom{enc}.")) (|OMopenFile| (($ (|String|) (|String|) (|OpenMathEncoding|)) "\\spad{OMopenFile(f,{}mode,{}enc)} opens file \\axiom{\\spad{f}} for reading or writing OpenMath objects (depending on \\axiom{\\spad{mode}} which can be \\spad{\"r\"},{} \\spad{\"w\"} or \"a\" for read,{} write and append respectively),{} in the encoding \\axiom{\\spad{enc}}."))) NIL NIL -(-760) +(-759) ((|constructor| (NIL "\\spadtype{OpenMathEncoding} is the set of valid OpenMath encodings.")) (|OMencodingBinary| (($) "\\spad{OMencodingBinary()} is the constant for the OpenMath binary encoding.")) (|OMencodingSGML| (($) "\\spad{OMencodingSGML()} is the constant for the deprecated OpenMath SGML encoding.")) (|OMencodingXML| (($) "\\spad{OMencodingXML()} is the constant for the OpenMath \\spad{XML} encoding.")) (|OMencodingUnknown| (($) "\\spad{OMencodingUnknown()} is the constant for unknown encoding types. If this is used on an input device,{} the encoding will be autodetected. It is invalid to use it on an output device."))) NIL NIL -(-761) +(-760) ((|constructor| (NIL "\\spadtype{OpenMathErrorKind} represents different kinds of OpenMath errors: specifically parse errors,{} unknown \\spad{CD} or symbol errors,{} and read errors.")) (|OMReadError?| (((|Boolean|) $) "\\spad{OMReadError?(u)} tests whether \\spad{u} is an OpenMath read error.")) (|OMUnknownSymbol?| (((|Boolean|) $) "\\spad{OMUnknownSymbol?(u)} tests whether \\spad{u} is an OpenMath unknown symbol error.")) (|OMUnknownCD?| (((|Boolean|) $) "\\spad{OMUnknownCD?(u)} tests whether \\spad{u} is an OpenMath unknown \\spad{CD} error.")) (|OMParseError?| (((|Boolean|) $) "\\spad{OMParseError?(u)} tests whether \\spad{u} is an OpenMath parsing error.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(u)} creates an OpenMath error object of an appropriate type if \\axiom{\\spad{u}} is one of \\axiom{OMParseError},{} \\axiom{OMReadError},{} \\axiom{OMUnknownCD} or \\axiom{OMUnknownSymbol},{} otherwise it raises a runtime error."))) NIL NIL -(-762) +(-761) ((|constructor| (NIL "\\spadtype{OpenMathError} is the domain of OpenMath errors.")) (|omError| (($ (|OpenMathErrorKind|) (|List| (|Symbol|))) "\\spad{omError(k,{}l)} creates an instance of OpenMathError.")) (|errorInfo| (((|List| (|Symbol|)) $) "\\spad{errorInfo(u)} returns information about the error \\spad{u}.")) (|errorKind| (((|OpenMathErrorKind|) $) "\\spad{errorKind(u)} returns the type of error which \\spad{u} represents."))) NIL NIL -(-763 R) +(-762 R) ((|constructor| (NIL "\\spadtype{ExpressionToOpenMath} provides support for converting objects of type \\spadtype{Expression} into OpenMath."))) NIL NIL -(-764 P R) +(-763 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) ((-4227 . T) (-4228 . T) (-4230 . T)) ((|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-210)))) -(-765) +(-764) ((|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."))) NIL NIL -(-766) +(-765) ((|constructor| (NIL "\\spadtype{OpenMathPackage} provides some simple utilities to make reading OpenMath objects easier.")) (|OMunhandledSymbol| (((|Exit|) (|String|) (|String|)) "\\spad{OMunhandledSymbol(s,{}cd)} raises an error if AXIOM reads a symbol which it is unable to handle. Note that this is different from an unexpected symbol.")) (|OMsupportsSymbol?| (((|Boolean|) (|String|) (|String|)) "\\spad{OMsupportsSymbol?(s,{}cd)} returns \\spad{true} if AXIOM supports symbol \\axiom{\\spad{s}} from \\spad{CD} \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMsupportsCD?| (((|Boolean|) (|String|)) "\\spad{OMsupportsCD?(cd)} returns \\spad{true} if AXIOM supports \\axiom{\\spad{cd}},{} \\spad{false} otherwise.")) (|OMlistSymbols| (((|List| (|String|)) (|String|)) "\\spad{OMlistSymbols(cd)} lists all the symbols in \\axiom{\\spad{cd}}.")) (|OMlistCDs| (((|List| (|String|))) "\\spad{OMlistCDs()} lists all the \\spad{CDs} supported by AXIOM.")) (|OMreadStr| (((|Any|) (|String|)) "\\spad{OMreadStr(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMreadFile| (((|Any|) (|String|)) "\\spad{OMreadFile(f)} reads an OpenMath object from \\axiom{\\spad{f}} and passes it to AXIOM.")) (|OMread| (((|Any|) (|OpenMathDevice|)) "\\spad{OMread(dev)} reads an OpenMath object from \\axiom{\\spad{dev}} and passes it to AXIOM."))) NIL NIL -(-767 S) +(-766 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4233 . T) (-4223 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4223 . T) (-4234 . T) (-2092 . T)) NIL -(-768) +(-767) ((|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."))) NIL NIL -(-769 R S) +(-768 R S) ((|constructor| (NIL "Lifting of maps to one-point completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|) (|OnePointCompletion| |#2|)) "\\spad{map(f,{} r,{} i)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = \\spad{i}.") (((|OnePointCompletion| |#2|) (|Mapping| |#2| |#1|) (|OnePointCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(infinity) = infinity."))) NIL NIL -(-770 R) +(-769 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."))) -((-4230 |has| |#1| (-782))) -((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-506))) (-3703 (|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-21))) (-3703 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-782))))) -(-771 R) +((-4230 |has| |#1| (-781))) +((|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-506))) (-3703 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-21))) (-3703 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-781))))) +(-770 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) ((-4228 |has| |#1| (-157)) (-4227 |has| |#1| (-157)) (-4230 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135)))) -(-772) +(-771) ((|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)."))) NIL NIL -(-773) +(-772) ((|numericalOptimization| (((|Result|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.") (((|Result|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{numericalOptimization(args)} performs the optimization of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization 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.") (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve an optimization 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 -(-774) +(-773) ((|goodnessOfFit| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{goodnessOfFit(lf,{}start)} is a top level ANNA function to check to goodness of fit of a least squares model \\spadignore{i.e.} the minimization of a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation. goodnessOfFit(\\spad{lf},{}\\spad{start}) is a top level function to iterate over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then checks the goodness of fit of the least squares model.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{goodnessOfFit(prob)} is a top level ANNA function to check to goodness of fit of a least squares model as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}. It then calls the numerical routine \\axiomType{E04YCF} to get estimates of the variance-covariance matrix of the regression coefficients of the least-squares problem. \\blankline It thus returns both the results of the optimization and the variance-covariance calculation.")) (|optimize| (((|Result|) (|List| (|Expression| (|Float|))) (|List| (|Float|))) "\\spad{optimize(lf,{}start)} is a top level ANNA function to minimize a set of functions,{} \\axiom{\\spad{lf}},{} of one or more variables without constraints \\spadignore{i.e.} a least-squares problem. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|))) "\\spad{optimize(f,{}start)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables without constraints. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with simple constraints. The bounds on the variables are defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Float|)) (|List| (|OrderedCompletion| (|Float|))) (|List| (|Expression| (|Float|))) (|List| (|OrderedCompletion| (|Float|)))) "\\spad{optimize(f,{}start,{}lower,{}cons,{}upper)} is a top level ANNA function to minimize a function,{} \\axiom{\\spad{f}},{} of one or more variables with the given constraints. \\blankline These constraints may be simple constraints on the variables in which case \\axiom{\\spad{cons}} would be an empty list and the bounds on those variables defined in \\axiom{\\spad{lower}} and \\axiom{\\spad{upper}},{} or a mixture of simple,{} linear and non-linear constraints,{} where \\axiom{\\spad{cons}} contains the linear and non-linear constraints and the bounds on these are added to \\axiom{\\spad{upper}} and \\axiom{\\spad{lower}}. \\blankline The parameter \\axiom{\\spad{start}} is a list of the initial guesses of the values of the variables. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|)) "\\spad{optimize(prob)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.") (((|Result|) (|NumericalOptimizationProblem|) (|RoutinesTable|)) "\\spad{optimize(prob,{}routines)} is a top level ANNA function to minimize a function or a set of functions with any constraints as defined within \\axiom{\\spad{prob}}. \\blankline It iterates over the \\axiom{domains} listed in \\axiom{\\spad{routines}} of \\axiomType{NumericalOptimizationCategory} to get the name and other relevant information of the best \\axiom{measure} and then optimize the function on that \\axiom{domain}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalOptimizationProblem|) (|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 optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} 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|)))) (|NumericalOptimizationProblem|)) "\\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 optimization problem defined by \\axiom{\\spad{prob}} by checking various attributes of the functions and calculating a measure of compatibility of each routine to these attributes. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalOptimizationCategory} 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."))) NIL NIL -(-775) +(-774) ((|retract| (((|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|)))))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Union| (|:| |noa| (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) (|:| |lsa| (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |lfn| (|List| (|Expression| (|DoubleFloat|)))) (|:| |init| (|List| (|DoubleFloat|))))) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |init| (|List| (|DoubleFloat|))) (|:| |lb| (|List| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |cf| (|List| (|Expression| (|DoubleFloat|)))) (|:| |ub| (|List| (|OrderedCompletion| (|DoubleFloat|)))))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-776 R S) +(-775 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f,{} r,{} p,{} m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f,{} r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-777 R) +(-776 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."))) -((-4230 |has| |#1| (-782))) -((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-506))) (-3703 (|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-21))) (-3703 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-782))))) -(-778) +((-4230 |has| |#1| (-781))) +((|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-506))) (-3703 (|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-21))) (-3703 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-781))))) +(-777) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-779 -2617 S) +(-778 -2623 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 -(-780) +(-779) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-781 S) +(-780 S) ((|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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) NIL NIL -(-782) +(-781) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\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|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) ((-4230 . T)) NIL -(-783 S) +(-782 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-784) +(-783) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\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|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) NIL NIL -(-785 S R) +(-784 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| ((|#2| $) "\\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") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\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| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|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| ((|#2| $) "\\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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-157)))) -(-786 R) +(-785 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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)}.}"))) ((-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-787 R C) +(-786 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 (-337))) (|HasCategory| |#1| (QUOTE (-513)))) -(-788 R |sigma| -1202) +(-787 R |sigma| -1202) ((|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."))) ((-4227 . T) (-4228 . T) (-4230 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-337)))) -(-789 |x| R |sigma| -1202) +(-788 |x| R |sigma| -1202) ((|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."))) ((-4227 . T) (-4228 . T) (-4230 . T)) ((|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-337)))) -(-790 R) +(-789 R) ((|constructor| (NIL "This package provides orthogonal polynomials as functions on a ring.")) (|legendreP| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{legendreP(n,{}x)} is the \\spad{n}-th Legendre polynomial,{} \\spad{P[n](x)}. These are defined by \\spad{1/sqrt(1-2*x*t+t**2) = sum(P[n](x)*t**n,{} n = 0..)}.")) (|laguerreL| ((|#1| (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(m,{}n,{}x)} is the associated Laguerre polynomial,{} \\spad{L<m>[n](x)}. This is the \\spad{m}-th derivative of \\spad{L[n](x)}.") ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{laguerreL(n,{}x)} is the \\spad{n}-th Laguerre polynomial,{} \\spad{L[n](x)}. These are defined by \\spad{exp(-t*x/(1-t))/(1-t) = sum(L[n](x)*t**n/n!,{} n = 0..)}.")) (|hermiteH| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{hermiteH(n,{}x)} is the \\spad{n}-th Hermite polynomial,{} \\spad{H[n](x)}. These are defined by \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n = 0..)}.")) (|chebyshevU| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevU(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the second kind,{} \\spad{U[n](x)}. These are defined by \\spad{1/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}.")) (|chebyshevT| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{chebyshevT(n,{}x)} is the \\spad{n}-th Chebyshev polynomial of the first kind,{} \\spad{T[n](x)}. These are defined by \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x) *t**n,{} n = 0..)}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) -(-791) +(-790) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date created : 14 August 1988 Date Last Updated : 11 March 1991 Description : A domain used in order to take the free \\spad{R}-module on the Integers \\spad{I}. This is actually the forgetful functor from OrderedRings to OrderedSets applied to \\spad{I}")) (|value| (((|Integer|) $) "\\spad{value(x)} returns the integer associated with \\spad{x}")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} returns the element corresponding to \\spad{i}"))) NIL NIL -(-792) +(-791) ((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (^= (($ $ $) "\\spad{f ^= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-793) +(-792) ((|constructor| (NIL "OutPackage allows pretty-printing from programs.")) (|outputList| (((|Void|) (|List| (|Any|))) "\\spad{outputList(l)} displays the concatenated components of the list \\spad{l} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}; quotes are stripped from strings.")) (|output| (((|Void|) (|String|) (|OutputForm|)) "\\spad{output(s,{}x)} displays the string \\spad{s} followed by the form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output\\spad{''} stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-794 |VariableList|) +(-793 |VariableList|) ((|constructor| (NIL "This domain implements ordered variables")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} returns a member of the variable set or failed"))) NIL NIL -(-795 R |vl| |wl| |wtlevel|) +(-794 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"))) ((-4228 |has| |#1| (-157)) (-4227 |has| |#1| (-157)) (-4230 . T)) ((|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337)))) -(-796 R PS UP) +(-795 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-797 R |x| |pt|) +(-796 R |x| |pt|) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Trager,{}Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|pade| (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}s)} computes the quotient of polynomials (if it exists) with numerator degree at most \\spad{nd} and denominator degree at most \\spad{dd} which matches the series \\spad{s} to order \\spad{nd + dd}.") (((|Union| (|Fraction| (|UnivariatePolynomial| |#2| |#1|)) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) (|UnivariateTaylorSeries| |#1| |#2| |#3|) (|UnivariateTaylorSeries| |#1| |#2| |#3|)) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) NIL NIL -(-798 |p|) +(-797 |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}."))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-799 |p|) +(-798 |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)."))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-800 |p|) +(-799 |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)."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-799 |#1|) (QUOTE (-838))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-799 |#1|) (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-135))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-799 |#1|) (QUOTE (-946))) (|HasCategory| (-799 |#1|) (QUOTE (-757))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-799 |#1|) (QUOTE (-1060))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-799 |#1|) (QUOTE (-210))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -482) (QUOTE (-1084)) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -284) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (LIST (QUOTE -261) (LIST (QUOTE -799) (|devaluate| |#1|)) (LIST (QUOTE -799) (|devaluate| |#1|)))) (|HasCategory| (-799 |#1|) (QUOTE (-282))) (|HasCategory| (-799 |#1|) (QUOTE (-506))) (|HasCategory| (-799 |#1|) (QUOTE (-784))) (-3703 (|HasCategory| (-799 |#1|) (QUOTE (-757))) (|HasCategory| (-799 |#1|) (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-799 |#1|) (QUOTE (-838)))) (|HasCategory| (-799 |#1|) (QUOTE (-133))))) -(-801 |p| PADIC) +((|HasCategory| (-798 |#1|) (QUOTE (-837))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-798 |#1|) (QUOTE (-133))) (|HasCategory| (-798 |#1|) (QUOTE (-135))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-798 |#1|) (QUOTE (-946))) (|HasCategory| (-798 |#1|) (QUOTE (-756))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-798 |#1|) (QUOTE (-1060))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-798 |#1|) (QUOTE (-210))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -482) (QUOTE (-1084)) (LIST (QUOTE -798) (|devaluate| |#1|)))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -284) (LIST (QUOTE -798) (|devaluate| |#1|)))) (|HasCategory| (-798 |#1|) (LIST (QUOTE -261) (LIST (QUOTE -798) (|devaluate| |#1|)) (LIST (QUOTE -798) (|devaluate| |#1|)))) (|HasCategory| (-798 |#1|) (QUOTE (-282))) (|HasCategory| (-798 |#1|) (QUOTE (-506))) (|HasCategory| (-798 |#1|) (QUOTE (-783))) (-3703 (|HasCategory| (-798 |#1|) (QUOTE (-756))) (|HasCategory| (-798 |#1|) (QUOTE (-783)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-798 |#1|) (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-798 |#1|) (QUOTE (-837)))) (|HasCategory| (-798 |#1|) (QUOTE (-133))))) +(-800 |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)}."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-946))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -261) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-784))) (-3703 (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-784)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) -(-802 S T$) +((|HasCategory| |#2| (QUOTE (-837))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-946))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -261) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-783))) (-3703 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-783)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-133))))) +(-801 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 (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))))) -(-803) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))))) +(-802) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL NIL -(-804) +(-803) ((|constructor| (NIL "This package provides a coerce from polynomials over algebraic numbers to \\spadtype{Expression AlgebraicNumber}.")) (|coerce| (((|Expression| (|Integer|)) (|Fraction| (|Polynomial| (|AlgebraicNumber|)))) "\\spad{coerce(rf)} converts \\spad{rf},{} a fraction of polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}.") (((|Expression| (|Integer|)) (|Polynomial| (|AlgebraicNumber|))) "\\spad{coerce(p)} converts the polynomial \\spad{p} with algebraic number coefficients to \\spadtype{Expression Integer}."))) NIL NIL -(-805 CF1 CF2) +(-804 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-806 |ComponentFunction|) +(-805 |ComponentFunction|) ((|constructor| (NIL "ParametricPlaneCurve is used for plotting parametric plane curves in the affine plane.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function for \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component \\spad{i} of the plane curve is.")) (|curve| (($ |#1| |#1|) "\\spad{curve(c1,{}c2)} creates a plane curve from 2 component functions \\spad{c1} and \\spad{c2}."))) NIL NIL -(-807 CF1 CF2) +(-806 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-808 |ComponentFunction|) +(-807 |ComponentFunction|) ((|constructor| (NIL "ParametricSpaceCurve is used for plotting parametric space curves in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(c,{}i)} returns a coordinate function of \\spad{c} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the space curve is.")) (|curve| (($ |#1| |#1| |#1|) "\\spad{curve(c1,{}c2,{}c3)} creates a space curve from 3 component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-809) +(-808) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad script parser.} Related Constructors: Syntax. See Also: Syntax.")) (|getSyntaxFormsFromFile| (((|List| (|Syntax|)) (|String|)) "\\spad{getSyntaxFormsFromFile(f)} parses the source file \\spad{f} (supposedly containing Spad scripts) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that source location information is not part of result."))) NIL NIL -(-810 CF1 CF2) +(-809 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,{}x)} \\undocumented"))) NIL NIL -(-811 |ComponentFunction|) +(-810 |ComponentFunction|) ((|constructor| (NIL "ParametricSurface is used for plotting parametric surfaces in affine 3-space.")) (|coordinate| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coordinate(s,{}i)} returns a coordinate function of \\spad{s} using 1-based indexing according to \\spad{i}. This indicates what the function for the coordinate component,{} \\spad{i},{} of the surface is.")) (|surface| (($ |#1| |#1| |#1|) "\\spad{surface(c1,{}c2,{}c3)} creates a surface from 3 parametric component functions \\spad{c1},{} \\spad{c2},{} and \\spad{c3}."))) NIL NIL -(-812) +(-811) ((|constructor| (NIL "PartitionsAndPermutations contains functions for generating streams of integer partitions,{} and streams of sequences of integers composed from a multi-set.")) (|permutations| (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{permutations(n)} is the stream of permutations \\indented{1}{formed from \\spad{1,{}2,{}3,{}...,{}n}.}")) (|sequences| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|))) "\\spad{sequences([l0,{}l1,{}l2,{}..,{}ln])} is the set of \\indented{1}{all sequences formed from} \\spad{l0} 0\\spad{'s},{}\\spad{l1} 1\\spad{'s},{}\\spad{l2} 2\\spad{'s},{}...,{}\\spad{ln} \\spad{n}\\spad{'s}.") (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{sequences(l1,{}l2)} is the stream of all sequences that \\indented{1}{can be composed from the multiset defined from} \\indented{1}{two lists of integers \\spad{l1} and \\spad{l2}.} \\indented{1}{For example,{}the pair \\spad{([1,{}2,{}4],{}[2,{}3,{}5])} represents} \\indented{1}{multi-set with 1 \\spad{2},{} 2 \\spad{3}\\spad{'s},{} and 4 \\spad{5}\\spad{'s}.}")) (|shufflein| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|Stream| (|List| (|Integer|)))) "\\spad{shufflein(l,{}st)} maps shuffle(\\spad{l},{}\\spad{u}) on to all \\indented{1}{members \\spad{u} of \\spad{st},{} concatenating the results.}")) (|shuffle| (((|Stream| (|List| (|Integer|))) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{shuffle(l1,{}l2)} forms the stream of all shuffles of \\spad{l1} \\indented{1}{and \\spad{l2},{} \\spadignore{i.e.} all sequences that can be formed from} \\indented{1}{merging \\spad{l1} and \\spad{l2}.}")) (|conjugates| (((|Stream| (|List| (|Integer|))) (|Stream| (|List| (|Integer|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|Integer|)) (|List| (|Integer|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}.")) (|partitions| (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l)} is the stream of all \\indented{1}{partitions whose number of} \\indented{1}{parts and largest part are no greater than \\spad{p} and \\spad{l}.}") (((|Stream| (|List| (|Integer|))) (|Integer|)) "\\spad{partitions(n)} is the stream of all partitions of \\spad{n}.") (((|Stream| (|List| (|Integer|))) (|Integer|) (|Integer|) (|Integer|)) "\\spad{partitions(p,{}l,{}n)} is the stream of partitions \\indented{1}{of \\spad{n} whose number of parts is no greater than \\spad{p}} \\indented{1}{and whose largest part is no greater than \\spad{l}.}"))) NIL NIL -(-813 R) +(-812 R) ((|constructor| (NIL "An object \\spad{S} is Patternable over an object \\spad{R} if \\spad{S} can lift the conversions from \\spad{R} into \\spadtype{Pattern(Integer)} and \\spadtype{Pattern(Float)} to itself."))) NIL NIL -(-814 R S L) +(-813 R S L) ((|constructor| (NIL "A PatternMatchListResult is an object internally returned by the pattern matcher when matching on lists. It is either a failed match,{} or a pair of PatternMatchResult,{} one for atoms (elements of the list),{} and one for lists.")) (|lists| (((|PatternMatchResult| |#1| |#3|) $) "\\spad{lists(r)} returns the list of matches that match lists.")) (|atoms| (((|PatternMatchResult| |#1| |#2|) $) "\\spad{atoms(r)} returns the list of matches that match atoms (elements of the lists).")) (|makeResult| (($ (|PatternMatchResult| |#1| |#2|) (|PatternMatchResult| |#1| |#3|)) "\\spad{makeResult(r1,{}r2)} makes the combined result [\\spad{r1},{}\\spad{r2}].")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-815 S) +(-814 S) ((|constructor| (NIL "A set \\spad{R} is PatternMatchable over \\spad{S} if elements of \\spad{R} can be matched to patterns over \\spad{S}.")) (|patternMatch| (((|PatternMatchResult| |#1| $) $ (|Pattern| |#1|) (|PatternMatchResult| |#1| $)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}. res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion). Initially,{} res is just the result of \\spadfun{new} which is an empty list of matches."))) NIL NIL -(-816 |Base| |Subject| |Pat|) +(-815 |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 -((|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))) (-12 (-2400 (|HasCategory| |#2| (QUOTE (-970)))) (-2400 (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))))) (-12 (|HasCategory| |#2| (QUOTE (-970))) (-2400 (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084))))))) -(-817 R A B) +((|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))) (-12 (-2416 (|HasCategory| |#2| (QUOTE (-970)))) (-2416 (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))))) (-12 (|HasCategory| |#2| (QUOTE (-970))) (-2416 (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084))))))) +(-816 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL NIL -(-818 R S) +(-817 R S) ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-819 R -2212) +(-818 R -2244) ((|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 -(-820 R S) +(-819 R S) ((|constructor| (NIL "Lifts maps to patterns.")) (|map| (((|Pattern| |#2|) (|Mapping| |#2| |#1|) (|Pattern| |#1|)) "\\spad{map(f,{} p)} applies \\spad{f} to all the leaves of \\spad{p} and returns the result as a pattern over \\spad{S}."))) NIL NIL -(-821 R) +(-820 R) ((|constructor| (NIL "Patterns for use by the pattern matcher.")) (|optpair| (((|Union| (|List| $) "failed") (|List| $)) "\\spad{optpair(l)} returns \\spad{l} has the form \\spad{[a,{} b]} and a is optional,{} and \"failed\" otherwise.")) (|variables| (((|List| $) $) "\\spad{variables(p)} returns the list of matching variables appearing in \\spad{p}.")) (|getBadValues| (((|List| (|Any|)) $) "\\spad{getBadValues(p)} returns the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (($ $ (|Any|)) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|resetBadValues| (($ $) "\\spad{resetBadValues(p)} initializes the list of \"bad values\" for \\spad{p} to \\spad{[]}. Note: \\spad{p} is not allowed to match any of its \"bad values\".")) (|hasTopPredicate?| (((|Boolean|) $) "\\spad{hasTopPredicate?(p)} tests if \\spad{p} has a top-level predicate.")) (|topPredicate| (((|Record| (|:| |var| (|List| (|Symbol|))) (|:| |pred| (|Any|))) $) "\\spad{topPredicate(x)} returns \\spad{[[a1,{}...,{}an],{} f]} where the top-level predicate of \\spad{x} is \\spad{f(a1,{}...,{}an)}. Note: \\spad{n} is 0 if \\spad{x} has no top-level predicate.")) (|setTopPredicate| (($ $ (|List| (|Symbol|)) (|Any|)) "\\spad{setTopPredicate(x,{} [a1,{}...,{}an],{} f)} returns \\spad{x} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.")) (|patternVariable| (($ (|Symbol|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{patternVariable(x,{} c?,{} o?,{} m?)} creates a pattern variable \\spad{x},{} which is constant if \\spad{c? = true},{} optional if \\spad{o? = true},{} and multiple if \\spad{m? = true}.")) (|withPredicates| (($ $ (|List| (|Any|))) "\\spad{withPredicates(p,{} [p1,{}...,{}pn])} makes a copy of \\spad{p} and attaches the predicate \\spad{p1} and ... and \\spad{pn} to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p,{} [p1,{}...,{}pn])} attaches the predicate \\spad{p1} and ... and \\spad{pn} to \\spad{p}.")) (|predicates| (((|List| (|Any|)) $) "\\spad{predicates(p)} returns \\spad{[p1,{}...,{}pn]} such that the predicate attached to \\spad{p} is \\spad{p1} and ... and \\spad{pn}.")) (|hasPredicate?| (((|Boolean|) $) "\\spad{hasPredicate?(p)} tests if \\spad{p} has predicates attached to it.")) (|optional?| (((|Boolean|) $) "\\spad{optional?(p)} tests if \\spad{p} is a single matching variable which can match an identity.")) (|multiple?| (((|Boolean|) $) "\\spad{multiple?(p)} tests if \\spad{p} is a single matching variable allowing list matching or multiple term matching in a sum or product.")) (|generic?| (((|Boolean|) $) "\\spad{generic?(p)} tests if \\spad{p} is a single matching variable.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests if \\spad{p} contains no matching variables.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(p)} tests if \\spad{p} is a symbol.")) (|quoted?| (((|Boolean|) $) "\\spad{quoted?(p)} tests if \\spad{p} is of the form \\spad{'s} for a symbol \\spad{s}.")) (|inR?| (((|Boolean|) $) "\\spad{inR?(p)} tests if \\spad{p} is an atom (\\spadignore{i.e.} an element of \\spad{R}).")) (|copy| (($ $) "\\spad{copy(p)} returns a recursive copy of \\spad{p}.")) (|convert| (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the pattern \\spad{[a1,{}...,{}an]}.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(p)} returns the nesting level of \\spad{p}.")) (/ (($ $ $) "\\spad{a / b} returns the pattern \\spad{a / b}.")) (** (($ $ $) "\\spad{a ** b} returns the pattern \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** n} returns the pattern \\spad{a ** n}.")) (* (($ $ $) "\\spad{a * b} returns the pattern \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the pattern \\spad{a + b}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,{} [a1,{}...,{}an])} returns \\spad{op(a1,{}...,{}an)}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| $)) "failed") $) "\\spad{isPower(p)} returns \\spad{[a,{} b]} if \\spad{p = a ** b},{} and \"failed\" otherwise.")) (|isList| (((|Union| (|List| $) "failed") $) "\\spad{isList(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = [a1,{}...,{}an]},{} \"failed\" otherwise.")) (|isQuotient| (((|Union| (|Record| (|:| |num| $) (|:| |den| $)) "failed") $) "\\spad{isQuotient(p)} returns \\spad{[a,{} b]} if \\spad{p = a / b},{} and \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[q,{} n]} if \\spad{n > 0} and \\spad{p = q ** n},{} and \"failed\" otherwise.")) (|isOp| (((|Union| (|Record| (|:| |op| (|BasicOperator|)) (|:| |arg| (|List| $))) "failed") $) "\\spad{isOp(p)} returns \\spad{[op,{} [a1,{}...,{}an]]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.") (((|Union| (|List| $) "failed") $ (|BasicOperator|)) "\\spad{isOp(p,{} op)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = op(a1,{}...,{}an)},{} and \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} and \\spad{p = a1 * ... * an},{} and \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{n > 1} \\indented{1}{and \\spad{p = a1 + ... + an},{}} and \"failed\" otherwise.")) ((|One|) (($) "1")) ((|Zero|) (($) "0"))) NIL NIL -(-822 |VarSet|) +(-821 |VarSet|) ((|constructor| (NIL "This domain provides the internal representation of polynomials in non-commutative variables written over the Poincare-Birkhoff-Witt basis. See the \\spadtype{XPBWPolynomial} domain constructor. See Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\spad{varList([l1]*[l2]*...[ln])} returns the list of variables in the word \\spad{l1*l2*...*ln}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?([l1]*[l2]*...[ln])} returns \\spad{true} iff \\spad{n} equals \\spad{1}.")) (|rest| (($ $) "\\spad{rest([l1]*[l2]*...[ln])} returns the list \\spad{l2,{} .... ln}.")) (|ListOfTerms| (((|List| (|LyndonWord| |#1|)) $) "\\spad{ListOfTerms([l1]*[l2]*...[ln])} returns the list of words \\spad{l1,{} l2,{} .... ln}.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length([l1]*[l2]*...[ln])} returns the length of the word \\spad{l1*l2*...*ln}.")) (|first| (((|LyndonWord| |#1|) $) "\\spad{first([l1]*[l2]*...[ln])} returns the Lyndon word \\spad{l1}.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} return \\spad{v}") (((|OrderedFreeMonoid| |#1|) $) "\\spad{coerce([l1]*[l2]*...[ln])} returns the word \\spad{l1*l2*...*ln},{} where \\spad{[l_i]} is the backeted form of the Lyndon word \\spad{l_i}.")) ((|One|) (($) "\\spad{1} returns the empty list."))) NIL NIL -(-823 UP R) +(-822 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,{}q)} \\undocumented"))) NIL NIL -(-824) +(-823) ((|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 -(-825 UP -4049) +(-824 UP -4049) ((|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 -(-826) +(-825) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalPDEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical PDE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{PartialDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of PDEs by checking various attributes of the system of PDEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}) and the boundary values (\\axiom{\\spad{bounds}}). A default value for tolerance is used. There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|Float|) (|Float|) (|Float|) (|Float|) (|NonNegativeInteger|) (|NonNegativeInteger|) (|List| (|Expression| (|Float|))) (|List| (|List| (|Expression| (|Float|)))) (|String|) (|DoubleFloat|)) "\\spad{solve(xmin,{}ymin,{}xmax,{}ymax,{}ngx,{}ngy,{}pde,{}bounds,{}st,{}tol)} is a top level ANNA function to solve numerically a system of partial differential equations. This is defined as a list of coefficients (\\axiom{\\spad{pde}}),{} a grid (\\axiom{\\spad{xmin}},{} \\axiom{\\spad{ymin}},{} \\axiom{\\spad{xmax}},{} \\axiom{\\spad{ymax}},{} \\axiom{\\spad{ngx}},{} \\axiom{\\spad{ngy}}),{} the boundary values (\\axiom{\\spad{bounds}}) and a tolerance requirement (\\axiom{\\spad{tol}}). There is also a parameter (\\axiom{\\spad{st}}) which should contain the value \"elliptic\" if the PDE is known to be elliptic,{} or \"unknown\" if it is uncertain. This causes the routine to check whether the PDE is elliptic. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|) (|RoutinesTable|)) "\\spad{solve(PDEProblem,{}routines)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the \\spad{routines} contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}") (((|Result|) (|NumericalPDEProblem|)) "\\spad{solve(PDEProblem)} is a top level ANNA function to solve numerically a system of partial differential equations. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of PDE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine. \\blankline \\spad{**} At the moment,{} only Second Order Elliptic Partial Differential Equations are solved \\spad{**}"))) NIL NIL -(-827) +(-826) ((|retract| (((|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-828 A S) +(-827 A S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#2|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-829 S) +(-828 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}."))) ((-4230 . T)) NIL -(-830 S) +(-829 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 -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) -(-831 |n| R) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) +(-830 |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 -(-832 S) +(-831 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."))) ((-4230 . T)) NIL -(-833 S) +(-832 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-834 S) +(-833 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|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."))) ((-4230 . T)) -((|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-784))) (-3703 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-784))))) -(-835 R E |VarSet| S) +((|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-783))) (-3703 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-783))))) +(-834 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-836 R S) +(-835 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-837 S) +(-836 S) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) NIL ((|HasCategory| |#1| (QUOTE (-133)))) -(-838) +(-837) ((|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}."))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-839 |p|) +(-838 |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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) ((|HasCategory| $ (QUOTE (-135))) (|HasCategory| $ (QUOTE (-133))) (|HasCategory| $ (QUOTE (-342)))) -(-840 R0 -4049 UP UPUP R) +(-839 R0 -4049 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 -(-841 UP UPUP R) +(-840 UP UPUP R) ((|constructor| (NIL "This package provides function for testing whether a divisor on a curve is a torsion divisor.")) (|torsionIfCan| (((|Union| (|Record| (|:| |order| (|NonNegativeInteger|)) (|:| |function| |#3|)) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsionIfCan(f)} \\undocumented")) (|torsion?| (((|Boolean|) (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{torsion?(f)} \\undocumented")) (|order| (((|Union| (|NonNegativeInteger|) "failed") (|FiniteDivisor| (|Fraction| (|Integer|)) |#1| |#2| |#3|)) "\\spad{order(f)} \\undocumented"))) NIL NIL -(-842 UP UPUP) +(-841 UP UPUP) ((|constructor| (NIL "\\indented{1}{Utilities for PFOQ and PFO} Author: Manuel Bronstein Date Created: 25 Aug 1988 Date Last Updated: 11 Jul 1990")) (|polyred| ((|#2| |#2|) "\\spad{polyred(u)} \\undocumented")) (|doubleDisc| (((|Integer|) |#2|) "\\spad{doubleDisc(u)} \\undocumented")) (|mix| (((|Integer|) (|List| (|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))))) "\\spad{mix(l)} \\undocumented")) (|badNum| (((|Integer|) |#2|) "\\spad{badNum(u)} \\undocumented") (((|Record| (|:| |den| (|Integer|)) (|:| |gcdnum| (|Integer|))) |#1|) "\\spad{badNum(p)} \\undocumented")) (|getGoodPrime| (((|PositiveInteger|) (|Integer|)) "\\spad{getGoodPrime n} returns the smallest prime not dividing \\spad{n}"))) NIL NIL -(-843 R) +(-842 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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-844 R) +(-843 R) ((|constructor| (NIL "The package \\spadtype{PartialFractionPackage} gives an easier to use interfact the domain \\spadtype{PartialFraction}. The user gives a fraction of polynomials,{} and a variable and the package converts it to the proper datatype for the \\spadtype{PartialFraction} domain.")) (|partialFraction| (((|Any|) (|Polynomial| |#1|) (|Factored| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(num,{} facdenom,{} var)} returns the partial fraction decomposition of the rational function whose numerator is \\spad{num} and whose factored denominator is \\spad{facdenom} with respect to the variable var.") (((|Any|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{partialFraction(rf,{} var)} returns the partial fraction decomposition of the rational function \\spad{rf} with respect to the variable var."))) NIL NIL -(-845 E OV R P) +(-844 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the \\spad{gcd} of the list of primitive polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,{}q)} computes the \\spad{gcd} of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the \\spad{gcd} of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,{}q)} computes the \\spad{gcd} of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-846) +(-845) ((|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 -(-847 -4049) +(-846 -4049) ((|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 -(-848 R) +(-847 R) ((|constructor| (NIL "\\indented{1}{Provides a coercion from the symbolic fractions in \\%\\spad{pi} with} integer coefficients to any Expression type. Date Created: 21 Feb 1990 Date Last Updated: 21 Feb 1990")) (|coerce| (((|Expression| |#1|) (|Pi|)) "\\spad{coerce(f)} returns \\spad{f} as an Expression(\\spad{R})."))) NIL NIL -(-849) +(-848) ((|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| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) ((-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL -(-850) +(-849) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) (((-4235 "*") . T)) NIL -(-851 -4049 P) +(-850 -4049 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-852 |xx| -4049) +(-851 |xx| -4049) ((|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 -(-853 R |Var| |Expon| GR) +(-852 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{^=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL -(-854 S) +(-853 S) ((|constructor| (NIL "PlotFunctions1 provides facilities for plotting curves where functions \\spad{SF} \\spad{->} \\spad{SF} are specified by giving an expression")) (|plotPolar| (((|Plot|) |#1| (|Symbol|)) "\\spad{plotPolar(f,{}theta)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges from 0 to 2 \\spad{pi}") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}theta,{}seg)} plots the graph of \\spad{r = f(theta)} as \\spad{theta} ranges over an interval")) (|plot| (((|Plot|) |#1| |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}t,{}seg)} plots the graph of \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over an interval.") (((|Plot|) |#1| (|Symbol|) (|Segment| (|DoubleFloat|))) "\\spad{plot(fcn,{}x,{}seg)} plots the graph of \\spad{y = f(x)} on a interval"))) NIL NIL -(-855) +(-854) ((|constructor| (NIL "Plot3D supports parametric plots defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example,{} floating point numbers and infinite continued fractions are real number systems. The facilities at this point are limited to 3-dimensional parametric plots.")) (|debug3D| (((|Boolean|) (|Boolean|)) "\\spad{debug3D(true)} turns debug mode on; debug3D(\\spad{false}) turns debug mode off.")) (|numFunEvals3D| (((|Integer|)) "\\spad{numFunEvals3D()} returns the number of points computed.")) (|setAdaptive3D| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive3D(true)} turns adaptive plotting on; setAdaptive3D(\\spad{false}) turns adaptive plotting off.")) (|adaptive3D?| (((|Boolean|)) "\\spad{adaptive3D?()} determines whether plotting be done adaptively.")) (|setScreenResolution3D| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution3D(i)} sets the screen resolution for a 3d graph to \\spad{i}.")) (|screenResolution3D| (((|Integer|)) "\\spad{screenResolution3D()} returns the screen resolution for a 3d graph.")) (|setMaxPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints3D(i)} sets the maximum number of points in a plot to \\spad{i}.")) (|maxPoints3D| (((|Integer|)) "\\spad{maxPoints3D()} returns the maximum number of points in a plot.")) (|setMinPoints3D| (((|Integer|) (|Integer|)) "\\spad{setMinPoints3D(i)} sets the minimum number of points in a plot to \\spad{i}.")) (|minPoints3D| (((|Integer|)) "\\spad{minPoints3D()} returns the minimum number of points in a plot.")) (|tValues| (((|List| (|List| (|DoubleFloat|))) $) "\\spad{tValues(p)} returns a list of lists of the values of the parameter for which a point is computed,{} one list for each curve in the plot \\spad{p}.")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}.")) (|refine| (($ $) "\\spad{refine(x)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s,{}t)} \\undocumented")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f1,{}f2,{}f3,{}f4,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}x,{}y,{}z,{}w)} \\undocumented") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(f,{}g,{}h,{}a..b)} plots {/emx = \\spad{f}(\\spad{t}),{} \\spad{y} = \\spad{g}(\\spad{t}),{} \\spad{z} = \\spad{h}(\\spad{t})} as \\spad{t} ranges over {/em[a,{}\\spad{b}]}."))) NIL NIL -(-856) +(-855) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,{}r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r,{}s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,{}r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,{}2*\\%\\spad{pi}]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,{}a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,{}b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),{}g(t)),{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,{}r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b,{}c..d,{}e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}; \\spad{x}-range of \\spad{[c,{}d]} and \\spad{y}-range of \\spad{[e,{}f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}g,{}a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,{}b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b,{}c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,{}...,{}fm],{}a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b,{}c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}; \\spad{y}-range of \\spad{[c,{}d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,{}a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,{}b]}."))) NIL NIL -(-857) +(-856) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-858 R -4049) +(-857 R -4049) ((|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 -(-859) +(-858) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list.")) (|optional| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation)..")) (|constant| (((|Expression| (|Integer|)) (|Symbol|)) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-860 S A B) +(-859 S A B) ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-861 S R -4049) +(-860 S R -4049) ((|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 -(-862 I) +(-861 I) ((|constructor| (NIL "This package provides pattern matching functions on integers.")) (|patternMatch| (((|PatternMatchResult| (|Integer|) |#1|) |#1| (|Pattern| (|Integer|)) (|PatternMatchResult| (|Integer|) |#1|)) "\\spad{patternMatch(n,{} pat,{} res)} matches the pattern \\spad{pat} to the integer \\spad{n}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-863 S E) +(-862 S E) ((|constructor| (NIL "This package provides pattern matching functions on kernels.")) (|patternMatch| (((|PatternMatchResult| |#1| |#2|) (|Kernel| |#2|) (|Pattern| |#1|) (|PatternMatchResult| |#1| |#2|)) "\\spad{patternMatch(f(e1,{}...,{}en),{} pat,{} res)} matches the pattern \\spad{pat} to \\spad{f(e1,{}...,{}en)}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-864 S R L) +(-863 S R L) ((|constructor| (NIL "This package provides pattern matching functions on lists.")) (|patternMatch| (((|PatternMatchListResult| |#1| |#2| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchListResult| |#1| |#2| |#3|)) "\\spad{patternMatch(l,{} pat,{} res)} matches the pattern \\spad{pat} to the list \\spad{l}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-865 S E V R P) +(-864 S E V R P) ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL -((|HasCategory| |#3| (LIST (QUOTE -815) (|devaluate| |#1|)))) -(-866 R -4049 -2212) +((|HasCategory| |#3| (LIST (QUOTE -814) (|devaluate| |#1|)))) +(-865 R -4049 -2244) ((|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 -(-867 -2212) +(-866 -2244) ((|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 -(-868 S R Q) +(-867 S R Q) ((|constructor| (NIL "This package provides pattern matching functions on quotients.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(a/b,{} pat,{} res)} matches the pattern \\spad{pat} to the quotient \\spad{a/b}; res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL NIL -(-869 S) +(-868 S) ((|constructor| (NIL "This package provides pattern matching functions on symbols.")) (|patternMatch| (((|PatternMatchResult| |#1| (|Symbol|)) (|Symbol|) (|Pattern| |#1|) (|PatternMatchResult| |#1| (|Symbol|))) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches (necessary for recursion)."))) NIL NIL -(-870 S R P) +(-869 S R P) ((|constructor| (NIL "This package provides tools for the pattern matcher.")) (|patternMatchTimes| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatchTimes(lsubj,{} lpat,{} res,{} match)} matches the product of patterns \\spad{reduce(*,{}lpat)} to the product of subjects \\spad{reduce(*,{}lsubj)}; \\spad{r} contains the previous matches and match is a pattern-matching function on \\spad{P}.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) (|List| |#3|) (|List| (|Pattern| |#1|)) (|Mapping| |#3| (|List| |#3|)) (|PatternMatchResult| |#1| |#3|) (|Mapping| (|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|))) "\\spad{patternMatch(lsubj,{} lpat,{} op,{} res,{} match)} matches the list of patterns \\spad{lpat} to the list of subjects \\spad{lsubj},{} allowing for commutativity; \\spad{op} is the operator such that \\spad{op}(\\spad{lpat}) should match \\spad{op}(\\spad{lsubj}) at the end,{} \\spad{r} contains the previous matches,{} and match is a pattern-matching function on \\spad{P}."))) NIL NIL -(-871) +(-870) ((|constructor| (NIL "This package provides various polynomial number theoretic functions over the integers.")) (|legendre| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{legendre(n)} returns the \\spad{n}th Legendre polynomial \\spad{P[n](x)}. Note: Legendre polynomials,{} denoted \\spad{P[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{1/sqrt(1-2*t*x+t**2) = sum(P[n](x)*t**n,{} n=0..infinity)}.")) (|laguerre| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{laguerre(n)} returns the \\spad{n}th Laguerre polynomial \\spad{L[n](x)}. Note: Laguerre polynomials,{} denoted \\spad{L[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(x*t/(t-1))/(1-t) = sum(L[n](x)*t**n/n!,{} n=0..infinity)}.")) (|hermite| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{hermite(n)} returns the \\spad{n}th Hermite polynomial \\spad{H[n](x)}. Note: Hermite polynomials,{} denoted \\spad{H[n](x)},{} are computed from the two term recurrence. The generating function is: \\spad{exp(2*t*x-t**2) = sum(H[n](x)*t**n/n!,{} n=0..infinity)}.")) (|fixedDivisor| (((|Integer|) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{fixedDivisor(a)} for \\spad{a(x)} in \\spad{Z[x]} is the largest integer \\spad{f} such that \\spad{f} divides \\spad{a(x=k)} for all integers \\spad{k}. Note: fixed divisor of \\spad{a} is \\spad{reduce(gcd,{}[a(x=k) for k in 0..degree(a)])}.")) (|euler| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler polynomial \\spad{E[n](x)}. Note: Euler polynomials denoted \\spad{E(n,{}x)} computed by solving the differential equation \\spad{differentiate(E(n,{}x),{}x) = n E(n-1,{}x)} where \\spad{E(0,{}x) = 1} and initial condition comes from \\spad{E(n) = 2**n E(n,{}1/2)}.")) (|cyclotomic| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{cyclotomic(n)} returns the \\spad{n}th cyclotomic polynomial \\spad{phi[n](x)}. Note: \\spad{phi[n](x)} is the factor of \\spad{x**n - 1} whose roots are the primitive \\spad{n}th roots of unity.")) (|chebyshevU| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevU(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{U[n](x)}. Note: Chebyshev polynomials of the second kind,{} denoted \\spad{U[n](x)},{} computed from the two term recurrence. The generating function \\spad{1/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|chebyshevT| (((|SparseUnivariatePolynomial| (|Integer|)) (|Integer|)) "\\spad{chebyshevT(n)} returns the \\spad{n}th Chebyshev polynomial \\spad{T[n](x)}. Note: Chebyshev polynomials of the first kind,{} denoted \\spad{T[n](x)},{} computed from the two term recurrence. The generating function \\spad{(1-t*x)/(1-2*t*x+t**2) = sum(T[n](x)*t**n,{} n=0..infinity)}.")) (|bernoulli| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli polynomial \\spad{B[n](x)}. Note: Bernoulli polynomials denoted \\spad{B(n,{}x)} computed by solving the differential equation \\spad{differentiate(B(n,{}x),{}x) = n B(n-1,{}x)} where \\spad{B(0,{}x) = 1} and initial condition comes from \\spad{B(n) = B(n,{}0)}."))) NIL NIL -(-872 R) +(-871 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-970)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) -(-873 |lv| R) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-970)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) +(-872 |lv| R) ((|constructor| (NIL "Package with the conversion functions among different kind of polynomials")) (|pToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToDmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{DMP}.")) (|dmpToP| (((|Polynomial| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToP(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{POLY}.")) (|hdmpToP| (((|Polynomial| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToP(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{POLY}.")) (|pToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|Polynomial| |#2|)) "\\spad{pToHdmp(p)} converts \\spad{p} from a \\spadtype{POLY} to a \\spadtype{HDMP}.")) (|hdmpToDmp| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{hdmpToDmp(p)} converts \\spad{p} from a \\spadtype{HDMP} to a \\spadtype{DMP}.")) (|dmpToHdmp| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{dmpToHdmp(p)} converts \\spad{p} from a \\spadtype{DMP} to a \\spadtype{HDMP}."))) NIL NIL -(-874 |TheField| |ThePols|) +(-873 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealPolynomialUtilitiesPackage} provides common functions used by interval coding.")) (|lazyVariations| (((|NonNegativeInteger|) (|List| |#1|) (|Integer|) (|Integer|)) "\\axiom{lazyVariations(\\spad{l},{}\\spad{s1},{}\\spad{sn})} is the number of sign variations in the list of non null numbers [s1::l]\\spad{@sn},{}")) (|sturmVariationsOf| (((|NonNegativeInteger|) (|List| |#1|)) "\\axiom{sturmVariationsOf(\\spad{l})} is the number of sign variations in the list of numbers \\spad{l},{} note that the first term counts as a sign")) (|boundOfCauchy| ((|#1| |#2|) "\\axiom{boundOfCauchy(\\spad{p})} bounds the roots of \\spad{p}")) (|sturmSequence| (((|List| |#2|) |#2|) "\\axiom{sturmSequence(\\spad{p}) = sylvesterSequence(\\spad{p},{}\\spad{p'})}")) (|sylvesterSequence| (((|List| |#2|) |#2| |#2|) "\\axiom{sylvesterSequence(\\spad{p},{}\\spad{q})} is the negated remainder sequence of \\spad{p} and \\spad{q} divided by the last computed term"))) NIL -((|HasCategory| |#1| (QUOTE (-782)))) -(-875 R S) +((|HasCategory| |#1| (QUOTE (-781)))) +(-874 R S) ((|constructor| (NIL "\\indented{2}{This package takes a mapping between coefficient rings,{} and lifts} it to a mapping between polynomials over those rings.")) (|map| (((|Polynomial| |#2|) (|Mapping| |#2| |#1|) (|Polynomial| |#1|)) "\\spad{map(f,{} p)} produces a new polynomial as a result of applying the function \\spad{f} to every coefficient of the polynomial \\spad{p}."))) NIL NIL -(-876 |x| R) +(-875 |x| R) ((|constructor| (NIL "This package is primarily to help the interpreter do coercions. It allows you to view a polynomial as a univariate polynomial in one of its variables with coefficients which are again a polynomial in all the other variables.")) (|univariate| (((|UnivariatePolynomial| |#1| (|Polynomial| |#2|)) (|Polynomial| |#2|) (|Variable| |#1|)) "\\spad{univariate(p,{} x)} converts the polynomial \\spad{p} to a one of type \\spad{UnivariatePolynomial(x,{}Polynomial(R))},{} ie. as a member of \\spad{R[...][x]}."))) NIL NIL -(-877 S R E |VarSet|) +(-876 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 (-838))) (|HasAttribute| |#2| (QUOTE -4231)) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#4| (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#4| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#4| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#4| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-784)))) -(-878 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-837))) (|HasAttribute| |#2| (QUOTE -4231)) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#4| (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#4| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#4| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#4| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-783)))) +(-877 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}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) NIL -(-879 E V R P -4049) +(-878 E V R P -4049) ((|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 -(-880 E |Vars| R P S) +(-879 E |Vars| R P S) ((|constructor| (NIL "This package provides a very general map function,{} which given a set \\spad{S} and polynomials over \\spad{R} with maps from the variables into \\spad{S} and the coefficients into \\spad{S},{} maps polynomials into \\spad{S}. \\spad{S} is assumed to support \\spad{+},{} \\spad{*} and \\spad{**}.")) (|map| ((|#5| (|Mapping| |#5| |#2|) (|Mapping| |#5| |#3|) |#4|) "\\spad{map(varmap,{} coefmap,{} p)} takes a \\spad{varmap},{} a mapping from the variables of polynomial \\spad{p} into \\spad{S},{} \\spad{coefmap},{} a mapping from coefficients of \\spad{p} into \\spad{S},{} and \\spad{p},{} and produces a member of \\spad{S} using the corresponding arithmetic. in \\spad{S}"))) NIL NIL -(-881 R) +(-880 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}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) -(-882 E V R P -4049) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| (-1084) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) +(-881 E V R P -4049) ((|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 (-425)))) -(-883) +(-882) ((|constructor| (NIL "PlottablePlaneCurveCategory is the category of curves in the plane which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x}-coordinates and \\spad{y}-coordinates of the points on the curve.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-884 R L) +(-883 R L) ((|constructor| (NIL "\\spadtype{PrecomputedAssociatedEquations} stores some generic precomputations which speed up the computations of the associated equations needed for factoring operators.")) (|firstUncouplingMatrix| (((|Union| (|Matrix| |#1|) "failed") |#2| (|PositiveInteger|)) "\\spad{firstUncouplingMatrix(op,{} m)} returns the matrix A such that \\spad{A w = (W',{}W'',{}...,{}W^N)} in the corresponding associated equations for right-factors of order \\spad{m} of \\spad{op}. Returns \"failed\" if the matrix A has not been precomputed for the particular combination \\spad{degree(L),{} m}."))) NIL NIL -(-885 A B) +(-884 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on primitive arrays} with unary and binary functions involving different underlying types")) (|map| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1|) (|PrimitiveArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of primitive array \\spad{a} resulting in a new primitive array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the primitive array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|PrimitiveArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|PrimitiveArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of primitive array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) NIL NIL -(-886 S) +(-885 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"))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) -(-887) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) +(-886) ((|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 -(-888 -4049) +(-887 -4049) ((|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 -(-889 I) +(-888 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin\\spad{'s} probabilistic primality test and the utility functions \\spadfun{nextPrime},{} \\spadfun{prevPrime} and \\spadfun{primes}.")) (|primes| (((|List| |#1|) |#1| |#1|) "\\spad{primes(a,{}b)} returns a list of all primes \\spad{p} with \\spad{a <= p <= b}")) (|prevPrime| ((|#1| |#1|) "\\spad{prevPrime(n)} returns the largest prime strictly smaller than \\spad{n}")) (|nextPrime| ((|#1| |#1|) "\\spad{nextPrime(n)} returns the smallest prime strictly larger than \\spad{n}")) (|prime?| (((|Boolean|) |#1|) "\\spad{prime?(n)} returns \\spad{true} if \\spad{n} is prime and \\spad{false} if not. The algorithm used is Rabin\\spad{'s} probabilistic primality test (reference: Knuth Volume 2 Semi Numerical Algorithms). If \\spad{prime? n} returns \\spad{false},{} \\spad{n} is proven composite. If \\spad{prime? n} returns \\spad{true},{} prime? may be in error however,{} the probability of error is very low. and is zero below 25*10**9 (due to a result of Pomerance et al),{} below 10**12 and 10**13 due to results of Pinch,{} and below 341550071728321 due to a result of Jaeschke. Specifically,{} this implementation does at least 10 pseudo prime tests and so the probability of error is \\spad{< 4**(-10)}. The running time of this method is cubic in the length of the input \\spad{n},{} that is \\spad{O( (log n)**3 )},{} for n<10**20. beyond that,{} the algorithm is quartic,{} \\spad{O( (log n)**4 )}. Two improvements due to Davenport have been incorporated which catches some trivial strong pseudo-primes,{} such as [Jaeschke,{} 1991] 1377161253229053 * 413148375987157,{} which the original algorithm regards as prime"))) NIL NIL -(-890) +(-889) ((|constructor| (NIL "PrintPackage provides a print function for output forms.")) (|print| (((|Void|) (|OutputForm|)) "\\spad{print(o)} writes the output form \\spad{o} on standard output using the two-dimensional formatter."))) NIL NIL -(-891 R E) +(-890 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}"))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4227 . T) (-4228 . T) (-4230 . T)) ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-425))) (-12 (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-124)))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231))) -(-892 A B) +(-891 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"))) ((-4230 -12 (|has| |#2| (-446)) (|has| |#1| (-446)))) -((-12 (|HasCategory| |#1| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-729)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-446)))) (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#2| (QUOTE (-342)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-446)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| 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(|HasCategory| |#1| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-729))))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-729))))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-446))) (|HasCategory| |#2| (QUOTE (-446)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663)))) (-12 (|HasCategory| |#1| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-729))))) (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-783)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-729))) (|HasCategory| |#2| (QUOTE (-729)))) (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-783)))))) +(-892) +((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) +NIL +NIL (-893 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|equivOperands| (((|Pair| $ $) $) "\\spad{equivOperands p} extracts the operands to the logical equivalence; otherwise errors.")) (|equiv?| (((|Boolean|) $) "\\spad{equiv? p} is \\spad{true} when \\spad{`p'} is a logical equivalence.")) (|impliesOperands| (((|Pair| $ $) $) "\\spad{impliesOperands p} extracts the operands to the logical implication; otherwise errors.")) (|implies?| (((|Boolean|) $) "\\spad{implies? p} is \\spad{true} when \\spad{`p'} is a logical implication.")) (|orOperands| (((|Pair| $ $) $) "\\spad{orOperands p} extracts the operands to the logical disjunction; otherwise errors.")) (|or?| (((|Boolean|) $) "\\spad{or? p} is \\spad{true} when \\spad{`p'} is a logical disjunction.")) (|andOperands| (((|Pair| $ $) $) "\\spad{andOperands p} extracts the operands of the logical conjunction; otherwise errors.")) (|and?| (((|Boolean|) $) "\\spad{and? p} is \\spad{true} when \\spad{`p'} is a logical conjunction.")) (|notOperand| (($ $) "\\spad{notOperand returns} the operand to the logical `not' operator; otherwise errors.")) (|not?| (((|Boolean|) $) "\\spad{not? p} is \\spad{true} when \\spad{`p'} is a logical negation")) (|variable| (((|Symbol|) $) "\\spad{variable p} extracts the varible name from \\spad{`p'}; otherwise errors.")) (|variable?| (((|Boolean|) $) "variables? \\spad{p} returns \\spad{true} when \\spad{`p'} really is a variable.")) (|term| ((|#1| $) "\\spad{term p} extracts the term value from \\spad{`p'}; otherwise errors.")) (|term?| (((|Boolean|) $) "\\spad{term? p} returns \\spad{true} when \\spad{`p'} really is a term")) (|variables| (((|Set| (|Symbol|)) $) "\\spad{variables(p)} returns the set of propositional variables appearing in the proposition \\spad{`p'}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional variable.") (($ |#1|) "\\spad{coerce(t)} turns the term \\spad{`t'} into a propositional formula"))) NIL -((|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791))))) (-894) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,{}q)} returns the logical equivalence of \\spad{`p'},{} \\spad{`q'}.")) (|implies| (($ $ $) "\\spad{implies(p,{}q)} returns the logical implication of \\spad{`q'} by \\spad{`p'}.")) (|or| (($ $ $) "\\spad{p or q} returns the logical disjunction of \\spad{`p'},{} \\spad{`q'}.")) (|and| (($ $ $) "\\spad{p and q} returns the logical conjunction of \\spad{`p'},{} \\spad{`q'}.")) (|not| (($ $) "\\spad{not p} returns the logical negation of \\spad{`p'}."))) NIL NIL (-895 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-896 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}}"))) @@ -3538,7 +3538,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-513)))) (-902 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."))) -((-4233 . T) (-2046 . T)) +((-4233 . T) (-2092 . T)) NIL (-903 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."))) @@ -3554,7 +3554,7 @@ NIL NIL (-906 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}."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-907 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3599,10 +3599,10 @@ NIL (-917 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 (-838))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-946))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-1060)))) +((|HasCategory| |#2| (QUOTE (-837))) (|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-946))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-1060)))) (-918 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}."))) -((-2046 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-2092 . T) (-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-919 |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}."))) @@ -3610,12 +3610,12 @@ NIL NIL (-920 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."))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-921 S R) ((|constructor| (NIL "\\spadtype{QuaternionCategory} describes the category of quaternions and implements functions that are not representation specific.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(q)} returns \\spad{q} as a rational number,{} or \"failed\" if this is not possible. Note: if \\spad{rational?(q)} is \\spad{true},{} the conversion can be done and the rational number will be returned.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(q)} tries to convert \\spad{q} into a rational number. Error: if this is not possible. If \\spad{rational?(q)} is \\spad{true},{} the conversion will be done and the rational number returned.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(q)} returns {\\it \\spad{true}} if all the imaginary parts of \\spad{q} are zero and the real part can be converted into a rational number,{} and {\\it \\spad{false}} otherwise.")) (|abs| ((|#2| $) "\\spad{abs(q)} computes the absolute value of quaternion \\spad{q} (sqrt of norm).")) (|real| ((|#2| $) "\\spad{real(q)} extracts the real part of quaternion \\spad{q}.")) (|quatern| (($ |#2| |#2| |#2| |#2|) "\\spad{quatern(r,{}i,{}j,{}k)} constructs a quaternion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(q)} computes the norm of \\spad{q} (the sum of the squares of the components).")) (|imagK| ((|#2| $) "\\spad{imagK(q)} extracts the imaginary \\spad{k} part of quaternion \\spad{q}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(q)} extracts the imaginary \\spad{j} part of quaternion \\spad{q}.")) (|imagI| ((|#2| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) NIL -((|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-265)))) +((|HasCategory| |#2| (QUOTE (-506))) (|HasCategory| |#2| (QUOTE (-979))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-265)))) (-922 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}."))) ((-4226 |has| |#1| (-265)) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -3627,11 +3627,11 @@ NIL (-924 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.}"))) ((-4226 |has| |#1| (-265)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-265))) (-3703 (|HasCategory| |#1| (QUOTE (-265))) (|HasCategory| |#1| (QUOTE (-337)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-506))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))))) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-265))) (-3703 (|HasCategory| |#1| (QUOTE (-265))) (|HasCategory| |#1| (QUOTE (-337)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -482) (QUOTE (-1084)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -261) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-979))) (|HasCategory| |#1| (QUOTE (-506))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))))) (-925 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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-926 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 @@ -3643,11 +3643,11 @@ NIL (-928 -4049 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) ((-4226 |has| (-381 |#2|) (-337)) (-4231 |has| (-381 |#2|) (-337)) (-4225 |has| (-381 |#2|) (-337)) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-381 |#2|) (QUOTE (-133))) (|HasCategory| (-381 |#2|) (QUOTE (-135))) (|HasCategory| (-381 |#2|) (QUOTE (-323))) (|HasCategory| (-381 |#2|) (QUOTE (-337))) (-3703 (|HasCategory| (-381 |#2|) (QUOTE (-337))) (|HasCategory| (-381 |#2|) (QUOTE (-323)))) (|HasCategory| (-381 |#2|) (QUOTE (-342))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-342))) (-3703 (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) +((|HasCategory| (-381 |#2|) (QUOTE (-133))) (|HasCategory| (-381 |#2|) (QUOTE (-135))) (|HasCategory| (-381 |#2|) (QUOTE (-323))) (|HasCategory| (-381 |#2|) (QUOTE (-337))) (-3703 (|HasCategory| (-381 |#2|) (QUOTE (-337))) (|HasCategory| (-381 |#2|) (QUOTE (-323)))) (|HasCategory| (-381 |#2|) (QUOTE (-342))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-342))) (-3703 (|HasCategory| (-381 |#2|) (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-12 (|HasCategory| (-381 |#2|) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (-3703 (-12 (|HasCategory| (-381 |#2|) (QUOTE (-210))) (|HasCategory| (-381 |#2|) (QUOTE (-337)))) (|HasCategory| (-381 |#2|) (QUOTE (-323))))) (-929 |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."))) ((-4225 . T) (-4231 . T) (-4226 . T) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| (-521) (QUOTE (-838))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-521) (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-135))) (|HasCategory| (-521) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-946))) (|HasCategory| (-521) (QUOTE (-757))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-1060))) (|HasCategory| (-521) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| (-521) (QUOTE (-210))) (|HasCategory| (-521) (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| (-521) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -284) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -261) (QUOTE (-521)) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-282))) (|HasCategory| (-521) (QUOTE (-506))) (|HasCategory| (-521) (QUOTE (-784))) (-3703 (|HasCategory| (-521) (QUOTE (-757))) (|HasCategory| (-521) (QUOTE (-784)))) (|HasCategory| (-521) (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-838)))) (|HasCategory| (-521) (QUOTE (-133))))) +((|HasCategory| (-521) (QUOTE (-837))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-1084)))) (|HasCategory| (-521) (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-135))) (|HasCategory| (-521) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-946))) (|HasCategory| (-521) (QUOTE (-756))) (|HasCategory| (-521) (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-1060))) (|HasCategory| (-521) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| (-521) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| (-521) (QUOTE (-210))) (|HasCategory| (-521) (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| (-521) (LIST (QUOTE -482) (QUOTE (-1084)) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -284) (QUOTE (-521)))) (|HasCategory| (-521) (LIST (QUOTE -261) (QUOTE (-521)) (QUOTE (-521)))) (|HasCategory| (-521) (QUOTE (-282))) (|HasCategory| (-521) (QUOTE (-506))) (|HasCategory| (-521) (QUOTE (-783))) (-3703 (|HasCategory| (-521) (QUOTE (-756))) (|HasCategory| (-521) (QUOTE (-783)))) (|HasCategory| (-521) (LIST (QUOTE -583) (QUOTE (-521)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| (-521) (QUOTE (-837)))) (|HasCategory| (-521) (QUOTE (-133))))) (-930) ((|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 @@ -3670,7 +3670,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4234)) (|HasCategory| |#2| (QUOTE (-1013)))) (-935 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}."))) -((-2046 . T)) +((-2092 . T)) NIL (-936 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)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\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}}"))) @@ -3735,7 +3735,7 @@ NIL (-951 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."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-791))))) (-952 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 @@ -3767,7 +3767,7 @@ NIL (-959) ((|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.}"))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (QUOTE (-1084))) (LIST (QUOTE |:|) (QUOTE -3045) (QUOTE (-51))))))) (|HasCategory| (-1084) (QUOTE (-784))) (|HasCategory| (-51) (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-1013)))) (-12 (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -284) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (QUOTE (-1084))) (LIST (QUOTE |:|) (QUOTE -3050) (QUOTE (-51))))))) (|HasCategory| (-1084) (QUOTE (-783))) (|HasCategory| (-51) (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-1013)))) (-12 (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -284) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791)))))) (-960 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL @@ -3799,7 +3799,7 @@ NIL (-967 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}."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| (-716 |#1| (-794 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-716 |#1| (-794 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-716 |#1| (-794 |#2|)) (QUOTE (-1013))) (|HasCategory| (-716 |#1| (-794 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -716) (|devaluate| |#1|) (LIST (QUOTE -794) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| (-794 |#2|) (QUOTE (-342))) (|HasCategory| (-716 |#1| (-794 |#2|)) (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| (-716 |#1| (-793 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-716 |#1| (-793 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-716 |#1| (-793 |#2|)) (QUOTE (-1013))) (|HasCategory| (-716 |#1| (-793 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -716) (|devaluate| |#1|) (LIST (QUOTE -793) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| (-793 |#2|) (QUOTE (-342))) (|HasCategory| (-716 |#1| (-793 |#2|)) (LIST (QUOTE -561) (QUOTE (-791))))) (-968) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,{}j,{}k,{}l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,{}f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL @@ -3822,12 +3822,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-282))) (|HasCategory| |#4| (QUOTE (-337))) (|HasCategory| |#4| (QUOTE (-513))) (|HasCategory| |#4| (QUOTE (-157)))) (-973 |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"))) -((-4233 . T) (-2046 . T) (-4228 . T) (-4227 . T)) +((-4233 . T) (-2092 . T) (-4228 . T) (-4227 . T)) NIL (-974 |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}."))) ((-4233 . T) (-4228 . T) (-4227 . T)) -((|HasCategory| |#3| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#3| (QUOTE (-337))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-282))) (|HasCategory| |#3| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-157))) (-3703 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-337)))) (|HasCategory| |#3| (LIST (QUOTE -561) (QUOTE (-792)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))) (-3703 (-12 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-337))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))))) +((|HasCategory| |#3| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#3| (QUOTE (-337))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-282))) (|HasCategory| |#3| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-157))) (-3703 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (QUOTE (-337)))) (|HasCategory| |#3| (LIST (QUOTE -561) (QUOTE (-791)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))) (-3703 (-12 (|HasCategory| |#3| (QUOTE (-157))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-337))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (LIST (QUOTE -284) (|devaluate| |#3|)))))) (-975 |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 @@ -3859,7 +3859,7 @@ NIL (-982) ((|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}"))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (QUOTE (-1084))) (LIST (QUOTE |:|) (QUOTE -3045) (QUOTE (-51))))))) (|HasCategory| (-1084) (QUOTE (-784))) (|HasCategory| (-51) (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-1013)))) (-12 (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -284) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (QUOTE (-1084))) (LIST (QUOTE |:|) (QUOTE -3050) (QUOTE (-51))))))) (|HasCategory| (-1084) (QUOTE (-783))) (|HasCategory| (-51) (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-1013)))) (-12 (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -284) (QUOTE (-51))))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-51) (LIST (QUOTE -561) (QUOTE (-791)))))) (-983 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 @@ -3886,7 +3886,7 @@ NIL NIL (-989 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}."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-990 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."))) @@ -3915,7 +3915,7 @@ NIL (-996 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."))) ((-4226 |has| |#1| (-337)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) ((-4235 "*") . T) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084))))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084))))) (-12 (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337)))) (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337)))) (|HasCategory| |#1| (QUOTE (-323))))) +((|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-323)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084))))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084))))) (-12 (|HasCategory| |#1| (QUOTE (-323))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337)))) (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (QUOTE (-337)))) (|HasCategory| |#1| (QUOTE (-323))))) (-997 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 @@ -3939,7 +3939,7 @@ NIL (-1002 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"))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| (-1003 (-1084)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-210))) (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) (-1003 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 @@ -3947,7 +3947,7 @@ NIL (-1004 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value. For example,{} if \\spad{s = l..h by k},{} then the list \\spad{[f(l),{} f(l+k),{}...,{} f(lN)]} is computed,{} where \\spad{lN <= h < lN+k}.") (((|Segment| |#2|) (|Mapping| |#2| |#1|) (|Segment| |#1|)) "\\spad{map(f,{}l..h)} returns a new segment \\spad{f(l)..f(h)}."))) NIL -((|HasCategory| |#1| (QUOTE (-782)))) +((|HasCategory| |#1| (QUOTE (-781)))) (-1005 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,{}v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL @@ -3958,15 +3958,15 @@ NIL ((|HasCategory| |#1| (QUOTE (-1013)))) (-1007 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."))) -((-2046 . T)) +((-2092 . T)) NIL (-1008 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-782))) (|HasCategory| |#1| (QUOTE (-1013)))) +((|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1013)))) (-1009 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-2046 . T)) +((-2092 . T)) NIL (-1010 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3974,7 +3974,7 @@ NIL NIL (-1011 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4223 . T) (-2046 . T)) +((-4223 . T) (-2092 . T)) NIL (-1012 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}."))) @@ -3991,7 +3991,7 @@ NIL (-1015 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)}}"))) ((-4233 . T) (-4223 . T) (-4234 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-784))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-783))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-342))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791))))) (-1016 |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 @@ -4018,7 +4018,7 @@ NIL NIL (-1022 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.}"))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-1023) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4035,7 +4035,7 @@ NIL (-1026 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. 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((|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 @@ -4058,7 +4058,7 @@ NIL NIL (-1032 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| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4233 . T) (-4234 . T) (-2046 . T)) +((-4233 . T) (-4234 . T) (-2092 . T)) NIL (-1033 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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."))) @@ -4066,7 +4066,7 @@ NIL ((|HasCategory| |#3| (QUOTE (-337))) (|HasAttribute| |#3| (QUOTE (-4235 "*"))) (|HasCategory| |#3| (QUOTE (-157)))) (-1034 |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."))) -((-2046 . T) (-4233 . T) (-4227 . T) (-4228 . T) (-4230 . T)) +((-2092 . T) (-4233 . T) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-1035 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}."))) @@ -4075,14 +4075,14 @@ NIL (-1036 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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-838))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-838)))) (|HasCategory| |#1| (QUOTE (-133))))) +((|HasCategory| |#1| (QUOTE (-837))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-425))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (|HasCategory| |#1| (QUOTE (-425))) (|HasCategory| |#1| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-837)))) (|HasCategory| |#1| (QUOTE (-133))))) (-1037 |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}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4228 . T) (-4227 . T) (-4230 . T)) ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-135))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-513))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-337)))) (-1038 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}"))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-1039 UP -4049) ((|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"))) @@ -4103,7 +4103,7 @@ NIL (-1043 S A) ((|constructor| (NIL "This package exports sorting algorithnms")) (|insertionSort!| ((|#2| |#2|) "\\spad{insertionSort! }\\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{insertionSort!(a,{}f)} \\undocumented")) (|bubbleSort!| ((|#2| |#2|) "\\spad{bubbleSort!(a)} \\undocumented") ((|#2| |#2| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{bubbleSort!(a,{}f)} \\undocumented"))) NIL -((|HasCategory| |#1| (QUOTE (-784)))) +((|HasCategory| |#1| (QUOTE (-783)))) (-1044 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL @@ -4131,18 +4131,18 @@ NIL (-1050 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."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-1049 |#1| |#2|) (QUOTE (-1013))) (-12 (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -284) (LIST (QUOTE -1049) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1049 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -561) (QUOTE (-792)))) (-12 (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -284) (LIST (QUOTE -1049) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1049 |#1| |#2|) (QUOTE (-1013)))))) +((|HasCategory| (-1049 |#1| |#2|) (QUOTE (-1013))) (-12 (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -284) (LIST (QUOTE -1049) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1049 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -561) (QUOTE (-791)))) (-12 (|HasCategory| (-1049 |#1| |#2|) (LIST (QUOTE -284) (LIST (QUOTE -1049) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1049 |#1| |#2|) (QUOTE (-1013)))))) (-1051 |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}."))) ((-4230 . T) (-4222 |has| |#2| (-6 (-4235 "*"))) (-4233 . T) (-4227 . T) (-4228 . T)) -((|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-337))) (-3703 (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-3703 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-157)))) +((|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (QUOTE (-282))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-337))) (-3703 (|HasAttribute| |#2| (QUOTE (-4235 "*"))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasCategory| |#2| (QUOTE (-210)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-3703 (-12 (|HasCategory| |#2| (QUOTE (-210))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-157)))) (-1052 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|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1053) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-1054 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.}"))) @@ -4151,23 +4151,23 @@ NIL (-1055 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."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-791))))) (-1056 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}."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1057 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 (-1058 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})}."))) -((-2046 . T)) +((-2092 . T)) NIL (-1059 |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."))) ((-4234 . T)) -((|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|)))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|)))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1060) ((|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 @@ -4191,19 +4191,19 @@ NIL (-1065 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."))) ((-4234 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1066) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-1067) NIL ((-4234 . T) (-4233 . T)) -((|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| (-132) (QUOTE (-1013))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-3703 (-12 (|HasCategory| (-132) (QUOTE (-784))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| (-132) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-132) (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| (-132) (QUOTE (-1013))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-3703 (-12 (|HasCategory| (-132) (QUOTE (-783))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132))))) (-12 (|HasCategory| (-132) (QUOTE (-1013))) (|HasCategory| (-132) (LIST (QUOTE -284) (QUOTE (-132)))))) (|HasCategory| (-132) (LIST (QUOTE -561) (QUOTE (-791))))) (-1068 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (QUOTE (-1067))) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#1|)))))) (|HasCategory| (-1067) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (QUOTE (-1067))) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#1|)))))) (|HasCategory| (-1067) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-1013)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1069 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 @@ -4230,8 +4230,8 @@ NIL NIL (-1075 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n),{} n = a..b)} returns \\spad{f}(a) + \\spad{f}(a+1) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n),{} n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL @@ -4251,15 +4251,15 @@ NIL (-1080 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) 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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}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|))))) (|HasCategory| (-707) (QUOTE (-1025))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (|HasSignature| |#1| (LIST (QUOTE -2189) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2184) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4084) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|))))) (|HasCategory| (-707) (QUOTE (-1025))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (|HasSignature| |#1| (LIST (QUOTE -2223) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -1749) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4085) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) (-1083) ((|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 @@ -4303,7 +4303,7 @@ NIL (-1093 |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}"))) ((-4233 . T) (-4234 . T)) -((|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2529) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3045) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#2| (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792))))) (-3703 (|HasCategory| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (LIST (QUOTE -561) (QUOTE (-792)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (-12 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -284) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -2535) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -3050) (|devaluate| |#2|)))))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#2| (QUOTE (-1013))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -284) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791))))) (-3703 (|HasCategory| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (LIST (QUOTE -561) (QUOTE (-791)))) (|HasCategory| |#2| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1094 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 @@ -4314,7 +4314,7 @@ NIL NIL (-1096 |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})}."))) -((-4234 . T) (-2046 . T)) +((-4234 . T) (-2092 . T)) NIL (-1097 |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."))) @@ -4355,7 +4355,7 @@ NIL (-1106 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (QUOTE (-1013))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1107 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL @@ -4375,14 +4375,14 @@ NIL (-1111 R -4049) ((|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 -562) (LIST (QUOTE -821) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -815) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -815) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (LIST (QUOTE -562) (LIST (QUOTE -820) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -814) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -814) (|devaluate| |#1|))))) (-1112 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 (-342)))) (-1113 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|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-1114 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) @@ -4399,19 +4399,19 @@ NIL (-1117 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 (-1013))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791))))) (-1118 -4049) ((|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 (-1119) ((|constructor| (NIL "The fundamental Type."))) -((-2046 . T)) +((-2092 . T)) NIL (-1120 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 (-784)))) +((|HasCategory| |#1| (QUOTE (-783)))) (-1121) ((|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 @@ -4438,16 +4438,16 @@ NIL ((|HasCategory| |#2| (QUOTE (-337)))) (-1127 |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)}."))) -(((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-2046 |has| |#1| (-337)) (-4227 . T) (-4228 . T) (-4230 . T)) +(((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-2092 |has| |#1| (-337)) (-4227 . T) (-4228 . T) (-4230 . T)) NIL (-1128 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. 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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 @@ -4455,11 +4455,11 @@ NIL (-1131 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 (-782)))) +((|HasCategory| |#1| (QUOTE (-781)))) (-1132 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 (-782))) (|HasCategory| |#1| (QUOTE (-1013)))) +((|HasCategory| |#1| (QUOTE (-781))) (|HasCategory| |#1| (QUOTE (-1013)))) (-1133 |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 @@ -4483,7 +4483,7 @@ NIL (-1138 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#2| $) "\\spad{fmecg(p1,{}e,{}r,{}p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} converts the variable \\spad{x} to a univariate polynomial."))) (((-4235 "*") |has| |#2| (-157)) (-4226 |has| |#2| (-513)) (-4229 |has| |#2| (-337)) (-4231 |has| |#2| (-6 -4231)) (-4228 . T) (-4227 . T) (-4230 . T)) -((|HasCategory| |#2| (QUOTE (-838))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-157))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-513)))) (-12 (|HasCategory| (-998) (LIST (QUOTE -815) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-353))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -815) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -815) (QUOTE (-521))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-353)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -821) (QUOTE (-521)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#2| (QUOTE (-784))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -829) (QUOTE (-1084)))) (-3703 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE -4231)) (|HasCategory| |#2| (QUOTE (-425))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-838)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-838)))) (|HasCategory| |#2| (QUOTE (-133))))) +((|HasCategory| |#2| (QUOTE (-837))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-157))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-513)))) (-12 (|HasCategory| (-998) (LIST (QUOTE -814) (QUOTE (-353)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-353))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -814) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -814) (QUOTE (-521))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-353)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -562) (LIST (QUOTE -820) (QUOTE (-521)))))) (-12 (|HasCategory| (-998) (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#2| (LIST (QUOTE -562) (QUOTE (-497))))) (|HasCategory| |#2| (QUOTE (-783))) (|HasCategory| |#2| (LIST (QUOTE -583) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-135))) (|HasCategory| |#2| (QUOTE (-133))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (QUOTE (-521)))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-1060))) (|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (-3703 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (LIST (QUOTE -961) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasCategory| |#2| (QUOTE (-210))) (|HasAttribute| |#2| (QUOTE -4231)) (|HasCategory| |#2| (QUOTE (-425))) (-3703 (|HasCategory| |#2| (QUOTE (-157))) (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-513))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (|HasCategory| |#2| (QUOTE (-337))) (|HasCategory| |#2| (QUOTE (-425))) (|HasCategory| |#2| (QUOTE (-837)))) (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-837)))) (-3703 (-12 (|HasCategory| $ (QUOTE (-133))) (|HasCategory| |#2| (QUOTE (-837)))) (|HasCategory| |#2| (QUOTE (-133))))) (-1139 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 @@ -4499,7 +4499,7 @@ NIL (-1142 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 -829) (QUOTE (-1084)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2189) (LIST (|devaluate| |#2|) (QUOTE (-1084)))))) +((|HasCategory| |#2| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1025))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -2223) (LIST (|devaluate| |#2|) (QUOTE (-1084)))))) (-1143 |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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -4527,11 +4527,11 @@ NIL (-1149 |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)}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|))))) (|HasCategory| (-381 (-521)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasSignature| |#1| (LIST (QUOTE -2189) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2184) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4084) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|))))) (|HasCategory| (-381 (-521)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasSignature| |#1| (LIST (QUOTE -2223) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -1749) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4085) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) (-1150 |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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4231 |has| |#1| (-337)) (-4225 |has| |#1| (-337)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|))))) (|HasCategory| (-381 (-521)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasSignature| |#1| (LIST (QUOTE -2189) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2184) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4084) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521))) (|devaluate| |#1|))))) (|HasCategory| (-381 (-521)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (-3703 (|HasCategory| |#1| (QUOTE (-337))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -381) (QUOTE (-521)))))) (|HasSignature| |#1| (LIST (QUOTE -2223) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -1749) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4085) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) (-1151 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") $) "\\spad{limitPlus(f(var))} returns \\spad{limit(var -> cen+,{}f(var))}."))) (((-4235 "*") |has| (-1150 |#2| |#3| |#4|) (-157)) (-4226 |has| (-1150 |#2| |#3| |#4|) (-513)) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -4542,7 +4542,7 @@ NIL ((|HasAttribute| |#1| (QUOTE -4234))) (-1153 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-2046 . T)) +((-2092 . T)) NIL (-1154 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) @@ -4551,7 +4551,7 @@ NIL (-1155 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|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 (-521)))) (|HasCategory| |#2| (QUOTE (-887))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasSignature| |#2| (LIST (QUOTE -4084) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2184) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1084))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (QUOTE (-337)))) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#2| (QUOTE (-886))) (|HasCategory| |#2| (QUOTE (-1105))) (|HasSignature| |#2| (LIST (QUOTE -4085) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -1749) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1084))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#2| (QUOTE (-337)))) (-1156 |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."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4227 . T) (-4228 . T) (-4230 . T)) @@ -4559,7 +4559,7 @@ NIL (-1157 |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}."))) (((-4235 "*") |has| |#1| (-157)) (-4226 |has| |#1| (-513)) (-4227 . T) (-4228 . T) (-4230 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -829) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|))))) (|HasCategory| (-707) (QUOTE (-1025))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (|HasSignature| |#1| (LIST (QUOTE -2189) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-887))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -2184) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4084) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#1| (QUOTE (-157))) (-3703 (|HasCategory| |#1| (QUOTE (-157))) (|HasCategory| |#1| (QUOTE (-513)))) (|HasCategory| |#1| (QUOTE (-133))) (|HasCategory| |#1| (QUOTE (-135))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -828) (QUOTE (-1084)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-707)) (|devaluate| |#1|))))) (|HasCategory| (-707) (QUOTE (-1025))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-707))))) (|HasSignature| |#1| (LIST (QUOTE -2223) (LIST (|devaluate| |#1|) (QUOTE (-1084)))))) (|HasCategory| |#1| (QUOTE (-337))) (-3703 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-521)))) (|HasCategory| |#1| (QUOTE (-886))) (|HasCategory| |#1| (QUOTE (-1105))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -381) (QUOTE (-521))))) (|HasSignature| |#1| (LIST (QUOTE -1749) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1084))))) (|HasSignature| |#1| (LIST (QUOTE -4085) (LIST (LIST (QUOTE -587) (QUOTE (-1084))) (|devaluate| |#1|))))))) (-1158 |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 @@ -4570,7 +4570,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-513)))) (-1160) ((|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."))) -((-2046 . T)) +((-2092 . T)) NIL (-1161 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) @@ -4582,7 +4582,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-927))) (|HasCategory| |#2| (QUOTE (-970))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) (-1163 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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4234 . T) (-4233 . T) (-2046 . T)) +((-4234 . T) (-4233 . T) (-2092 . T)) NIL (-1164 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) @@ -4591,7 +4591,7 @@ NIL (-1165 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| (-521) (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-970)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-792)))))) +((|HasCategory| |#1| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| (-521) (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013))) (-3703 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-970))) (-12 (|HasCategory| |#1| (QUOTE (-927))) (|HasCategory| |#1| (QUOTE (-970)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-783))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))) (-3703 (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (LIST (QUOTE -284) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -561) (QUOTE (-791)))))) (-1166) ((|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 @@ -4635,7 +4635,7 @@ NIL (-1176 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}}."))) ((-4234 . T) (-4233 . T)) -((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-792))))) +((|HasCategory| |#4| (LIST (QUOTE -562) (QUOTE (-497)))) (|HasCategory| |#4| (QUOTE (-1013))) (-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (LIST (QUOTE -284) (|devaluate| |#4|)))) (|HasCategory| |#1| (QUOTE (-513))) (|HasCategory| |#3| (QUOTE (-342))) (|HasCategory| |#4| (LIST (QUOTE -561) (QUOTE (-791))))) (-1177 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}."))) ((-4227 . T) (-4228 . T) (-4230 . T)) @@ -4716,4 +4716,4 @@ NIL NIL NIL NIL -((-1196 NIL 2233082 2233087 2233092 2233097) (-3 NIL 2233062 2233067 2233072 2233077) (-2 NIL 2233042 2233047 2233052 2233057) (-1 NIL 2233022 2233027 2233032 2233037) (0 NIL 2233002 2233007 2233012 2233017) (-1191 "ZMOD.spad" 2232811 2232824 2232940 2232997) (-1190 "ZLINDEP.spad" 2231855 2231866 2232801 2232806) (-1189 "ZDSOLVE.spad" 2221704 2221726 2231845 2231850) (-1188 "YSTREAM.spad" 2221197 2221208 2221694 2221699) (-1187 "XRPOLY.spad" 2220417 2220437 2221053 2221122) (-1186 "XPR.spad" 2218146 2218159 2220135 2220234) (-1185 "XPOLY.spad" 2217701 2217712 2218002 2218071) (-1184 "XPOLYC.spad" 2217018 2217034 2217627 2217696) (-1183 "XPBWPOLY.spad" 2215455 2215475 2216798 2216867) (-1182 "XF.spad" 2213916 2213931 2215357 2215450) (-1181 "XF.spad" 2212357 2212374 2213800 2213805) (-1180 "XFALG.spad" 2209381 2209397 2212283 2212352) (-1179 "XEXPPKG.spad" 2208632 2208658 2209371 2209376) (-1178 "XDPOLY.spad" 2208246 2208262 2208488 2208557) (-1177 "XALG.spad" 2207844 2207855 2208202 2208241) (-1176 "WUTSET.spad" 2203683 2203700 2207490 2207517) (-1175 "WP.spad" 2202697 2202741 2203541 2203608) (-1174 "WFFINTBS.spad" 2200260 2200282 2202687 2202692) (-1173 "WEIER.spad" 2198474 2198485 2200250 2200255) (-1172 "VSPACE.spad" 2198147 2198158 2198442 2198469) (-1171 "VSPACE.spad" 2197840 2197853 2198137 2198142) (-1170 "VOID.spad" 2197430 2197439 2197830 2197835) (-1169 "VIEW.spad" 2195052 2195061 2197420 2197425) (-1168 "VIEWDEF.spad" 2190249 2190258 2195042 2195047) (-1167 "VIEW3D.spad" 2174084 2174093 2190239 2190244) (-1166 "VIEW2D.spad" 2161821 2161830 2174074 2174079) (-1165 "VECTOR.spad" 2160498 2160509 2160749 2160776) (-1164 "VECTOR2.spad" 2159125 2159138 2160488 2160493) (-1163 "VECTCAT.spad" 2157013 2157024 2159081 2159120) (-1162 "VECTCAT.spad" 2154722 2154735 2156792 2156797) (-1161 "VARIABLE.spad" 2154502 2154517 2154712 2154717) (-1160 "UTYPE.spad" 2154136 2154145 2154482 2154497) (-1159 "UTSODETL.spad" 2153429 2153453 2154092 2154097) (-1158 "UTSODE.spad" 2151617 2151637 2153419 2153424) (-1157 "UTS.spad" 2146406 2146434 2150084 2150181) (-1156 "UTSCAT.spad" 2143857 2143873 2146304 2146401) (-1155 "UTSCAT.spad" 2140952 2140970 2143401 2143406) (-1154 "UTS2.spad" 2140545 2140580 2140942 2140947) (-1153 "URAGG.spad" 2135167 2135178 2140525 2140540) (-1152 "URAGG.spad" 2129763 2129776 2135123 2135128) (-1151 "UPXSSING.spad" 2127409 2127435 2128847 2128980) (-1150 "UPXS.spad" 2124436 2124464 2125541 2125690) (-1149 "UPXSCONS.spad" 2122193 2122213 2122568 2122717) (-1148 "UPXSCCA.spad" 2120651 2120671 2122039 2122188) (-1147 "UPXSCCA.spad" 2119251 2119273 2120641 2120646) (-1146 "UPXSCAT.spad" 2117832 2117848 2119097 2119246) (-1145 "UPXS2.spad" 2117373 2117426 2117822 2117827) (-1144 "UPSQFREE.spad" 2115785 2115799 2117363 2117368) (-1143 "UPSCAT.spad" 2113378 2113402 2115683 2115780) (-1142 "UPSCAT.spad" 2110677 2110703 2112984 2112989) (-1141 "UPOLYC.spad" 2105655 2105666 2110519 2110672) (-1140 "UPOLYC.spad" 2100525 2100538 2105391 2105396) (-1139 "UPOLYC2.spad" 2099994 2100013 2100515 2100520) (-1138 "UP.spad" 2097044 2097059 2097552 2097705) (-1137 "UPMP.spad" 2095934 2095947 2097034 2097039) (-1136 "UPDIVP.spad" 2095497 2095511 2095924 2095929) (-1135 "UPDECOMP.spad" 2093734 2093748 2095487 2095492) (-1134 "UPCDEN.spad" 2092941 2092957 2093724 2093729) (-1133 "UP2.spad" 2092303 2092324 2092931 2092936) (-1132 "UNISEG.spad" 2091656 2091667 2092222 2092227) (-1131 "UNISEG2.spad" 2091149 2091162 2091612 2091617) (-1130 "UNIFACT.spad" 2090250 2090262 2091139 2091144) (-1129 "ULS.spad" 2080809 2080837 2081902 2082331) (-1128 "ULSCONS.spad" 2074852 2074872 2075224 2075373) (-1127 "ULSCCAT.spad" 2072449 2072469 2074672 2074847) (-1126 "ULSCCAT.spad" 2070180 2070202 2072405 2072410) (-1125 "ULSCAT.spad" 2068396 2068412 2070026 2070175) (-1124 "ULS2.spad" 2067908 2067961 2068386 2068391) (-1123 "UFD.spad" 2066973 2066982 2067834 2067903) (-1122 "UFD.spad" 2066100 2066111 2066963 2066968) (-1121 "UDVO.spad" 2064947 2064956 2066090 2066095) (-1120 "UDPO.spad" 2062374 2062385 2064903 2064908) (-1119 "TYPE.spad" 2062296 2062305 2062354 2062369) (-1118 "TWOFACT.spad" 2060946 2060961 2062286 2062291) (-1117 "TUPLE.spad" 2060332 2060343 2060845 2060850) (-1116 "TUBETOOL.spad" 2057169 2057178 2060322 2060327) (-1115 "TUBE.spad" 2055810 2055827 2057159 2057164) (-1114 "TS.spad" 2054399 2054415 2055375 2055472) (-1113 "TSETCAT.spad" 2041514 2041531 2054355 2054394) (-1112 "TSETCAT.spad" 2028627 2028646 2041470 2041475) (-1111 "TRMANIP.spad" 2022993 2023010 2028333 2028338) (-1110 "TRIMAT.spad" 2021952 2021977 2022983 2022988) (-1109 "TRIGMNIP.spad" 2020469 2020486 2021942 2021947) (-1108 "TRIGCAT.spad" 2019981 2019990 2020459 2020464) (-1107 "TRIGCAT.spad" 2019491 2019502 2019971 2019976) (-1106 "TREE.spad" 2018062 2018073 2019098 2019125) (-1105 "TRANFUN.spad" 2017893 2017902 2018052 2018057) (-1104 "TRANFUN.spad" 2017722 2017733 2017883 2017888) (-1103 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1988251 1988755 1988760) (-1084 "SYMBOL.spad" 1985576 1985585 1988230 1988235) (-1083 "SWITCH.spad" 1982333 1982342 1985566 1985571) (-1082 "SUTS.spad" 1979232 1979260 1980800 1980897) (-1081 "SUPXS.spad" 1976246 1976274 1977364 1977513) (-1080 "SUP.spad" 1973023 1973034 1973804 1973957) (-1079 "SUPFRACF.spad" 1972128 1972146 1973013 1973018) (-1078 "SUP2.spad" 1971518 1971531 1972118 1972123) (-1077 "SUMRF.spad" 1970484 1970495 1971508 1971513) (-1076 "SUMFS.spad" 1970117 1970134 1970474 1970479) (-1075 "SULS.spad" 1960663 1960691 1961769 1962198) (-1074 "SUCH.spad" 1960343 1960358 1960653 1960658) (-1073 "SUBSPACE.spad" 1952350 1952365 1960333 1960338) (-1072 "SUBRESP.spad" 1951510 1951524 1952306 1952311) (-1071 "STTF.spad" 1947609 1947625 1951500 1951505) (-1070 "STTFNC.spad" 1944077 1944093 1947599 1947604) (-1069 "STTAYLOR.spad" 1936475 1936486 1943958 1943963) (-1068 "STRTBL.spad" 1934980 1934997 1935129 1935156) (-1067 "STRING.spad" 1934389 1934398 1934403 1934430) (-1066 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1897375 1898579 1898584) (-1047 "SPECOUT.spad" 1895916 1895925 1897356 1897361) (-1046 "spad-parser.spad" 1895381 1895390 1895906 1895911) (-1045 "SPACEC.spad" 1879394 1879405 1895371 1895376) (-1044 "SPACE3.spad" 1879170 1879181 1879384 1879389) (-1043 "SORTPAK.spad" 1878715 1878728 1879126 1879131) (-1042 "SOLVETRA.spad" 1876472 1876483 1878705 1878710) (-1041 "SOLVESER.spad" 1874992 1875003 1876462 1876467) (-1040 "SOLVERAD.spad" 1871002 1871013 1874982 1874987) (-1039 "SOLVEFOR.spad" 1869422 1869440 1870992 1870997) (-1038 "SNTSCAT.spad" 1869010 1869027 1869378 1869417) (-1037 "SMTS.spad" 1867270 1867296 1868575 1868672) (-1036 "SMP.spad" 1864712 1864732 1865102 1865229) (-1035 "SMITH.spad" 1863555 1863580 1864702 1864707) (-1034 "SMATCAT.spad" 1861653 1861683 1863487 1863550) (-1033 "SMATCAT.spad" 1859695 1859727 1861531 1861536) (-1032 "SKAGG.spad" 1858644 1858655 1859651 1859690) (-1031 "SINT.spad" 1856952 1856961 1858510 1858639) (-1030 "SIMPAN.spad" 1856680 1856689 1856942 1856947) (-1029 "SIGNRF.spad" 1855788 1855799 1856670 1856675) (-1028 "SIGNEF.spad" 1855057 1855074 1855778 1855783) (-1027 "SHP.spad" 1852975 1852990 1855013 1855018) (-1026 "SHDP.spad" 1844365 1844392 1844874 1845003) (-1025 "SGROUP.spad" 1843831 1843840 1844355 1844360) (-1024 "SGROUP.spad" 1843295 1843306 1843821 1843826) (-1023 "SGCF.spad" 1836176 1836185 1843285 1843290) (-1022 "SFRTCAT.spad" 1835092 1835109 1836132 1836171) (-1021 "SFRGCD.spad" 1834155 1834175 1835082 1835087) (-1020 "SFQCMPK.spad" 1828792 1828812 1834145 1834150) (-1019 "SFORT.spad" 1828227 1828241 1828782 1828787) (-1018 "SEXOF.spad" 1828070 1828110 1828217 1828222) (-1017 "SEX.spad" 1827962 1827971 1828060 1828065) (-1016 "SEXCAT.spad" 1825066 1825106 1827952 1827957) (-1015 "SET.spad" 1823366 1823377 1824487 1824526) (-1014 "SETMN.spad" 1821800 1821817 1823356 1823361) (-1013 "SETCAT.spad" 1821285 1821294 1821790 1821795) (-1012 "SETCAT.spad" 1820768 1820779 1821275 1821280) (-1011 "SETAGG.spad" 1817291 1817302 1820736 1820763) (-1010 "SETAGG.spad" 1813834 1813847 1817281 1817286) (-1009 "SEGXCAT.spad" 1812946 1812959 1813814 1813829) (-1008 "SEG.spad" 1812759 1812770 1812865 1812870) (-1007 "SEGCAT.spad" 1811578 1811589 1812739 1812754) (-1006 "SEGBIND.spad" 1810650 1810661 1811533 1811538) (-1005 "SEGBIND2.spad" 1810346 1810359 1810640 1810645) (-1004 "SEG2.spad" 1809771 1809784 1810302 1810307) (-1003 "SDVAR.spad" 1809047 1809058 1809761 1809766) (-1002 "SDPOL.spad" 1806440 1806451 1806731 1806858) (-1001 "SCPKG.spad" 1804519 1804530 1806430 1806435) (-1000 "SCOPE.spad" 1803664 1803673 1804509 1804514) (-999 "SCACHE.spad" 1802347 1802357 1803654 1803659) (-998 "SAOS.spad" 1802220 1802228 1802337 1802342) (-997 "SAERFFC.spad" 1801934 1801953 1802210 1802215) (-996 "SAE.spad" 1800113 1800128 1800723 1800858) (-995 "SAEFACT.spad" 1799815 1799834 1800103 1800108) (-994 "RURPK.spad" 1797457 1797472 1799805 1799810) (-993 "RULESET.spad" 1796899 1796922 1797447 1797452) (-992 "RULE.spad" 1795104 1795127 1796889 1796894) (-991 "RULECOLD.spad" 1794957 1794969 1795094 1795099) (-990 "RSETGCD.spad" 1791336 1791355 1794947 1794952) (-989 "RSETCAT.spad" 1781109 1781125 1791292 1791331) (-988 "RSETCAT.spad" 1770914 1770932 1781099 1781104) (-987 "RSDCMPK.spad" 1769367 1769386 1770904 1770909) (-986 "RRCC.spad" 1767752 1767781 1769357 1769362) (-985 "RRCC.spad" 1766135 1766166 1767742 1767747) (-984 "RPOLCAT.spad" 1745496 1745510 1766003 1766130) (-983 "RPOLCAT.spad" 1724572 1724588 1745081 1745086) (-982 "ROUTINE.spad" 1720436 1720444 1723219 1723246) (-981 "ROMAN.spad" 1719669 1719677 1720302 1720431) (-980 "ROIRC.spad" 1718750 1718781 1719659 1719664) (-979 "RNS.spad" 1717654 1717662 1718652 1718745) (-978 "RNS.spad" 1716644 1716654 1717644 1717649) (-977 "RNG.spad" 1716380 1716388 1716634 1716639) (-976 "RMODULE.spad" 1716019 1716029 1716370 1716375) (-975 "RMCAT2.spad" 1715428 1715484 1716009 1716014) (-974 "RMATRIX.spad" 1714108 1714126 1714595 1714634) (-973 "RMATCAT.spad" 1709630 1709660 1714052 1714103) (-972 "RMATCAT.spad" 1705054 1705086 1709478 1709483) (-971 "RINTERP.spad" 1704943 1704962 1705044 1705049) (-970 "RING.spad" 1704301 1704309 1704923 1704938) (-969 "RING.spad" 1703667 1703677 1704291 1704296) (-968 "RIDIST.spad" 1703052 1703060 1703657 1703662) (-967 "RGCHAIN.spad" 1701632 1701647 1702537 1702564) (-966 "RF.spad" 1699247 1699257 1701622 1701627) (-965 "RFFACTOR.spad" 1698710 1698720 1699237 1699242) (-964 "RFFACT.spad" 1698446 1698457 1698700 1698705) (-963 "RFDIST.spad" 1697435 1697443 1698436 1698441) (-962 "RETSOL.spad" 1696853 1696865 1697425 1697430) (-961 "RETRACT.spad" 1696203 1696213 1696843 1696848) (-960 "RETRACT.spad" 1695551 1695563 1696193 1696198) (-959 "RESULT.spad" 1693612 1693620 1694198 1694225) (-958 "RESRING.spad" 1692960 1693006 1693550 1693607) (-957 "RESLATC.spad" 1692285 1692295 1692950 1692955) (-956 "REPSQ.spad" 1692015 1692025 1692275 1692280) (-955 "REP.spad" 1689568 1689576 1692005 1692010) (-954 "REPDB.spad" 1689274 1689284 1689558 1689563) (-953 "REP2.spad" 1678847 1678857 1689116 1689121) (-952 "REP1.spad" 1672838 1672848 1678797 1678802) (-951 "REGSET.spad" 1670636 1670652 1672484 1672511) (-950 "REF.spad" 1669966 1669976 1670591 1670596) (-949 "REDORDER.spad" 1669143 1669159 1669956 1669961) (-948 "RECLOS.spad" 1667933 1667952 1668636 1668729) (-947 "REALSOLV.spad" 1667066 1667074 1667923 1667928) (-946 "REAL.spad" 1666939 1666947 1667056 1667061) (-945 "REAL0Q.spad" 1664222 1664236 1666929 1666934) (-944 "REAL0.spad" 1661051 1661065 1664212 1664217) (-943 "RDIV.spad" 1660703 1660727 1661041 1661046) (-942 "RDIST.spad" 1660267 1660277 1660693 1660698) (-941 "RDETRS.spad" 1659064 1659081 1660257 1660262) (-940 "RDETR.spad" 1657172 1657189 1659054 1659059) (-939 "RDEEFS.spad" 1656246 1656262 1657162 1657167) (-938 "RDEEF.spad" 1655243 1655259 1656236 1656241) (-937 "RCFIELD.spad" 1652427 1652435 1655145 1655238) (-936 "RCFIELD.spad" 1649697 1649707 1652417 1652422) (-935 "RCAGG.spad" 1647600 1647610 1649677 1649692) (-934 "RCAGG.spad" 1645440 1645452 1647519 1647524) (-933 "RATRET.spad" 1644801 1644811 1645430 1645435) (-932 "RATFACT.spad" 1644494 1644505 1644791 1644796) (-931 "RANDSRC.spad" 1643814 1643822 1644484 1644489) (-930 "RADUTIL.spad" 1643569 1643577 1643804 1643809) (-929 "RADIX.spad" 1640362 1640375 1642039 1642132) (-928 "RADFF.spad" 1638779 1638815 1638897 1639053) (-927 "RADCAT.spad" 1638373 1638381 1638769 1638774) (-926 "RADCAT.spad" 1637965 1637975 1638363 1638368) (-925 "QUEUE.spad" 1637308 1637318 1637572 1637599) (-924 "QUAT.spad" 1635894 1635904 1636236 1636301) (-923 "QUATCT2.spad" 1635513 1635531 1635884 1635889) (-922 "QUATCAT.spad" 1633678 1633688 1635443 1635508) (-921 "QUATCAT.spad" 1631595 1631607 1633362 1633367) (-920 "QUAGG.spad" 1630409 1630419 1631551 1631590) (-919 "QFORM.spad" 1629872 1629886 1630399 1630404) (-918 "QFCAT.spad" 1628563 1628573 1629762 1629867) (-917 "QFCAT.spad" 1626860 1626872 1628061 1628066) (-916 "QFCAT2.spad" 1626551 1626567 1626850 1626855) (-915 "QEQUAT.spad" 1626108 1626116 1626541 1626546) (-914 "QCMPACK.spad" 1620855 1620874 1626098 1626103) (-913 "QALGSET.spad" 1616930 1616962 1620769 1620774) (-912 "QALGSET2.spad" 1614926 1614944 1616920 1616925) (-911 "PWFFINTB.spad" 1612236 1612257 1614916 1614921) (-910 "PUSHVAR.spad" 1611565 1611584 1612226 1612231) (-909 "PTRANFN.spad" 1607691 1607701 1611555 1611560) (-908 "PTPACK.spad" 1604779 1604789 1607681 1607686) (-907 "PTFUNC2.spad" 1604600 1604614 1604769 1604774) (-906 "PTCAT.spad" 1603682 1603692 1604556 1604595) (-905 "PSQFR.spad" 1602989 1603013 1603672 1603677) (-904 "PSEUDLIN.spad" 1601847 1601857 1602979 1602984) (-903 "PSETPK.spad" 1587280 1587296 1601725 1601730) (-902 "PSETCAT.spad" 1581188 1581211 1587248 1587275) (-901 "PSETCAT.spad" 1575082 1575107 1581144 1581149) (-900 "PSCURVE.spad" 1574065 1574073 1575072 1575077) (-899 "PSCAT.spad" 1572832 1572861 1573963 1574060) (-898 "PSCAT.spad" 1571689 1571720 1572822 1572827) (-897 "PRTITION.spad" 1570532 1570540 1571679 1571684) (-896 "PRS.spad" 1560094 1560111 1570488 1570493) (-895 "PRQAGG.spad" 1559513 1559523 1560050 1560089) (-894 "PROPLOG.spad" 1558916 1558924 1559503 1559508) (-893 "PROPFRML.spad" 1556781 1556792 1558852 1558857) (-892 "PRODUCT.spad" 1554461 1554473 1554747 1554802) (-891 "PR.spad" 1552850 1552862 1553555 1553682) (-890 "PRINT.spad" 1552602 1552610 1552840 1552845) (-889 "PRIMES.spad" 1550853 1550863 1552592 1552597) (-888 "PRIMELT.spad" 1548834 1548848 1550843 1550848) (-887 "PRIMCAT.spad" 1548457 1548465 1548824 1548829) (-886 "PRIMARR.spad" 1547462 1547472 1547640 1547667) (-885 "PRIMARR2.spad" 1546185 1546197 1547452 1547457) (-884 "PREASSOC.spad" 1545557 1545569 1546175 1546180) (-883 "PPCURVE.spad" 1544694 1544702 1545547 1545552) (-882 "POLYROOT.spad" 1543466 1543488 1544650 1544655) (-881 "POLY.spad" 1540766 1540776 1541283 1541410) (-880 "POLYLIFT.spad" 1540027 1540050 1540756 1540761) (-879 "POLYCATQ.spad" 1538129 1538151 1540017 1540022) (-878 "POLYCAT.spad" 1531535 1531556 1537997 1538124) (-877 "POLYCAT.spad" 1524243 1524266 1530707 1530712) (-876 "POLY2UP.spad" 1523691 1523705 1524233 1524238) (-875 "POLY2.spad" 1523286 1523298 1523681 1523686) (-874 "POLUTIL.spad" 1522227 1522256 1523242 1523247) (-873 "POLTOPOL.spad" 1520975 1520990 1522217 1522222) (-872 "POINT.spad" 1519816 1519826 1519903 1519930) (-871 "PNTHEORY.spad" 1516482 1516490 1519806 1519811) (-870 "PMTOOLS.spad" 1515239 1515253 1516472 1516477) (-869 "PMSYM.spad" 1514784 1514794 1515229 1515234) (-868 "PMQFCAT.spad" 1514371 1514385 1514774 1514779) (-867 "PMPRED.spad" 1513840 1513854 1514361 1514366) (-866 "PMPREDFS.spad" 1513284 1513306 1513830 1513835) (-865 "PMPLCAT.spad" 1512354 1512372 1513216 1513221) (-864 "PMLSAGG.spad" 1511935 1511949 1512344 1512349) (-863 "PMKERNEL.spad" 1511502 1511514 1511925 1511930) (-862 "PMINS.spad" 1511078 1511088 1511492 1511497) (-861 "PMFS.spad" 1510651 1510669 1511068 1511073) (-860 "PMDOWN.spad" 1509937 1509951 1510641 1510646) (-859 "PMASS.spad" 1508949 1508957 1509927 1509932) (-858 "PMASSFS.spad" 1507918 1507934 1508939 1508944) (-857 "PLOTTOOL.spad" 1507698 1507706 1507908 1507913) (-856 "PLOT.spad" 1502529 1502537 1507688 1507693) (-855 "PLOT3D.spad" 1498949 1498957 1502519 1502524) (-854 "PLOT1.spad" 1498090 1498100 1498939 1498944) (-853 "PLEQN.spad" 1485306 1485333 1498080 1498085) (-852 "PINTERP.spad" 1484922 1484941 1485296 1485301) (-851 "PINTERPA.spad" 1484704 1484720 1484912 1484917) (-850 "PI.spad" 1484311 1484319 1484678 1484699) (-849 "PID.spad" 1483267 1483275 1484237 1484306) (-848 "PICOERCE.spad" 1482924 1482934 1483257 1483262) (-847 "PGROEB.spad" 1481521 1481535 1482914 1482919) (-846 "PGE.spad" 1472774 1472782 1481511 1481516) (-845 "PGCD.spad" 1471656 1471673 1472764 1472769) (-844 "PFRPAC.spad" 1470799 1470809 1471646 1471651) (-843 "PFR.spad" 1467456 1467466 1470701 1470794) (-842 "PFOTOOLS.spad" 1466714 1466730 1467446 1467451) (-841 "PFOQ.spad" 1466084 1466102 1466704 1466709) (-840 "PFO.spad" 1465503 1465530 1466074 1466079) (-839 "PF.spad" 1465077 1465089 1465308 1465401) (-838 "PFECAT.spad" 1462743 1462751 1465003 1465072) (-837 "PFECAT.spad" 1460437 1460447 1462699 1462704) (-836 "PFBRU.spad" 1458307 1458319 1460427 1460432) (-835 "PFBR.spad" 1455845 1455868 1458297 1458302) (-834 "PERM.spad" 1451526 1451536 1455675 1455690) (-833 "PERMGRP.spad" 1446262 1446272 1451516 1451521) (-832 "PERMCAT.spad" 1444814 1444824 1446242 1446257) (-831 "PERMAN.spad" 1443346 1443360 1444804 1444809) (-830 "PENDTREE.spad" 1442619 1442629 1442975 1442980) (-829 "PDRING.spad" 1441110 1441120 1442599 1442614) (-828 "PDRING.spad" 1439609 1439621 1441100 1441105) (-827 "PDEPROB.spad" 1438566 1438574 1439599 1439604) (-826 "PDEPACK.spad" 1432568 1432576 1438556 1438561) (-825 "PDECOMP.spad" 1432030 1432047 1432558 1432563) (-824 "PDECAT.spad" 1430384 1430392 1432020 1432025) (-823 "PCOMP.spad" 1430235 1430248 1430374 1430379) (-822 "PBWLB.spad" 1428817 1428834 1430225 1430230) (-821 "PATTERN.spad" 1423248 1423258 1428807 1428812) (-820 "PATTERN2.spad" 1422984 1422996 1423238 1423243) (-819 "PATTERN1.spad" 1421286 1421302 1422974 1422979) (-818 "PATRES.spad" 1418833 1418845 1421276 1421281) (-817 "PATRES2.spad" 1418495 1418509 1418823 1418828) (-816 "PATMATCH.spad" 1416657 1416688 1418208 1418213) (-815 "PATMAB.spad" 1416082 1416092 1416647 1416652) (-814 "PATLRES.spad" 1415166 1415180 1416072 1416077) (-813 "PATAB.spad" 1414930 1414940 1415156 1415161) (-812 "PARTPERM.spad" 1412292 1412300 1414920 1414925) (-811 "PARSURF.spad" 1411720 1411748 1412282 1412287) (-810 "PARSU2.spad" 1411515 1411531 1411710 1411715) (-809 "script-parser.spad" 1411035 1411043 1411505 1411510) (-808 "PARSCURV.spad" 1410463 1410491 1411025 1411030) (-807 "PARSC2.spad" 1410252 1410268 1410453 1410458) (-806 "PARPCURV.spad" 1409710 1409738 1410242 1410247) (-805 "PARPC2.spad" 1409499 1409515 1409700 1409705) (-804 "PAN2EXPR.spad" 1408911 1408919 1409489 1409494) (-803 "PALETTE.spad" 1407881 1407889 1408901 1408906) (-802 "PAIR.spad" 1406864 1406877 1407469 1407474) (-801 "PADICRC.spad" 1404197 1404215 1405372 1405465) (-800 "PADICRAT.spad" 1402215 1402227 1402436 1402529) (-799 "PADIC.spad" 1401910 1401922 1402141 1402210) (-798 "PADICCT.spad" 1400451 1400463 1401836 1401905) (-797 "PADEPAC.spad" 1399130 1399149 1400441 1400446) (-796 "PADE.spad" 1397870 1397886 1399120 1399125) (-795 "OWP.spad" 1396854 1396884 1397728 1397795) (-794 "OVAR.spad" 1396635 1396658 1396844 1396849) (-793 "OUT.spad" 1395719 1395727 1396625 1396630) (-792 "OUTFORM.spad" 1385133 1385141 1395709 1395714) (-791 "OSI.spad" 1384608 1384616 1385123 1385128) (-790 "ORTHPOL.spad" 1383069 1383079 1384525 1384530) (-789 "OREUP.spad" 1382429 1382457 1382751 1382790) (-788 "ORESUP.spad" 1381730 1381754 1382111 1382150) (-787 "OREPCTO.spad" 1379549 1379561 1381650 1381655) (-786 "OREPCAT.spad" 1373606 1373616 1379505 1379544) (-785 "OREPCAT.spad" 1367553 1367565 1373454 1373459) (-784 "ORDSET.spad" 1366719 1366727 1367543 1367548) (-783 "ORDSET.spad" 1365883 1365893 1366709 1366714) (-782 "ORDRING.spad" 1365273 1365281 1365863 1365878) (-781 "ORDRING.spad" 1364671 1364681 1365263 1365268) (-780 "ORDMON.spad" 1364526 1364534 1364661 1364666) (-779 "ORDFUNS.spad" 1363652 1363668 1364516 1364521) (-778 "ORDFIN.spad" 1363586 1363594 1363642 1363647) (-777 "ORDCOMP.spad" 1362054 1362064 1363136 1363165) (-776 "ORDCOMP2.spad" 1361339 1361351 1362044 1362049) (-775 "OPTPROB.spad" 1359919 1359927 1361329 1361334) (-774 "OPTPACK.spad" 1352304 1352312 1359909 1359914) (-773 "OPTCAT.spad" 1349979 1349987 1352294 1352299) (-772 "OPQUERY.spad" 1349528 1349536 1349969 1349974) (-771 "OP.spad" 1349270 1349280 1349350 1349417) (-770 "ONECOMP.spad" 1348018 1348028 1348820 1348849) (-769 "ONECOMP2.spad" 1347436 1347448 1348008 1348013) (-768 "OMSERVER.spad" 1346438 1346446 1347426 1347431) (-767 "OMSAGG.spad" 1346214 1346224 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1122033) (-672 "MRING.spad" 1118842 1118854 1121579 1121646) (-671 "MRF2.spad" 1118410 1118424 1118832 1118837) (-670 "MRATFAC.spad" 1117956 1117973 1118400 1118405) (-669 "MPRFF.spad" 1115986 1116005 1117946 1117951) (-668 "MPOLY.spad" 1113424 1113439 1113783 1113910) (-667 "MPCPF.spad" 1112688 1112707 1113414 1113419) (-666 "MPC3.spad" 1112503 1112543 1112678 1112683) (-665 "MPC2.spad" 1112145 1112178 1112493 1112498) (-664 "MONOTOOL.spad" 1110480 1110497 1112135 1112140) (-663 "MONOID.spad" 1109654 1109662 1110470 1110475) (-662 "MONOID.spad" 1108826 1108836 1109644 1109649) (-661 "MONOGEN.spad" 1107572 1107585 1108686 1108821) (-660 "MONOGEN.spad" 1106340 1106355 1107456 1107461) (-659 "MONADWU.spad" 1104354 1104362 1106330 1106335) (-658 "MONADWU.spad" 1102366 1102376 1104344 1104349) (-657 "MONAD.spad" 1101510 1101518 1102356 1102361) (-656 "MONAD.spad" 1100652 1100662 1101500 1101505) (-655 "MOEBIUS.spad" 1099338 1099352 1100632 1100647) (-654 "MODULE.spad" 1099208 1099218 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(-577 "LIECAT.spad" 982351 982363 982803 982808) (-576 "LIB.spad" 980399 980407 981010 981025) (-575 "LGROBP.spad" 977752 977771 980389 980394) (-574 "LF.spad" 976671 976687 977742 977747) (-573 "LFCAT.spad" 975690 975698 976661 976666) (-572 "LEXTRIPK.spad" 971193 971208 975680 975685) (-571 "LEXP.spad" 969196 969223 971173 971188) (-570 "LEADCDET.spad" 967580 967597 969186 969191) (-569 "LAZM3PK.spad" 966284 966306 967570 967575) (-568 "LAUPOL.spad" 964975 964988 965879 965948) (-567 "LAPLACE.spad" 964548 964564 964965 964970) (-566 "LA.spad" 963988 964002 964470 964509) (-565 "LALG.spad" 963764 963774 963968 963983) (-564 "LALG.spad" 963548 963560 963754 963759) (-563 "KOVACIC.spad" 962261 962278 963538 963543) (-562 "KONVERT.spad" 961983 961993 962251 962256) (-561 "KOERCE.spad" 961720 961730 961973 961978) (-560 "KERNEL.spad" 960255 960265 961504 961509) (-559 "KERNEL2.spad" 959958 959970 960245 960250) (-558 "KDAGG.spad" 959049 959071 959926 959953) (-557 "KDAGG.spad" 958160 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180363 180368) (-148 "COMMONOP.spad" 179652 179660 180109 180114) (-147 "COMM.spad" 179461 179469 179642 179647) (-146 "COMBOPC.spad" 178366 178374 179451 179456) (-145 "COMBINAT.spad" 177111 177121 178356 178361) (-144 "COMBF.spad" 174479 174495 177101 177106) (-143 "COLOR.spad" 173316 173324 174469 174474) (-142 "CMPLXRT.spad" 173025 173042 173306 173311) (-141 "CLIP.spad" 169117 169125 173015 173020) (-140 "CLIF.spad" 167756 167772 169073 169112) (-139 "CLAGG.spad" 164231 164241 167736 167751) (-138 "CLAGG.spad" 160587 160599 164094 164099) (-137 "CINTSLPE.spad" 159912 159925 160577 160582) (-136 "CHVAR.spad" 157990 158012 159902 159907) (-135 "CHARZ.spad" 157905 157913 157970 157985) (-134 "CHARPOL.spad" 157413 157423 157895 157900) (-133 "CHARNZ.spad" 157166 157174 157393 157408) (-132 "CHAR.spad" 155056 155064 157156 157161) (-131 "CFCAT.spad" 154372 154380 155046 155051) (-130 "CDEN.spad" 153530 153544 154362 154367) (-129 "CCLASS.spad" 151679 151687 152941 152980) (-128 "CARTEN.spad" 146782 146806 151669 151674) (-127 "CARTEN2.spad" 146168 146195 146772 146777) (-126 "CARD.spad" 143457 143465 146142 146163) (-125 "CACHSET.spad" 143079 143087 143447 143452) (-124 "CABMON.spad" 142632 142640 143069 143074) (-123 "BTREE.spad" 141701 141711 142239 142266) (-122 "BTOURN.spad" 140704 140714 141308 141335) (-121 "BTCAT.spad" 140080 140090 140660 140699) (-120 "BTCAT.spad" 139488 139500 140070 140075) (-119 "BTAGG.spad" 138504 138512 139444 139483) (-118 "BTAGG.spad" 137552 137562 138494 138499) (-117 "BSTREE.spad" 136287 136297 137159 137186) (-116 "BRILL.spad" 134482 134493 136277 136282) (-115 "BRAGG.spad" 133396 133406 134462 134477) (-114 "BRAGG.spad" 132284 132296 133352 133357) (-113 "BPADICRT.spad" 130268 130280 130523 130616) (-112 "BPADIC.spad" 129932 129944 130194 130263) (-111 "BOUNDZRO.spad" 129588 129605 129922 129927) (-110 "BOP.spad" 125052 125060 129578 129583) (-109 "BOP1.spad" 122438 122448 125008 125013) (-108 "BOOLEAN.spad" 121691 121699 122428 122433) (-107 "BMODULE.spad" 121403 121415 121659 121686) (-106 "BITS.spad" 120822 120830 121039 121066) (-105 "BINFILE.spad" 120165 120173 120812 120817) (-104 "BINDING.spad" 119572 119580 120155 120160) (-103 "BINARY.spad" 117465 117473 118042 118135) (-102 "BGAGG.spad" 116650 116660 117433 117460) (-101 "BGAGG.spad" 115855 115867 116640 116645) (-100 "BFUNCT.spad" 115419 115427 115835 115850) (-99 "BEZOUT.spad" 114554 114580 115369 115374) (-98 "BBTREE.spad" 111374 111383 114161 114188) (-97 "BASTYPE.spad" 111047 111054 111364 111369) (-96 "BASTYPE.spad" 110718 110727 111037 111042) (-95 "BALFACT.spad" 110158 110170 110708 110713) (-94 "AUTOMOR.spad" 109605 109614 110138 110153) (-93 "ATTREG.spad" 106324 106331 109357 109600) (-92 "ATTRBUT.spad" 102347 102354 106304 106319) (-91 "ATRIG.spad" 101817 101824 102337 102342) (-90 "ATRIG.spad" 101285 101294 101807 101812) (-89 "ASTACK.spad" 100618 100627 100892 100919) (-88 "ASSOCEQ.spad" 99418 99429 100574 100579) (-87 "ASP9.spad" 98499 98512 99408 99413) (-86 "ASP8.spad" 97542 97555 98489 98494) (-85 "ASP80.spad" 96864 96877 97532 97537) (-84 "ASP7.spad" 96024 96037 96854 96859) (-83 "ASP78.spad" 95475 95488 96014 96019) (-82 "ASP77.spad" 94844 94857 95465 95470) (-81 "ASP74.spad" 93936 93949 94834 94839) (-80 "ASP73.spad" 93207 93220 93926 93931) (-79 "ASP6.spad" 91839 91852 93197 93202) (-78 "ASP55.spad" 90348 90361 91829 91834) (-77 "ASP50.spad" 88165 88178 90338 90343) (-76 "ASP4.spad" 87460 87473 88155 88160) (-75 "ASP49.spad" 86459 86472 87450 87455) (-74 "ASP42.spad" 84866 84905 86449 86454) (-73 "ASP41.spad" 83445 83484 84856 84861) (-72 "ASP35.spad" 82433 82446 83435 83440) (-71 "ASP34.spad" 81734 81747 82423 82428) (-70 "ASP33.spad" 81294 81307 81724 81729) (-69 "ASP31.spad" 80434 80447 81284 81289) (-68 "ASP30.spad" 79326 79339 80424 80429) (-67 "ASP29.spad" 78792 78805 79316 79321) (-66 "ASP28.spad" 70065 70078 78782 78787) (-65 "ASP27.spad" 68962 68975 70055 70060) (-64 "ASP24.spad" 68049 68062 68952 68957) (-63 "ASP20.spad" 67265 67278 68039 68044) (-62 "ASP1.spad" 66646 66659 67255 67260) (-61 "ASP19.spad" 61332 61345 66636 66641) (-60 "ASP12.spad" 60746 60759 61322 61327) (-59 "ASP10.spad" 60017 60030 60736 60741) (-58 "ARRAY2.spad" 59377 59386 59624 59651) (-57 "ARRAY1.spad" 58212 58221 58560 58587) (-56 "ARRAY12.spad" 56881 56892 58202 58207) (-55 "ARR2CAT.spad" 52531 52552 56837 56876) (-54 "ARR2CAT.spad" 48213 48236 52521 52526) (-53 "APPRULE.spad" 47457 47479 48203 48208) (-52 "APPLYORE.spad" 47072 47085 47447 47452) (-51 "ANY.spad" 45414 45421 47062 47067) (-50 "ANY1.spad" 44485 44494 45404 45409) (-49 "ANTISYM.spad" 42924 42940 44465 44480) (-48 "ANON.spad" 42837 42844 42914 42919) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-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 +((-1196 NIL 2233052 2233057 2233062 2233067) (-3 NIL 2233032 2233037 2233042 2233047) (-2 NIL 2233012 2233017 2233022 2233027) (-1 NIL 2232992 2232997 2233002 2233007) (0 NIL 2232972 2232977 2232982 2232987) (-1191 "ZMOD.spad" 2232781 2232794 2232910 2232967) (-1190 "ZLINDEP.spad" 2231825 2231836 2232771 2232776) (-1189 "ZDSOLVE.spad" 2221674 2221696 2231815 2231820) (-1188 "YSTREAM.spad" 2221167 2221178 2221664 2221669) (-1187 "XRPOLY.spad" 2220387 2220407 2221023 2221092) (-1186 "XPR.spad" 2218116 2218129 2220105 2220204) (-1185 "XPOLY.spad" 2217671 2217682 2217972 2218041) (-1184 "XPOLYC.spad" 2216988 2217004 2217597 2217666) (-1183 "XPBWPOLY.spad" 2215425 2215445 2216768 2216837) (-1182 "XF.spad" 2213886 2213901 2215327 2215420) (-1181 "XF.spad" 2212327 2212344 2213770 2213775) (-1180 "XFALG.spad" 2209351 2209367 2212253 2212322) (-1179 "XEXPPKG.spad" 2208602 2208628 2209341 2209346) (-1178 "XDPOLY.spad" 2208216 2208232 2208458 2208527) (-1177 "XALG.spad" 2207814 2207825 2208172 2208211) (-1176 "WUTSET.spad" 2203653 2203670 2207460 2207487) (-1175 "WP.spad" 2202667 2202711 2203511 2203578) (-1174 "WFFINTBS.spad" 2200230 2200252 2202657 2202662) (-1173 "WEIER.spad" 2198444 2198455 2200220 2200225) (-1172 "VSPACE.spad" 2198117 2198128 2198412 2198439) (-1171 "VSPACE.spad" 2197810 2197823 2198107 2198112) (-1170 "VOID.spad" 2197400 2197409 2197800 2197805) (-1169 "VIEW.spad" 2195022 2195031 2197390 2197395) (-1168 "VIEWDEF.spad" 2190219 2190228 2195012 2195017) (-1167 "VIEW3D.spad" 2174054 2174063 2190209 2190214) (-1166 "VIEW2D.spad" 2161791 2161800 2174044 2174049) (-1165 "VECTOR.spad" 2160468 2160479 2160719 2160746) (-1164 "VECTOR2.spad" 2159095 2159108 2160458 2160463) (-1163 "VECTCAT.spad" 2156983 2156994 2159051 2159090) (-1162 "VECTCAT.spad" 2154692 2154705 2156762 2156767) (-1161 "VARIABLE.spad" 2154472 2154487 2154682 2154687) (-1160 "UTYPE.spad" 2154106 2154115 2154452 2154467) (-1159 "UTSODETL.spad" 2153399 2153423 2154062 2154067) (-1158 "UTSODE.spad" 2151587 2151607 2153389 2153394) (-1157 "UTS.spad" 2146376 2146404 2150054 2150151) (-1156 "UTSCAT.spad" 2143827 2143843 2146274 2146371) (-1155 "UTSCAT.spad" 2140922 2140940 2143371 2143376) (-1154 "UTS2.spad" 2140515 2140550 2140912 2140917) (-1153 "URAGG.spad" 2135137 2135148 2140495 2140510) (-1152 "URAGG.spad" 2129733 2129746 2135093 2135098) (-1151 "UPXSSING.spad" 2127379 2127405 2128817 2128950) (-1150 "UPXS.spad" 2124406 2124434 2125511 2125660) (-1149 "UPXSCONS.spad" 2122163 2122183 2122538 2122687) (-1148 "UPXSCCA.spad" 2120621 2120641 2122009 2122158) (-1147 "UPXSCCA.spad" 2119221 2119243 2120611 2120616) (-1146 "UPXSCAT.spad" 2117802 2117818 2119067 2119216) (-1145 "UPXS2.spad" 2117343 2117396 2117792 2117797) (-1144 "UPSQFREE.spad" 2115755 2115769 2117333 2117338) (-1143 "UPSCAT.spad" 2113348 2113372 2115653 2115750) (-1142 "UPSCAT.spad" 2110647 2110673 2112954 2112959) (-1141 "UPOLYC.spad" 2105625 2105636 2110489 2110642) (-1140 "UPOLYC.spad" 2100495 2100508 2105361 2105366) (-1139 "UPOLYC2.spad" 2099964 2099983 2100485 2100490) (-1138 "UP.spad" 2097014 2097029 2097522 2097675) (-1137 "UPMP.spad" 2095904 2095917 2097004 2097009) (-1136 "UPDIVP.spad" 2095467 2095481 2095894 2095899) (-1135 "UPDECOMP.spad" 2093704 2093718 2095457 2095462) (-1134 "UPCDEN.spad" 2092911 2092927 2093694 2093699) (-1133 "UP2.spad" 2092273 2092294 2092901 2092906) (-1132 "UNISEG.spad" 2091626 2091637 2092192 2092197) (-1131 "UNISEG2.spad" 2091119 2091132 2091582 2091587) (-1130 "UNIFACT.spad" 2090220 2090232 2091109 2091114) (-1129 "ULS.spad" 2080779 2080807 2081872 2082301) (-1128 "ULSCONS.spad" 2074822 2074842 2075194 2075343) (-1127 "ULSCCAT.spad" 2072419 2072439 2074642 2074817) (-1126 "ULSCCAT.spad" 2070150 2070172 2072375 2072380) (-1125 "ULSCAT.spad" 2068366 2068382 2069996 2070145) (-1124 "ULS2.spad" 2067878 2067931 2068356 2068361) (-1123 "UFD.spad" 2066943 2066952 2067804 2067873) (-1122 "UFD.spad" 2066070 2066081 2066933 2066938) (-1121 "UDVO.spad" 2064917 2064926 2066060 2066065) (-1120 "UDPO.spad" 2062344 2062355 2064873 2064878) (-1119 "TYPE.spad" 2062266 2062275 2062324 2062339) (-1118 "TWOFACT.spad" 2060916 2060931 2062256 2062261) (-1117 "TUPLE.spad" 2060302 2060313 2060815 2060820) (-1116 "TUBETOOL.spad" 2057139 2057148 2060292 2060297) (-1115 "TUBE.spad" 2055780 2055797 2057129 2057134) (-1114 "TS.spad" 2054369 2054385 2055345 2055442) (-1113 "TSETCAT.spad" 2041484 2041501 2054325 2054364) (-1112 "TSETCAT.spad" 2028597 2028616 2041440 2041445) (-1111 "TRMANIP.spad" 2022963 2022980 2028303 2028308) (-1110 "TRIMAT.spad" 2021922 2021947 2022953 2022958) (-1109 "TRIGMNIP.spad" 2020439 2020456 2021912 2021917) (-1108 "TRIGCAT.spad" 2019951 2019960 2020429 2020434) (-1107 "TRIGCAT.spad" 2019461 2019472 2019941 2019946) (-1106 "TREE.spad" 2018032 2018043 2019068 2019095) (-1105 "TRANFUN.spad" 2017863 2017872 2018022 2018027) (-1104 "TRANFUN.spad" 2017692 2017703 2017853 2017858) (-1103 "TOPSP.spad" 2017366 2017375 2017682 2017687) (-1102 "TOOLSIGN.spad" 2017029 2017040 2017356 2017361) (-1101 "TEXTFILE.spad" 2015586 2015595 2017019 2017024) (-1100 "TEX.spad" 2012603 2012612 2015576 2015581) (-1099 "TEX1.spad" 2012159 2012170 2012593 2012598) (-1098 "TEMUTL.spad" 2011714 2011723 2012149 2012154) (-1097 "TBCMPPK.spad" 2009807 2009830 2011704 2011709) (-1096 "TBAGG.spad" 2008831 2008854 2009775 2009802) (-1095 "TBAGG.spad" 2007875 2007900 2008821 2008826) (-1094 "TANEXP.spad" 2007251 2007262 2007865 2007870) (-1093 "TABLE.spad" 2005662 2005685 2005932 2005959) (-1092 "TABLEAU.spad" 2005143 2005154 2005652 2005657) (-1091 "TABLBUMP.spad" 2001926 2001937 2005133 2005138) (-1090 "SYSSOLP.spad" 1999399 1999410 2001916 2001921) (-1089 "SYNTAX.spad" 1995684 1995693 1999389 1999394) (-1088 "SYMTAB.spad" 1993740 1993749 1995674 1995679) (-1087 "SYMS.spad" 1989725 1989734 1993730 1993735) (-1086 "SYMPOLY.spad" 1988735 1988746 1988817 1988944) (-1085 "SYMFUNC.spad" 1988210 1988221 1988725 1988730) (-1084 "SYMBOL.spad" 1985546 1985555 1988200 1988205) (-1083 "SWITCH.spad" 1982303 1982312 1985536 1985541) (-1082 "SUTS.spad" 1979202 1979230 1980770 1980867) (-1081 "SUPXS.spad" 1976216 1976244 1977334 1977483) (-1080 "SUP.spad" 1972993 1973004 1973774 1973927) (-1079 "SUPFRACF.spad" 1972098 1972116 1972983 1972988) (-1078 "SUP2.spad" 1971488 1971501 1972088 1972093) (-1077 "SUMRF.spad" 1970454 1970465 1971478 1971483) (-1076 "SUMFS.spad" 1970087 1970104 1970444 1970449) (-1075 "SULS.spad" 1960633 1960661 1961739 1962168) (-1074 "SUCH.spad" 1960313 1960328 1960623 1960628) (-1073 "SUBSPACE.spad" 1952320 1952335 1960303 1960308) (-1072 "SUBRESP.spad" 1951480 1951494 1952276 1952281) (-1071 "STTF.spad" 1947579 1947595 1951470 1951475) (-1070 "STTFNC.spad" 1944047 1944063 1947569 1947574) (-1069 "STTAYLOR.spad" 1936445 1936456 1943928 1943933) (-1068 "STRTBL.spad" 1934950 1934967 1935099 1935126) (-1067 "STRING.spad" 1934359 1934368 1934373 1934400) (-1066 "STRICAT.spad" 1934135 1934144 1934315 1934354) (-1065 "STREAM.spad" 1930903 1930914 1933660 1933675) (-1064 "STREAM3.spad" 1930448 1930463 1930893 1930898) (-1063 "STREAM2.spad" 1929516 1929529 1930438 1930443) (-1062 "STREAM1.spad" 1929220 1929231 1929506 1929511) (-1061 "STINPROD.spad" 1928126 1928142 1929210 1929215) (-1060 "STEP.spad" 1927327 1927336 1928116 1928121) (-1059 "STBL.spad" 1925853 1925881 1926020 1926035) (-1058 "STAGG.spad" 1924918 1924929 1925833 1925848) (-1057 "STAGG.spad" 1923991 1924004 1924908 1924913) (-1056 "STACK.spad" 1923342 1923353 1923598 1923625) (-1055 "SREGSET.spad" 1921046 1921063 1922988 1923015) (-1054 "SRDCMPK.spad" 1919591 1919611 1921036 1921041) (-1053 "SRAGG.spad" 1914676 1914685 1919547 1919586) (-1052 "SRAGG.spad" 1909793 1909804 1914666 1914671) (-1051 "SQMATRIX.spad" 1907419 1907437 1908327 1908414) (-1050 "SPLTREE.spad" 1901971 1901984 1906855 1906882) (-1049 "SPLNODE.spad" 1898559 1898572 1901961 1901966) (-1048 "SPFCAT.spad" 1897336 1897345 1898549 1898554) (-1047 "SPECOUT.spad" 1895886 1895895 1897326 1897331) (-1046 "spad-parser.spad" 1895351 1895360 1895876 1895881) (-1045 "SPACEC.spad" 1879364 1879375 1895341 1895346) (-1044 "SPACE3.spad" 1879140 1879151 1879354 1879359) (-1043 "SORTPAK.spad" 1878685 1878698 1879096 1879101) (-1042 "SOLVETRA.spad" 1876442 1876453 1878675 1878680) (-1041 "SOLVESER.spad" 1874962 1874973 1876432 1876437) (-1040 "SOLVERAD.spad" 1870972 1870983 1874952 1874957) (-1039 "SOLVEFOR.spad" 1869392 1869410 1870962 1870967) (-1038 "SNTSCAT.spad" 1868980 1868997 1869348 1869387) (-1037 "SMTS.spad" 1867240 1867266 1868545 1868642) (-1036 "SMP.spad" 1864682 1864702 1865072 1865199) (-1035 "SMITH.spad" 1863525 1863550 1864672 1864677) (-1034 "SMATCAT.spad" 1861623 1861653 1863457 1863520) (-1033 "SMATCAT.spad" 1859665 1859697 1861501 1861506) (-1032 "SKAGG.spad" 1858614 1858625 1859621 1859660) (-1031 "SINT.spad" 1856922 1856931 1858480 1858609) (-1030 "SIMPAN.spad" 1856650 1856659 1856912 1856917) (-1029 "SIGNRF.spad" 1855758 1855769 1856640 1856645) (-1028 "SIGNEF.spad" 1855027 1855044 1855748 1855753) (-1027 "SHP.spad" 1852945 1852960 1854983 1854988) (-1026 "SHDP.spad" 1844335 1844362 1844844 1844973) (-1025 "SGROUP.spad" 1843801 1843810 1844325 1844330) (-1024 "SGROUP.spad" 1843265 1843276 1843791 1843796) (-1023 "SGCF.spad" 1836146 1836155 1843255 1843260) (-1022 "SFRTCAT.spad" 1835062 1835079 1836102 1836141) (-1021 "SFRGCD.spad" 1834125 1834145 1835052 1835057) (-1020 "SFQCMPK.spad" 1828762 1828782 1834115 1834120) (-1019 "SFORT.spad" 1828197 1828211 1828752 1828757) (-1018 "SEXOF.spad" 1828040 1828080 1828187 1828192) (-1017 "SEX.spad" 1827932 1827941 1828030 1828035) (-1016 "SEXCAT.spad" 1825036 1825076 1827922 1827927) (-1015 "SET.spad" 1823336 1823347 1824457 1824496) (-1014 "SETMN.spad" 1821770 1821787 1823326 1823331) (-1013 "SETCAT.spad" 1821255 1821264 1821760 1821765) (-1012 "SETCAT.spad" 1820738 1820749 1821245 1821250) (-1011 "SETAGG.spad" 1817261 1817272 1820706 1820733) (-1010 "SETAGG.spad" 1813804 1813817 1817251 1817256) (-1009 "SEGXCAT.spad" 1812916 1812929 1813784 1813799) (-1008 "SEG.spad" 1812729 1812740 1812835 1812840) (-1007 "SEGCAT.spad" 1811548 1811559 1812709 1812724) (-1006 "SEGBIND.spad" 1810620 1810631 1811503 1811508) (-1005 "SEGBIND2.spad" 1810316 1810329 1810610 1810615) (-1004 "SEG2.spad" 1809741 1809754 1810272 1810277) (-1003 "SDVAR.spad" 1809017 1809028 1809731 1809736) (-1002 "SDPOL.spad" 1806410 1806421 1806701 1806828) (-1001 "SCPKG.spad" 1804489 1804500 1806400 1806405) (-1000 "SCOPE.spad" 1803634 1803643 1804479 1804484) (-999 "SCACHE.spad" 1802317 1802327 1803624 1803629) (-998 "SAOS.spad" 1802190 1802198 1802307 1802312) (-997 "SAERFFC.spad" 1801904 1801923 1802180 1802185) (-996 "SAE.spad" 1800083 1800098 1800693 1800828) (-995 "SAEFACT.spad" 1799785 1799804 1800073 1800078) (-994 "RURPK.spad" 1797427 1797442 1799775 1799780) (-993 "RULESET.spad" 1796869 1796892 1797417 1797422) (-992 "RULE.spad" 1795074 1795097 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(-616 "MAGMA.spad" 1039059 1039076 1041259 1041264) (-615 "M3D.spad" 1036757 1036767 1038439 1038444) (-614 "LZSTAGG.spad" 1033975 1033985 1036737 1036752) (-613 "LZSTAGG.spad" 1031201 1031213 1033965 1033970) (-612 "LWORD.spad" 1027906 1027923 1031191 1031196) (-611 "LSQM.spad" 1026134 1026148 1026532 1026583) (-610 "LSPP.spad" 1025667 1025684 1026124 1026129) (-609 "LSMP.spad" 1024507 1024535 1025657 1025662) (-608 "LSMP1.spad" 1022311 1022325 1024497 1024502) (-607 "LSAGG.spad" 1021968 1021978 1022267 1022306) (-606 "LSAGG.spad" 1021657 1021669 1021958 1021963) (-605 "LPOLY.spad" 1020611 1020630 1021513 1021582) (-604 "LPEFRAC.spad" 1019868 1019878 1020601 1020606) (-603 "LO.spad" 1019269 1019283 1019802 1019829) (-602 "LOGIC.spad" 1018871 1018879 1019259 1019264) (-601 "LOGIC.spad" 1018471 1018481 1018861 1018866) (-600 "LODOOPS.spad" 1017389 1017401 1018461 1018466) (-599 "LODO.spad" 1016775 1016791 1017071 1017110) (-598 "LODOF.spad" 1015819 1015836 1016732 1016737) (-597 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(-577 "LIECAT.spad" 982327 982339 982779 982784) (-576 "LIB.spad" 980375 980383 980986 981001) (-575 "LGROBP.spad" 977728 977747 980365 980370) (-574 "LF.spad" 976647 976663 977718 977723) (-573 "LFCAT.spad" 975666 975674 976637 976642) (-572 "LEXTRIPK.spad" 971169 971184 975656 975661) (-571 "LEXP.spad" 969172 969199 971149 971164) (-570 "LEADCDET.spad" 967556 967573 969162 969167) (-569 "LAZM3PK.spad" 966260 966282 967546 967551) (-568 "LAUPOL.spad" 964951 964964 965855 965924) (-567 "LAPLACE.spad" 964524 964540 964941 964946) (-566 "LA.spad" 963964 963978 964446 964485) (-565 "LALG.spad" 963740 963750 963944 963959) (-564 "LALG.spad" 963524 963536 963730 963735) (-563 "KOVACIC.spad" 962237 962254 963514 963519) (-562 "KONVERT.spad" 961959 961969 962227 962232) (-561 "KOERCE.spad" 961696 961706 961949 961954) (-560 "KERNEL.spad" 960231 960241 961480 961485) (-559 "KERNEL2.spad" 959934 959946 960221 960226) (-558 "KDAGG.spad" 959025 959047 959902 959929) (-557 "KDAGG.spad" 958136 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677866) (-393 "FRUTIL.spad" 675936 675946 676984 676989) (-392 "FR.spad" 669633 669643 674963 675032) (-391 "FRNAALG.spad" 664720 664730 669575 669628) (-390 "FRNAALG.spad" 659819 659831 664676 664681) (-389 "FRNAAF2.spad" 659273 659291 659809 659814) (-388 "FRMOD.spad" 658668 658698 659205 659210) (-387 "FRIDEAL.spad" 657863 657884 658648 658663) (-386 "FRIDEAL2.spad" 657465 657497 657853 657858) (-385 "FRETRCT.spad" 656976 656986 657455 657460) (-384 "FRETRCT.spad" 656355 656367 656836 656841) (-383 "FRAMALG.spad" 654683 654696 656311 656350) (-382 "FRAMALG.spad" 653043 653058 654673 654678) (-381 "FRAC.spad" 650146 650156 650549 650722) (-380 "FRAC2.spad" 649749 649761 650136 650141) (-379 "FR2.spad" 649083 649095 649739 649744) (-378 "FPS.spad" 645892 645900 648973 649078) (-377 "FPS.spad" 642729 642739 645812 645817) (-376 "FPC.spad" 641771 641779 642631 642724) (-375 "FPC.spad" 640899 640909 641761 641766) (-374 "FPATMAB.spad" 640651 640661 640879 640894) (-373 "FPARFRAC.spad" 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"FLOATCP.spad" 604669 604683 607242 607247) (-351 "FLINEXP.spad" 604381 604391 604649 604664) (-350 "FLINEXP.spad" 604047 604059 604317 604322) (-349 "FLASORT.spad" 603367 603379 604037 604042) (-348 "FLALG.spad" 601013 601032 603293 603362) (-347 "FLAGG.spad" 598019 598029 600981 601008) (-346 "FLAGG.spad" 594938 594950 597902 597907) (-345 "FLAGG2.spad" 593619 593635 594928 594933) (-344 "FINRALG.spad" 591648 591661 593575 593614) (-343 "FINRALG.spad" 589603 589618 591532 591537) (-342 "FINITE.spad" 588755 588763 589593 589598) (-341 "FINAALG.spad" 577736 577746 588697 588750) (-340 "FINAALG.spad" 566729 566741 577692 577697) (-339 "FILE.spad" 566312 566322 566719 566724) (-338 "FILECAT.spad" 564830 564847 566302 566307) (-337 "FIELD.spad" 564236 564244 564732 564825) (-336 "FIELD.spad" 563728 563738 564226 564231) (-335 "FGROUP.spad" 562337 562347 563708 563723) (-334 "FGLMICPK.spad" 561124 561139 562327 562332) (-333 "FFX.spad" 560499 560514 560840 560933) (-332 "FFSLPE.spad" 559988 560009 560489 560494) (-331 "FFPOLY.spad" 551240 551251 559978 559983) (-330 "FFPOLY2.spad" 550300 550317 551230 551235) (-329 "FFP.spad" 549697 549717 550016 550109) (-328 "FF.spad" 549145 549161 549378 549471) (-327 "FFNBX.spad" 547657 547677 548861 548954) (-326 "FFNBP.spad" 546170 546187 547373 547466) (-325 "FFNB.spad" 544635 544656 545851 545944) (-324 "FFINTBAS.spad" 542049 542068 544625 544630) (-323 "FFIELDC.spad" 539624 539632 541951 542044) (-322 "FFIELDC.spad" 537285 537295 539614 539619) (-321 "FFHOM.spad" 536033 536050 537275 537280) (-320 "FFF.spad" 533468 533479 536023 536028) (-319 "FFCGX.spad" 532315 532335 533184 533277) (-318 "FFCGP.spad" 531204 531224 532031 532124) (-317 "FFCG.spad" 529996 530017 530885 530978) (-316 "FFCAT.spad" 522897 522919 529835 529991) (-315 "FFCAT.spad" 515877 515901 522817 522822) (-314 "FFCAT2.spad" 515622 515662 515867 515872) (-313 "FEXPR.spad" 507335 507381 515382 515421) (-312 "FEVALAB.spad" 507041 507051 507325 507330) (-311 "FEVALAB.spad" 506532 506544 506818 506823) (-310 "FDIV.spad" 505974 505998 506522 506527) (-309 "FDIVCAT.spad" 504016 504040 505964 505969) (-308 "FDIVCAT.spad" 502056 502082 504006 504011) (-307 "FDIV2.spad" 501710 501750 502046 502051) (-306 "FCPAK1.spad" 500263 500271 501700 501705) (-305 "FCOMP.spad" 499642 499652 500253 500258) (-304 "FC.spad" 489467 489475 499632 499637) (-303 "FAXF.spad" 482402 482416 489369 489462) (-302 "FAXF.spad" 475389 475405 482358 482363) (-301 "FARRAY.spad" 473535 473545 474572 474599) (-300 "FAMR.spad" 471655 471667 473433 473530) (-299 "FAMR.spad" 469759 469773 471539 471544) (-298 "FAMONOID.spad" 469409 469419 469713 469718) (-297 "FAMONC.spad" 467631 467643 469399 469404) (-296 "FAGROUP.spad" 467237 467247 467527 467554) (-295 "FACUTIL.spad" 465433 465450 467227 467232) (-294 "FACTFUNC.spad" 464609 464619 465423 465428) (-293 "EXPUPXS.spad" 461442 461465 462741 462890) (-292 "EXPRTUBE.spad" 458670 458678 461432 461437) (-291 "EXPRODE.spad" 455542 455558 458660 458665) (-290 "EXPR.spad" 450844 450854 451558 451961) (-289 "EXPR2UPS.spad" 446936 446949 450834 450839) (-288 "EXPR2.spad" 446639 446651 446926 446931) (-287 "EXPEXPAN.spad" 443580 443605 444214 444307) (-286 "EXIT.spad" 443251 443259 443570 443575) (-285 "EVALCYC.spad" 442709 442723 443241 443246) (-284 "EVALAB.spad" 442273 442283 442699 442704) (-283 "EVALAB.spad" 441835 441847 442263 442268) (-282 "EUCDOM.spad" 439377 439385 441761 441830) (-281 "EUCDOM.spad" 436981 436991 439367 439372) (-280 "ESTOOLS.spad" 428821 428829 436971 436976) (-279 "ESTOOLS2.spad" 428422 428436 428811 428816) (-278 "ESTOOLS1.spad" 428107 428118 428412 428417) (-277 "ES.spad" 420654 420662 428097 428102) (-276 "ES.spad" 413109 413119 420554 420559) (-275 "ESCONT.spad" 409882 409890 413099 413104) (-274 "ESCONT1.spad" 409631 409643 409872 409877) (-273 "ES2.spad" 409126 409142 409621 409626) (-272 "ES1.spad" 408692 408708 409116 409121) (-271 "ERROR.spad" 406013 406021 408682 408687) (-270 "EQTBL.spad" 404485 404507 404694 404721) (-269 "EQ.spad" 399369 399379 402168 402277) (-268 "EQ2.spad" 399085 399097 399359 399364) (-267 "EP.spad" 395399 395409 399075 399080) (-266 "ENV.spad" 394101 394109 395389 395394) (-265 "ENTIRER.spad" 393769 393777 394045 394096) (-264 "EMR.spad" 392970 393011 393695 393764) (-263 "ELTAGG.spad" 391210 391229 392960 392965) (-262 "ELTAGG.spad" 389414 389435 391166 391171) (-261 "ELTAB.spad" 388861 388879 389404 389409) (-260 "ELFUTS.spad" 388240 388259 388851 388856) (-259 "ELEMFUN.spad" 387929 387937 388230 388235) (-258 "ELEMFUN.spad" 387616 387626 387919 387924) (-257 "ELAGG.spad" 385547 385557 387584 387611) (-256 "ELAGG.spad" 383427 383439 385466 385471) (-255 "EFUPXS.spad" 380203 380233 383383 383388) (-254 "EFULS.spad" 377039 377062 380159 380164) (-253 "EFSTRUC.spad" 374994 375010 377029 377034) (-252 "EF.spad" 369760 369776 374984 374989) (-251 "EAB.spad" 368036 368044 369750 369755) (-250 "E04UCFA.spad" 367572 367580 368026 368031) (-249 "E04NAFA.spad" 367149 367157 367562 367567) (-248 "E04MBFA.spad" 366729 366737 367139 367144) (-247 "E04JAFA.spad" 366265 366273 366719 366724) (-246 "E04GCFA.spad" 365801 365809 366255 366260) (-245 "E04FDFA.spad" 365337 365345 365791 365796) (-244 "E04DGFA.spad" 364873 364881 365327 365332) (-243 "E04AGNT.spad" 360715 360723 364863 364868) (-242 "DVARCAT.spad" 357400 357410 360705 360710) (-241 "DVARCAT.spad" 354083 354095 357390 357395) (-240 "DSMP.spad" 351517 351531 351822 351949) (-239 "DROPT.spad" 345462 345470 351507 351512) (-238 "DROPT1.spad" 345125 345135 345452 345457) (-237 "DROPT0.spad" 339952 339960 345115 345120) (-236 "DRAWPT.spad" 338107 338115 339942 339947) (-235 "DRAW.spad" 330707 330720 338097 338102) (-234 "DRAWHACK.spad" 330015 330025 330697 330702) (-233 "DRAWCX.spad" 327457 327465 330005 330010) (-232 "DRAWCURV.spad" 326994 327009 327447 327452) (-231 "DRAWCFUN.spad" 316166 316174 326984 326989) (-230 "DQAGG.spad" 314322 314332 316122 316161) (-229 "DPOLCAT.spad" 309663 309679 314190 314317) (-228 "DPOLCAT.spad" 305090 305108 309619 309624) (-227 "DPMO.spad" 299077 299093 299215 299511) (-226 "DPMM.spad" 293077 293095 293202 293498) (-225 "domain.spad" 292348 292356 293067 293072) (-224 "DMP.spad" 289573 289588 290145 290272) (-223 "DLP.spad" 288921 288931 289563 289568) (-222 "DLIST.spad" 287333 287343 288104 288131) (-221 "DLAGG.spad" 285734 285744 287313 287328) (-220 "DIVRING.spad" 285181 285189 285678 285729) (-219 "DIVRING.spad" 284672 284682 285171 285176) (-218 "DISPLAY.spad" 282852 282860 284662 284667) (-217 "DIRPROD.spad" 274111 274127 274751 274880) (-216 "DIRPROD2.spad" 272919 272937 274101 274106) (-215 "DIRPCAT.spad" 271851 271867 272773 272914) (-214 "DIRPCAT.spad" 270523 270541 271447 271452) (-213 "DIOSP.spad" 269348 269356 270513 270518) (-212 "DIOPS.spad" 268320 268330 269316 269343) (-211 "DIOPS.spad" 267278 267290 268276 268281) (-210 "DIFRING.spad" 266570 266578 267258 267273) (-209 "DIFRING.spad" 265870 265880 266560 266565) (-208 "DIFEXT.spad" 265029 265039 265850 265865) (-207 "DIFEXT.spad" 264105 264117 264928 264933) (-206 "DIAGG.spad" 263723 263733 264073 264100) (-205 "DIAGG.spad" 263361 263373 263713 263718) (-204 "DHMATRIX.spad" 261665 261675 262818 262845) (-203 "DFSFUN.spad" 255073 255081 261655 261660) (-202 "DFLOAT.spad" 251596 251604 254963 255068) (-201 "DFINTTLS.spad" 249805 249821 251586 251591) (-200 "DERHAM.spad" 247715 247747 249785 249800) (-199 "DEQUEUE.spad" 247033 247043 247322 247349) (-198 "DEGRED.spad" 246648 246662 247023 247028) (-197 "DEFINTRF.spad" 244173 244183 246638 246643) (-196 "DEFINTEF.spad" 242669 242685 244163 244168) (-195 "DECIMAL.spad" 240553 240561 241139 241232) (-194 "DDFACT.spad" 238352 238369 240543 240548) (-193 "DBLRESP.spad" 237950 237974 238342 238347) (-192 "DBASE.spad" 236522 236532 237940 237945) (-191 "D03FAFA.spad" 236350 236358 236512 236517) (-190 "D03EEFA.spad" 236170 236178 236340 236345) (-189 "D03AGNT.spad" 235250 235258 236160 236165) (-188 "D02EJFA.spad" 234712 234720 235240 235245) (-187 "D02CJFA.spad" 234190 234198 234702 234707) (-186 "D02BHFA.spad" 233680 233688 234180 234185) (-185 "D02BBFA.spad" 233170 233178 233670 233675) (-184 "D02AGNT.spad" 227974 227982 233160 233165) (-183 "D01WGTS.spad" 226293 226301 227964 227969) (-182 "D01TRNS.spad" 226270 226278 226283 226288) (-181 "D01GBFA.spad" 225792 225800 226260 226265) (-180 "D01FCFA.spad" 225314 225322 225782 225787) (-179 "D01ASFA.spad" 224782 224790 225304 225309) (-178 "D01AQFA.spad" 224228 224236 224772 224777) (-177 "D01APFA.spad" 223652 223660 224218 224223) (-176 "D01ANFA.spad" 223146 223154 223642 223647) (-175 "D01AMFA.spad" 222656 222664 223136 223141) (-174 "D01ALFA.spad" 222196 222204 222646 222651) (-173 "D01AKFA.spad" 221722 221730 222186 222191) (-172 "D01AJFA.spad" 221245 221253 221712 221717) (-171 "D01AGNT.spad" 217304 217312 221235 221240) (-170 "CYCLOTOM.spad" 216810 216818 217294 217299) (-169 "CYCLES.spad" 213642 213650 216800 216805) (-168 "CVMP.spad" 213059 213069 213632 213637) (-167 "CTRIGMNP.spad" 211549 211565 213049 213054) (-166 "CTORCALL.spad" 211137 211145 211539 211544) (-165 "CSTTOOLS.spad" 210380 210393 211127 211132) (-164 "CRFP.spad" 204084 204097 210370 210375) (-163 "CRAPACK.spad" 203127 203137 204074 204079) (-162 "CPMATCH.spad" 202627 202642 203052 203057) (-161 "CPIMA.spad" 202332 202351 202617 202622) (-160 "COORDSYS.spad" 197225 197235 202322 202327) (-159 "CONTOUR.spad" 196627 196635 197215 197220) (-158 "CONTFRAC.spad" 192239 192249 196529 196622) (-157 "COMRING.spad" 191913 191921 192177 192234) (-156 "COMPPROP.spad" 191427 191435 191903 191908) (-155 "COMPLPAT.spad" 191194 191209 191417 191422) (-154 "COMPLEX.spad" 185227 185237 185471 185732) (-153 "COMPLEX2.spad" 184940 184952 185217 185222) (-152 "COMPFACT.spad" 184542 184556 184930 184935) (-151 "COMPCAT.spad" 182598 182608 184264 184537) (-150 "COMPCAT.spad" 180361 180373 182029 182034) (-149 "COMMUPC.spad" 180107 180125 180351 180356) (-148 "COMMONOP.spad" 179640 179648 180097 180102) (-147 "COMM.spad" 179449 179457 179630 179635) (-146 "COMBOPC.spad" 178354 178362 179439 179444) (-145 "COMBINAT.spad" 177099 177109 178344 178349) (-144 "COMBF.spad" 174467 174483 177089 177094) (-143 "COLOR.spad" 173304 173312 174457 174462) (-142 "CMPLXRT.spad" 173013 173030 173294 173299) (-141 "CLIP.spad" 169105 169113 173003 173008) (-140 "CLIF.spad" 167744 167760 169061 169100) (-139 "CLAGG.spad" 164219 164229 167724 167739) (-138 "CLAGG.spad" 160575 160587 164082 164087) (-137 "CINTSLPE.spad" 159900 159913 160565 160570) (-136 "CHVAR.spad" 157978 158000 159890 159895) (-135 "CHARZ.spad" 157893 157901 157958 157973) (-134 "CHARPOL.spad" 157401 157411 157883 157888) (-133 "CHARNZ.spad" 157154 157162 157381 157396) (-132 "CHAR.spad" 155044 155052 157144 157149) (-131 "CFCAT.spad" 154360 154368 155034 155039) (-130 "CDEN.spad" 153518 153532 154350 154355) (-129 "CCLASS.spad" 151667 151675 152929 152968) (-128 "CARTEN.spad" 146770 146794 151657 151662) (-127 "CARTEN2.spad" 146156 146183 146760 146765) (-126 "CARD.spad" 143445 143453 146130 146151) (-125 "CACHSET.spad" 143067 143075 143435 143440) (-124 "CABMON.spad" 142620 142628 143057 143062) (-123 "BTREE.spad" 141689 141699 142227 142254) (-122 "BTOURN.spad" 140692 140702 141296 141323) (-121 "BTCAT.spad" 140068 140078 140648 140687) (-120 "BTCAT.spad" 139476 139488 140058 140063) (-119 "BTAGG.spad" 138492 138500 139432 139471) (-118 "BTAGG.spad" 137540 137550 138482 138487) (-117 "BSTREE.spad" 136275 136285 137147 137174) (-116 "BRILL.spad" 134470 134481 136265 136270) (-115 "BRAGG.spad" 133384 133394 134450 134465) (-114 "BRAGG.spad" 132272 132284 133340 133345) (-113 "BPADICRT.spad" 130256 130268 130511 130604) (-112 "BPADIC.spad" 129920 129932 130182 130251) (-111 "BOUNDZRO.spad" 129576 129593 129910 129915) (-110 "BOP.spad" 125040 125048 129566 129571) (-109 "BOP1.spad" 122426 122436 124996 125001) (-108 "BOOLEAN.spad" 121679 121687 122416 122421) (-107 "BMODULE.spad" 121391 121403 121647 121674) (-106 "BITS.spad" 120810 120818 121027 121054) (-105 "BINFILE.spad" 120153 120161 120800 120805) (-104 "BINDING.spad" 119572 119580 120143 120148) (-103 "BINARY.spad" 117465 117473 118042 118135) (-102 "BGAGG.spad" 116650 116660 117433 117460) (-101 "BGAGG.spad" 115855 115867 116640 116645) (-100 "BFUNCT.spad" 115419 115427 115835 115850) (-99 "BEZOUT.spad" 114554 114580 115369 115374) (-98 "BBTREE.spad" 111374 111383 114161 114188) (-97 "BASTYPE.spad" 111047 111054 111364 111369) (-96 "BASTYPE.spad" 110718 110727 111037 111042) (-95 "BALFACT.spad" 110158 110170 110708 110713) (-94 "AUTOMOR.spad" 109605 109614 110138 110153) (-93 "ATTREG.spad" 106324 106331 109357 109600) (-92 "ATTRBUT.spad" 102347 102354 106304 106319) (-91 "ATRIG.spad" 101817 101824 102337 102342) (-90 "ATRIG.spad" 101285 101294 101807 101812) (-89 "ASTACK.spad" 100618 100627 100892 100919) (-88 "ASSOCEQ.spad" 99418 99429 100574 100579) (-87 "ASP9.spad" 98499 98512 99408 99413) (-86 "ASP8.spad" 97542 97555 98489 98494) (-85 "ASP80.spad" 96864 96877 97532 97537) (-84 "ASP7.spad" 96024 96037 96854 96859) (-83 "ASP78.spad" 95475 95488 96014 96019) (-82 "ASP77.spad" 94844 94857 95465 95470) (-81 "ASP74.spad" 93936 93949 94834 94839) (-80 "ASP73.spad" 93207 93220 93926 93931) (-79 "ASP6.spad" 91839 91852 93197 93202) (-78 "ASP55.spad" 90348 90361 91829 91834) (-77 "ASP50.spad" 88165 88178 90338 90343) (-76 "ASP4.spad" 87460 87473 88155 88160) (-75 "ASP49.spad" 86459 86472 87450 87455) (-74 "ASP42.spad" 84866 84905 86449 86454) (-73 "ASP41.spad" 83445 83484 84856 84861) (-72 "ASP35.spad" 82433 82446 83435 83440) (-71 "ASP34.spad" 81734 81747 82423 82428) (-70 "ASP33.spad" 81294 81307 81724 81729) (-69 "ASP31.spad" 80434 80447 81284 81289) (-68 "ASP30.spad" 79326 79339 80424 80429) (-67 "ASP29.spad" 78792 78805 79316 79321) (-66 "ASP28.spad" 70065 70078 78782 78787) (-65 "ASP27.spad" 68962 68975 70055 70060) (-64 "ASP24.spad" 68049 68062 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T)) -((($) -3703 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-970))) ((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-970)))) +((($) -3703 (|has| |#2| (-157)) (|has| |#2| (-781)) (|has| |#2| (-970))) ((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-970)))) (-3703 (|has| |#1| (-21)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-513)) (|has| |#1| (-970))) (((|#1|) . T)) (-3703 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-513)) (|has| |#1| (-970))) @@ -612,38 +612,38 @@ (((|#1|) . T) (($) . T)) (|has| |#4| (-157)) (|has| |#3| (-157)) -(((#0=(-381 (-881 |#1|)) #0#) . T)) -(-3703 (|has| |#1| (-784)) (|has| |#1| (-1013))) +(((#0=(-381 (-880 |#1|)) #0#) . 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T)) -(-3703 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-970))) +(-3703 (|has| |#3| (-157)) (|has| |#3| (-781)) (|has| |#3| (-970))) (|has| |#3| (-729)) -(-3703 (|has| |#3| (-729)) (|has| |#3| (-782))) -(|has| |#3| (-782)) +(-3703 (|has| |#3| (-729)) (|has| |#3| (-781))) +(|has| |#3| (-781)) ((((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513))) ((|#2|) |has| |#1| (-337)) ((|#1|) |has| |#1| (-157))) (((|#1|) |has| |#1| (-157)) (((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513)))) (((|#2|) . T)) -((((-792)) . T)) -((((-792)) . T)) -((((-792)) . T)) -((((-792)) . T)) -(((|#1| (-1065 |#1|)) |has| |#1| (-782))) +((((-791)) . T)) +((((-791)) . T)) +((((-791)) . T)) +((((-791)) . T)) +(((|#1| (-1065 |#1|)) |has| |#1| (-781))) ((((-521) |#2|) . T)) (|has| |#1| (-1013)) (((|#1|) . T)) @@ -651,23 +651,23 @@ (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (|has| |#1| (-1013)) (((|#2|) . T)) -((((-497)) |has| |#2| (-562 (-497))) (((-821 (-353))) |has| |#2| (-562 (-821 (-353)))) (((-821 (-521))) |has| |#2| (-562 (-821 (-521))))) +((((-497)) |has| |#2| (-562 (-497))) (((-820 (-353))) |has| |#2| (-562 (-820 (-353)))) (((-820 (-521))) |has| |#2| (-562 (-820 (-521))))) (((|#4|) -3703 (|has| |#4| (-157)) (|has| |#4| (-337)))) (((|#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)))) -((((-792)) . T)) +((((-791)) . T)) (((|#1|) . T)) -(-3703 (|has| |#2| (-425)) (|has| |#2| (-838))) -(-3703 (|has| |#1| (-425)) (|has| |#1| (-838))) -(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-838))) -((($ $) . T) ((#0=(-1084) $) |has| |#1| (-210)) ((#0# |#1|) |has| |#1| (-210)) ((#1=(-755 (-1084)) |#1|) . T) ((#1# $) . T)) -(-3703 (|has| |#1| (-425)) (|has| |#1| (-838))) +(-3703 (|has| |#2| (-425)) (|has| |#2| (-837))) +(-3703 (|has| |#1| (-425)) (|has| |#1| (-837))) +(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-837))) +((($ $) . T) ((#0=(-1084) $) |has| |#1| (-210)) ((#0# |#1|) |has| |#1| (-210)) ((#1=(-754 (-1084)) |#1|) . T) ((#1# $) . T)) +(-3703 (|has| |#1| (-425)) (|has| |#1| (-837))) ((((-521) |#2|) . T)) -((((-792)) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-791)) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -((($) -3703 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-970))) ((|#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-970)))) +((($) -3703 (|has| |#3| (-157)) (|has| |#3| (-781)) (|has| |#3| (-970))) ((|#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-970)))) ((((-521) |#1|) . T)) (|has| (-381 |#2|) (-135)) (|has| (-381 |#2|) (-133)) @@ -675,16 +675,16 @@ (|has| |#1| (-37 (-381 (-521)))) (((|#1|) . T)) (((|#2|) . T) (($) . T) (((-381 (-521))) . T)) -((((-792)) . T)) +((((-791)) . T)) (|has| |#1| (-513)) (|has| |#1| (-513)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) -((((-792)) . T)) -((((-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) +((((-791)) . T)) +((((-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))) . T)) (|has| |#1| (-37 (-381 (-521)))) -((((-362) (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))) . T)) +((((-362) (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))) . T)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#2| (-1060)) (-3703 (|has| |#1| (-337)) (|has| |#1| (-513))) @@ -694,10 +694,10 @@ (|has| |#1| (-513)) ((((-112 |#1|)) . T)) ((((-521) |#1|) . T)) -(-3703 (|has| |#1| (-157)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) +(-3703 (|has| |#1| (-157)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) (((|#2|) . T)) -((((-792)) . T)) -((((-756 |#1|)) . T)) +((((-791)) . T)) +((((-755 |#1|)) . T)) (((|#2|) |has| |#2| (-157))) ((((-1084) (-51)) . T)) (((|#1|) . T)) @@ -705,9 +705,9 @@ (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-513)) (((|#1|) |has| |#1| (-157))) -((((-792)) . T)) +((((-791)) . T)) ((((-497)) |has| |#1| (-562 (-497)))) -(-3703 (|has| |#1| (-784)) (|has| |#1| (-1013))) +(-3703 (|has| |#1| (-783)) (|has| |#1| (-1013))) (((|#2|) |has| |#2| (-284 |#2|))) (((#0=(-521) #0#) . T) ((#1=(-381 (-521)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -717,7 +717,7 @@ (((#0=(-521) #0#) . T) ((#1=(-381 (-521)) #1#) . T) (($ $) . T)) ((($) . T) (((-521)) . T) (((-381 (-521))) . T)) (|has| |#2| (-342)) -(-3703 (|has| |#1| (-784)) (|has| |#1| (-1013))) +(-3703 (|has| |#1| (-783)) (|has| |#1| (-1013))) (((|#1|) . T) (((-381 (-521))) . T) (($) . T)) (((|#1|) . T) (((-381 (-521))) . T) (($) . T)) (((|#1|) . T) (((-381 (-521))) . T) (($) . T)) @@ -726,21 +726,21 @@ (((|#1| |#2|) . T)) ((((-521)) . T) (((-381 (-521))) . T) (($) . T)) ((((-1082 |#1| |#2| |#3|) $) -12 (|has| (-1082 |#1| |#2| |#3|) (-261 (-1082 |#1| |#2| |#3|) (-1082 |#1| |#2| |#3|))) (|has| |#1| (-337))) (($ $) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) ((($) . 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T)) -((($) -3703 (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) +((($) -3703 (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) ((((-381 (-521))) . T) (((-521)) . T)) ((((-521) (-132)) . T)) ((((-132)) . T)) @@ -751,56 +751,56 @@ ((((-108)) . T)) (((|#1|) . T)) ((((-497)) |has| |#1| (-562 (-497))) (((-202)) . #0=(|has| |#1| (-946))) (((-353)) . #0#)) -((((-792)) . T)) -(|has| |#1| (-757)) -(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) -(|has| |#1| (-784)) +((((-791)) . T)) +(|has| |#1| (-756)) +(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) +(|has| |#1| (-783)) (-3703 (|has| |#1| (-157)) (|has| |#1| (-513))) (|has| |#1| (-513)) -(|has| |#1| (-838)) +(|has| |#1| (-837)) (((|#1|) . T)) (|has| |#1| (-1013)) -((((-792)) . 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T)) (((|#1|) . T)) ((((-381 (-521))) . T) (($) . T)) ((($) . T) (((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) ((|#1|) . T)) -(|has| |#1| (-765)) +(|has| |#1| (-764)) ((((-381 (-521))) |has| |#1| (-961 (-381 (-521)))) (((-521)) |has| |#1| (-961 (-521))) ((|#1|) . T)) (|has| |#1| (-1013)) (((|#1| $) |has| |#1| (-261 |#1| |#1|))) @@ -809,10 +809,10 @@ (((|#4|) |has| |#4| (-1013))) (((|#3|) |has| |#3| (-1013))) (|has| |#3| (-342)) -(((|#1|) . T) (((-792)) . T)) +(((|#1|) . T) (((-791)) . T)) ((((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513))) (((-1157 |#1| |#2| |#3|)) |has| |#1| (-337)) ((|#1|) |has| |#1| (-157))) (((|#1|) |has| |#1| (-157)) (((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513)))) -((((-792)) . T)) +((((-791)) . T)) ((($) |has| |#1| (-513)) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) (((|#2|) . T)) (((|#1| |#1|) |has| |#1| (-157))) @@ -827,14 +827,14 @@ ((((-132)) . T)) (((|#1|) . T)) ((((-132)) . T)) -((($) -3703 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-970))) ((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-970)))) +((($) -3703 (|has| |#2| (-157)) (|has| |#2| (-781)) (|has| |#2| (-970))) ((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-970)))) ((((-132)) . T)) (((|#1| |#2| |#3|) . T)) (-3703 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-513)) (|has| |#1| (-970))) (|has| $ (-135)) (|has| $ (-135)) (|has| |#1| (-1013)) -((((-792)) . T)) +((((-791)) . T)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) (-3703 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-446)) (|has| |#1| (-513)) (|has| |#1| (-970)) (|has| |#1| (-1025))) @@ -848,20 +848,20 @@ (|has| |#1| (-513)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) -((((-792)) . T)) +((((-791)) . T)) (|has| |#2| (-133)) (|has| |#2| (-135)) (((|#2|) . T) (($) . T)) (|has| |#1| (-135)) (|has| |#1| (-133)) -(|has| |#4| (-782)) -(((|#2| (-217 (-3475 |#1|) (-707)) (-794 |#1|)) . T)) -(|has| |#3| (-782)) +(|has| |#4| (-781)) +(((|#2| (-217 (-3478 |#1|) (-707)) (-793 |#1|)) . T)) +(|has| |#3| (-781)) (((|#1| (-493 |#3|) |#3|) . T)) (|has| |#1| (-135)) (|has| |#1| (-133)) (((#0=(-381 (-521)) #0#) |has| |#2| (-337)) (($ $) . T)) -((((-799 |#1|)) . T)) +((((-798 |#1|)) . T)) (|has| |#1| (-135)) (|has| |#1| (-342)) (|has| |#1| (-342)) @@ -869,21 +869,21 @@ (|has| |#1| (-133)) ((((-381 (-521))) |has| |#2| (-337)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -(-3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838))) +(-3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837))) (-3703 (|has| |#1| (-323)) (|has| |#1| (-342))) ((((-1051 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-157)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-210)) (|has| |#2| (-970))) -(((|#2|) . T) (((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) -(-3703 (|has| |#3| (-729)) (|has| |#3| (-782))) -(-3703 (|has| |#3| (-729)) (|has| |#3| (-782))) -((((-792)) . T)) +(((|#2|) . T) (((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) +(-3703 (|has| |#3| (-729)) (|has| |#3| (-781))) +(-3703 (|has| |#3| (-729)) (|has| |#3| (-781))) +((((-791)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-636)) . T)) -(-3703 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-970))) +(-3703 (|has| |#2| (-157)) (|has| |#2| (-781)) (|has| |#2| (-970))) (|has| |#1| (-513)) (((|#1|) . T)) (((|#1|) . T)) @@ -892,50 +892,50 @@ (((|#1|) . T)) (((|#1|) . T)) ((((-1084) (-51)) . T)) -((((-792)) . T)) -((((-497)) . T) (((-821 (-521))) . T) (((-353)) . T) (((-202)) . T)) +((((-791)) . T)) +((((-497)) . T) (((-820 (-521))) . T) (((-353)) . T) (((-202)) . T)) (((|#1|) . T)) -((((-792)) . T)) -((((-497)) . T) (((-821 (-521))) . T) (((-353)) . T) (((-202)) . T)) +((((-791)) . T)) +((((-497)) . T) (((-820 (-521))) . T) (((-353)) . T) (((-202)) . T)) (((|#1| (-521)) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1| (-381 (-521))) . T)) (((|#3|) . T) (((-560 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-381 (-521))) . T) (($) . T)) (((#0=(-1082 |#1| |#2| |#3|) #0#) -12 (|has| (-1082 |#1| |#2| |#3|) (-284 (-1082 |#1| |#2| |#3|))) (|has| |#1| (-337))) (((-1084) #0#) -12 (|has| (-1082 |#1| |#2| |#3|) (-482 (-1084) (-1082 |#1| |#2| |#3|))) (|has| |#1| (-337)))) ((((-521)) . T) (($) . T) (((-381 (-521))) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) |has| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (-284 (-2 (|:| -2529 |#1|) (|:| -3045 |#2|))))) -(((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))) |has| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (-284 (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))))) -((((-792)) . T)) +(((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) |has| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (-284 (-2 (|:| -2535 |#1|) (|:| -3050 |#2|))))) +(((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))) |has| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (-284 (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))))) +((((-791)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) (((|#1|) . T)) ((($) . T) ((|#2|) . T)) ((((-1084) (-51)) . T)) (((|#3|) . T)) -((($ $) . T) ((#0=(-794 |#1|) $) . T) ((#0# |#2|) . T)) -(|has| |#1| (-765)) +((($ $) . T) ((#0=(-793 |#1|) $) . T) ((#0# |#2|) . T)) +(|has| |#1| (-764)) (|has| |#1| (-1013)) (((|#2| |#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-970))) (($ $) |has| |#2| (-157))) (((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)))) -((((-521) (-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T) ((|#1| |#2|) . T)) +((((-521) (-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T) ((|#1| |#2|) . T)) (((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-970))) (($) |has| |#2| (-157))) ((((-707)) . T)) ((((-521)) . T)) (|has| |#1| (-513)) -((((-792)) . T)) +((((-791)) . T)) (((|#1| (-381 (-521)) (-998)) . T)) (|has| |#1| (-133)) (((|#1|) . T)) @@ -948,21 +948,21 @@ (-3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-513))) (-3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-513))) (-3703 (|has| |#1| (-157)) (|has| |#1| (-513))) -((((-821 (-521))) . T) (((-821 (-353))) . T) (((-497)) . T) (((-1084)) . T)) -((((-792)) . T)) -(-3703 (|has| |#1| (-784)) (|has| |#1| (-1013))) +((((-820 (-521))) . T) (((-820 (-353))) . T) (((-497)) . T) (((-1084)) . T)) +((((-791)) . T)) +(-3703 (|has| |#1| (-783)) (|has| |#1| (-1013))) ((($) . T)) -((((-792)) . T)) -(-3703 (|has| |#2| (-157)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838))) +((((-791)) . T)) +(-3703 (|has| |#2| (-157)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837))) (((|#2|) |has| |#2| (-157))) -((($) -3703 (|has| |#2| (-337)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838))) ((|#2|) |has| |#2| (-157)) (((-381 (-521))) |has| |#2| (-37 (-381 (-521))))) -((((-799 |#1|)) . T)) -(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-782)) (|has| |#2| (-970)) (|has| |#2| (-1013))) +((($) -3703 (|has| |#2| (-337)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837))) ((|#2|) |has| |#2| (-157)) (((-381 (-521))) |has| |#2| (-37 (-381 (-521))))) +((((-798 |#1|)) . T)) +(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-781)) (|has| |#2| (-970)) (|has| |#2| (-1013))) (-12 (|has| |#3| (-210)) (|has| |#3| (-970))) (|has| |#2| (-1060)) -(((#0=(-51)) . T) (((-2 (|:| -2529 (-1084)) (|:| -3045 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2535 (-1084)) (|:| -3050 #0#))) . T)) (((|#1| |#2|) . T)) -(-3703 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-970))) +(-3703 (|has| |#3| (-157)) (|has| |#3| (-781)) (|has| |#3| (-970))) (((|#1| (-521) (-998)) . T)) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (((|#1| (-381 (-521)) (-998)) . T)) @@ -972,7 +972,7 @@ (((|#1| |#2|) . T)) (|has| |#2| (-342)) (-12 (|has| |#1| (-342)) (|has| |#2| (-342))) -((((-792)) . T)) +((((-791)) . T)) ((((-1084) |#1|) |has| |#1| (-482 (-1084) |#1|)) ((|#1| |#1|) |has| |#1| (-284 |#1|))) (-3703 (|has| |#1| (-133)) (|has| |#1| (-342))) (-3703 (|has| |#1| (-133)) (|has| |#1| (-342))) @@ -982,28 +982,28 @@ ((((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513))) (((-1082 |#1| |#2| |#3|)) |has| |#1| (-337)) ((|#1|) |has| |#1| (-157))) (((|#1|) |has| |#1| (-157)) (((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513)))) ((($) |has| |#1| (-513)) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) -((((-792)) . T)) +((((-791)) . T)) (|has| |#1| (-323)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) ((#0=(-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) #0#) |has| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (-284 (-2 (|:| -2529 |#1|) (|:| -3045 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) ((#0=(-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) #0#) |has| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (-284 (-2 (|:| -2535 |#1|) (|:| -3050 |#2|))))) (|has| |#1| (-513)) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -((((-792)) . T)) +((((-791)) . T)) (((|#1| |#2|) . T)) -(-3703 (|has| |#2| (-425)) (|has| |#2| (-838))) -(-3703 (|has| |#1| (-784)) (|has| |#1| (-1013))) -(-3703 (|has| |#1| (-425)) (|has| |#1| (-838))) +(-3703 (|has| |#2| (-425)) (|has| |#2| (-837))) +(-3703 (|has| |#1| (-783)) (|has| |#1| (-1013))) +(-3703 (|has| |#1| (-425)) (|has| |#1| (-837))) ((((-381 (-521))) . T) (((-521)) . T)) ((((-521)) . T)) -((((-381 (-521))) |has| |#2| (-37 (-381 (-521)))) ((|#2|) |has| |#2| (-157)) (($) -3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838)))) +((((-381 (-521))) |has| |#2| (-37 (-381 (-521)))) ((|#2|) |has| |#2| (-157)) (($) -3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837)))) ((($) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#1|) . T)) -((((-799 |#1|)) . T) (($) . T) (((-381 (-521))) . T)) -((((-792)) . T)) +((((-798 |#1|)) . T) (($) . T) (((-381 (-521))) . T)) +((((-791)) . T)) (((|#3| |#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-970))) (($ $) |has| |#3| (-157))) (|has| |#1| (-946)) -((((-792)) . T)) +((((-791)) . T)) (((|#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-970))) (($) |has| |#3| (-157))) ((((-521) (-108)) . T)) (((|#1|) |has| |#1| (-284 |#1|))) @@ -1011,7 +1011,7 @@ (|has| |#1| (-342)) (|has| |#1| (-342)) ((((-1084) $) |has| |#1| (-482 (-1084) $)) (($ $) |has| |#1| (-284 $)) ((|#1| |#1|) |has| |#1| (-284 |#1|)) (((-1084) |#1|) |has| |#1| (-482 (-1084) |#1|))) -((((-1084)) |has| |#1| (-829 (-1084)))) +((((-1084)) |has| |#1| (-828 (-1084)))) (-3703 (-12 (|has| |#1| (-210)) (|has| |#1| (-337))) (|has| |#1| (-323))) ((((-362) (-1031)) . T)) (((|#1| |#4|) . T)) @@ -1019,24 +1019,24 @@ ((((-362) |#1|) . T)) (-3703 (|has| |#1| (-337)) (|has| |#1| (-323))) (|has| |#1| (-1013)) -((((-792)) . T)) -((((-792)) . T)) -((((-839 |#1|)) . T)) -((((-381 (-521))) |has| |#2| (-37 (-381 (-521)))) ((|#2|) |has| |#2| (-157)) (($) -3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838)))) -((((-381 (-521))) |has| |#1| (-37 (-381 (-521)))) ((|#1|) |has| |#1| (-157)) (($) -3703 (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838)))) +((((-791)) . T)) +((((-791)) . T)) +((((-838 |#1|)) . T)) +((((-381 (-521))) |has| |#2| (-37 (-381 (-521)))) ((|#2|) |has| |#2| (-157)) (($) -3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837)))) +((((-381 (-521))) |has| |#1| (-37 (-381 (-521)))) ((|#1|) |has| |#1| (-157)) (($) -3703 (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) -(((#0=(-799 |#1|)) |has| #0# (-284 #0#))) +(((#0=(-798 |#1|)) |has| #0# (-284 #0#))) (((|#1| |#2|) . T)) -(-3703 (|has| |#2| (-729)) (|has| |#2| (-782))) -(-3703 (|has| |#2| (-729)) (|has| |#2| (-782))) +(-3703 (|has| |#2| (-729)) (|has| |#2| (-781))) +(-3703 (|has| |#2| (-729)) (|has| |#2| (-781))) (-12 (|has| |#1| (-729)) (|has| |#2| (-729))) (((|#1|) . T)) (-12 (|has| |#1| (-729)) (|has| |#2| (-729))) -(-3703 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-970))) +(-3703 (|has| |#2| (-157)) (|has| |#2| (-781)) (|has| |#2| (-970))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . 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T)) (((|#1|) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) (((|#3|) . T)) (((|#3|) . T)) (((|#1|) . T)) @@ -1378,34 +1378,34 @@ (|has| |#1| (-135)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) -((((-2 (|:| -2529 (-1084)) (|:| -3045 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) +((((-2 (|:| -2535 (-1084)) (|:| -3050 (-51)))) . T)) ((((-1082 |#1| |#2| |#3|)) |has| |#1| (-337))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) ((((-1084) (-51)) . T)) ((($ $) . T)) (((|#1| (-521)) . T)) -((((-839 |#1|)) . T)) -(((|#1|) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-970))) (($) -3703 (|has| |#1| (-829 (-1084))) (|has| |#1| (-970)))) +((((-838 |#1|)) . T)) +(((|#1|) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-970))) (($) -3703 (|has| |#1| (-828 (-1084))) (|has| |#1| (-970)))) (((|#1|) . T) (((-521)) |has| |#1| (-961 (-521))) (((-381 (-521))) |has| |#1| (-961 (-381 (-521))))) -(|has| |#1| (-784)) -(|has| |#1| (-784)) +(|has| |#1| (-783)) +(|has| |#1| (-783)) ((((-521) |#2|) . T)) ((((-521)) . T)) ((((-1157 |#1| |#2| |#3|)) -12 (|has| (-1157 |#1| |#2| |#3|) (-284 (-1157 |#1| |#2| |#3|))) (|has| |#1| (-337)))) -(|has| |#1| (-784)) -((((-627 |#2|)) . T) (((-792)) . T)) +(|has| |#1| (-783)) +((((-627 |#2|)) . T) (((-791)) . T)) (((|#1| |#2|) . T)) -((((-381 (-881 |#1|))) . T)) +((((-381 (-880 |#1|))) . T)) (((|#4| |#4|) -12 (|has| |#4| (-284 |#4|)) (|has| |#4| (-1013)))) (((|#4| |#4|) -12 (|has| |#4| (-284 |#4|)) (|has| |#4| (-1013)))) (((|#1|) |has| |#1| (-157))) (((|#4| |#4|) -12 (|has| |#4| (-284 |#4|)) (|has| |#4| (-1013)))) (((|#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)))) -(|has| |#2| (-784)) -(|has| |#1| (-784)) -(-3703 (|has| |#2| (-337)) (|has| |#2| (-425)) (|has| |#2| (-838))) +(|has| |#2| (-783)) +(|has| |#1| (-783)) +(-3703 (|has| |#2| (-337)) (|has| |#2| (-425)) (|has| |#2| (-837))) ((($ $) . T) ((#0=(-381 (-521)) #0#) . T)) ((((-521) |#2|) . T)) (((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)))) @@ -1413,13 +1413,13 @@ (((|#3| |#3|) -12 (|has| |#3| (-284 |#3|)) (|has| |#3| (-1013)))) ((($) . T) (((-381 (-521))) . T)) ((((-521) (-108)) . T)) -(|has| |#1| (-757)) -(|has| |#1| (-757)) +(|has| |#1| (-756)) +(|has| |#1| (-756)) (((|#1|) . T)) (-3703 (|has| |#1| (-282)) (|has| |#1| (-337)) (|has| |#1| (-323))) -(|has| |#1| (-782)) -(|has| |#1| (-782)) -(|has| |#1| (-782)) +(|has| |#1| (-781)) +(|has| |#1| (-781)) +(|has| |#1| (-781)) (((|#1|) . T) (((-381 (-521))) . T) (($) . T)) (|has| |#1| (-37 (-381 (-521)))) ((((-521)) . T) (($) . T) (((-381 (-521))) . T)) @@ -1427,11 +1427,11 @@ (|has| |#1| (-37 (-381 (-521)))) (-3703 (|has| |#1| (-337)) (|has| |#1| (-323))) (|has| |#1| (-37 (-381 (-521)))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) -((((-1084)) |has| |#1| (-829 (-1084))) (((-998)) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) +((((-1084)) |has| |#1| (-828 (-1084))) (((-998)) . T)) (((|#1|) . T)) -(|has| |#1| (-782)) -(((#0=(-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) #0#) |has| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (-284 (-2 (|:| -2529 (-1067)) (|:| -3045 (-51)))))) +(|has| |#1| (-781)) +(((#0=(-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) #0#) |has| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (-284 (-2 (|:| -2535 (-1067)) (|:| -3050 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (|has| |#1| (-1013)) (((|#1|) . T)) @@ -1443,13 +1443,13 @@ (((|#2|) . T)) (((|#1|) . T)) (((|#1| (-493 |#2|) |#2|) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#1| (-707) (-998)) . T)) (((|#3|) . T)) (((|#1|) . T)) ((((-132)) . T)) (((|#2|) |has| |#2| (-157))) -(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-782)) (|has| |#2| (-970)) (|has| |#2| (-1013))) +(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-781)) (|has| |#2| (-970)) (|has| |#2| (-1013))) (((|#1|) . T)) (|has| |#1| (-133)) (|has| |#1| (-135)) @@ -1464,31 +1464,30 @@ ((($) . T) ((|#1|) . T) (((-381 (-521))) . T)) (((|#2|) . T)) ((((-1082 |#1| |#2| |#3|)) |has| |#1| (-337))) -((($) |has| |#1| (-782))) -(|has| |#1| (-838)) -((((-792)) . T)) +((($) |has| |#1| (-781))) +(|has| |#1| (-837)) +((((-791)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (((|#1|) . T)) (((|#1| |#2|) . 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T)) -(-3703 (-12 (|has| |#1| (-337)) (|has| |#2| (-757))) (-12 (|has| |#1| (-337)) (|has| |#2| (-784)))) +(-3703 (-12 (|has| |#1| (-337)) (|has| |#2| (-756))) (-12 (|has| |#1| (-337)) (|has| |#2| (-783)))) (-3703 (|has| |#1| (-337)) (|has| |#1| (-513))) -((((-839 |#1|)) . T)) +((((-838 |#1|)) . T)) (((|#1| (-465 |#1| |#3|) (-465 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-707)) . T)) @@ -1496,25 +1495,25 @@ ((((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513))) (((-1082 |#1| |#2| |#3|)) |has| |#1| (-337)) ((|#1|) |has| |#1| (-157))) (((|#1|) |has| |#1| (-157)) (((-381 (-521))) -3703 (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-337))) (($) -3703 (|has| |#1| (-337)) (|has| |#1| (-513)))) ((($) |has| |#1| (-513)) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) -((((-2 (|:| -2529 (-1084)) (|:| -3045 (-51)))) . T)) +((((-2 (|:| -2535 (-1084)) (|:| -3050 (-51)))) . 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T)) +(((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) |has| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (-284 (-2 (|:| -2535 |#1|) (|:| -3050 |#2|))))) (((|#1|) |has| |#1| (-157))) ((($) |has| |#1| (-513)) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) @@ -1634,40 +1633,40 @@ (((|#2|) -3703 (|has| |#2| (-157)) (|has| |#2| (-337)))) ((((-1150 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) -(|has| |#1| (-757)) -(|has| |#1| (-757)) +(|has| |#1| (-756)) +(|has| |#1| (-756)) (((|#1| (-521) (-998)) . T)) ((($) |has| |#1| (-284 $)) ((|#1|) |has| |#1| (-284 |#1|))) -(|has| |#1| (-782)) -(|has| |#1| (-782)) +(|has| |#1| (-781)) +(|has| |#1| (-781)) (((|#1| (-521) (-998)) . T)) -(-3703 (|has| |#1| (-829 (-1084))) (|has| |#1| (-970))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . 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T)) (((|#1| |#1|) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-970)))) (((|#1|) . T)) ((((-521)) . T)) @@ -1675,23 +1674,23 @@ (((|#1|) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-970)))) (((|#2|) |has| |#2| (-337))) ((($) . T) ((|#1|) . T) (((-381 (-521))) |has| |#1| (-337))) -(|has| |#1| (-784)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +(|has| |#1| (-783)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -2529 (-1084)) (|:| -3045 (-51)))) |has| (-2 (|:| -2529 (-1084)) (|:| -3045 (-51))) (-284 (-2 (|:| -2529 (-1084)) (|:| -3045 (-51)))))) -(-3703 (|has| |#1| (-425)) (|has| |#1| (-838))) +((((-2 (|:| -2535 (-1084)) (|:| -3050 (-51)))) |has| (-2 (|:| -2535 (-1084)) (|:| -3050 (-51))) (-284 (-2 (|:| -2535 (-1084)) (|:| -3050 (-51)))))) +(-3703 (|has| |#1| (-425)) (|has| |#1| (-837))) (((|#2|) . T) (((-521)) |has| |#2| (-583 (-521)))) -((((-792)) . T)) -((((-792)) . T)) -((((-497)) . T) (((-521)) . T) (((-821 (-521))) . T) (((-353)) . T) (((-202)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) +((((-497)) . T) (((-521)) . T) (((-820 (-521))) . T) (((-353)) . T) (((-202)) . T)) +((((-791)) . T)) (|has| |#1| (-37 (-381 (-521)))) ((((-521)) . T) (($) . T) (((-381 (-521))) . T)) ((((-521)) . T) (($) . T) (((-381 (-521))) . T)) (|has| |#1| (-210)) (((|#1|) . T)) (((|#1| (-521)) . T)) -(|has| |#1| (-782)) +(|has| |#1| (-781)) (((|#1| (-1082 |#1| |#2| |#3|)) . T)) (((|#1| |#1|) . T)) (((|#1| |#1|) . T)) @@ -1713,37 +1712,37 @@ (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) (((|#1|) . T)) -(-3703 (|has| |#2| (-157)) (|has| |#2| (-782)) (|has| |#2| (-970))) +(-3703 (|has| |#2| (-157)) (|has| |#2| (-781)) (|has| |#2| (-970))) (((|#1| |#1|) . T) ((#0=(-381 (-521)) #0#) . T) (($ $) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#1|) . T) (((-381 (-521))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) -((((-792)) -3703 (|has| |#1| (-561 (-792))) (|has| |#1| (-1013)))) +((((-791)) -3703 (|has| |#1| (-561 (-791))) (|has| |#1| (-1013)))) (|has| |#1| (-337)) (|has| |#1| (-337)) (|has| (-381 |#2|) (-210)) -(|has| |#1| (-838)) +(|has| |#1| (-837)) (((|#2|) |has| |#2| (-970))) -(((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) |has| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (-284 (-2 (|:| -2529 |#1|) (|:| -3045 |#2|))))) +(((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) (((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) |has| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (-284 (-2 (|:| -2535 |#1|) (|:| -3050 |#2|))))) (|has| |#1| (-337)) (((|#1|) |has| |#1| (-157))) (((|#1| |#1|) . T)) -((((-799 |#1|)) . T)) -((((-792)) . T)) +((((-798 |#1|)) . T)) +((((-791)) . T)) (((|#1|) . T)) (((|#2|) |has| |#2| (-1013))) -(|has| |#2| (-784)) +(|has| |#2| (-783)) (((|#1|) . T)) ((((-381 (-521))) . T) (((-521)) . T) (((-560 $)) . T)) (((|#1|) . T)) -((((-792)) . T)) +((((-791)) . T)) ((($) . T)) -(|has| |#1| (-784)) -((((-792)) . T)) +(|has| |#1| (-783)) +((((-791)) . T)) (((|#1| (-493 |#2|) |#2|) . T)) (((|#1| (-521) (-998)) . T)) -((((-839 |#1|)) . T)) -((((-792)) . T)) +((((-838 |#1|)) . T)) +((((-791)) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1| (-381 (-521)) (-998)) . T)) @@ -1757,45 +1756,45 @@ (((|#1|) . T)) ((((-381 |#2|)) . T) (((-381 (-521))) . T) (($) . T)) (|has| |#2| (-210)) -(((|#2| (-493 (-794 |#1|)) (-794 |#1|)) . T)) -((((-792)) . T)) +(((|#2| (-493 (-793 |#1|)) (-793 |#1|)) . T)) +((((-791)) . T)) ((($) |has| |#1| (-513)) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) -((((-792)) . T)) +((((-791)) . T)) (((|#1| |#3|) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#1|) |has| |#1| (-157))) ((((-636)) . T)) ((((-636)) . 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T)) -(|has| |#2| (-784)) +(|has| |#2| (-783)) (((|#3|) |has| |#3| (-970))) -(|has| |#2| (-838)) -(|has| |#1| (-838)) +(|has| |#2| (-837)) +(|has| |#1| (-837)) (|has| |#1| (-337)) -(|has| |#1| (-784)) -((((-1084)) |has| |#2| (-829 (-1084)))) -((((-792)) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +(|has| |#1| (-783)) +((((-1084)) |has| |#2| (-828 (-1084)))) +((((-791)) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) ((((-381 (-521))) . T) (($) . T)) (|has| |#1| (-446)) (|has| |#1| (-342)) @@ -1812,8 +1811,8 @@ ((($) . T)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) -(((|#2|) . T) (((-792)) . T)) -(((|#2|) . T) (((-792)) . T)) +(((|#2|) . T) (((-791)) . T)) +(((|#2|) . T) (((-791)) . T)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) @@ -1822,17 +1821,17 @@ (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) -(|has| |#1| (-784)) -((((-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))) . T)) +(|has| |#1| (-783)) +((((-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-135)) (|has| |#1| (-133)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) |has| (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)) (-284 (-2 (|:| -2529 |#1|) (|:| -3045 |#2|)))) ((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013)))) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) |has| (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)) (-284 (-2 (|:| -2535 |#1|) (|:| -3050 |#2|)))) ((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) (|has| |#1| (-342)) -(|has| |#1| (-784)) +(|has| |#1| (-783)) (((|#2|) . T) (((-381 (-521))) |has| |#1| (-961 (-381 (-521)))) (((-521)) |has| |#1| (-961 (-521))) ((|#1|) . T)) ((((-112 |#1|)) . T)) (((|#2|) |has| |#2| (-157))) @@ -1840,12 +1839,12 @@ ((((-521)) . T)) (|has| |#1| (-337)) (|has| |#1| (-337)) -((((-792)) . T)) -((((-792)) . T)) -((((-497)) |has| |#1| (-562 (-497))) (((-821 (-521))) |has| |#1| (-562 (-821 (-521)))) (((-821 (-353))) |has| |#1| (-562 (-821 (-353)))) (((-353)) . #0=(|has| |#1| (-946))) (((-202)) . #0#)) +((((-791)) . T)) +((((-791)) . T)) +((((-497)) |has| |#1| (-562 (-497))) (((-820 (-521))) |has| |#1| (-562 (-820 (-521)))) (((-820 (-353))) |has| |#1| (-562 (-820 (-353)))) (((-353)) . #0=(|has| |#1| (-946))) (((-202)) . #0#)) (((|#1|) |has| |#1| (-337))) -((((-792)) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-791)) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) ((($ $) . T) (((-560 $) $) . T)) (-3703 (|has| |#1| (-337)) (|has| |#1| (-513))) ((($) . T) (((-1151 |#1| |#2| |#3| |#4|)) . T) (((-381 (-521))) . T)) @@ -1854,21 +1853,21 @@ (|has| |#1| (-337)) (|has| |#1| (-337)) ((((-353)) . T) (((-521)) . T) (((-381 (-521))) . T)) -((((-587 (-716 |#1| (-794 |#2|)))) . T) (((-792)) . T)) -((((-497)) |has| (-716 |#1| (-794 |#2|)) (-562 (-497)))) +((((-587 (-716 |#1| (-793 |#2|)))) . T) (((-791)) . T)) +((((-497)) |has| (-716 |#1| (-793 |#2|)) (-562 (-497)))) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) ((((-353)) . T)) (((|#3|) -12 (|has| |#3| (-284 |#3|)) (|has| |#3| (-1013)))) -((((-792)) . T)) -(-3703 (|has| |#2| (-425)) (|has| |#2| (-838))) +((((-791)) . T)) +(-3703 (|has| |#2| (-425)) (|has| |#2| (-837))) (((|#1|) . T)) -(|has| |#1| (-784)) -(|has| |#1| (-784)) -((((-792)) -3703 (|has| |#1| (-561 (-792))) (|has| |#1| (-1013)))) +(|has| |#1| (-783)) +(|has| |#1| (-783)) +((((-791)) -3703 (|has| |#1| (-561 (-791))) (|has| |#1| (-1013)))) ((((-497)) |has| |#1| (-562 (-497)))) (((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013)))) (|has| |#1| (-1013)) -((((-792)) . T)) +((((-791)) . T)) ((((-381 (-521))) . T) (((-521)) . T) (((-560 $)) . T)) (|has| |#1| (-133)) (|has| |#1| (-135)) @@ -1888,37 +1887,37 @@ (|has| |#1| (-210)) (|has| |#1| (-337)) (((|#3|) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) ((((-521)) |has| |#2| (-583 (-521))) ((|#2|) . T)) (((|#2|) . T)) (|has| |#1| (-1013)) (((|#1| |#2|) . T)) (((|#1|) . T) (((-521)) |has| |#1| (-583 (-521)))) (((|#3|) |has| |#3| (-157))) -(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-782)) (|has| |#2| (-970)) (|has| |#2| (-1013))) +(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-781)) (|has| |#2| (-970)) (|has| |#2| (-1013))) ((((-521)) . T)) (((|#1| $) |has| |#1| (-261 |#1| |#1|))) ((((-381 (-521))) . T) (($) . T) (((-381 |#1|)) . T) ((|#1|) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#3|) . T)) (((|#1| |#1|) . T) (($ $) -3703 (|has| |#1| (-265)) (|has| |#1| (-337))) ((#0=(-381 (-521)) #0#) |has| |#1| (-337))) -((((-2 (|:| -2529 (-1084)) (|:| -3045 (-51)))) . T)) +((((-2 (|:| -2535 (-1084)) (|:| -3050 (-51)))) . T)) ((($) . T)) ((((-521) |#1|) . T)) -((((-1084)) |has| (-381 |#2|) (-829 (-1084)))) +((((-1084)) |has| (-381 |#2|) (-828 (-1084)))) (((|#1|) . T) (($) -3703 (|has| |#1| (-265)) (|has| |#1| (-337))) (((-381 (-521))) |has| |#1| (-337))) ((((-497)) |has| |#2| (-562 (-497)))) -((((-627 |#2|)) . T) (((-792)) . T)) +((((-627 |#2|)) . T) (((-791)) . T)) (((|#1|) . T)) (((|#4|) -12 (|has| |#4| (-284 |#4|)) (|has| |#4| (-1013)))) (((|#4|) -12 (|has| |#4| (-284 |#4|)) (|has| |#4| (-1013)))) -((((-799 |#1|)) . T)) +((((-798 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -(-3703 (|has| |#4| (-729)) (|has| |#4| (-782))) -(-3703 (|has| |#3| (-729)) (|has| |#3| (-782))) -((((-792)) . T)) -((((-792)) . T)) +(-3703 (|has| |#4| (-729)) (|has| |#4| (-781))) +(-3703 (|has| |#3| (-729)) (|has| |#3| (-781))) +((((-791)) . T)) +((((-791)) . T)) (((|#4|) -12 (|has| |#4| (-284 |#4|)) (|has| |#4| (-1013)))) (((|#2|) |has| |#2| (-970))) (((|#1|) . T)) @@ -1937,14 +1936,14 @@ ((((-381 (-521))) |has| #0=(-381 |#2|) (-961 (-381 (-521)))) (((-521)) |has| #0# (-961 (-521))) ((#0#) . T)) (((|#2|) . T) (((-521)) |has| |#2| (-583 (-521)))) (((|#1| (-707)) . T)) -(|has| |#1| (-784)) +(|has| |#1| (-783)) (((|#1|) . T) (((-521)) |has| |#1| (-583 (-521)))) ((($) -3703 (|has| |#1| (-337)) (|has| |#1| (-323))) (((-381 (-521))) -3703 (|has| |#1| (-337)) (|has| |#1| (-323))) ((|#1|) . T)) ((((-521)) . T)) (|has| |#1| (-37 (-381 (-521)))) -((((-2 (|:| -2529 (-1067)) (|:| -3045 (-51)))) |has| (-2 (|:| -2529 (-1067)) (|:| -3045 (-51))) (-284 (-2 (|:| -2529 (-1067)) (|:| -3045 (-51)))))) +((((-2 (|:| -2535 (-1067)) (|:| -3050 (-51)))) |has| (-2 (|:| -2535 (-1067)) (|:| -3050 (-51))) (-284 (-2 (|:| -2535 (-1067)) (|:| -3050 (-51)))))) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -(|has| |#1| (-782)) +(|has| |#1| (-781)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) @@ -1966,28 +1965,28 @@ (|has| |#1| (-37 (-381 (-521)))) (((|#1| |#2|) . T)) ((((-132)) . T)) -((((-716 |#1| (-794 |#2|))) . T)) -((((-792)) -3703 (|has| |#1| (-561 (-792))) (|has| |#1| (-1013)))) +((((-716 |#1| (-793 |#2|))) . T)) +((((-791)) -3703 (|has| |#1| (-561 (-791))) (|has| |#1| (-1013)))) (|has| |#1| (-1105)) (((|#1|) . T)) -(-3703 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-342)) (|has| |#3| (-729)) (|has| |#3| (-782)) (|has| |#3| (-970)) (|has| |#3| (-1013))) +(-3703 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-342)) (|has| |#3| (-729)) (|has| |#3| (-781)) (|has| |#3| (-970)) (|has| |#3| (-1013))) ((((-1084) |#1|) |has| |#1| (-482 (-1084) |#1|))) (((|#2|) . T)) -((($ $) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) ((|#1| |#1|) . T) ((#0=(-381 (-521)) #0#) |has| |#1| (-37 (-381 (-521))))) -((($) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) ((|#1|) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) -((((-839 |#1|)) . T)) +((($ $) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) ((|#1| |#1|) . T) ((#0=(-381 (-521)) #0#) |has| |#1| (-37 (-381 (-521))))) +((($) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) ((|#1|) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) +((((-838 |#1|)) . T)) ((($) . T)) -((((-381 (-881 |#1|))) . T)) +((((-381 (-880 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) ((((-497)) |has| |#4| (-562 (-497)))) -((((-792)) . T) (((-587 |#4|)) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-791)) . T) (((-587 |#4|)) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) (((|#1|) . T)) -(|has| |#1| (-782)) -(((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))) |has| (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|)) (-284 (-2 (|:| -2529 (-1067)) (|:| -3045 |#1|))))) +(|has| |#1| (-781)) +(((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013))) (((-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))) |has| (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|)) (-284 (-2 (|:| -2535 (-1067)) (|:| -3050 |#1|))))) (|has| |#1| (-1013)) (|has| |#1| (-337)) -(|has| |#1| (-784)) +(|has| |#1| (-783)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2001,30 +2000,30 @@ (|has| |#1| (-135)) (|has| |#1| (-135)) (|has| |#1| (-133)) -((((-792)) -3703 (|has| |#1| (-561 (-792))) (|has| |#1| (-1013)))) +((((-791)) -3703 (|has| |#1| (-561 (-791))) (|has| |#1| (-1013)))) ((((-1157 |#1| |#2| |#3|)) |has| |#1| (-337))) -(|has| |#1| (-782)) +(|has| |#1| (-781)) (((|#1| |#2|) . T)) (((|#1|) . T) (((-521)) |has| |#1| (-583 (-521)))) ((((-521)) |has| |#1| (-583 (-521))) ((|#1|) . T)) -((((-839 |#1|)) . T) (((-381 (-521))) . T) (($) . T)) +((((-838 |#1|)) . T) (((-381 (-521))) . T) (($) . T)) (|has| |#1| (-1013)) (((|#1|) . T) (($) . T) (((-381 (-521))) . T) (((-521)) . T)) (|has| |#2| (-133)) (|has| |#2| (-135)) -((((-839 |#1|)) . T) (((-381 (-521))) . T) (($) . T)) +((((-838 |#1|)) . T) (((-381 (-521))) . T) (($) . T)) (|has| |#1| (-1013)) (((|#2|) |has| |#2| (-157))) (((|#2|) . T)) (((|#1| |#1|) . T)) (((|#3|) |has| |#3| (-337))) ((((-381 |#2|)) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#1|) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) ((((-497)) |has| |#1| (-562 (-497)))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) ((((-1084) |#1|) |has| |#1| (-482 (-1084) |#1|)) ((|#1| |#1|) |has| |#1| (-284 |#1|))) (((|#1|) -3703 (|has| |#1| (-157)) (|has| |#1| (-337)))) ((((-290 |#1|)) . T)) @@ -2032,13 +2031,13 @@ (((|#2|) . T)) ((((-381 (-521))) . T) (((-636)) . T) (($) . T)) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -(((#0=(-716 |#1| (-794 |#2|)) #0#) |has| (-716 |#1| (-794 |#2|)) (-284 (-716 |#1| (-794 |#2|))))) -((((-794 |#1|)) . T)) +(((#0=(-716 |#1| (-793 |#2|)) #0#) |has| (-716 |#1| (-793 |#2|)) (-284 (-716 |#1| (-793 |#2|))))) +((((-793 |#1|)) . T)) (((|#2|) |has| |#2| (-157))) (((|#1|) |has| |#1| (-157))) (((|#2|) . T)) -((((-1084)) |has| |#1| (-829 (-1084))) (((-998)) . T)) -((((-1084)) |has| |#1| (-829 (-1084))) (((-1003 (-1084))) . T)) +((((-1084)) |has| |#1| (-828 (-1084))) (((-998)) . T)) +((((-1084)) |has| |#1| (-828 (-1084))) (((-1003 (-1084))) . T)) (((|#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013)))) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (|has| |#1| (-37 (-381 (-521)))) @@ -2047,11 +2046,11 @@ (|has| |#1| (-133)) (|has| |#1| (-135)) ((($ $) . T)) -(-3703 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-446)) (|has| |#1| (-663)) (|has| |#1| (-829 (-1084))) (|has| |#1| (-970)) (|has| |#1| (-1025)) (|has| |#1| (-1013))) +(-3703 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-446)) (|has| |#1| (-663)) (|has| |#1| (-828 (-1084))) (|has| |#1| (-970)) (|has| |#1| (-1025)) (|has| |#1| (-1013))) (|has| |#1| (-513)) (((|#2|) . T)) ((((-521)) . T)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) (-3703 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-513)) (|has| |#1| (-970))) @@ -2061,13 +2060,13 @@ (((|#1|) . T)) ((($) . T)) (((|#1|) . T)) -((((-792)) . T)) +((((-791)) . T)) (((|#2|) |has| |#2| (-6 (-4235 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((((-381 (-521))) |has| |#2| (-961 (-381 (-521)))) (((-521)) |has| |#2| (-961 (-521))) ((|#2|) . T) (((-794 |#1|)) . T)) +((((-381 (-521))) |has| |#2| (-961 (-381 (-521)))) (((-521)) |has| |#2| (-961 (-521))) ((|#2|) . T) (((-793 |#1|)) . T)) ((($) . T) (((-112 |#1|)) . T) (((-381 (-521))) . T)) ((((-1036 |#1| |#2|)) . T) ((|#2|) . T) ((|#1|) . T) (((-521)) |has| |#1| (-961 (-521))) (((-381 (-521))) |has| |#1| (-961 (-381 (-521))))) ((((-1080 |#1|)) . T) (((-998)) . T) ((|#1|) . T) (((-521)) |has| |#1| (-961 (-521))) (((-381 (-521))) |has| |#1| (-961 (-381 (-521))))) @@ -2075,7 +2074,7 @@ (|has| |#1| (-1013)) ((($) . T)) (|has| |#1| (-1013)) -((((-521)) -12 (|has| |#1| (-815 (-521))) (|has| |#2| (-815 (-521)))) (((-353)) -12 (|has| |#1| (-815 (-353))) (|has| |#2| (-815 (-353))))) +((((-521)) -12 (|has| |#1| (-814 (-521))) (|has| |#2| (-814 (-521)))) (((-353)) -12 (|has| |#1| (-814 (-353))) (|has| |#2| (-814 (-353))))) (((|#1| |#2|) . T)) ((((-1084) |#1|) . T)) (((|#4|) . T)) @@ -2083,8 +2082,8 @@ ((((-1084) (-51)) . T)) ((((-1150 |#2| |#3| |#4|) (-293 |#2| |#3| |#4|)) . T)) ((((-381 (-521))) |has| |#1| (-961 (-381 (-521)))) (((-521)) |has| |#1| (-961 (-521))) ((|#1|) . T)) -((((-792)) . T)) -(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-782)) (|has| |#2| (-970)) (|has| |#2| (-1013))) +((((-791)) . T)) +(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-342)) (|has| |#2| (-729)) (|has| |#2| (-781)) (|has| |#2| (-970)) (|has| |#2| (-1013))) (((#0=(-1151 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-381 (-521)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-157)) ((#0=(-381 (-521)) #0#) |has| |#1| (-513)) (($ $) |has| |#1| (-513))) (((|#1|) . T) (($) . T) (((-381 (-521))) . T)) @@ -2103,18 +2102,18 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013)))) (((|#2| |#3|) . T)) -(-3703 (|has| |#2| (-337)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838))) +(-3703 (|has| |#2| (-337)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837))) (((|#1| (-493 |#2|)) . T)) (((|#1| (-707)) . T)) (((|#1| (-493 (-1003 (-1084)))) . T)) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) -(|has| |#2| (-838)) -(-3703 (|has| |#2| (-729)) (|has| |#2| (-782))) -((((-792)) . T)) +(|has| |#2| (-837)) +(-3703 (|has| |#2| (-729)) (|has| |#2| (-781))) +((((-791)) . T)) ((($ $) . T) ((#0=(-1150 |#2| |#3| |#4|) #0#) . T) ((#1=(-381 (-521)) #1#) |has| #0# (-37 (-381 (-521))))) -((((-839 |#1|)) . T)) -(-12 (|has| |#1| (-337)) (|has| |#2| (-757))) +((((-838 |#1|)) . T)) +(-12 (|has| |#1| (-337)) (|has| |#2| (-756))) ((($) . T) (((-381 (-521))) . T)) ((($) . T)) ((($) . T)) @@ -2124,65 +2123,65 @@ ((($) . T) ((#0=(-1150 |#2| |#3| |#4|)) . T) (((-381 (-521))) |has| #0# (-37 (-381 (-521))))) (((|#1| |#2|) . 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T)) -(-3703 (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) -(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) +(-3703 (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) +(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-729)) (|has| |#2| (-782)) (|has| |#2| (-970))) -(-3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-782)) (|has| |#2| (-970))) -(|has| |#1| (-838)) -(|has| |#1| (-838)) +(-3703 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-729)) (|has| |#2| (-781)) (|has| |#2| (-970))) +(-3703 (|has| |#2| (-157)) (|has| |#2| (-337)) (|has| |#2| (-781)) (|has| |#2| (-970))) +(|has| |#1| (-837)) +(|has| |#1| (-837)) (((|#2|) . T)) (((|#1|) . T)) -((((-792)) . T)) +((((-791)) . T)) ((((-521)) . T)) (((#0=(-381 (-521)) #0#) . T) (($ $) . T)) ((((-381 (-521))) . T) (($) . T)) @@ -2239,29 +2238,29 @@ (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) -(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) -(|has| |#1| (-757)) -(((#0=(-839 |#1|) #0#) . T) (($ $) . T) ((#1=(-381 (-521)) #1#) . T)) +(-3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) +(|has| |#1| (-756)) +(((#0=(-838 |#1|) #0#) . T) (($ $) . T) ((#1=(-381 (-521)) #1#) . T)) ((((-381 |#2|)) . T)) -(|has| |#1| (-782)) -((((-792)) -3703 (|has| |#1| (-561 (-792))) (|has| |#1| (-1013)))) +(|has| |#1| (-781)) +((((-791)) -3703 (|has| |#1| (-561 (-791))) (|has| |#1| (-1013)))) (((|#1| |#1|) . T) ((#0=(-381 (-521)) #0#) . T) ((#1=(-521) #1#) . T) (($ $) . T)) -((((-839 |#1|)) . T) (($) . T) (((-381 (-521))) . T)) +((((-838 |#1|)) . T) (($) . T) (((-381 (-521))) . T)) (((|#2|) |has| |#2| (-970)) (((-521)) -12 (|has| |#2| (-583 (-521))) (|has| |#2| (-970)))) (((|#1|) . T) (((-381 (-521))) . T) (((-521)) . T) (($) . T)) (((|#1| |#2| |#3| |#4|) . T)) (|has| |#1| (-135)) (|has| |#1| (-133)) (((|#2|) . T)) -((((-792)) . T)) +((((-791)) . T)) (-3703 (|has| |#1| (-133)) (|has| |#1| (-342))) (-3703 (|has| |#1| (-133)) (|has| |#1| (-342))) (-3703 (|has| |#1| (-133)) (|has| |#1| (-342))) -((((-2 (|:| -2529 (-1084)) (|:| -3045 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -2529 (-1084)) (|:| -3045 #0#))) . T)) +((((-2 (|:| -2535 (-1084)) (|:| -3050 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -2535 (-1084)) (|:| -3050 #0#))) . T)) (|has| |#1| (-323)) ((((-521)) . T)) -((((-792)) . T)) +((((-791)) . T)) (((#0=(-1151 |#1| |#2| |#3| |#4|) $) |has| #0# (-261 #0# #0#))) (|has| |#1| (-337)) (((#0=(-998) |#1|) . T) ((#0# $) . T) (($ $) . T)) @@ -2277,11 +2276,11 @@ ((((-381 (-521))) . T) (((-636)) . T) (($) . T)) (((|#3| |#3|) . T)) (|has| |#2| (-210)) -((((-794 |#1|)) . T)) -((((-1084)) |has| |#1| (-829 (-1084))) ((|#3|) . T)) +((((-793 |#1|)) . T)) +((((-1084)) |has| |#1| (-828 (-1084))) ((|#3|) . T)) (-12 (|has| |#1| (-337)) (|has| |#2| (-946))) ((((-1082 |#1| |#2| |#3|)) |has| |#1| (-337))) -((((-792)) . T)) +((((-791)) . T)) (|has| |#1| (-337)) (|has| |#1| (-337)) ((((-381 (-521))) . T) (($) . T) (((-381 |#1|)) . T) ((|#1|) . T)) @@ -2291,7 +2290,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-521)) . T)) -(-3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) +(-3703 (|has| |#1| (-157)) (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-837))) (((|#2|) . T) (((-521)) |has| |#2| (-583 (-521)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2301,10 +2300,10 @@ (((|#1|) . T) (($) . T)) (((|#1| (-1165 |#1|) (-1165 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) (((#0=(-112 |#1|) #0#) . T) ((#1=(-381 (-521)) #1#) . T) (($ $) . T)) -((((-381 (-521))) |has| |#2| (-961 (-381 (-521)))) (((-521)) |has| |#2| (-961 (-521))) ((|#2|) . T) (((-794 |#1|)) . T)) +((((-381 (-521))) |has| |#2| (-961 (-381 (-521)))) (((-521)) |has| |#2| (-961 (-521))) ((|#2|) . T) (((-793 |#1|)) . T)) ((((-1036 |#1| |#2|)) . T) ((|#3|) . T) ((|#1|) . T) (((-521)) |has| |#1| (-961 (-521))) (((-381 (-521))) |has| |#1| (-961 (-381 (-521)))) ((|#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2313,7 +2312,7 @@ ((((-612 |#1|)) . T)) ((($) . T) (((-381 (-521))) |has| |#2| (-37 (-381 (-521)))) ((|#2|) . T)) ((((-112 |#1|)) . T) (((-381 (-521))) . T) (($) . T)) -((((-521)) -12 (|has| |#1| (-815 (-521))) (|has| |#3| (-815 (-521)))) (((-353)) -12 (|has| |#1| (-815 (-353))) (|has| |#3| (-815 (-353))))) +((((-521)) -12 (|has| |#1| (-814 (-521))) (|has| |#3| (-814 (-521)))) (((-353)) -12 (|has| |#1| (-814 (-353))) (|has| |#3| (-814 (-353))))) (((|#2|) . T) ((|#6|) . T)) (((|#1|) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521)))) (($) . T)) ((((-132)) . T)) @@ -2321,48 +2320,48 @@ ((($) . T) ((|#1|) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) ((($) . T) ((|#1|) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) (((|#1|) . T)) -(|has| |#2| (-838)) -(|has| |#1| (-838)) -(|has| |#1| (-838)) +(|has| |#2| (-837)) +(|has| |#1| (-837)) +(|has| |#1| (-837)) (((|#4|) . T)) (|has| |#2| (-946)) ((($) . T)) -(|has| |#1| (-838)) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +(|has| |#1| (-837)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) (((|#1|) . T) (($) . T)) ((($) . T)) (|has| |#1| (-337)) -((((-839 |#1|)) . T)) -((($) -3703 (|has| |#1| (-337)) (|has| |#1| (-425)) (|has| |#1| (-513)) (|has| |#1| (-838))) ((|#1|) |has| |#1| (-157)) (((-381 (-521))) |has| |#1| (-37 (-381 (-521))))) +((((-838 |#1|)) . 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T)) (|has| |#1| (-513)) ((((-381 (-521))) . T) (($) . T)) ((($) . T)) @@ -2372,11 +2371,11 @@ (|has| |#1| (-37 (-381 (-521)))) (-3703 (|has| |#1| (-282)) (|has| |#1| (-337)) (|has| |#1| (-323))) (|has| |#1| (-37 (-381 (-521)))) -(-12 (|has| |#1| (-506)) (|has| |#1| (-765))) -((((-792)) . T)) -((((-1084)) -3703 (-12 (|has| |#1| (-15 * (|#1| (-521) |#1|))) (|has| |#1| (-829 (-1084)))) (-12 (|has| |#1| (-337)) (|has| |#2| (-829 (-1084)))))) +(-12 (|has| |#1| (-506)) (|has| |#1| (-764))) +((((-791)) . T)) +((((-1084)) -3703 (-12 (|has| |#1| (-15 * (|#1| (-521) |#1|))) (|has| |#1| (-828 (-1084)))) (-12 (|has| |#1| (-337)) (|has| |#2| (-828 (-1084)))))) (|has| |#1| (-337)) -((((-1084)) -12 (|has| |#1| (-15 * (|#1| (-381 (-521)) |#1|))) (|has| |#1| (-829 (-1084))))) +((((-1084)) -12 (|has| |#1| (-15 * (|#1| (-381 (-521)) |#1|))) (|has| |#1| (-828 (-1084))))) (|has| |#1| (-337)) ((((-381 (-521))) . T) (($) . T)) ((($) . T) (((-381 (-521))) |has| |#1| (-37 (-381 (-521)))) ((|#1|) . T)) @@ -2384,7 +2383,7 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-337))) (((|#2|) |has| |#1| (-337))) -((((-2 (|:| -2529 |#1|) (|:| -3045 |#2|))) . T)) +((((-2 (|:| -2535 |#1|) (|:| -3050 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) @@ -2392,20 +2391,20 @@ (((|#2|) . T)) ((((-1084) #0=(-1151 |#1| |#2| |#3| |#4|)) |has| #0# (-482 (-1084) #0#)) ((#0# #0#) |has| #0# (-284 #0#))) ((((-560 $) $) . T) (($ $) . T)) -((((-154 (-202))) . T) (((-154 (-353))) . T) (((-1080 (-636))) . T) (((-821 (-353))) . T)) -((((-792)) . T)) +((((-154 (-202))) . T) (((-154 (-353))) . T) (((-1080 (-636))) . T) (((-820 (-353))) . T)) +((((-791)) . T)) (|has| |#1| (-513)) (|has| |#1| (-513)) (|has| (-381 |#2|) (-210)) (((|#1| (-381 (-521))) . T)) ((($ $) . T)) -((((-1084)) |has| |#2| (-829 (-1084)))) +((((-1084)) |has| |#2| (-828 (-1084)))) ((($) . T)) -((((-792)) . T)) +((((-791)) . T)) ((((-381 (-521))) . T) (($) . 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T)) (((|#1|) |has| |#1| (-284 |#1|))) @@ -2524,31 +2524,31 @@ (|has| |#1| (-337)) (|has| |#1| (-513)) (|has| |#1| (-1013)) -((((-716 |#1| (-794 |#2|))) |has| (-716 |#1| (-794 |#2|)) (-284 (-716 |#1| (-794 |#2|))))) -(-3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838))) +((((-716 |#1| (-793 |#2|))) |has| (-716 |#1| (-793 |#2|)) (-284 (-716 |#1| (-793 |#2|))))) +(-3703 (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-837))) (((|#1|) . T)) (((|#2| |#3|) . T)) -(|has| |#2| (-838)) +(|has| |#2| (-837)) (((|#1|) . T)) (((|#1| (-493 |#2|)) . T)) (((|#1| (-707)) . T)) (|has| |#1| (-210)) (((|#1| (-493 (-1003 (-1084)))) . T)) (|has| |#2| (-337)) -((((-2 (|:| -2529 (-1067)) (|:| -3045 (-51)))) . T)) +((((-2 (|:| -2535 (-1067)) (|:| -3050 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -((((-792)) . T)) -((((-792)) . T)) -(-3703 (|has| |#3| (-729)) (|has| |#3| (-782))) -((((-792)) . T)) -((((-792)) . T)) +((((-791)) . T)) +((((-791)) . T)) +(-3703 (|has| |#3| (-729)) (|has| |#3| (-781))) +((((-791)) . T)) +((((-791)) . T)) (((|#1|) . T)) ((($ $) . T) (((-560 $) $) . T)) (((|#1|) . T)) ((((-521)) . T)) (((|#3|) . T)) -((((-792)) . T)) +((((-791)) . T)) (-3703 (|has| |#1| (-282)) (|has| |#1| (-337)) (|has| |#1| (-323))) (-3703 (|has| |#1| (-133)) (|has| |#1| (-135)) (|has| |#1| (-157)) (|has| |#1| (-513)) (|has| |#1| (-970))) (((#0=(-534 |#1|) #0#) . T) (($ $) . T) ((#1=(-381 (-521)) #1#) . T)) @@ -2561,9 +2561,9 @@ (((|#2|) |has| |#2| (-6 (-4235 "*")))) (((|#1|) . T)) (((|#1|) . T)) -((((-792)) |has| |#1| (-561 (-792)))) +((((-791)) |has| |#1| (-561 (-791)))) ((((-269 |#3|)) . T)) -(((#0=(-381 (-521)) #0#) |has| |#2| (-37 (-381 (-521)))) ((|#2| |#2|) . T) (($ $) -3703 (|has| |#2| (-157)) (|has| |#2| (-425)) (|has| |#2| (-513)) (|has| |#2| (-838)))) +(((#0=(-381 (-521)) #0#) |has| |#2| (-37 (-381 (-521)))) ((|#2| |#2|) . 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T)) (((|#1| |#1|) |has| |#1| (-157))) (-3703 (|has| |#1| (-337)) (|has| |#1| (-513))) -(-3703 (|has| |#1| (-21)) (|has| |#1| (-782))) +(-3703 (|has| |#1| (-21)) (|has| |#1| (-781))) (((|#2|) . T)) -(-3703 (|has| |#1| (-21)) (|has| |#1| (-782))) +(-3703 (|has| |#1| (-21)) (|has| |#1| (-781))) (((|#1|) |has| |#1| (-157))) (((|#1|) . T)) (((|#1|) . T)) -((((-792)) -3703 (-12 (|has| |#1| (-561 (-792))) (|has| |#2| (-561 (-792)))) (-12 (|has| |#1| (-1013)) (|has| |#2| (-1013))))) +((((-791)) -3703 (-12 (|has| |#1| (-561 (-791))) (|has| |#2| (-561 (-791)))) (-12 (|has| |#1| (-1013)) (|has| |#2| (-1013))))) ((((-381 |#2|) |#3|) . T)) ((((-381 (-521))) . T) (($) . T)) (|has| |#1| (-37 (-381 (-521)))) @@ -3084,19 +3084,19 @@ (((|#1|) . T) (((-381 (-521))) . T) (((-521)) . T) (($) . T)) (((#0=(-521) #0#) . T)) ((($) . T) (((-381 (-521))) . 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T)) (|has| |#1| (-37 (-381 (-521)))) (|has| |#1| (-37 (-381 (-521)))) @@ -3124,65 +3124,65 @@ ((((-381 (-521))) . T) (((-636)) . T) (($) . T)) ((((-1082 |#1| |#2| |#3|)) . T)) ((((-1082 |#1| |#2| |#3|)) . T) (((-1075 |#1| |#2| |#3|)) . T)) -((((-792)) . T)) -((((-792)) -3703 (|has| |#1| (-561 (-792))) (|has| |#1| (-1013)))) +((((-791)) . T)) +((((-791)) -3703 (|has| |#1| (-561 (-791))) (|has| |#1| (-1013)))) ((((-521) |#1|) . T)) ((((-1082 |#1| |#2| |#3|)) |has| |#1| (-337))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-337)) -(((|#3|) . T) ((|#2|) . T) (($) -3703 (|has| |#4| (-157)) (|has| |#4| (-782)) (|has| |#4| (-970))) ((|#4|) -3703 (|has| |#4| (-157)) (|has| |#4| (-337)) (|has| |#4| (-970)))) -(((|#2|) . T) (($) -3703 (|has| |#3| (-157)) (|has| |#3| (-782)) (|has| |#3| (-970))) ((|#3|) -3703 (|has| |#3| (-157)) (|has| |#3| (-337)) (|has| |#3| (-970)))) +(((|#3|) . T) ((|#2|) . 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T)) (((|#2| $) |has| |#2| (-261 |#2| |#2|))) -(((|#1| (-587 |#1|)) |has| |#1| (-782))) +(((|#1| (-587 |#1|)) |has| |#1| (-781))) (-3703 (|has| |#1| (-210)) (|has| |#1| (-323))) (-3703 (|has| |#1| (-337)) (|has| |#1| (-323))) (|has| |#1| (-1013)) @@ -3192,17 +3192,17 @@ (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) -((((-1084)) |has| |#1| (-829 (-1084)))) +((((-1084)) |has| |#1| (-828 (-1084)))) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (((|#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013)))) (((|#1| (-552 |#1| |#3|) (-552 |#1| |#2|)) . T)) (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . 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-210) 134799) ((-126 . -784) T) ((-599 . -1013) T) ((-1093 . -554) 134778) ((-507 . -1096) 134757) ((-310 . -1013) T) ((-293 . -337) 134736) ((-381 . -135) 134715) ((-381 . -133) 134694) ((-892 . -1025) 134593) ((-217 . -829) 134526) ((-752 . -1025) 134457) ((-595 . -786) 134441) ((-451 . -554) 134420) ((-507 . -102) 134370) ((-929 . -351) 134352) ((-929 . -312) 134334) ((-92 . -1013) T) ((-892 . -23) 134145) ((-450 . -21) T) ((-450 . -25) T) ((-752 . -23) 134016) ((-1084 . -561) 133998) ((-57 . -19) 133982) ((-1084 . -562) 133904) ((-1080 . -663) T) ((-1036 . -663) T) ((-484 . -19) 133888) ((-465 . -19) 133872) ((-57 . -554) 133849) ((-1002 . -1013) T) ((-830 . -97) 133827) ((-788 . -663) T) ((-718 . -1013) T) ((-484 . -554) 133804) ((-465 . -554) 133781) ((-716 . -1013) T) ((-716 . -984) 133748) ((-434 . -1013) T) ((-427 . -1013) T) ((-538 . -654) 133723) ((-590 . -1013) T) ((-929 . -829) NIL) ((-1157 . -46) 133700) ((-571 . -1025) T) ((-611 . -124) T) ((-1151 . -97) T) ((-1150 . -46) 133670) ((-1129 . -46) 133647) ((-1114 . -157) 133598) ((-996 . -1123) 133549) ((-251 . -1013) T) ((-83 . -414) T) ((-83 . -369) T) ((-1081 . -282) 133528) ((-1075 . -282) 133507) ((-49 . -1013) T) ((-996 . -513) 133458) ((-648 . -157) T) ((-546 . -46) 133435) ((-202 . -589) 133400) ((-534 . -1013) T) ((-485 . -1013) T) ((-333 . -1123) T) ((-327 . -1123) T) ((-319 . -1123) T) ((-458 . -757) T) ((-458 . -849) T) ((-293 . -1025) T) ((-103 . -1123) T) ((-313 . -784) T) ((-195 . -849) T) ((-195 . -757) T) ((-651 . -976) 133370) ((-333 . -513) T) ((-327 . -513) T) ((-319 . -513) T) ((-103 . -513) T) ((-599 . -654) 133340) ((-1075 . -946) NIL) ((-293 . -23) T) ((-65 . -1119) T) ((-925 . -561) 133272) ((-631 . -208) 133254) ((-651 . -107) 133219) ((-587 . -33) T) ((-222 . -460) 133203) ((-1015 . -1011) 133187) ((-156 . -1013) T) ((-881 . -838) 133166) ((-453 . -838) 133145) ((-1187 . -21) T) ((-1187 . -25) T) ((-1185 . -124) T) ((-1183 . -124) T) ((-1002 . -654) 132994) ((-981 . -589) 132981) ((-881 . -589) 132906) ((-497 . -561) 132888) ((-497 . -562) 132869) ((-718 . -654) 132698) ((-716 . -654) 132547) ((-1176 . -97) T) ((-993 . -97) T) ((-355 . -25) T) ((-355 . -21) T) ((-453 . -589) 132472) ((-434 . -654) 132443) ((-427 . -654) 132292) ((-913 . -97) T) ((-674 . -97) T) ((-493 . -25) T) ((-1129 . -1119) 132271) ((-1161 . -561) 132237) ((-1129 . -815) NIL) ((-1129 . -813) 132189) ((-129 . -97) T) ((-43 . -124) T) ((-1093 . -562) NIL) ((-1093 . -561) 132171) ((-1051 . -1034) 132116) ((-317 . -977) T) ((-605 . -561) 132098) ((-264 . -1025) T) ((-329 . -561) 132080) ((-326 . -561) 132062) ((-318 . -561) 132044) ((-240 . -562) 131792) ((-240 . -561) 131774) ((-224 . -561) 131756) ((-224 . -562) 131617) ((-967 . -1113) 131546) ((-830 . -284) 131484) ((-1191 . -1060) T) ((-1150 . -961) 131419) ((-1129 . -961) 131385) ((-1114 . -482) 131352) ((-1050 . -561) 131334) ((-756 . -663) T) ((-552 . -263) 131311) ((-534 . -654) 131276) ((-451 . -562) NIL) ((-451 . -561) 131258) 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128218) ((-325 . -133) T) ((-333 . -1025) T) ((-327 . -1025) T) ((-319 . -1025) T) ((-929 . -282) T) ((-843 . -282) T) ((-801 . -220) T) ((-103 . -1025) T) ((-801 . -210) 128197) ((-1149 . -107) 128018) ((-1128 . -107) 127807) ((-222 . -1153) 127791) ((-521 . -782) T) ((-333 . -23) T) ((-328 . -323) T) ((-290 . -284) 127778) ((-287 . -284) 127719) ((-327 . -23) T) ((-293 . -124) T) ((-319 . -23) T) ((-929 . -946) T) ((-103 . -23) T) ((-222 . -554) 127696) ((-1151 . -37) 127588) ((-1138 . -838) 127567) ((-108 . -1013) T) ((-959 . -97) T) ((-1138 . -589) 127492) ((-800 . -730) NIL) ((-789 . -589) 127466) ((-800 . -727) NIL) ((-753 . -815) NIL) ((-800 . -663) T) ((-1002 . -482) 127339) ((-718 . -482) 127287) ((-716 . -482) 127239) ((-528 . -589) 127226) ((-753 . -961) 127056) ((-427 . -482) 126999) ((-362 . -363) T) ((-58 . -1119) T) ((-566 . -784) 126978) ((-469 . -602) T) ((-1055 . -902) 126947) ((-928 . -425) T) ((-636 . -782) T) ((-478 . -728) T) ((-447 . -976) 126782) ((-317 . -1013) T) ((-287 . -1060) NIL) ((-264 . -124) T) ((-368 . -1013) T) ((-631 . -344) 126749) ((-799 . -977) T) ((-200 . -565) 126726) ((-301 . -261) 126703) ((-447 . -107) 126524) ((-1149 . -970) T) ((-1128 . -970) T) ((-753 . -351) 126508) ((-154 . -663) T) ((-595 . -97) T) ((-1149 . -220) 126487) ((-1149 . -210) 126439) ((-1128 . -210) 126344) ((-1128 . -220) 126323) ((-928 . -376) NIL) ((-611 . -583) 126271) ((-290 . -37) 126181) ((-287 . -37) 126110) ((-67 . -561) 126092) ((-293 . -462) 126058) ((-1093 . -263) 126037) ((-1026 . -1025) 125968) ((-81 . -1119) T) ((-59 . -561) 125950) ((-451 . -263) 125929) ((-1178 . -961) 125906) ((-1073 . -1013) T) ((-1026 . -23) 125777) ((-753 . -829) 125713) ((-1138 . -663) T) ((-1015 . -1119) T) ((-1002 . -265) 125644) ((-822 . -97) T) ((-718 . -265) 125555) ((-301 . -19) 125539) ((-57 . -263) 125516) ((-716 . -265) 125447) ((-789 . -663) T) ((-113 . -782) NIL) ((-484 . -263) 125424) ((-301 . -554) 125401) ((-465 . -263) 125378) ((-427 . -265) 125309) 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T) ((-469 . -784) T) ((-329 . -976) 124556) ((-326 . -976) 124508) ((-318 . -976) 124460) ((-227 . -1119) T) ((-226 . -1119) T) ((-240 . -976) 124303) ((-224 . -976) 124146) ((-605 . -107) 124125) ((-329 . -107) 124063) ((-326 . -107) 124001) ((-318 . -107) 123939) ((-240 . -107) 123768) ((-224 . -107) 123597) ((-754 . -1123) 123576) ((-568 . -385) 123560) ((-43 . -21) T) ((-43 . -25) T) ((-752 . -583) 123468) ((-754 . -513) 123447) ((-227 . -961) 123276) ((-226 . -961) 123105) ((-122 . -115) 123089) ((-839 . -976) 123054) ((-636 . -977) T) ((-649 . -97) T) ((-317 . -157) T) ((-140 . -21) T) ((-140 . -25) T) ((-86 . -561) 123036) ((-839 . -107) 122992) ((-39 . -654) 122937) ((-799 . -1013) T) ((-301 . -562) 122898) ((-301 . -561) 122810) ((-1128 . -728) 122763) ((-1128 . -732) 122716) ((-227 . -351) 122686) ((-226 . -351) 122656) ((-595 . -37) 122626) ((-556 . -33) T) ((-454 . -1025) 122557) ((-448 . -33) T) ((-1026 . -124) 122428) ((-892 . -25) 122239) ((-803 . -561) 122221) ((-892 . 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-37) 119999) ((-1165 . -1163) 119983) ((-325 . -376) T) ((-1165 . -1013) 119933) ((-533 . -654) 119920) ((-521 . -654) 119907) ((-464 . -654) 119872) ((-290 . -573) 119851) ((-771 . -663) T) ((-764 . -663) T) ((-587 . -1119) T) ((-996 . -583) 119799) ((-1080 . -829) 119743) ((-1036 . -829) 119727) ((-603 . -976) 119711) ((-103 . -583) 119693) ((-454 . -124) 119564) ((-1086 . -1025) T) ((-881 . -46) 119533) ((-568 . -1013) T) ((-603 . -107) 119512) ((-301 . -263) 119489) ((-453 . -46) 119446) ((-1086 . -23) T) ((-113 . -1013) T) ((-98 . -97) 119424) ((-1175 . -1025) T) ((-974 . -124) T) ((-948 . -977) T) ((-756 . -961) 119408) ((-928 . -661) 119380) ((-1175 . -23) T) ((-636 . -654) 119345) ((-538 . -561) 119327) ((-360 . -961) 119311) ((-328 . -977) T) ((-359 . -124) T) ((-298 . -961) 119295) ((-202 . -815) 119277) ((-929 . -849) T) ((-89 . -33) T) ((-929 . -757) T) ((-843 . -849) T) ((-458 . -1123) T) ((-1100 . -561) 119259) ((-1018 . -1013) T) ((-195 . -1123) T) ((-924 . -284) 119224) 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. -157) T) ((-648 . -107) 114365) ((-1191 . -977) T) ((-1138 . -351) 114349) ((-392 . -1123) 114327) ((-287 . -782) NIL) ((-392 . -513) T) ((-202 . -282) T) ((-1128 . -727) 114280) ((-1128 . -730) 114233) ((-1149 . -663) T) ((-1128 . -663) T) ((-47 . -654) 114198) ((-202 . -946) T) ((-325 . -1172) 114175) ((-1151 . -385) 114141) ((-655 . -663) T) ((-1138 . -829) 114085) ((-108 . -561) 114067) ((-108 . -562) 114049) ((-655 . -446) T) ((-454 . -21) 113960) ((-123 . -460) 113944) ((-117 . -460) 113928) ((-454 . -25) 113780) ((-568 . -265) T) ((-538 . -976) 113755) ((-411 . -1013) T) ((-981 . -282) T) ((-113 . -265) T) ((-1017 . -97) T) ((-928 . -97) T) ((-538 . -107) 113723) ((-1051 . -284) 113661) ((-1114 . -970) T) ((-981 . -946) T) ((-64 . -1119) T) ((-974 . -25) T) ((-974 . -21) T) ((-648 . -970) T) ((-359 . -21) T) ((-359 . -25) T) ((-631 . -482) NIL) ((-948 . -157) T) ((-648 . -220) T) ((-981 . -506) T) ((-471 . -97) T) ((-328 . -157) T) ((-317 . -561) 113643) ((-368 . -561) 113625) 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. -97) T) ((-627 . -55) 101403) ((-636 . -970) T) ((-49 . -589) 101377) ((-264 . -425) T) ((-449 . -1113) 101346) ((0 . -97) T) ((-534 . -589) 101311) ((-485 . -589) 101256) ((-48 . -97) T) ((-839 . -961) 101243) ((-636 . -220) T) ((-996 . -383) 101222) ((-668 . -583) 101170) ((-924 . -1013) T) ((-649 . -157) 101061) ((-458 . -918) 101043) ((-240 . -351) 101027) ((-224 . -351) 101011) ((-373 . -1013) T) ((-313 . -37) 100995) ((-950 . -97) 100973) ((-195 . -918) 100955) ((-158 . -37) 100887) ((-1149 . -282) 100866) ((-1128 . -282) 100845) ((-599 . -663) T) ((-94 . -561) 100827) ((-1075 . -583) 100779) ((-456 . -25) T) ((-456 . -21) T) ((-1128 . -946) 100732) ((-568 . -970) T) ((-353 . -378) T) ((-364 . -97) T) ((-240 . -829) 100678) ((-224 . -829) 100655) ((-113 . -970) T) ((-753 . -1025) T) ((-1002 . -663) T) ((-568 . -210) 100634) ((-566 . -97) T) ((-718 . -663) T) ((-716 . -663) T) ((-387 . -1025) T) ((-113 . -220) T) ((-39 . -342) NIL) ((-113 . -210) NIL) ((-427 . -663) T) ((-753 . 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. -135) 89411) ((-353 . -513) T) ((-1081 . -135) 89390) ((-1081 . -133) 89369) ((-1075 . -133) 89276) ((-381 . -265) T) ((-1075 . -135) 89183) ((-1037 . -135) 89162) ((-1037 . -133) 89141) ((-293 . -37) 88982) ((-154 . -124) T) ((-287 . -732) NIL) ((-287 . -728) NIL) ((-595 . -970) T) ((-47 . -589) 88947) ((-919 . -21) T) ((-123 . -935) 88931) ((-117 . -935) 88915) ((-919 . -25) T) ((-830 . -115) 88899) ((-1067 . -97) T) ((-753 . -784) 88878) ((-1138 . -124) T) ((-1080 . -25) T) ((-1080 . -21) T) ((-789 . -124) T) ((-1036 . -25) T) ((-1036 . -21) T) ((-788 . -25) T) ((-788 . -21) T) ((-718 . -282) 88857) ((-588 . -97) 88835) ((-576 . -97) T) ((-1068 . -284) 88630) ((-528 . -124) T) ((-566 . -782) 88609) ((-1065 . -460) 88593) ((-1059 . -139) 88543) ((-1055 . -561) 88505) ((-1055 . -562) 88466) ((-948 . -727) T) ((-948 . -730) T) ((-948 . -663) T) ((-455 . -284) 88404) ((-426 . -391) 88374) ((-325 . -157) T) ((-264 . -37) 88361) ((-250 . -97) T) ((-249 . -97) T) ((-248 . -97) T) ((-247 . -97) T) ((-246 . -97) T) ((-245 . -97) T) ((-244 . -97) T) ((-317 . -961) 88338) ((-191 . -97) T) ((-190 . -97) T) ((-188 . -97) T) ((-187 . -97) T) ((-186 . -97) T) ((-185 . -97) T) ((-182 . -97) T) ((-181 . -97) T) ((-649 . -976) 88161) ((-180 . -97) T) ((-179 . -97) T) ((-178 . -97) T) ((-177 . -97) T) ((-176 . -97) T) ((-175 . -97) T) ((-174 . -97) T) ((-173 . -97) T) ((-172 . -97) T) ((-328 . -663) T) ((-649 . -107) 87970) ((-611 . -208) 87954) ((-534 . -282) T) ((-485 . -282) T) ((-269 . -482) 87903) ((-103 . -284) NIL) ((-70 . -369) T) ((-1026 . -97) 87714) ((-770 . -385) 87698) ((-1031 . -732) T) ((-1031 . -728) T) ((-638 . -1013) T) ((-353 . -337) T) ((-154 . -462) 87676) ((-199 . -561) 87608) ((-126 . -1013) T) ((-112 . -1013) T) ((-47 . -663) T) ((-967 . -460) 87573) ((-129 . -399) 87555) ((-129 . -342) T) ((-951 . -97) T) ((-480 . -477) 87534) ((-449 . -97) T) ((-436 . -97) T) ((-958 . -1025) T) ((-1082 . -34) 87500) ((-1082 . -91) 87466) ((-1082 . -1108) 87432) ((-1082 . 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. -37) 86133) ((-319 . -37) 86098) ((-78 . -414) T) ((-78 . -369) T) ((-202 . -25) T) ((-202 . -21) T) ((-771 . -1025) T) ((-103 . -37) 86048) ((-764 . -1025) T) ((-710 . -1013) T) ((-112 . -654) 86035) ((-612 . -961) 86019) ((-560 . -97) T) ((-771 . -23) T) ((-764 . -23) T) ((-1065 . -261) 85996) ((-1026 . -284) 85934) ((-1015 . -212) 85918) ((-62 . -370) T) ((-62 . -369) T) ((-106 . -97) T) ((-39 . -351) 85895) ((-594 . -786) 85879) ((-981 . -21) T) ((-981 . -25) T) ((-752 . -208) 85849) ((-881 . -25) T) ((-881 . -21) T) ((-566 . -977) T) ((-453 . -25) T) ((-453 . -21) T) ((-951 . -284) 85787) ((-818 . -561) 85769) ((-814 . -561) 85751) ((-227 . -784) 85702) ((-226 . -784) 85653) ((-490 . -482) 85586) ((-800 . -583) 85563) ((-449 . -284) 85501) ((-436 . -284) 85439) ((-325 . -265) T) ((-1065 . -1153) 85423) ((-1051 . -561) 85385) ((-1051 . -562) 85346) ((-1049 . -97) T) ((-924 . -976) 85242) ((-39 . -829) 85194) ((-1065 . -554) 85171) ((-1191 . -589) 85158) ((-982 . -139) 85104) 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. -1025) T) ((-224 . -1025) T) ((-568 . -282) 78251) ((-1059 . -284) 78055) ((-605 . -23) T) ((-454 . -208) 78025) ((-140 . -977) T) ((-329 . -23) T) ((-326 . -23) T) ((-318 . -23) T) ((-113 . -282) T) ((-240 . -23) T) ((-224 . -23) T) ((-928 . -970) T) ((-649 . -838) 78004) ((-928 . -210) 77976) ((-928 . -220) T) ((-113 . -946) NIL) ((-839 . -1025) T) ((-1150 . -425) 77955) ((-1129 . -425) 77934) ((-490 . -561) 77866) ((-649 . -589) 77791) ((-381 . -976) 77743) ((-473 . -561) 77725) ((-839 . -23) T) ((-458 . -284) NIL) ((-447 . -124) T) ((-195 . -284) NIL) ((-381 . -107) 77663) ((-752 . -977) 77594) ((-674 . -1011) 77578) ((-1149 . -462) 77544) ((-1128 . -462) 77510) ((-129 . -1011) 77492) ((-450 . -265) T) ((-1186 . -970) T) ((-982 . -97) T) ((-469 . -482) NIL) ((-640 . -97) T) ((-454 . -215) 77471) ((-1080 . -133) 77450) ((-1080 . -135) 77429) ((-1036 . -135) 77408) ((-1036 . -133) 77387) ((-579 . -976) 77371) ((-555 . -976) 77355) ((-611 . -1013) T) ((-611 . -973) 77295) ((-1082 . 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. -97) T) ((-75 . -370) T) ((-75 . -369) T) ((-594 . -597) 74638) ((-129 . -1119) T) ((-800 . -135) T) ((-800 . -133) NIL) ((-325 . -970) T) ((-68 . -357) T) ((-68 . -369) T) ((-1074 . -97) T) ((-611 . -482) 74571) ((-627 . -284) 74509) ((-891 . -37) 74406) ((-672 . -37) 74376) ((-507 . -284) 74180) ((-290 . -1119) T) ((-325 . -210) T) ((-325 . -220) T) ((-287 . -1119) T) ((-264 . -1013) T) ((-1088 . -561) 74162) ((-648 . -1123) T) ((-1065 . -592) 74146) ((-1114 . -513) 74125) ((-648 . -513) T) ((-290 . -813) 74109) ((-290 . -815) 74034) ((-287 . -813) 73995) ((-287 . -815) NIL) ((-736 . -284) 73960) ((-293 . -654) 73801) ((-298 . -297) 73778) ((-456 . -97) T) ((-447 . -25) T) ((-447 . -21) T) ((-392 . -37) 73752) ((-290 . -961) 73420) ((-202 . -1105) T) ((-202 . -1108) T) ((-3 . -561) 73402) ((-287 . -961) 73332) ((-2 . -1013) T) ((-2 . |RecordCategory|) T) ((-770 . -561) 73314) ((-1026 . -977) 73245) ((-533 . -849) T) ((-521 . -757) T) ((-521 . -849) T) ((-464 . -849) T) ((-128 . 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. -592) 129942) ((-1002 . -157) 129853) ((-885 . -347) 129837) ((-981 . -730) T) ((-981 . -727) T) ((-718 . -157) 129728) ((-716 . -157) 129639) ((-752 . -46) 129601) ((-981 . -663) T) ((-301 . -460) 129585) ((-880 . -663) T) ((-427 . -157) 129496) ((-222 . -261) 129473) ((-453 . -663) T) ((-1176 . -284) 129411) ((-1157 . -828) 129324) ((-1150 . -828) 129230) ((-1149 . -976) 129065) ((-1129 . -828) 128898) ((-1128 . -976) 128706) ((-1114 . -265) 128685) ((-1055 . -139) 128669) ((-991 . -97) T) ((-855 . -882) T) ((-73 . -1119) T) ((-674 . -284) 128607) ((-154 . -837) 128560) ((-605 . -356) 128532) ((-30 . -882) T) ((-1 . -561) 128514) ((-1031 . -97) T) ((-996 . -23) T) ((-49 . -565) 128498) ((-996 . -1025) T) ((-928 . -383) 128470) ((-546 . -828) 128383) ((-412 . -97) T) ((-129 . -284) NIL) ((-800 . -970) T) ((-769 . -783) 128362) ((-79 . -1119) T) ((-648 . -265) T) ((-39 . -977) T) ((-534 . -157) T) ((-485 . -157) T) ((-479 . -561) 128344) ((-154 . -589) 128254) ((-475 . -561) 128236) ((-325 . -135) 128218) ((-325 . -133) T) ((-333 . -1025) T) ((-327 . -1025) T) ((-319 . -1025) T) ((-929 . -282) T) ((-842 . -282) T) ((-800 . -220) T) ((-103 . -1025) T) ((-800 . -210) 128197) ((-1149 . -107) 128018) ((-1128 . -107) 127807) ((-222 . -1153) 127791) ((-521 . -781) T) ((-333 . -23) T) ((-328 . -323) T) ((-290 . -284) 127778) ((-287 . -284) 127719) ((-327 . -23) T) ((-293 . -124) T) ((-319 . -23) T) ((-929 . -946) T) ((-103 . -23) T) ((-222 . -554) 127696) ((-1151 . -37) 127588) ((-1138 . -837) 127567) ((-108 . -1013) T) ((-959 . -97) T) ((-1138 . -589) 127492) ((-799 . -730) NIL) ((-788 . -589) 127466) ((-799 . -727) NIL) ((-752 . -814) NIL) ((-799 . -663) T) ((-1002 . -482) 127339) ((-718 . -482) 127287) ((-716 . -482) 127239) ((-528 . -589) 127226) ((-752 . -961) 127056) ((-427 . -482) 126999) ((-362 . -363) T) ((-58 . -1119) T) ((-566 . -783) 126978) ((-469 . -602) T) ((-1055 . -902) 126947) ((-928 . -425) T) ((-636 . -781) T) ((-478 . -728) T) ((-447 . -976) 126782) ((-317 . -1013) T) ((-287 . -1060) NIL) ((-264 . -124) T) ((-368 . -1013) T) ((-631 . -344) 126749) ((-798 . -977) T) ((-200 . -565) 126726) ((-301 . -261) 126703) ((-447 . -107) 126524) ((-1149 . -970) T) ((-1128 . -970) T) ((-752 . -351) 126508) ((-154 . -663) T) ((-595 . -97) T) ((-1149 . -220) 126487) ((-1149 . -210) 126439) ((-1128 . -210) 126344) ((-1128 . -220) 126323) ((-928 . -376) NIL) ((-611 . -583) 126271) ((-290 . -37) 126181) ((-287 . -37) 126110) ((-67 . -561) 126092) ((-293 . -462) 126058) ((-1093 . -263) 126037) ((-1026 . -1025) 125968) ((-81 . -1119) T) ((-59 . -561) 125950) ((-451 . -263) 125929) ((-1178 . -961) 125906) ((-1073 . -1013) T) ((-1026 . -23) 125777) ((-752 . -828) 125713) ((-1138 . -663) T) ((-1015 . -1119) T) ((-1002 . -265) 125644) ((-821 . -97) T) ((-718 . -265) 125555) ((-301 . -19) 125539) ((-57 . -263) 125516) ((-716 . -265) 125447) ((-788 . -663) T) ((-113 . -781) NIL) ((-484 . -263) 125424) ((-301 . -554) 125401) ((-465 . -263) 125378) ((-427 . -265) 125309) ((-959 . -284) 125160) ((-528 . -663) T) ((-603 . -561) 125142) ((-222 . -562) 125103) ((-222 . -561) 125015) ((-1056 . -33) T) ((-871 . -1119) T) ((-317 . -654) 124960) ((-611 . -25) T) ((-611 . -21) T) ((-447 . -970) T) ((-579 . -391) 124925) ((-555 . -391) 124890) ((-1031 . -1060) T) ((-534 . -265) T) ((-485 . -265) T) ((-1150 . -282) 124869) ((-447 . -210) 124821) ((-447 . -220) 124800) ((-1129 . -282) 124779) ((-996 . -124) T) ((-800 . -731) 124758) ((-132 . -97) T) ((-39 . -1013) T) ((-800 . -728) 124737) ((-587 . -935) 124721) ((-533 . -977) T) ((-521 . -977) T) ((-464 . -977) T) ((-381 . -425) T) ((-333 . -124) T) ((-290 . -374) 124705) ((-287 . -374) 124666) ((-327 . -124) T) ((-319 . -124) T) ((-1129 . -946) NIL) ((-1008 . -561) 124633) ((-103 . -124) T) ((-1031 . -37) 124620) ((-849 . -1013) T) ((-707 . -1013) T) ((-612 . -1013) T) ((-638 . -135) T) ((-112 . -135) T) ((-1185 . -21) T) ((-1185 . -25) T) ((-1183 . -21) T) ((-1183 . -25) T) ((-605 . -976) 124604) 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122221) ((-891 . -21) 122176) ((-751 . -21) 122087) ((-751 . -25) 121939) ((-568 . -977) T) ((-1086 . -513) 121918) ((-1080 . -46) 121895) ((-329 . -970) T) ((-326 . -970) T) ((-454 . -23) 121766) ((-318 . -970) T) ((-240 . -970) T) ((-224 . -970) T) ((-1036 . -46) 121738) ((-113 . -977) T) ((-958 . -589) 121712) ((-885 . -33) T) ((-329 . -210) 121691) ((-329 . -220) T) ((-326 . -210) 121670) ((-224 . -300) 121627) ((-326 . -220) T) ((-318 . -210) 121606) ((-318 . -220) T) ((-240 . -300) 121578) ((-240 . -210) 121557) ((-1065 . -139) 121541) ((-227 . -828) 121474) ((-226 . -828) 121407) ((-998 . -783) T) ((-1132 . -1119) T) ((-388 . -1025) T) ((-974 . -23) T) ((-838 . -970) T) ((-296 . -589) 121389) ((-948 . -781) T) ((-1114 . -927) 121355) ((-1081 . -848) 121334) ((-1075 . -848) 121313) ((-838 . -220) T) ((-753 . -337) 121292) ((-359 . -23) T) ((-123 . -1013) 121270) ((-117 . -1013) 121248) ((-838 . -210) T) ((-1075 . -756) NIL) ((-353 . -589) 121213) ((-798 . -654) 121200) ((-967 . -139) 121165) ((-39 . -157) T) ((-631 . -385) 121147) ((-649 . -284) 121134) ((-770 . -589) 121094) ((-763 . -589) 121068) ((-293 . -25) T) ((-293 . -21) T) ((-599 . -261) 121047) ((-533 . -1013) T) ((-521 . -1013) T) ((-464 . -1013) T) ((-222 . -263) 121024) ((-287 . -208) 120985) ((-1080 . -814) NIL) ((-1036 . -814) 120844) ((-1080 . -961) 120727) ((-1036 . -961) 120612) ((-166 . -561) 120594) ((-787 . -961) 120492) ((-718 . -261) 120419) ((-753 . -1025) T) ((-958 . -663) T) ((-552 . -592) 120403) ((-967 . -902) 120332) ((-924 . -97) T) ((-753 . -23) T) ((-649 . -1060) 120310) ((-631 . -977) T) ((-552 . -347) 120294) ((-325 . -425) T) ((-317 . -265) T) ((-1166 . -1013) T) ((-373 . -97) T) ((-264 . -21) T) ((-264 . -25) T) ((-335 . -663) T) ((-636 . -1013) T) ((-335 . -446) T) ((-1114 . -561) 120276) ((-1080 . -351) 120260) ((-1036 . -351) 120244) ((-948 . -385) 120206) ((-129 . -206) 120188) ((-353 . -730) T) ((-353 . -727) T) ((-798 . -157) T) ((-353 . -663) T) ((-648 . -561) 120170) ((-649 . -37) 119999) ((-1165 . -1163) 119983) ((-325 . -376) T) ((-1165 . -1013) 119933) ((-533 . -654) 119920) ((-521 . -654) 119907) ((-464 . -654) 119872) ((-290 . -573) 119851) ((-770 . -663) T) ((-763 . -663) T) ((-587 . -1119) T) ((-996 . -583) 119799) ((-1080 . -828) 119743) ((-1036 . -828) 119727) ((-603 . -976) 119711) ((-103 . -583) 119693) ((-454 . -124) 119564) ((-1086 . -1025) T) ((-880 . -46) 119533) ((-568 . -1013) T) ((-603 . -107) 119512) ((-301 . -263) 119489) ((-453 . -46) 119446) ((-1086 . -23) T) ((-113 . -1013) T) ((-98 . -97) 119424) ((-1175 . -1025) T) ((-974 . -124) T) ((-948 . -977) T) ((-755 . -961) 119408) ((-928 . -661) 119380) ((-1175 . -23) T) ((-636 . -654) 119345) ((-538 . -561) 119327) ((-360 . -961) 119311) ((-328 . -977) T) ((-359 . -124) T) ((-298 . -961) 119295) ((-202 . -814) 119277) ((-929 . -848) T) ((-89 . -33) T) ((-929 . -756) T) ((-842 . -848) T) ((-458 . -1123) T) ((-1100 . -561) 119259) ((-1018 . -1013) T) ((-195 . -1123) T) ((-924 . -284) 119224) ((-202 . -961) 119184) ((-39 . -265) T) ((-996 . -21) T) ((-996 . -25) T) ((-1031 . -764) T) ((-458 . -513) T) ((-333 . -25) T) ((-195 . -513) T) ((-333 . -21) T) ((-327 . -25) T) ((-327 . -21) T) ((-651 . -589) 119144) ((-319 . -25) T) ((-319 . -21) T) ((-103 . -25) T) ((-103 . -21) T) ((-47 . -977) T) ((-533 . -157) T) ((-521 . -157) T) ((-464 . -157) T) ((-599 . -561) 119126) ((-674 . -673) 119110) ((-310 . -561) 119092) ((-66 . -357) T) ((-66 . -369) T) ((-1015 . -102) 119076) ((-981 . -814) 119058) ((-880 . -814) 118983) ((-594 . -1025) T) ((-568 . -654) 118970) ((-453 . -814) NIL) ((-1055 . -97) T) ((-981 . -961) 118952) ((-92 . -561) 118934) ((-450 . -135) T) ((-880 . -961) 118816) ((-113 . -654) 118761) ((-594 . -23) T) ((-453 . -961) 118639) ((-1002 . -562) NIL) ((-1002 . -561) 118621) ((-718 . -562) NIL) ((-718 . -561) 118582) ((-716 . -562) 118217) ((-716 . -561) 118131) ((-1026 . -583) 118039) ((-434 . -561) 118021) ((-427 . -561) 118003) ((-427 . -562) 117864) ((-959 . -206) 117810) ((-122 . -33) T) ((-753 . -124) T) ((-800 . -837) 117789) ((-590 . -561) 117771) ((-329 . -1182) 117755) ((-326 . -1182) 117739) ((-318 . -1182) 117723) ((-123 . -482) 117656) ((-117 . -482) 117589) ((-479 . -728) T) ((-479 . -731) T) ((-478 . -730) T) ((-98 . -284) 117527) ((-199 . -97) 117505) ((-631 . -1013) T) ((-636 . -157) T) ((-800 . -589) 117457) ((-63 . -358) T) ((-251 . -561) 117439) ((-63 . -369) T) ((-880 . -351) 117423) ((-798 . -265) T) ((-49 . -561) 117405) ((-924 . -37) 117353) ((-534 . -561) 117335) ((-453 . -351) 117319) ((-534 . -562) 117301) ((-485 . -561) 117283) ((-838 . -1182) 117270) ((-799 . -1119) T) ((-638 . -425) T) ((-464 . -482) 117236) ((-458 . -337) T) ((-329 . -342) 117215) ((-326 . -342) 117194) ((-318 . -342) 117173) ((-195 . -337) T) ((-651 . -663) T) ((-112 . -425) T) ((-1186 . -1177) 117157) ((-799 . -812) 117134) ((-799 . -814) NIL) ((-891 . -783) 117033) ((-751 . -783) 116984) ((-595 . -597) 116968) ((-1106 . -33) T) ((-156 . -561) 116950) ((-1026 . -21) 116861) ((-1026 . -25) 116713) ((-799 . -961) 116690) ((-880 . -828) 116671) ((-1138 . -46) 116648) ((-838 . -342) T) ((-57 . -592) 116632) ((-484 . -592) 116616) ((-453 . -828) 116593) ((-69 . -414) T) ((-69 . -369) T) ((-465 . -592) 116577) ((-57 . -347) 116561) ((-568 . -157) T) ((-484 . -347) 116545) ((-465 . -347) 116529) ((-763 . -646) 116513) ((-1080 . -282) 116492) ((-1086 . -124) T) ((-113 . -157) T) ((-1055 . -284) 116430) ((-154 . -1119) T) ((-579 . -681) 116414) ((-555 . -681) 116398) ((-1175 . -124) T) ((-1150 . -848) 116377) ((-1129 . -848) 116356) ((-1129 . -756) NIL) ((-631 . -654) 116306) ((-1128 . -837) 116259) ((-948 . -1013) T) ((-799 . -351) 116236) ((-799 . -312) 116213) ((-833 . -1025) T) ((-154 . -812) 116197) ((-154 . -814) 116122) ((-458 . -1025) T) ((-328 . -1013) T) ((-195 . -1025) T) ((-74 . -414) T) ((-74 . -369) T) ((-154 . -961) 116020) ((-293 . -783) T) ((-1165 . -482) 115953) ((-1149 . -589) 115850) ((-1128 . -589) 115720) ((-800 . -730) 115699) ((-800 . -727) 115678) ((-800 . -663) T) ((-458 . -23) T) ((-200 . -561) 115660) ((-158 . -425) T) ((-199 . -284) 115598) ((-84 . -414) T) ((-84 . -369) T) ((-195 . -23) T) ((-1187 . -1180) 115577) ((-533 . -265) T) ((-521 . -265) T) ((-616 . -961) 115561) ((-464 . -265) T) ((-128 . -443) 115516) ((-47 . -1013) T) ((-649 . -208) 115500) ((-799 . -828) NIL) ((-1138 . -814) NIL) ((-817 . -97) T) ((-813 . -97) T) ((-362 . -1013) T) ((-154 . -351) 115484) ((-154 . -312) 115468) ((-1138 . -961) 115351) ((-788 . -961) 115249) ((-1051 . -97) T) ((-594 . -124) T) ((-113 . -482) 115157) ((-603 . -728) 115136) ((-603 . -731) 115115) ((-528 . -961) 115097) ((-269 . -1172) 115067) ((-794 . -97) T) ((-890 . -513) 115046) ((-1114 . -976) 114929) ((-454 . -583) 114837) ((-832 . -1013) T) ((-948 . -654) 114774) ((-648 . -976) 114739) ((-552 . -33) T) ((-1056 . -1119) T) ((-1114 . -107) 114608) ((-447 . -589) 114505) ((-328 . -654) 114450) ((-154 . -828) 114409) ((-636 . -265) T) ((-631 . -157) T) ((-648 . -107) 114365) ((-1191 . -977) T) ((-1138 . -351) 114349) ((-392 . -1123) 114327) ((-287 . -781) NIL) ((-392 . -513) T) ((-202 . -282) T) ((-1128 . -727) 114280) ((-1128 . -730) 114233) ((-1149 . -663) T) ((-1128 . -663) T) ((-47 . -654) 114198) ((-202 . -946) T) ((-325 . -1172) 114175) ((-1151 . -385) 114141) ((-655 . -663) T) ((-1138 . -828) 114085) ((-108 . -561) 114067) ((-108 . -562) 114049) ((-655 . -446) T) ((-454 . -21) 113960) ((-123 . -460) 113944) ((-117 . -460) 113928) ((-454 . -25) 113780) ((-568 . -265) T) ((-538 . -976) 113755) ((-411 . -1013) T) ((-981 . -282) T) ((-113 . -265) T) ((-1017 . -97) T) ((-928 . -97) T) ((-538 . -107) 113723) ((-1051 . -284) 113661) ((-1114 . -970) T) ((-981 . -946) T) ((-64 . -1119) T) ((-974 . -25) T) ((-974 . -21) T) ((-648 . -970) T) ((-359 . -21) T) ((-359 . -25) T) ((-631 . -482) NIL) ((-948 . -157) T) ((-648 . -220) T) ((-981 . -506) T) ((-471 . -97) T) ((-328 . -157) T) ((-317 . -561) 113643) ((-368 . -561) 113625) ((-447 . -663) T) ((-1031 . -781) T) ((-820 . -961) 113593) ((-103 . -783) T) ((-599 . -976) 113577) ((-458 . -124) T) ((-1151 . -977) T) ((-195 . -124) T) ((-1065 . -97) 113555) ((-94 . -1013) T) ((-222 . -607) 113539) ((-222 . -592) 113523) ((-599 . -107) 113502) ((-290 . -385) 113486) ((-222 . -347) 113470) ((-1068 . -212) 113417) ((-924 . -208) 113401) ((-72 . -1119) T) ((-47 . -157) T) ((-638 . -361) T) ((-638 . -131) T) ((-1186 . -97) T) ((-1002 . -976) 113244) ((-240 . -837) 113223) ((-224 . -837) 113202) ((-718 . -976) 113025) ((-716 . -976) 112868) ((-556 . -1119) T) ((-1073 . -561) 112850) ((-1002 . -107) 112679) ((-967 . -97) T) ((-448 . -1119) T) ((-434 . -976) 112650) ((-427 . -976) 112493) ((-605 . -589) 112477) ((-799 . -282) T) ((-718 . -107) 112286) ((-716 . -107) 112115) ((-329 . -589) 112067) ((-326 . -589) 112019) ((-318 . -589) 111971) ((-240 . -589) 111896) ((-224 . -589) 111821) ((-1067 . -783) T) ((-1003 . -961) 111805) ((-434 . -107) 111766) ((-427 . -107) 111595) ((-992 . -961) 111572) ((-925 . -33) T) ((-893 . -561) 111533) ((-885 . -1119) T) ((-122 . -935) 111517) ((-890 . -1025) T) ((-799 . -946) NIL) ((-672 . -1025) T) ((-652 . -1025) T) ((-1165 . -460) 111501) ((-1051 . -37) 111461) ((-890 . -23) T) ((-776 . -97) T) ((-753 . -21) T) ((-753 . -25) T) ((-672 . -23) T) ((-652 . -23) T) ((-106 . -602) T) ((-838 . -589) 111426) ((-534 . -976) 111391) ((-485 . -976) 111336) ((-204 . -55) 111294) ((-426 . -23) T) ((-381 . -97) T) ((-239 . -97) T) ((-631 . -265) T) ((-794 . -37) 111264) ((-534 . -107) 111220) ((-485 . -107) 111149) ((-392 . -1025) T) ((-290 . -977) 111040) ((-287 . -977) T) ((-599 . -970) T) ((-1191 . -1013) T) ((-154 . -282) 110971) ((-392 . -23) T) ((-39 . -561) 110953) ((-39 . -562) 110937) ((-103 . -918) 110919) ((-112 . -797) 110903) ((-47 . -482) 110869) ((-1106 . -935) 110853) ((-1089 . -561) 110835) ((-1093 . -33) T) ((-849 . -561) 110817) ((-1026 . -783) 110768) ((-707 . -561) 110750) 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. -210) T) ((-464 . -220) T) ((-464 . -210) T) ((-707 . -728) T) ((-707 . -731) T) ((-1059 . -212) 102633) ((-1002 . -837) 102612) ((-112 . -37) 102599) ((-188 . -736) T) ((-187 . -736) T) ((-186 . -736) T) ((-185 . -736) T) ((-800 . -946) 102578) ((-1176 . -460) 102562) ((-718 . -837) 102541) ((-716 . -837) 102520) ((-1093 . -1119) T) ((-427 . -837) 102499) ((-674 . -460) 102483) ((-1002 . -589) 102408) ((-718 . -589) 102333) ((-568 . -976) 102320) ((-451 . -1119) T) ((-317 . -342) T) ((-129 . -460) 102302) ((-716 . -589) 102227) ((-1050 . -1119) T) ((-434 . -589) 102198) ((-240 . -814) 102057) ((-224 . -814) NIL) ((-113 . -976) 102002) ((-427 . -589) 101927) ((-605 . -961) 101904) ((-568 . -107) 101889) ((-329 . -961) 101873) ((-326 . -961) 101857) ((-318 . -961) 101841) ((-240 . -961) 101687) ((-224 . -961) 101565) ((-113 . -107) 101494) ((-57 . -1119) T) ((-486 . -1119) T) ((-484 . -1119) T) ((-466 . -1119) T) ((-465 . -1119) T) ((-411 . -561) 101476) ((-408 . -561) 101458) ((-3 . 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. -1143) 96698) ((-1093 . -1096) 96677) ((-991 . -561) 96659) ((-588 . -139) 96643) ((-576 . -139) 96589) ((-1093 . -102) 96539) ((-451 . -1096) 96518) ((-458 . -135) T) ((-458 . -133) NIL) ((-1031 . -562) 96433) ((-412 . -561) 96415) ((-195 . -135) T) ((-195 . -133) NIL) ((-1031 . -561) 96397) ((-51 . -97) T) ((-1129 . -583) 96349) ((-451 . -102) 96299) ((-919 . -23) T) ((-1187 . -37) 96269) ((-1080 . -1025) T) ((-1036 . -1025) T) ((-981 . -1123) T) ((-787 . -1025) T) ((-880 . -1123) 96248) ((-453 . -1123) 96227) ((-668 . -783) 96206) ((-981 . -513) T) ((-880 . -513) 96137) ((-1080 . -23) T) ((-1036 . -23) T) ((-787 . -23) T) ((-453 . -513) 96068) ((-1051 . -654) 96000) ((-1055 . -482) 95933) ((-959 . -562) NIL) ((-959 . -561) 95915) ((-794 . -654) 95885) ((-1114 . -46) 95854) ((-227 . -124) T) ((-226 . -124) T) ((-1017 . -1013) T) ((-928 . -1013) T) ((-60 . -561) 95836) ((-1075 . -783) NIL) ((-948 . -728) T) ((-948 . -731) T) ((-1191 . -976) 95823) ((-1191 . -107) 95808) ((-798 . -589) 95795) ((-1157 . -25) T) ((-1157 . -21) T) ((-1150 . -21) T) ((-1150 . -25) T) ((-1129 . -21) T) ((-1129 . -25) T) ((-951 . -139) 95779) ((-800 . -756) 95758) ((-800 . -848) T) ((-649 . -261) 95685) ((-547 . -21) T) ((-547 . -25) T) ((-546 . -21) T) ((-39 . -663) T) ((-199 . -482) 95618) ((-546 . -25) T) ((-449 . -139) 95602) ((-436 . -139) 95586) ((-849 . -663) T) ((-707 . -729) T) ((-707 . -730) T) ((-471 . -1013) T) ((-707 . -663) T) ((-202 . -337) T) ((-1065 . -1013) 95564) ((-799 . -1123) T) ((-595 . -561) 95546) ((-799 . -513) T) ((-631 . -342) NIL) ((-333 . -1172) 95530) ((-611 . -97) T) ((-327 . -1172) 95514) ((-319 . -1172) 95498) ((-1186 . -1013) T) ((-487 . -783) 95477) ((-753 . -425) 95456) ((-967 . -1013) T) ((-967 . -989) 95385) ((-951 . -902) 95354) ((-755 . -1025) T) ((-928 . -654) 95299) ((-360 . -1025) T) ((-449 . -902) 95268) ((-436 . -902) 95237) ((-106 . -139) 95219) ((-71 . -561) 95201) ((-821 . -561) 95183) ((-996 . -661) 95162) ((-1191 . -970) T) ((-752 . 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92673) ((-1178 . -25) T) ((-1178 . -21) T) ((-1117 . -97) 92651) ((-1019 . -369) T) ((-568 . -589) 92638) ((-427 . -814) NIL) ((-615 . -97) 92616) ((-1002 . -961) 92445) ((-799 . -23) T) ((-718 . -961) 92307) ((-716 . -961) 92166) ((-113 . -589) 92111) ((-427 . -961) 91989) ((-590 . -961) 91973) ((-571 . -97) T) ((-199 . -460) 91957) ((-1165 . -33) T) ((-579 . -654) 91941) ((-555 . -654) 91925) ((-611 . -37) 91885) ((-293 . -97) T) ((-83 . -561) 91867) ((-49 . -961) 91851) ((-1031 . -976) 91838) ((-1002 . -351) 91822) ((-58 . -55) 91784) ((-636 . -730) T) ((-636 . -727) T) ((-534 . -961) 91771) ((-485 . -961) 91748) ((-636 . -663) T) ((-290 . -970) 91639) ((-298 . -124) T) ((-287 . -970) T) ((-154 . -1025) T) ((-718 . -351) 91623) ((-716 . -351) 91607) ((-44 . -139) 91557) ((-929 . -918) 91539) ((-427 . -351) 91523) ((-381 . -157) T) ((-290 . -220) 91502) ((-287 . -220) T) ((-287 . -210) NIL) ((-269 . -1013) 91285) ((-202 . -124) T) ((-1031 . -107) 91270) ((-154 . -23) T) ((-735 . -135) 91249) ((-735 . -133) 91228) ((-227 . -583) 91136) ((-226 . -583) 91044) ((-293 . -259) 91010) ((-1065 . -482) 90943) ((-1044 . -1013) T) ((-202 . -979) T) ((-751 . -284) 90881) ((-1002 . -828) 90816) ((-718 . -828) 90760) ((-716 . -828) 90744) ((-1185 . -37) 90714) ((-1183 . -37) 90684) ((-1138 . -1025) T) ((-788 . -1025) T) ((-427 . -828) 90661) ((-790 . -1013) T) ((-1138 . -23) T) ((-528 . -1025) T) ((-788 . -23) T) ((-568 . -663) T) ((-329 . -848) T) ((-326 . -848) T) ((-264 . -97) T) ((-318 . -848) T) ((-981 . -124) T) ((-880 . -124) T) ((-113 . -730) NIL) ((-113 . -727) NIL) ((-113 . -663) T) ((-631 . -837) NIL) ((-967 . -482) 90562) ((-453 . -124) T) ((-528 . -23) T) ((-615 . -284) 90500) ((-579 . -698) T) ((-555 . -698) T) ((-1129 . -783) NIL) ((-928 . -265) T) ((-227 . -21) T) ((-631 . -589) 90450) ((-325 . -1013) T) ((-227 . -25) T) ((-226 . -21) T) ((-226 . -25) T) ((-140 . -37) 90434) ((-2 . -97) T) ((-838 . -848) T) ((-454 . -1172) 90404) ((-200 . -961) 90381) 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89435) ((-1082 . -133) 89414) ((-1082 . -135) 89393) ((-353 . -513) T) ((-1081 . -135) 89372) ((-1081 . -133) 89351) ((-1075 . -133) 89258) ((-381 . -265) T) ((-1075 . -135) 89165) ((-1037 . -135) 89144) ((-1037 . -133) 89123) ((-293 . -37) 88964) ((-154 . -124) T) ((-287 . -731) NIL) ((-287 . -728) NIL) ((-595 . -970) T) ((-47 . -589) 88929) ((-919 . -21) T) ((-123 . -935) 88913) ((-117 . -935) 88897) ((-919 . -25) T) ((-829 . -115) 88881) ((-1067 . -97) T) ((-752 . -783) 88860) ((-1138 . -124) T) ((-1080 . -25) T) ((-1080 . -21) T) ((-788 . -124) T) ((-1036 . -25) T) ((-1036 . -21) T) ((-787 . -25) T) ((-787 . -21) T) ((-718 . -282) 88839) ((-588 . -97) 88817) ((-576 . -97) T) ((-1068 . -284) 88612) ((-528 . -124) T) ((-566 . -781) 88591) ((-1065 . -460) 88575) ((-1059 . -139) 88525) ((-1055 . -561) 88487) ((-1055 . -562) 88448) ((-948 . -727) T) ((-948 . -730) T) ((-948 . -663) T) ((-455 . -284) 88386) ((-426 . -391) 88356) ((-325 . -157) T) ((-264 . -37) 88343) ((-250 . -97) T) 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87448) ((-1082 . -1108) 87414) ((-1082 . -1105) 87380) ((-1067 . -284) NIL) ((-87 . -370) T) ((-87 . -369) T) ((-996 . -1060) 87359) ((-1081 . -1105) 87325) ((-1081 . -1108) 87291) ((-958 . -23) T) ((-1081 . -91) 87257) ((-528 . -462) T) ((-1081 . -34) 87223) ((-1075 . -1105) 87189) ((-1075 . -1108) 87155) ((-1075 . -91) 87121) ((-335 . -1025) T) ((-333 . -1060) 87100) ((-327 . -1060) 87079) ((-319 . -1060) 87058) ((-1075 . -34) 87024) ((-1037 . -34) 86990) ((-1037 . -91) 86956) ((-103 . -1060) T) ((-1037 . -1108) 86922) ((-769 . -977) 86901) ((-588 . -284) 86839) ((-576 . -284) 86690) ((-1037 . -1105) 86656) ((-649 . -970) T) ((-981 . -583) 86638) ((-996 . -37) 86506) ((-880 . -583) 86454) ((-929 . -135) T) ((-929 . -133) NIL) ((-353 . -1025) T) ((-298 . -25) T) ((-296 . -23) T) ((-871 . -783) 86433) ((-649 . -300) 86410) ((-453 . -583) 86358) ((-39 . -961) 86248) ((-638 . -654) 86235) ((-649 . -210) T) ((-313 . -1013) T) ((-158 . -1013) T) ((-305 . -783) T) ((-392 . -425) 86185) ((-353 . -23) T) ((-333 . -37) 86150) ((-327 . -37) 86115) ((-319 . -37) 86080) ((-78 . -414) T) ((-78 . -369) T) ((-202 . -25) T) ((-202 . -21) T) ((-770 . -1025) T) ((-103 . -37) 86030) ((-763 . -1025) T) ((-710 . -1013) T) ((-112 . -654) 86017) ((-612 . -961) 86001) ((-560 . -97) T) ((-770 . -23) T) ((-763 . -23) T) ((-1065 . -261) 85978) ((-1026 . -284) 85916) ((-1015 . -212) 85900) ((-62 . -370) T) ((-62 . -369) T) ((-106 . -97) T) ((-39 . -351) 85877) ((-594 . -785) 85861) ((-981 . -21) T) ((-981 . -25) T) ((-751 . -208) 85831) ((-880 . -25) T) ((-880 . -21) T) ((-566 . -977) T) ((-453 . -25) T) ((-453 . -21) T) ((-951 . -284) 85769) ((-817 . -561) 85751) ((-813 . -561) 85733) ((-227 . -783) 85684) ((-226 . -783) 85635) ((-490 . -482) 85568) ((-799 . -583) 85545) ((-449 . -284) 85483) ((-436 . -284) 85421) ((-325 . -265) T) ((-1065 . -1153) 85405) ((-1051 . -561) 85367) ((-1051 . -562) 85328) ((-1049 . -97) T) ((-924 . -976) 85224) ((-39 . -828) 85176) ((-1065 . -554) 85153) 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-133) 84246) ((-1149 . -1123) 84225) ((-1129 . -133) 84132) ((-1129 . -135) 84039) ((-1128 . -1123) 84018) ((-353 . -124) T) ((-521 . -814) 84000) ((0 . -1013) T) ((-158 . -157) T) ((-154 . -21) T) ((-154 . -25) T) ((-48 . -1013) T) ((-1151 . -589) 83905) ((-1149 . -513) 83856) ((-651 . -1025) T) ((-1128 . -513) 83807) ((-521 . -961) 83789) ((-546 . -135) 83768) ((-546 . -133) 83747) ((-464 . -961) 83690) ((-85 . -358) T) ((-85 . -369) T) ((-800 . -337) T) ((-770 . -124) T) ((-763 . -124) T) ((-651 . -23) T) ((-471 . -561) 83672) ((-1187 . -977) T) ((-353 . -979) T) ((-950 . -1013) 83650) ((-829 . -33) T) ((-454 . -284) 83588) ((-1065 . -562) 83549) ((-1065 . -561) 83481) ((-1080 . -783) 83460) ((-44 . -97) T) ((-1036 . -783) 83439) ((-753 . -97) T) ((-1138 . -25) T) ((-1138 . -21) T) ((-788 . -25) T) ((-43 . -341) 83423) ((-788 . -21) T) ((-668 . -425) 83374) ((-1186 . -561) 83356) ((-528 . -25) T) ((-528 . -21) T) ((-364 . -1013) T) ((-974 . -284) 83294) ((-566 . -1013) T) ((-636 . -814) 83276) ((-1165 . -1119) T) ((-204 . -284) 83214) ((-132 . -342) T) ((-967 . -562) 83156) ((-967 . -561) 83099) ((-287 . -837) NIL) ((-636 . -961) 83044) ((-648 . -848) T) ((-447 . -1123) 83023) ((-1081 . -425) 83002) ((-1075 . -425) 82981) ((-304 . -97) T) ((-800 . -1025) T) ((-290 . -589) 82803) ((-287 . -589) 82732) ((-447 . -513) 82683) ((-313 . -482) 82649) ((-507 . -139) 82599) ((-39 . -282) T) ((-776 . -561) 82581) ((-638 . -265) T) ((-800 . -23) T) ((-353 . -462) T) ((-996 . -208) 82551) ((-480 . -97) T) ((-381 . -562) 82359) ((-381 . -561) 82341) ((-239 . -561) 82323) ((-112 . -265) T) ((-1151 . -663) T) ((-1149 . -337) 82302) ((-1128 . -337) 82281) ((-1176 . -33) T) ((-113 . -1119) T) ((-103 . -208) 82263) ((-1086 . -97) T) ((-450 . -1013) T) ((-490 . -460) 82247) ((-674 . -33) T) ((-454 . -37) 82217) ((-129 . -33) T) ((-113 . -812) 82194) ((-113 . -814) NIL) ((-568 . -961) 82079) ((-587 . -783) 82058) ((-1175 . -97) T) ((-270 . -97) T) ((-649 . -342) 82037) ((-113 . -961) 82014) ((-364 . -654) 81998) ((-566 . -654) 81982) ((-44 . -284) 81786) ((-752 . -133) 81765) ((-752 . -135) 81744) ((-1186 . -356) 81723) ((-755 . -783) T) ((-1167 . -1013) T) ((-1068 . -206) 81670) ((-360 . -783) 81649) ((-1157 . -1108) 81615) ((-1157 . -1105) 81581) ((-1150 . -1105) 81547) ((-483 . -124) T) ((-1150 . -1108) 81513) ((-1129 . -1105) 81479) ((-1129 . -1108) 81445) ((-1157 . -34) 81411) ((-1157 . -91) 81377) ((-579 . -561) 81346) ((-555 . -561) 81315) ((-202 . -783) T) ((-1150 . -91) 81281) ((-1150 . -34) 81247) ((-1149 . -1025) T) ((-1031 . -589) 81234) ((-1129 . -91) 81200) ((-1128 . -1025) T) ((-544 . -139) 81182) ((-996 . -323) 81161) ((-113 . -351) 81138) ((-113 . -312) 81115) ((-158 . -265) T) ((-1129 . -34) 81081) ((-798 . -282) T) ((-287 . -730) NIL) ((-287 . -727) NIL) ((-290 . -663) 80931) ((-287 . -663) T) ((-447 . -337) 80910) ((-333 . -323) 80889) ((-327 . -323) 80868) ((-319 . -323) 80847) ((-290 . -446) 80826) ((-1149 . -23) T) ((-1128 . -23) T) 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77337) ((-611 . -1013) T) ((-611 . -973) 77277) ((-1082 . -1156) 77261) ((-1082 . -1143) 77238) ((-458 . -1060) T) ((-1081 . -1148) 77199) ((-1081 . -1143) 77169) ((-1081 . -1146) 77153) ((-195 . -1060) T) ((-317 . -848) T) ((-754 . -242) 77137) ((-579 . -107) 77116) ((-555 . -107) 77095) ((-1075 . -1127) 77056) ((-776 . -970) 77035) ((-1075 . -1143) 77012) ((-483 . -25) T) ((-464 . -277) T) ((-479 . -23) T) ((-478 . -25) T) ((-476 . -25) T) ((-475 . -23) T) ((-1075 . -1125) 76996) ((-381 . -970) T) ((-293 . -977) T) ((-631 . -282) T) ((-103 . -781) T) ((-381 . -220) T) ((-381 . -210) 76975) ((-649 . -663) T) ((-458 . -37) 76925) ((-195 . -37) 76875) ((-447 . -462) 76841) ((-1067 . -1053) T) ((-1014 . -97) T) ((-638 . -561) 76823) ((-638 . -562) 76738) ((-651 . -21) T) ((-651 . -25) T) ((-126 . -561) 76720) ((-112 . -561) 76702) ((-143 . -25) T) ((-1185 . -1013) T) ((-800 . -583) 76650) ((-1183 . -1013) T) ((-890 . -97) T) ((-672 . -97) T) ((-652 . -97) T) ((-426 . -97) T) ((-752 . 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-369) T) ((-603 . -23) T) ((-611 . -698) T) ((-1117 . -1013) 75425) ((-325 . -976) 75370) ((-615 . -1013) 75348) ((-981 . -135) T) ((-880 . -135) 75327) ((-880 . -133) 75306) ((-735 . -97) T) ((-140 . -654) 75290) ((-453 . -135) 75269) ((-453 . -133) 75248) ((-325 . -107) 75177) ((-996 . -977) T) ((-296 . -783) 75156) ((-1157 . -899) 75126) ((-571 . -1013) T) ((-1150 . -899) 75089) ((-479 . -124) T) ((-475 . -124) T) ((-270 . -206) 75039) ((-333 . -977) T) ((-327 . -977) T) ((-319 . -977) T) ((-269 . -970) 74982) ((-1129 . -899) 74952) ((-353 . -783) T) ((-103 . -977) T) ((-924 . -663) T) ((-798 . -848) T) ((-776 . -731) 74931) ((-776 . -728) 74910) ((-392 . -284) 74849) ((-441 . -97) T) ((-546 . -899) 74819) ((-293 . -1013) T) ((-381 . -731) 74798) ((-381 . -728) 74777) ((-469 . -460) 74759) ((-1151 . -961) 74725) ((-1149 . -21) T) ((-1149 . -25) T) ((-1128 . -21) T) ((-1128 . -25) T) ((-751 . -654) 74667) ((-636 . -378) T) ((-1176 . -1119) T) ((-1026 . -385) 74636) ((-928 . -342) 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-1013) T) ((-202 . -976) 5785) ((-800 . -265) T) ((-195 . -828) NIL) ((-769 . -1025) 5764) ((-57 . -1013) 5714) ((-486 . -1013) 5692) ((-484 . -1013) 5642) ((-466 . -1013) 5620) ((-465 . -1013) 5570) ((-533 . -97) T) ((-521 . -97) T) ((-464 . -97) T) ((-447 . -157) 5501) ((-333 . -848) T) ((-327 . -848) T) ((-319 . -848) T) ((-202 . -107) 5457) ((-769 . -23) 5409) ((-401 . -663) T) ((-103 . -848) T) ((-39 . -37) 5354) ((-103 . -756) T) ((-534 . -323) T) ((-485 . -323) T) ((-1128 . -482) 5214) ((-290 . -425) 5193) ((-287 . -425) T) ((-770 . -261) 5172) ((-313 . -124) T) ((-158 . -124) T) ((-269 . -25) 5037) ((-269 . -21) 4921) ((-44 . -1096) 4900) ((-64 . -561) 4882) ((-820 . -561) 4864) ((-552 . -482) 4797) ((-44 . -102) 4747) ((-1015 . -399) 4731) ((-1015 . -342) 4710) ((-982 . -1119) T) ((-981 . -976) 4697) ((-880 . -976) 4540) ((-453 . -976) 4383) ((-605 . -654) 4367) ((-981 . -107) 4352) ((-880 . -107) 4181) ((-450 . -337) T) ((-329 . -654) 4133) ((-326 . -654) 4085) ((-318 . -654) 4037) ((-240 . -654) 3886) ((-224 . -654) 3735) ((-871 . -592) 3719) ((-453 . -107) 3548) ((-1166 . -97) T) ((-871 . -347) 3532) ((-1129 . -837) NIL) ((-72 . -561) 3514) ((-890 . -46) 3493) ((-566 . -1025) T) ((-1 . -1013) T) ((-636 . -97) T) ((-1165 . -97) 3443) ((-1157 . -589) 3368) ((-1150 . -589) 3265) ((-122 . -460) 3249) ((-1101 . -561) 3231) ((-1003 . -561) 3213) ((-364 . -23) T) ((-992 . -561) 3195) ((-85 . -1119) T) ((-1129 . -589) 3047) ((-838 . -654) 3012) ((-566 . -23) T) ((-556 . -561) 2994) ((-556 . -562) NIL) ((-448 . -562) NIL) ((-448 . -561) 2976) ((-479 . -1013) T) ((-475 . -1013) T) ((-325 . -25) T) ((-325 . -21) T) ((-123 . -284) 2914) ((-117 . -284) 2852) ((-547 . -589) 2839) ((-202 . -970) T) ((-546 . -589) 2764) ((-353 . -927) T) ((-202 . -220) T) ((-202 . -210) T) ((-885 . -562) 2725) ((-885 . -561) 2637) ((-798 . -37) 2624) ((-1149 . -265) 2575) ((-1128 . -265) 2526) ((-1031 . -425) T) ((-471 . -783) T) ((-290 . -1048) 2505) ((-924 . -135) 2484) ((-924 . -133) 2463) ((-464 . -284) 2450) ((-270 . -1096) 2429) ((-450 . -1025) T) ((-799 . -976) 2374) ((-568 . -97) T) ((-1106 . -460) 2358) ((-227 . -342) 2337) ((-226 . -342) 2316) ((-270 . -102) 2266) ((-981 . -970) T) ((-113 . -97) T) ((-880 . -970) T) ((-799 . -107) 2195) ((-450 . -23) T) ((-453 . -970) T) ((-981 . -210) T) ((-880 . -300) 2164) ((-453 . -300) 2121) ((-329 . -157) T) ((-326 . -157) T) ((-318 . -157) T) ((-240 . -157) 2032) ((-224 . -157) 1943) ((-890 . -961) 1841) ((-672 . -961) 1812) ((-1018 . -97) T) ((-1006 . -561) 1779) ((-958 . -561) 1761) ((-1157 . -663) T) ((-1150 . -663) T) ((-1129 . -727) NIL) ((-154 . -976) 1671) ((-1129 . -730) NIL) ((-838 . -157) T) ((-1129 . -663) T) ((-1176 . -139) 1655) ((-928 . -316) 1629) ((-925 . -482) 1562) ((-776 . -783) 1541) ((-521 . -1060) T) ((-447 . -265) 1492) ((-547 . -663) T) ((-335 . -561) 1474) ((-296 . -561) 1456) ((-392 . -961) 1354) ((-546 . -663) T) ((-381 . -783) 1305) ((-154 . -107) 1201) ((-769 . -124) 1153) ((-674 . -139) 1137) ((-1165 . -284) 1075) ((-458 . -282) T) ((-353 . -561) 1042) ((-487 . -935) 1026) ((-353 . -562) 940) ((-195 . -282) T) ((-129 . -139) 922) ((-651 . -261) 901) ((-458 . -946) T) ((-533 . -37) 888) ((-521 . -37) 875) ((-464 . -37) 840) ((-195 . -946) T) ((-799 . -970) T) ((-770 . -561) 822) ((-763 . -561) 804) ((-761 . -561) 786) ((-752 . -837) 765) ((-1187 . -1025) T) ((-1138 . -976) 588) ((-788 . -976) 572) ((-799 . -220) T) ((-799 . -210) NIL) ((-627 . -1119) T) ((-1187 . -23) T) ((-752 . -589) 497) ((-507 . -1119) T) ((-392 . -312) 481) ((-528 . -976) 468) ((-1138 . -107) 277) ((-638 . -583) 259) ((-788 . -107) 238) ((-355 . -23) T) ((-1093 . -482) 30))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 71963093..1896b473 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,5 +1,5 @@ -(30 . 3409778139) +(30 . 3409817876) (4236 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| @@ -275,7 +275,7 @@ |NumericalIntegrationCategory| |NumericalOrdinaryDifferentialEquations| |NumericalQuadrature| |NumericTubePlot| |OrderedAbelianGroup| |OrderedAbelianMonoid| - |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |ObjectProperty| + |OrderedAbelianMonoidSup| |OrderedAbelianSemiGroup| |OrderedCancellationAbelianMonoid| |OctonionCategory&| |OctonionCategory| |OctonionCategoryFunctions2| |Octonion| |OrdinaryDifferentialEquationsSolverCategory| |ConstantLODE| @@ -338,8 +338,8 @@ |PlottablePlaneCurveCategory| |PrecomputedAssociatedEquations| |PrimitiveArrayFunctions2| |PrimitiveArray| |PrimitiveFunctionCategory| |PrimitiveElement| |IntegerPrimesPackage| - |PrintPackage| |PolynomialRing| |Product| |PropositionalFormula| - |PropositionalLogic| |PriorityQueueAggregate| + |PrintPackage| |PolynomialRing| |Product| |Property| + |PropositionalFormula| |PropositionalLogic| |PriorityQueueAggregate| |PseudoRemainderSequence| |Partition| |PowerSeriesCategory&| |PowerSeriesCategory| |PlottableSpaceCurveCategory| |PolynomialSetCategory&| |PolynomialSetCategory| @@ -460,648 +460,644 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |Category| |subscript| |removeZeroes| - |normalizedAssociate| |lazyGintegrate| |mat| |delta| |updateStatus!| - |createPrimitiveElement| |monic?| |leastPower| |groebner?| - |rightAlternative?| |mathieu11| |evenlambert| |power!| - |clearTheIFTable| |f02wef| |insertionSort!| |rotatez| |zeroVector| - |Ci| |round| |makeYoungTableau| |e01bef| |argscript| |diagonal?| - |conjugate| |components| |maxrow| |PDESolve| |setprevious!| - |OMgetVariable| |putGraph| |makeprod| |dot| |subtractIfCan| |declare| - |squareFreeLexTriangular| |matrixConcat3D| |c06frf| |OMputEndError| - |dark| |localAbs| |leadingSupport| |getMultiplicationTable| - |flexible?| |complexNumeric| |mainCoefficients| |middle| - |controlPanel| |alphabetic| |rotatex| |s17aff| |subPolSet?| - |bivariatePolynomials| |depth| |log| |fglmIfCan| |odd?| - |cRationalPower| |recip| |pdf2df| |coefficients| |forLoop| - |virtualDegree| |setImagSteps| |intChoose| |createLowComplexityTable| - |rightDivide| |kernels| |leadingTerm| |cPower| |shallowCopy| |ode1| - |comment| |hasSolution?| |internal?| |central?| |fortranLiteralLine| - |decreasePrecision| |solve1| |leaves| |normal?| |univariate| - |constantCoefficientRicDE| |cardinality| |binaryFunction| |lambda| - |makeSUP| |showArrayValues| |lyndon| |coefChoose| |cSinh| - |getOperands| |f2df| |OMlistCDs| |rowEch| |subResultantGcdEuclidean| - |showSummary| |aspFilename| |retractIfCan| |overlap| - |subresultantSequence| |returns| |clikeUniv| |linearPolynomials| - |acscIfCan| |transpose| |perfectSqrt| |characteristicSerie| - |rewriteSetByReducingWithParticularGenerators| |innerint| |HenselLift| - |position!| |rowEchelon| |open?| |createMultiplicationMatrix| - |createGenericMatrix| |bipolarCylindrical| |tValues| |lflimitedint| - |merge| |showAttributes| |certainlySubVariety?| |measure2Result| - |pop!| |unprotectedRemoveRedundantFactors| |binaryTournament| |pole?| - |selectsecond| |exponential| |karatsubaDivide| |monicRightDivide| - |unexpand| |number?| |leftNorm| |nlde| |SFunction| |pushdterm| - |tryFunctionalDecomposition?| |nthFractionalTerm| |OMlistSymbols| - |OMputObject| |tableForDiscreteLogarithm| |headRemainder| - |FormatRoman| |infLex?| |lieAlgebra?| |clearTheFTable| BY - |initiallyReduce| |badNum| |hessian| |showAll?| Y |d03edf| - |ScanFloatIgnoreSpacesIfCan| |top| |divisors| |subspace| |logpart| - |iteratedInitials| |optional?| |OMbindTCP| |rule| |bsolve| |deref| - |continue| |matrix| |void| |s14baf| |possiblyInfinite?| |setEpilogue!| - |cyclotomicFactorization| |lowerPolynomial| |currentCategoryFrame| - |doubleRank| |infinityNorm| |innerEigenvectors| |setLabelValue| - |pattern| |composite| |e02bbf| - |solveLinearPolynomialEquationByRecursion| |jacobiIdentity?| |formula| - |generator| |mapExpon| |setPoly| |someBasis| |setProperty| - |complexNormalize| |sizeLess?| |map| |orOperands| |setMaxPoints3D| - |genericLeftTrace| |cAcsch| |gcdPrimitive| |exQuo| |nonLinearPart| - |lastSubResultantEuclidean| |useSingleFactorBound| - |generalizedContinuumHypothesisAssumed| |laurentIfCan| |returnTypeOf| - |hyperelliptic| |convergents| |root?| |lagrange| |pushup| - |LazardQuotient| |setEmpty!| |nrows| |startStats!| - |selectODEIVPRoutines| |functionIsContinuousAtEndPoints| |subTriSet?| - ~= |clipWithRanges| |cLog| |halfExtendedResultant2| |op| |contract| - |ncols| |remove| |retractable?| |iiacoth| |f07fef| |cyclePartition| - |messagePrint| |endOfFile?| |or?| |convert| |minimize| |true| - |complexElementary| |critMonD1| |reverseLex| |basisOfLeftNucleus| - |numerators| |validExponential| |baseRDEsys| |direction| |last| - |oblateSpheroidal| |spherical| |log10| |assoc| |multiple?| - |integralCoordinates| |laguerreL| |lo| |monicDivide| - |genericLeftTraceForm| |commonDenominator| |antiCommutative?| |match?| - |belong?| |acotIfCan| |incr| |hdmpToP| |real?| |unitsColorDefault| - |points| |cycleRagits| |fortran| |lazyIntegrate| |style| - |numberOfVariables| |toroidal| |showClipRegion| |limit| |hi| - |atanhIfCan| |OMputVariable| |writable?| |leftOne| |e02adf| - |irreducibleRepresentation| |symbolIfCan| |stFuncN| |rightRemainder| - |pdct| |rightGcd| |outputList| |retract| |makeSeries| |setCondition!| - |dominantTerm| |f04axf| |symbol| |numberOfComponents| |basisOfCenter| - |tanNa| |increasePrecision| |startPolynomial| |writeLine!| - |userOrdered?| |stoseInvertible?sqfreg| |copyInto!| |polygon| - |getGraph| ~ |fortranLogical| |OMputAtp| |prevPrime| |iiperm| - |sorted?| |null| |string| |integer| |setlast!| |point?| |Vectorise| - |aromberg| |s21bdf| |factors| |completeEchelonBasis| |rationalPower| - |ratDsolve| |indicialEquation| |leftRankPolynomial| |makeFR| - |rationalIfCan| |SturmHabicht| |expintegrate| |realEigenvectors| - |ef2edf| |mainCharacterization| |top!| |rightRankPolynomial| - |computeCycleLength| |getZechTable| = |mapmult| |term| |squareTop| - |removeRoughlyRedundantFactorsInPols| |bitLength| |curryLeft| |e02bcf| - |segment| |optpair| |setPrologue!| |monomialIntegrate| |cyclicCopy| - |open| |shiftRoots| |multiEuclidean| |binomThmExpt| |clearCache| < - |cTan| |asecIfCan| |genericRightDiscriminant| |pseudoRemainder| - |level| |nextIrreduciblePoly| |palgRDE| |currentSubProgram| > - |dmp2rfi| |jordanAdmissible?| |OMreadFile| |interpret| |firstDenom| - |decimal| |f07aef| <= |makeFloatFunction| |droot| |equivOperands| - |leader| |OMgetEndBVar| |incrementKthElement| |untab| >= |expr| |Nul| - |mainMonomials| |generate| |pascalTriangle| |list| |script| - |complexForm| |localUnquote| |getlo| |output| |leftDiscriminant| F2FG - |setDifference| |ode| |iiasech| |logGamma| |integerIfCan| |rootPoly| - |incrementBy| |composites| |integral?| |setIntersection| - |functionIsFracPolynomial?| |printCode| |checkPrecision| - |stoseInvertible?| + |pToHdmp| |expand| |setUnion| |sign| |conjugates| - |equation| |universe| |squareFreeFactors| |variable| - |powerSum| - |filterWhile| |comparison| |apply| |isTimes| |plotPolar| - |quasiRegular?| / |sort!| |filterUntil| |palgLODE| - |removeIrreducibleRedundantFactors| |tablePow| |lex| |e02daf| |select| - |f01mcf| |size| |bindings| |tex| |redPol| |cSec| - |numericalOptimization| |linearDependenceOverZ| - |generalInfiniteProduct| |normalizeAtInfinity| |t| |blue| |tanSum| - |invmod| |OMgetInteger| |palgint| |coerceImages| |cTanh| |randnum| - |clearFortranOutputStack| |ReduceOrder| |close| - |resultantEuclideannaif| |s18dcf| |fortranLiteral| |matrixDimensions| - |OMopenString| |crushedSet| |unvectorise| |bfKeys| |insert| - |intersect| |explicitlyEmpty?| |shift| |impliesOperands| |front| - |factorGroebnerBasis| |iidsum| |condition| |indices| |vedf2vef| - |pureLex| |charthRoot| |positiveSolve| SEGMENT |adaptive| |makeRecord| - |groebner| |edf2fi| |display| |OMputFloat| |showTheRoutinesTable| - |eisensteinIrreducible?| |heap| |rootProduct| |setPredicates| - |shellSort| |resetBadValues| |splitLinear| |fibonacci| |lazyEvaluate| - |setAdaptive3D| |iicot| |completeHermite| |numFunEvals3D| |mindegTerm| - |quadraticNorm| |mainMonomial| |idealiser| |pastel| |solveid| - |OMgetObject| |lintgcd| |c06ebf| |sumOfKthPowerDivisors| |f02aef| - |is?| |presuper| |edf2efi| |gbasis| |qinterval| |nextsubResultant2| - |c06gcf| |opeval| |orbit| |subresultantVector| |factorSFBRlcUnit| - |routines| |highCommonTerms| |input| |cCsch| |moduloP| - |selectOrPolynomials| |ParCond| |extractProperty| |e04ycf| - |superHeight| |e04mbf| |library| |numberOfImproperPartitions| - |leftMinimalPolynomial| |f04faf| |jacobi| |isList| |unit?| |exists?| - |pointPlot| |d01aqf| |result| |csch| |s17dcf| |epilogue| |coord| - |socf2socdf| |genericLeftDiscriminant| |printHeader| |asinh| - |distFact| |OMUnknownSymbol?| |hue| |powers| |irreducible?| - |eyeDistance| |acosh| |cup| |minset| |iisin| |nextPartition| - |cylindrical| |weight| |atanh| |integralMatrixAtInfinity| |removeZero| - |Si| |rightZero| |set| |legendreP| |poisson| - |lastSubResultantElseSplit| |acoth| |ScanRoman| |implies?| |mapDown!| - |OMReadError?| |ran| |satisfy?| |pr2dmp| |asech| - |rootOfIrreduciblePoly| |gcdprim| |transcendent?| |compile| |id| - |inrootof| |mainDefiningPolynomial| |dictionary| |nthFactor| - |leftTraceMatrix| |OMgetApp| |cSin| |every?| |simplifyExp| |read!| - |prinshINFO| |multiple| |totolex| |rootKerSimp| |ptree| |measure| - |hitherPlane| |symmetricTensors| |table| |OMserve| |monomRDEsys| - |getSyntaxFormsFromFile| |reseed| |applyQuote| |trunc| |iicoth| - |finiteBasis| |unaryFunction| |iExquo| |new| |lazyResidueClass| - |sdf2lst| |lyndonIfCan| |dequeue!| |setRow!| |extractBottom!| - |linearAssociatedExp| |endSubProgram| |totalLex| |createNormalPoly| - |unparse| |trapezoidalo| |variationOfParameters| |totalGroebner| - |nullary?| |compBound| |quatern| |Beta| |divide| |call| |powern| - |operators| |partition| |df2fi| |complex?| |ruleset| |setright!| - |tanIfCan| |wordInGenerators| |subNode?| |symFunc| |e01baf| |in?| - |show| |getExplanations| |besselJ| |fortranCarriageReturn| - |selectfirst| |s21bcf| |iiatanh| |createNormalPrimitivePoly| - |scalarTypeOf| |coercePreimagesImages| |mapdiv| |s19adf| |push| - |listOfLists| |external?| |modularGcd| |errorInfo| |reverse| - |makeResult| |representationType| |trace| |createZechTable| - |addPointLast| |bandedHessian| |d03faf| |suchThat| |topPredicate| - |conical| |d01apf| |complexNumericIfCan| |s19aaf| |makeop| - |monicRightFactorIfCan| |PollardSmallFactor| |linear?| - |primitivePart!| |insertRoot!| |besselK| |sinhcosh| |tower| - |invertIfCan| |reduceBasisAtInfinity| |addMatch| |recolor| - |getOperator| |constantIfCan| |isAbsolutelyIrreducible?| |superscript| - |center| |coleman| |approximants| |assign| |symmetricGroup| |objectOf| - |numberOfCycles| |toseInvertible?| |initial| |viewWriteAvailable| - |swap!| |sequences| |printInfo| |zeroSetSplit| |notOperand| - |fintegrate| |hexDigit?| |dAndcExp| |acschIfCan| - |factorSquareFreePolynomial| |left| |iomode| |bivariate?| |factor| - |imagJ| |e04gcf| |generalSqFr| |maxrank| |element?| - |SturmHabichtSequence| |identitySquareMatrix| |c06eaf| |right| - |directSum| |sqrt| |isPower| |acoshIfCan| |diagonalProduct| |property| - |iilog| |augment| |moreAlgebraic?| |real| |supersub| |schema| - |upDateBranches| |testModulus| |lowerCase!| |doublyTransitive?| - |integralBasisAtInfinity| |deleteProperty!| |pushdown| - |subscriptedVariables| |listYoungTableaus| |e02dff| |imag| |psolve| - |subResultantChain| |KrullNumber| |leadingBasisTerm| - |symmetricDifference| |symbolTable| |zeroDimPrime?| |getRef| |twist| - |s18adf| |ricDsolve| |oddInfiniteProduct| |directProduct| - |extendedEuclidean| |elliptic| |argumentListOf| - |countRealRootsMultiple| |modifyPoint| |loopPoints| |units| |ignore?| - |reduceByQuasiMonic| |insertTop!| |headReduced?| |pointColorPalette| - |changeVar| |df2st| |primPartElseUnitCanonical| |leftFactor| - |viewThetaDefault| |cAsinh| |cSech| |pushFortranOutputStack| - |expIfCan| |polyRicDE| |numberOfFractionalTerms| - |resultantReduitEuclidean| |stoseInternalLastSubResultant| |coth2tanh| - |constantOpIfCan| |option?| |OMsupportsCD?| |e02akf| |destruct| - |multiplyExponents| |degree| |popFortranOutputStack| - |generalizedEigenvectors| |conjug| |nextNormalPrimitivePoly| |prime| - |lprop| |extendIfCan| |genericLeftMinimalPolynomial| |optimize| - |semiDiscriminantEuclidean| |primlimintfrac| |cCoth| |genericLeftNorm| - |denomLODE| |outputAsFortran| |isobaric?| |maxPoints3D| |lazyPquo| - |OMputSymbol| |splitNodeOf!| |stronglyReduce| |radPoly| |rCoord| - |mainKernel| |ldf2lst| |wholeRadix| |expandTrigProducts| - |integralDerivationMatrix| |htrigs| |interval| |fortranTypeOf| - |mapMatrixIfCan| |rk4qc| |intermediateResultsIF| |extendedIntegrate| - |curryRight| |lastSubResultant| |code| |leftScalarTimes!| - |createIrreduciblePoly| |relationsIdeal| |strongGenerators| |push!| - |f01qef| |expint| |dfRange| |d01gbf| |changeThreshhold| - |var2StepsDefault| |imagi| |taylorQuoByVar| |nil| |moebius| |s15adf| - |plenaryPower| |OMputEndBVar| |quoted?| |print| |useNagFunctions| - |debug3D| |tableau| |removeSinhSq| |associative?| |UP2ifCan| - |asinhIfCan| |transform| |quasiMonicPolynomials| |light| |rischDEsys| - |e04dgf| |setref| |nthRootIfCan| |separate| |monicLeftDivide| |copies| - |setProperties!| |exprToXXP| |int| |d02gbf| |setAdaptive| - |internalIntegrate0| |cyclicGroup| |toseInvertibleSet| |cosSinInfo| - |e02baf| |second| |f2st| |rational| |cAcot| |csc2sin| |gcdcofactprim| - |wholePart| |algebraicDecompose| |initializeGroupForWordProblem| - |resultantnaif| |pointColorDefault| |scripted?| |third| |function| - |kovacic| |minPoints3D| |expt| |nullity| |d01asf| |evaluateInverse| - |decrease| |getBadValues| |expintfldpoly| |primitiveElement| |s13acf| - |reduceLODE| |cap| |GospersMethod| |sylvesterMatrix| - |exprHasAlgebraicWeight| |leadingIndex| |boundOfCauchy| |sechIfCan| - |zeroSetSplitIntoTriangularSystems| |resultant| |nil?| |cCsc| - |coerceListOfPairs| |leftAlternative?| |primes| |iidprod| - |sizePascalTriangle| |primeFactor| |OMopenFile| |denominators| - |fillPascalTriangle| |basisOfLeftNucloid| |associatedEquations| - |randomLC| |uniform| |reciprocalPolynomial| |drawCurves| |pow| - |hspace| |prindINFO| |linearlyDependent?| |brillhartIrreducible?| - |rightMult| |stoseIntegralLastSubResultant| |more?| |normalise| - |vectorise| |deleteRoutine!| |drawStyle| |list?| |vector| |infRittWu?| - |ratDenom| |postfix| |digit| |generators| |createPrimitiveNormalPoly| - |sub| |overset?| |algebraic?| |numericIfCan| |differentiate| - |setsubMatrix!| |minPol| |s17dgf| |numberOfDivisors| |orbits| |fTable| - |binarySearchTree| |mapUnivariateIfCan| |factorPolynomial| |extract!| - |resetNew| |rightTraceMatrix| |antisymmetric?| |listRepresentation| - |rdregime| |leftUnit| |precision| |case| |normalForm| |nextPrime| - |linear| |sylvesterSequence| |exprToGenUPS| |gradient| |computeBasis| - |divideExponents| |fixedDivisor| |integrate| |yCoord| |contains?| - |exactQuotient| |linearDependence| |coerce| |mapCoef| |OMgetError| - |rightScalarTimes!| |fortranCompilerName| |permanent| |high| |cCos| - |pquo| |OMgetAttr| |polynomial| |OMgetEndError| |construct| - |exponents| |radicalEigenvalues| |permutationGroup| |besselY| - |logIfCan| |maxRowIndex| |finiteBound| |B1solve| |negative?| - |completeSmith| D |powmod| |cycle| |f07fdf| |elements| - |alternatingGroup| |inGroundField?| |curve| |zero?| |member?| - |showTheSymbolTable| |lcm| |stiffnessAndStabilityFactor| - |pseudoDivide| |sncndn| |tanh2trigh| |choosemon| |leaf?| |exquo| - |laguerre| |reducedDiscriminant| |quoByVar| |coordinates| - |basisOfRightNucloid| |showTypeInOutput| |associatedSystem| |e02ajf| - |mirror| |bright| |setScreenResolution3D| |div| |atrapezoidal| - |double?| |hMonic| |viewPhiDefault| |curveColorPalette| |intcompBasis| - |mergeDifference| |standardBasisOfCyclicSubmodule| |chebyshevU| - |queue| |quo| |simplify| |bringDown| |totalDegree| |charClass| |gcd| - |close!| |getMeasure| |toseLastSubResultant| |cycleSplit!| |d01fcf| - |airyBi| |bottom!| |supDimElseRittWu?| |infiniteProduct| |over| - |union| |rootsOf| |checkForZero| |selectNonFiniteRoutines| |integers| - |minordet| |setValue!| |fprindINFO| |rem| |normalizedDivide| - |uniform01| |simpleBounds?| |false| |scaleRoots| |mulmod| - |squareMatrix| |frst| |OMgetEndObject| |OMwrite| |eval| |has?| - |setProperty!| |inconsistent?| |cross| |first| |child?| |reindex| - |iisinh| |polyPart| |solveLinearPolynomialEquationByFractions| - |idealiserMatrix| |setvalue!| |f02agf| |hasHi| |radix| |symmetric?| - |constantKernel| |rest| |noLinearFactor?| |critMTonD1| |setFormula!| - |inverseLaplace| |signAround| |duplicates| |innerSolve1| |duplicates?| - |exponentialOrder| |parametersOf| |substitute| |rur| |colorFunction| - |box| |zeroDimensional?| |/\\| |initials| |fixedPointExquo| |s21bbf| - |eigenMatrix| |any| |s13aaf| |s17ajf| |algint| |and?| - |removeDuplicates| |polygon?| |rangeIsFinite| |eulerE| |iisqrt3| - 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|tanQ| |monicModulo| |stFunc2| |random| |dimensions| |mathieu23| - |monicCompleteDecompose| |numberOfIrreduciblePoly| |coerceP| |s17adf| - |numerator| |groebnerFactorize| |cCot| |s21baf| |exp| |solid| - |purelyAlgebraic?| |normFactors| |lambert| |normalized?| |isMult| - |sincos| |euclideanNormalForm| |extendedSubResultantGcd| |bumptab| - |alphabetic?| |minimumDegree| |drawComplex| |OMconnInDevice| - |changeNameToObjf| |unary?| |hypergeometric0F1| |reducedSystem| - |divisor| |upperCase!| |firstNumer| |readable?| - |indiceSubResultantEuclidean| |mapExponents| |exprToUPS| |algDsolve| - |OMputEndApp| |tensorProduct| |restorePrecision| |figureUnits| - |realRoots| |multiEuclideanTree| |rules| |inHallBasis?| |An| - |clipBoolean| |aQuadratic| |legendre| |subst| |f02abf| |generic| - |LowTriBddDenomInv| |abs| |OMunhandledSymbol| - |setLegalFortranSourceExtensions| |upperCase| |imagK| - |generalizedInverse| |f02bbf| |newLine| |getMatch| - |fortranDoubleComplex| |setErrorBound| |primaryDecomp| |acosIfCan| - |iFTable| |collect| |pToDmp| |datalist| |rationalApproximation| - |midpoint| |iicsc| |stosePrepareSubResAlgo| |bumptab1| |trapezoidal| - |updatF| |diagonal| |binding| |rightMinimalPolynomial| |fortranDouble| - |complexZeros| |rightNorm| |implies| |leftRemainder| |aLinear| - |leftExtendedGcd| |space| |showIntensityFunctions| |divideIfCan!| - |objects| |multMonom| |identityMatrix| |xor| |lazy?| |gethi| |s18def| - |knownInfBasis| |bracket| |fixedPoint| |base| |mantissa| |traverse| - |removeSquaresIfCan| |leadingExponent| |invmultisect| |cfirst| - |squareFree| |structuralConstants| |infinite?| |summation| |checkRur| - |complexLimit| |pile| |double| |magnitude| |wrregime| |cAcsc| - |complexSolve| |prefix| |rubiksGroup| |nilFactor| |insert!| - |appendPoint| |setOrder| |rename!| |branchPointAtInfinity?| - |addPoint2| |divisorCascade| |setPosition| |makeEq| |putColorInfo| - |tubePoints| |algintegrate| |axes| |e02def| |brace| |constantRight| - |selectFiniteRoutines| |completeEval| |subCase?| |getDatabase| - 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|e01bgf| |factorAndSplit| |minimalPolynomial| |OMencodingBinary| - |even?| |outlineRender| |birth| |genericPosition| |insertMatch| - |OMgetString| |externalList| |conditionsForIdempotents| |phiCoord| - |f04jgf| |removeSuperfluousCases| |Zero| |triangulate| |ideal| - |discriminantEuclidean| |youngGroup| |ScanArabic| |complexEigenvalues| - |OMputInteger| |ODESolve| |subResultantGcd| |hasPredicate?| |One| - |s13adf| |less?| |sumOfDivisors| |groebSolve| |balancedBinaryTree| - |viewDefaults| |e02ahf| |hcrf| |showAllElements| |midpoints| |hclf| - |basisOfRightAnnihilator| |digit?| |comp| |ridHack1| |lhs| - |totalDifferential| |fmecg| |enterPointData| |selectPDERoutines| - |categoryFrame| |modularFactor| |fixedPoints| |palgintegrate| |rhs| - |parabolicCylindrical| |s17agf| |compose| |rotate| |ocf2ocdf| - |constructorName| |split| |nthCoef| |radicalEigenvector| - |ramifiedAtInfinity?| |f02axf| |f04adf| |f07adf| LODO2FUN - |setScreenResolution| |semiSubResultantGcdEuclidean2| - |stripCommentsAndBlanks| |prefixRagits| |next| |realElementary| - |numericalIntegration| |modifyPointData| |find| |localReal?| - |branchPoint?| |univariatePolynomialsGcds| |internalZeroSetSplit| - |iiacsc| |qelt| |drawToScale| |normDeriv2| |characteristicSet| - |increment| |addmod| |OMreadStr| |stFunc1| |rquo| |systemCommand| - |makeMulti| |tubeRadius| |consnewpol| |arity| |copy!| |e02gaf| - |nextLatticePermutation| |absolutelyIrreducible?| |mathieu24| |d02bbf| - |s19abf| |exponential1| |rootPower| |monomial?| |currentScope| |node?| - |scanOneDimSubspaces| |tab1| |Frobenius| |listexp| |constDsolve| - |mindeg| |normal| |stoseInvertible?reg| |reducedQPowers| - |computePowers| |rootSimp| |eigenvector| |cyclicEqual?| - |recoverAfterFail| |primitivePart| |leadingIdeal| |d01akf| |e01sbf| - |ParCondList| |mainValue| |numFunEvals| |clearTheSymbolTable| - |rischNormalize| |linGenPos| |append| |preprocess| |pseudoQuotient| - |rightFactorCandidate| |OMputApp| |divideIfCan| |revert| - |setButtonValue| |removeSuperfluousQuasiComponents| |cosIfCan| - |decompose| |listOfMonoms| |latex| |unit| NOT |delete| |idealSimplify| - |multiset| |trigs| |nthExpon| |symbolTableOf| |nary?| |yCoordinates| - |alphanumeric| |algSplitSimple| |c05nbf| |addMatchRestricted| OR - |quotedOperators| |delay| |semiSubResultantGcdEuclidean1| - |OMputEndAttr| |taylorRep| |graphCurves| |s18acf| |bitCoef| |quartic| - |f04mcf| |viewWriteDefault| AND |partialNumerators| |cycleEntry| - |combineFeatureCompatibility| |generalizedEigenvector| |quote| |term?| - |integralAtInfinity?| |d01alf| |f01qdf| |cyclic| |quasiComponent| - |quotient| |eulerPhi| |subMatrix| |OMconnOutDevice| |invertibleSet| - |countRealRoots| |imagI| |leftRegularRepresentation| |palgextint| - |pol| |halfExtendedSubResultantGcd2| |substring?| |setrest!| - |critBonD| |inverseColeman| |c06gsf| |euler| - |dimensionOfIrreducibleRepresentation| |power| |setVariableOrder| - |f04arf| |approxSqrt| |multisect| |outputGeneral| |e01bhf| - |nextNormalPoly| |showRegion| |zeroDim?| |failed?| |flagFactor| - |members| |rightUnits| |sn| |getVariableOrder| |f01maf| |sinIfCan| - |suffix?| |makeViewport3D| |makeCos| |interReduce| - |removeRoughlyRedundantFactorsInPol| |badValues| - |selectAndPolynomials| |univariatePolynomial| |matrixGcd| |minus!| - |cotIfCan| |airyAi| |polarCoordinates| |sqfrFactor| - |pmComplexintegrate| |var1Steps| |changeMeasure| |principalIdeal| - |coHeight| |f02bjf| |rightTrace| |d01bbf| |simplifyLog| - |initiallyReduced?| |linkToFortran| |prefix?| |xRange| |ord| |curve?| - |singularAtInfinity?| |explimitedint| |null?| |extractIfCan| |s17dlf| - |init| |normal01| |rewriteIdealWithRemainder| |coefficient| - |minPoints| |expandPower| |yRange| |solid?| |determinant| |minrank| - |lllp| |bipolar| |expextendedint| |cubic| |stopTableInvSet!| |fi2df| - |c06ekf| |clipPointsDefault| |semiResultantEuclideannaif| |zRange| - |eigenvalues| |generalPosition| |getStream| |remainder| |entry?| - |pade| |tryFunctionalDecomposition| |atanIfCan| |lists| |redmat| - |sumSquares| |normalDenom| |d02bhf| |tail| |parts| |prepareSubResAlgo| - |map!| * |tracePowMod| |vertConcat| |chineseRemainder| |diff| - |simpsono| |graphState| |inverse| |nextItem| |removeRedundantFactors| - |lift| |safetyMargin| |characteristic| |unitNormal| |calcRanges| - |qsetelt!| |fortranReal| |leviCivitaSymbol| |removeConstantTerm| - |splitSquarefree| |expressIdealMember| |lllip| |powerAssociative?| - |flatten| |stoseSquareFreePart| |reduce| |vspace| |split!| |c06fqf| - |chiSquare1| |lowerCase?| |differentialVariables| |swap| |dflist| - |HermiteIntegrate| |froot| |symbol?| |iiabs| |nor| |cot2trig| - |shanksDiscLogAlgorithm| |infix?| |csubst| |llprop| |rootSplit| - |besselI| |log2| |e02ddf| |roughEqualIdeals?| |collectUpper| - |radicalSolve| |arguments| |simplifyPower| |tube| - |leftCharacteristicPolynomial| |findCycle| |mask| |setMinPoints| - |ipow| |sizeMultiplication| |approximate| |hex| |moduleSum| - |OMputBVar| |trivialIdeal?| |freeOf?| |iicsch| |roman| - |diophantineSystem| |f01rdf| |mpsode| |complex| |iiacsch| - |rightRegularRepresentation| |subNodeOf?| |factorFraction| - |replaceKthElement| |bumprow| |splitConstant| |toScale| |iiacosh| - |goodnessOfFit| |addiag| |e02bef| |mr| |acsch| |fullPartialFraction| - |morphism| |bombieriNorm| |ptFunc| |explicitlyFinite?| |cCosh| - |f02adf| |setleaves!| |f02fjf| |symmetricRemainder| |norm| - |lSpaceBasis| |hasoln| |kmax| |atom?| |npcoef| |chebyshevT| - |readIfCan!| |reset| |semiResultantEuclidean2| - |inverseIntegralMatrixAtInfinity| |euclideanGroebner| |anfactor| - |lazyPseudoRemainder| |contours| |seriesSolve| |extension| |octon| - |root| |whileLoop| |semiDegreeSubResultantEuclidean| |positive?| - |outerProduct| |getMultiplicationMatrix| |laplace| |compiledFunction| - |graphs| |iisech| |normalElement| |edf2ef| |autoReduced?| |critpOrder| - |rowEchelonLocal| |polyRDE| |write| |ddFact| |complementaryBasis| - |outputAsScript| |bit?| |triangSolve| |save| |fullDisplay| |mkAnswer| - |mesh| |stack| |mainPrimitivePart| |leadingCoefficientRicDE| - |setfirst!| |bivariateSLPEBR| |isExpt| |concat!| |iiexp| |inR?| - |c06ecf| |low| |currentEnv| |getProperties| |antiAssociative?| - |LyndonWordsList| |removeCosSq| |f04maf| |wronskianMatrix| - |makeVariable| |startTableGcd!| |or| |newTypeLists| |one?| - |mightHaveRoots| |iiatan| |leftExactQuotient| |predicate| - |exteriorDifferential| |algebraicCoefficients?| |completeHensel| - |elRow2!| |OMencodingSGML| |sinhIfCan| |setleft!| - |halfExtendedResultant1| |and| |discriminant| |dequeue| |cAtanh| - |lyndon?| |oddintegers| |stopMusserTrials| |distribute| |s20acf| - |quotientByP| |argumentList!| |mergeFactors| |zeroDimPrimary?| - |factor1| |redpps| |empty| |normInvertible?| - |semiIndiceSubResultantEuclidean| |factorsOfDegree| - |particularSolution| |collectUnder| |radicalRoots| - |extractSplittingLeaf| |linearlyDependentOverZ?| |lfinfieldint| - |resultantReduit| |lfextlimint| |slash| |ode2| |palgint0| - |BumInSepFFE| |sumOfSquares| |lp| |slex| |monomial| |viewpoint| - |jordanAlgebra?| |showFortranOutputStack| |palglimint| |f04atf| F - |errorKind| |d02cjf| |fractRadix| |s17ahf| |hasTopPredicate?| - |setTex!| |bezoutMatrix| |axesColorDefault| |approxNthRoot| |s17aef| - |selectIntegrationRoutines| |tubeRadiusDefault| |fortranComplex| - |safeCeiling| |identification| |headReduce| |reducedForm| - |discreteLog| |meshFun2Var| |multivariate| |check| |isQuotient| - |moebiusMu| |sin2csc| FG2F |goodPoint| |drawComplexVectorField| |sPol| - |arg1| |repeating?| |scopes| |triangularSystems| |heapSort| - |represents| |variables| |solveInField| |setClosed| |unmakeSUP| - |e02agf| |float?| |s18aef| |bag| |arg2| |po| |hdmpToDmp| UP2UTS - |primintfldpoly| |horizConcat| |select!| |algebraicVariables| - |SturmHabichtMultiple| |varList| |expenseOfEvaluation| |leftLcm| - |symmetricPower| |cos2sec| |leftRank| |nonSingularModel| |separant| - |s18aff| |mapBivariate| |overlabel| - |generalizedContinuumHypothesisAssumed?| |tubePlot| |primextendedint| - |imagj| |csch2sinh| |OMputAttr| |inRadical?| |e01saf| |block| - |LiePoly| |symmetricProduct| |medialSet| |purelyTranscendental?| - |conditions| |OMputBind| |probablyZeroDim?| |numberOfNormalPoly| - |makeGraphImage| |groebgen| |abelianGroup| |leftMult| |linSolve| - |wordInStrongGenerators| |removeRedundantFactorsInContents| - |accuracyIF| |identity| |component| |palgLODE0| |setMinPoints3D| - |twoFactor| |denominator| |match| |wholeRagits| |LazardQuotient2| - |normalizeIfCan| |hash| |OMgetBind| |weierstrass| |height| |digits| - |OMputError| |orthonormalBasis| |setnext!| |weakBiRank| - |primPartElseUnitCanonical!| |internalSubQuasiComponent?| |variable?| - |concat| |crest| |critB| |algebraicOf| |count| |aCubic| |equality| - |extractTop!| |createMultiplicationTable| |invertibleElseSplit?| - |write!| |sturmSequence| |minimumExponent| |constantToUnaryFunction| - |operation| |stoseInvertibleSet| |buildSyntax| |clearTable!| - |lazyPremWithDefault| |extensionDegree| |linearAssociatedOrder| - |s14aaf| |relerror| |f04qaf| |rewriteIdealWithHeadRemainder| - |cscIfCan| |hermiteH| |internalSubPolSet?| |doubleResultant| - |OMputString| |chiSquare| |multinomial| |makeSin| |rightRank| - |enterInCache| |clip| |sturmVariationsOf| |euclideanSize| |reorder| - |gderiv| |removeCoshSq| |beauzamyBound| |torsionIfCan| - |commutativeEquality| |quadraticForm| |curveColor| |backOldPos| - |factorList| |padicallyExpand| |changeBase| |nonQsign| |associates?| - |vark| |e04jaf| |ScanFloatIgnoreSpaces| |nil| |infinite| - |arbitraryExponent| |approximate| |complex| |shallowMutable| - |canonical| |noetherian| |central| |partiallyOrderedSet| - |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| - |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| - |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| - |shallowlyMutable| |commutative|)
\ No newline at end of file + |Record| |Union| |Category| |makeSeries| |zeroDimensional?| GF2FG + |maxint| |e02aef| |delta| |leadingBasisTerm| |palgextint| |simplify| + |moebius| |hermite| |iiacos| |leftPower| |acscIfCan| |acschIfCan| + |unrankImproperPartitions0| |clearDenominator| |lexico| |curryRight| + |sort!| |mainSquareFreePart| |numerators| |iprint| |palgint| |minPol| + |curry| |indices| |belong?| |groebnerIdeal| |sts2stst| + |viewWriteDefault| |approximants| |leftGcd| |homogeneous?| |dmpToP| + |jordanAlgebra?| |declare| |overset?| |infieldint| |cyclicGroup| + |times!| |pushNewContour| |doubleDisc| |setCondition!| |nthExponent| + |complexNumeric| |imagk| |gcdPrimitive| |basis| |lllp| |countable?| + |OMsend| |hue| |OMreadFile| |completeEchelonBasis| |depth| |log| + |s17adf| |stoseInternalLastSubResultant| |reducedQPowers| |f02agf| + |numberOfCycles| |laurentIfCan| |zeroOf| |OMputEndObject| + |algebraicOf| |monicDecomposeIfCan| |droot| |generalizedEigenvector| + |kernels| |idealiserMatrix| |e01sff| |size?| |palgintegrate| |comment| + |reducedForm| |swap| |shallowCopy| |simplifyExp| + |rightMinimalPolynomial| |outputGeneral| |leaves| + |differentialVariables| |univariate| |ceiling| |cAsech| + |partialFraction| |compBound| |OMgetEndError| |tan2cot| |s18acf| + |composite| |lambda| |cycleTail| |hyperelliptic| |lazyGintegrate| + |fixedPoint| |atanIfCan| |showSummary| |retractIfCan| |quasiRegular| + |polynomialZeros| |traceMatrix| |tensorProduct| |exactQuotient| + |determinant| |virtualDegree| |hasPredicate?| |gcdprim| |nsqfree| + |log2| |f01maf| |cyclicParents| |expandTrigProducts| |gderiv| + |corrPoly| |principalIdeal| |extendIfCan| |prinb| |contract| + |realRoots| |showAttributes| |f02axf| |f07fef| |normDeriv2| |c06fuf| + |PDESolve| |genericRightNorm| |errorInfo| |partitions| |internal?| + |primPartElseUnitCanonical!| |constantCoefficientRicDE| + |deleteRoutine!| |indiceSubResultantEuclidean| |recoverAfterFail| + |acothIfCan| |setButtonValue| |column| |factorPolynomial| |bernoulli| + |OMopenFile| |polyRDE| |readIfCan!| |Is| |derivative| |alphanumeric?| + |graphImage| |exptMod| BY |ratpart| |pushdown| + |removeRoughlyRedundantFactorsInPol| |minColIndex| Y |e01saf| |birth| + |top| |useEisensteinCriterion| |OMencodingUnknown| |style| |B1solve| + |subNodeOf?| |bat1| |rule| |groebnerFactorize| |lfinfieldint| + |continue| |matrix| |void| |rationalPoints| |node?| + |expenseOfEvaluation| |heapSort| |cycleElt| |fractRadix| + |splitConstant| |getRef| |primeFrobenius| |cycleEntry| |LiePoly| + |divergence| |pattern| |qinterval| |chebyshevU| |setleft!| |formula| + |generator| |hconcat| |anfactor| |OMgetFloat| |nextColeman| + |leftRecip| |padicFraction| |content| |updateStatus!| |map| |maxrow| + |internalSubQuasiComponent?| |enterPointData| |back| |normal01| + |bivariateSLPEBR| |removeIrreducibleRedundantFactors| |newLine| + |yCoordinates| |range| |tubeRadius| |fillPascalTriangle| + |mapUnivariate| |Aleph| |f2df| |solve1| |primlimintfrac| |f2st| |int| + |binomThmExpt| |makeCos| |tanh2trigh| |nrows| + |genericLeftMinimalPolynomial| |simpsono| |genericLeftDiscriminant| + |leftRemainder| |showTypeInOutput| ~= |bezoutDiscriminant| + |dihedralGroup| |duplicates?| |op| |d03edf| |ncols| |remove| + |setLabelValue| |boundOfCauchy| |cothIfCan| |nthCoef| + |createLowComplexityTable| |cAcsc| |setelt!| |invertible?| |convert| + |rightOne| |true| |extendedSubResultantGcd| |euclideanNormalForm| + |factorList| |rootOf| |doubleFloatFormat| |stoseLastSubResultant| + |empty?| |untab| |rightCharacteristicPolynomial| |last| |lfextlimint| + |weights| |groebner| |assoc| |integralCoordinates| |maxPoints| + |f02ajf| |tRange| |OMencodingBinary| |lo| |trigs2explogs| |pointData| + |inverseIntegralMatrix| |match?| |insertBottom!| |graphs| |charClass| + |intermediateResultsIF| |ramified?| |incr| |setrest!| |unitNormalize| + |makeResult| |fortran| |cyclic?| |finiteBound| |llprop| + |problemPoints| |rootBound| |lfintegrate| |overbar| |hi| |npcoef| + |conjugate| |element?| |getZechTable| |float?| |subscriptedVariables| + |repSq| |normalizeIfCan| |f04qaf| |cscIfCan| |unit| |quasiRegular?| + |outputList| |retract| |LyndonBasis| |digamma| |coefficient| + |lSpaceBasis| |palgRDE0| |recur| |symbol| |simplifyPower| |monomRDE| + |tanSum| |dioSolve| |medialSet| |multiEuclidean| |e04ycf| |mathieu23| + |tryFunctionalDecomposition| |more?| |removeDuplicates!| ~ + |monicCompleteDecompose| |relerror| |hdmpToDmp| |number?| |lintgcd| + |relationsIdeal| |logpart| |string| |integer| |null| |outputForm| + |setScreenResolution| |numberOfDivisors| |e01sef| |euler| + |normInvertible?| |lllip| |transcendentalDecompose| |setProperty| + |readLine!| |polygon| |e01bff| |rightFactorCandidate| |showRegion| + |complexEigenvectors| |ScanRoman| |quasiAlgebraicSet| |symmetricPower| + |UnVectorise| |OMgetBind| |rdregime| |cosIfCan| |lowerCase!| = |nand| + |expintfldpoly| |noKaratsuba| |rootSimp| |eigenMatrix| |rootPower| + |rowEchelonLocal| |distance| |segment| |fortranCompilerName| + |tanh2coth| |setlast!| |cAcsch| |primitivePart| |open| |printInfo!| + |hex| |checkRur| |clearCache| < |inspect| |monomialIntegrate| + |getDatabase| |inverse| |debug3D| |level| |e01bhf| |c06gcf| + |nthRootIfCan| > |primlimitedint| |toseInvertibleSet| + |generalizedEigenvectors| |ListOfTerms| |interpret| |critB| |and?| + |shiftLeft| <= |selectPolynomials| |splitDenominator| + |viewDeltaXDefault| |characteristic| |leader| |explimitedint| |atoms| + |lagrange| >= |expr| |zeroVector| |e02agf| |generate| |cycleLength| + |f01rcf| |list| |script| |completeHensel| |makeGraphImage| + |setMaxPoints| |spherical| |output| |setDifference| |bumprow| + |stronglyReduce| |logIfCan| |critT| |roughUnitIdeal?| |removeCoshSq| + |incrementBy| |setIntersection| |semiDegreeSubResultantEuclidean| + |selectFiniteRoutines| |univariatePolynomialsGcds| |realZeros| |cSec| + |OMread| |checkPrecision| |legendre| + |algint| |asimpson| |expand| + |setUnion| |create| |equation| |localIntegralBasis| + |OMunhandledSymbol| |semiResultantEuclideannaif| |variable| - + |argument| |filterWhile| RF2UTS |pack!| |apply| |symmetricRemainder| + |maxRowIndex| |setEpilogue!| / |HenselLift| |cCos| |filterUntil| + |nil?| |multiplyCoefficients| |integralLastSubResultant| + |viewDeltaYDefault| |mainKernel| |OMputString| |select| |size| + |errorKind| |bindings| |tex| |mkIntegral| |reduction| |quadraticForm| + |morphism| |f02aef| |ellipticCylindrical| |hasTopPredicate?| |t| + |nodes| |weighted| |f02akf| |outputAsScript| |rationalApproximation| + |makeFloatFunction| |factorFraction| |rootsOf| |expenseOfEvaluationIF| + |setProperty!| |pascalTriangle| |d02bbf| |viewDefaults| |close| + |triangulate| |contractSolve| |getVariableOrder| |specialTrigs| + |clearTheSymbolTable| |setProperties!| |OMputApp| |idealSimplify| + |cycles| |semiSubResultantGcdEuclidean2| |iisech| |insert| |shift| + |minRowIndex| |linearPart| |graphCurves| |scopes| |palgLODE| + |multiple?| |alternating| |condition| |fullPartialFraction| + |explogs2trigs| |root?| |pomopo!| |midpoints| |getProperty| + |makeRecord| SEGMENT |continuedFraction| |parametersOf| |xn| + |meshPar2Var| |display| |associatedSystem| |mathieu12| |iiacosh| + |module| |getProperties| |hexDigit?| |getMeasure| |d01anf| + |newTypeLists| |safeCeiling| |perfectNthRoot| |usingTable?| + |fractionFreeGauss!| |invertibleSet| |recolor| |gradient| + |generalInfiniteProduct| |subResultantGcdEuclidean| |hermiteH| + |infieldIntegrate| |f01qef| |secIfCan| |dimensions| |categoryFrame| + |leftAlternative?| |leftMult| |subPolSet?| |s17dcf| |permutations| + |commonDenominator| |integrate| |revert| |strongGenerators| |nullary| + |f04maf| |nthExpon| |karatsuba| |genericLeftNorm| |paraboloidal| + |bitLength| |enqueue!| |Lazard| |zeroDim?| |OMputBind| |Gamma| + |polygon?| |input| |FormatRoman| |setErrorBound| |completeEval| + |symmetricDifference| |addPoint2| |linSolve| |padecf| |tube| |super| + |library| |rootRadius| |close!| |cCosh| |goto| |expint| + |purelyAlgebraic?| |hasHi| |perfectSqrt| |identityMatrix| |member?| + |result| |csch| |rightRank| |internalDecompose| |showTheSymbolTable| + |optAttributes| |e02dff| |generic| |d02gbf| |asinh| |stopMusserTrials| + |OMputInteger| |crushedSet| |objectOf| |lowerCase| |putColorInfo| + |intersect| |acosh| |yCoord| |laurentRep| |mindeg| |iicsc| + |bubbleSort!| |matrixGcd| |makeSUP| |atanh| |forLoop| + |reduceBasisAtInfinity| |selectPDERoutines| |f04adf| |coordinates| + |set| |eyeDistance| |nextIrreduciblePoly| |prime| |acoth| + |factorSquareFreePolynomial| |removeSuperfluousCases| + |linearDependenceOverZ| |OMencodingSGML| |iiatan| |linearDependence| + |basisOfNucleus| |LazardQuotient| |asech| |eigenvector| |compile| + LODO2FUN |realSolve| |generateIrredPoly| |id| |setPredicates| + |meatAxe| |limitedIntegrate| |fractionPart| |leastPower| |associates?| + |relativeApprox| |rationalPower| |head| |toroidal| |heap| + |startTable!| |multiple| |iibinom| |pdf2df| |ptree| |measure| + |minrank| |cycleRagits| |indiceSubResultant| |table| |prefixRagits| + |parent| |reduceByQuasiMonic| |hitherPlane| |applyQuote| |edf2fi| + |mapDown!| |upperCase?| |character?| |rightExtendedGcd| |imagJ| |new| + |primitivePart!| |setchildren!| |linears| |f07adf| + |exprHasWeightCosWXorSinWX| |innerSolve1| |var2Steps| + |singularitiesOf| |quartic| |OMputEndError| + |selectSumOfSquaresRoutines| |irreducibleFactor| |xCoord| |point?| + |iipow| |cyclotomicDecomposition| |sumOfSquares| |constantIfCan| + |semiIndiceSubResultantEuclidean| |curve| |initTable!| + |basisOfLeftAnnihilator| |call| |tubePoints| + |conditionsForIdempotents| |endOfFile?| |headReduce| |ruleset| + |setFormula!| |youngGroup| |infinityNorm| |e04ucf| |symmetric?| + |karatsubaOnce| |divide| |lazyPseudoRemainder| |show| |clipBoolean| + |resetNew| |setImagSteps| |removeZero| |has?| |computeInt| + |PollardSmallFactor| |vark| |commutativeEquality| |oddintegers| + |wordInGenerators| |singular?| |df2ef| |sin?| |sinhcosh| + |pointColorDefault| |lazy?| |reverse| |linearPolynomials| |coefChoose| + |trace| |restorePrecision| |failed?| |numberOfIrreduciblePoly| + |selectAndPolynomials| |suchThat| |scalarMatrix| |argumentListOf| + |distribute| |every?| |resetAttributeButtons| + |removeRoughlyRedundantFactorsInPols| |setright!| |plenaryPower| + |hypergeometric0F1| |numberOfImproperPartitions| |nextPrime| |digit| + |indicialEquationAtInfinity| |tower| |fortranLiteral| |lepol| |cCoth| + |slash| |semicolonSeparate| |center| |polyPart| |unitCanonical| + |innerint| |c06fpf| |iicot| |mesh| |initial| |upperCase| + |reducedSystem| |d02ejf| |pointPlot| |printInfo| |increase| |ldf2vmf| + |appendPoint| |red| |zeroMatrix| |left| |oneDimensionalArray| |expPot| + |d01akf| |factor| |complex?| |completeHermite| |rationalFunction| + |axesColorDefault| |rischNormalize| |OMgetError| |right| |cAcot| + |LazardQuotient2| |sqrt| |linear?| |leadingIndex| |property| + |resultantReduitEuclidean| |decreasePrecision| |iisin| + |matrixConcat3D| |d02gaf| |real| |groebner?| |vconcat| + |expextendedint| |listOfMonoms| |conjugates| |rk4f| + |subResultantChain| |leftDiscriminant| |f02xef| |mathieu11| |imag| + |squareMatrix| |any?| |SturmHabichtMultiple| |symbolTable| |getStream| + |d01amf| |mathieu22| |setMaxPoints3D| |reseed| |green| |directProduct| + |fTable| |equiv?| |interpolate| |leastMonomial| |nullity| |units| + |multisect| |f01bsf| |subNode?| |OMReadError?| |trigs| |iifact| + |commaSeparate| |multinomial| |superscript| |mapExpon| + |withPredicates| |pushFortranOutputStack| |tanhIfCan| |iidprod| + |dictionary| |explicitEntries?| |stripCommentsAndBlanks| |intChoose| + |f02wef| |semiResultantReduitEuclidean| |destruct| |dimension| + |regime| |exponential1| |popFortranOutputStack| |position!| + |curveColorPalette| |sumOfDivisors| |addMatch| |invertibleElseSplit?| + |optimize| |besselI| |OMputFloat| |insertMatch| |mirror| + |subtractIfCan| |integralRepresents| |outputAsFortran| |even?| + |uncouplingMatrices| |commutator| |poisson| |generalLambert| + |fracPart| |makeSin| |moduloP| |setfirst!| |ocf2ocdf| + |stoseInvertible?| |lieAlgebra?| |e02baf| |baseRDEsys| + |leadingCoefficientRicDE| |list?| |space| |numericIfCan| |rightGcd| + |sechIfCan| |code| |removeConstantTerm| |useNagFunctions| + |nonSingularModel| |fullDisplay| |powmod| |OMgetSymbol| + |doublyTransitive?| |basisOfRightNucleus| |clipParametric| |split| + |sec2cos| |nil| |print| |showScalarValues| |ReduceOrder| |perspective| + |toseInvertible?| |degree| |rootNormalize| |prime?| |normalDeriv| + |leadingTerm| |innerEigenvectors| |viewport2D| |balancedFactorisation| + |setClosed| |validExponential| |e02ddf| |approxSqrt| |OMgetVariable| + |f04asf| |OMputError| |Lazard2| |graeffe| |rightDiscriminant| |lquo| + |opeval| |setEmpty!| |pleskenSplit| |selectOrPolynomials| + |integralDerivationMatrix| |rewriteIdealWithRemainder| |tanQ| |second| + |possiblyInfinite?| |flexibleArray| |symmetricTensors| + |seriesToOutputForm| |hdmpToP| |tableForDiscreteLogarithm| |index?| + |acoshIfCan| |stopTableInvSet!| |palgLODE0| |third| |function| |rk4a| + |transform| |e02zaf| |s14baf| |variable?| |iflist2Result| + |hasSolution?| |interval| |complete| |tab| |normalizeAtInfinity| + |distFact| |OMlistCDs| |squareFreePolynomial| |horizConcat| |s18aef| + |orthonormalBasis| |airyBi| |s14abf| |nthFractionalTerm| |csc2sin| + |deepestInitial| |tan2trig| |iisinh| |f02aff| |redmat| |cotIfCan| + |meshPar1Var| |sizeLess?| |antisymmetric?| |halfExtendedResultant2| + |rotate| |hexDigit| |s17aef| |iisec| |rightZero| |totalGroebner| + |entry?| |d02bhf| |superHeight| |removeCosSq| |ddFact| |coleman| + |c06ekf| |coerceListOfPairs| |pdf2ef| |vector| |groebgen| |row| + |rightUnits| |zoom| |numberOfPrimitivePoly| |safetyMargin| |minGbasis| + |extend| |testDim| |differentiate| |palgRDE| |modifyPointData| + |separateDegrees| |totalDegree| |comparison| |jacobian| |myDegree| + |bits| |top!| |ratPoly| |f04atf| |mapGen| |indicialEquations| + |precision| |e02akf| |case| |getGraph| |linear| |closeComponent| + |stopTable!| |cCsch| |constantOpIfCan| |legendreP| |setAdaptive3D| + |setAdaptive| |signAround| |pmComplexintegrate| |exponential| + |collect| |coerce| |makeFR| |zeroSquareMatrix| |genericLeftTrace| + |argumentList!| |graphStates| |extractProperty| |OMcloseConn| |sample| + |polynomial| |lprop| |construct| |pushuconst| |sdf2lst| |push!| + |factorsOfDegree| |extensionDegree| |concat!| + |createMultiplicationMatrix| |fortranInteger| |exists?| D + |fortranLinkerArgs| |exponent| |stoseSquareFreePart| |f01rdf| + |symbolTableOf| |normalizedDivide| |leftZero| |genericRightTraceForm| + |palglimint0| |lcm| |normalise| |leftUnits| |s17def| |light| + |denominator| |ptFunc| |exquo| |rightRankPolynomial| |imagI| + |unaryFunction| |getMultiplicationMatrix| |c06gsf| |scalarTypeOf| + |associator| |bright| |exactQuotient!| |div| |compactFraction| + |positive?| |removeZeroes| |assign| |e04jaf| |printCode| |localAbs| + |OMputObject| |empty| |solveLinearPolynomialEquationByFractions| |quo| + |extendedEuclidean| |f02aaf| |subHeight| |gcd| |setProperties| + |balancedBinaryTree| |coth2tanh| |OMgetType| |polyred| |imagi| + |patternMatch| |compound?| |fractRagits| |union| |divideExponents| + |rootSplit| |sorted?| |simplifyLog| |rquo| |rem| |sup| |or?| + |degreeSubResultant| |limitedint| |false| |makeVariable| |OMgetAtp| + |mapExponents| |OMputVariable| |rectangularMatrix| |eval| |iiatanh| + |divisor| |wholeRadix| |pseudoQuotient| |d03eef| |first| + |printStatement| |firstSubsetGray| |torsion?| |equivOperands| + |SturmHabichtCoefficients| |noncommutativeJordanAlgebra?| |cyclotomic| + |toScale| |nextSubsetGray| |rest| |polyRicDE| |elRow1!| |convergents| + |bitTruth| |remainder| |radicalSolve| |sincos| |squareFree| + |basisOfCentroid| |LyndonCoordinates| |internalIntegrate| |substitute| + |box| |realElementary| |f01ref| |/\\| |Hausdorff| |compiledFunction| + |divideIfCan| |any| |nthr| |OMserve| |integralMatrixAtInfinity| + |setValue!| |removeDuplicates| |s19aaf| |Ci| |copies| + |splitSquarefree| |cyclicEqual?| |cyclicEntries| |sn| + |listYoungTableaus| |ord| |resultantEuclidean| |linGenPos| + |localUnquote| |cylindrical| |rowEchLocal| |isList| |primes| |reflect| + |hspace| |rootOfIrreduciblePoly| |e02bbf| |binaryFunction| |nthFlag| + |normal?| |linearlyDependent?| |psolve| |resultantReduit| + |create3Space| |move| |rightMult| |screenResolution3D| + |stiffnessAndStabilityOfODEIF| |showIntensityFunctions| + |basisOfCenter| |colorFunction| |f04faf| |rarrow| |euclideanGroebner| + |modularGcd| |composites| |explicitlyFinite?| |setStatus| |setelt| + |string?| |clearTheFTable| |numerator| |lazyVariations| + |minimumDegree| |changeNameToObjf| |algintegrate| |collectQuasiMonic| + |factor1| |numeric| |bandedJacobian| |invertIfCan| |coerceP| |minus!| + |monomials| |bivariatePolynomials| |radical| |primintfldpoly| |plus| + |not| |symmetricGroup| |infLex?| |wordsForStrongGenerators| |copy| + |exprHasLogarithmicWeights| |mkPrim| |cRationalPower| |OMgetEndBind| + |splitNodeOf!| |leaf?| |d02cjf| |rational?| |stoseInvertible?reg| + |conjug| |c06gqf| |leftRank| |characteristicSerie| |postfix| + |mainPrimitivePart| |properties| |writable?| |bernoulliB| |setPoly| + |OMgetEndObject| ^= |parametric?| |numberOfMonomials| + |basisOfRightNucloid| |Vectorise| |charthRoot| |ideal| |addPointLast| + |tubePointsDefault| |listexp| |monomRDEsys| |makeYoungTableau| + |autoCoerce| |c05pbf| |noLinearFactor?| |s17acf| |weierstrass| + |branchPoint?| |max| |dfRange| |hasoln| |cAcos| |iicosh| + |primitiveElement| |subscript| |taylorQuoByVar| |integers| |say| + |clip| |nextNormalPoly| |pointSizeDefault| |escape| |rotatex| |cCot| + |binomial| |f02fjf| |translate| |dAndcExp| |zag| |iiperm| |entries| + |harmonic| |pseudoDivide| |curryLeft| |numberOfFractionalTerms| + |leftCharacteristicPolynomial| |packageCall| |backOldPos| |invmod| + |preprocess| |open?| |Nul| |iitan| |times| |powerSum| |alphabetic| + |zeroDimPrime?| |polCase| |axes| |rightLcm| |adaptive3D?| |singRicDE| + |meshFun2Var| |factorials| |setsubMatrix!| |split!| |iiexp| |term| + |adaptive?| |OMputEndApp| |OMlistSymbols| |roughBase?| |quoByVar| + |mapmult| |basisOfCommutingElements| |stronglyReduced?| + |symmetricSquare| |rischDEsys| |expandLog| |tanNa| |replace| |length| + |monom| |torsionIfCan| |unparse| |cyclicCopy| |generalSqFr| |lighting| + |iiasec| |dflist| |scripts| |setAttributeButtonStep| |zeroDimPrimary?| + |bat| |key| |f02adf| |coHeight| |integerBound| |tubeRadiusDefault| + |octon| |selectfirst| |options| |rightFactorIfCan| |lineColorDefault| + |common| |laplacian| |rotate!| |removeRedundantFactorsInContents| + |norm| |elt| |gbasis| |e02daf| |nullary?| |binarySearchTree| + |OMopenString| |wholePart| |po| |extractClosed| |filename| + |OMputEndBind| |rdHack1| |const| |setPrologue!| |tanintegrate| + |pr2dmp| |normFactors| |algebraic?| |brillhartTrials| |f07aef| |chvar| + |over| |predicates| |expandPower| |not?| |mainContent| |BumInSepFFE| + |extension| |sign| |setnext!| |changeVar| |HermiteIntegrate| |ref| + |ldf2lst| |fglmIfCan| |parse| |pmintegrate| |cAtanh| |rightPower| + |tanAn| |s01eaf| |s13acf| |cond| |iroot| |s17dgf| |OMreceive| |orbits| + |intcompBasis| |e02def| |rombergo| |collectUnder| |cn| |minPoints3D| + |setvalue!| |rightRecip| |sinh2csch| |polar| |lfunc| |lexGroebner| + |fixedPointExquo| |blue| |ef2edf| |laplace| |addiag| |elliptic?| + |symbol?| |deepestTail| |unary?| |stFunc2| |associatedEquations| + |functionIsOscillatory| |possiblyNewVariety?| |finiteBasis| |dim| + |squareFreeLexTriangular| |points| |initiallyReduced?| + |basisOfMiddleNucleus| |commutative?| |read!| |critBonD| |totalLex| + |queue| |multMonom| |dark| |degreeSubResultantEuclidean| |ffactor| + |redPol| |quatern| |unvectorise| |intPatternMatch| + |createGenericMatrix| |denominators| |parabolicCylindrical| + |constantToUnaryFunction| |lfextendedint| |reify| |s21bdf| |iiacoth| + |userOrdered?| |width| |mainDefiningPolynomial| |incrementKthElement| + |startTableGcd!| |ran| |integral?| |moebiusMu| |addBadValue| + |minIndex| |trapezoidalo| |stiffnessAndStabilityFactor| |minimize| + |lyndon?| |transcendent?| |csubst| |newReduc| |fortranReal| + |getSyntaxFormsFromFile| |diagonal| |OMputEndAtp| |rightExactQuotient| + |bottom!| |OMgetBVar| |permutationRepresentation| |kovacic| + |taylorRep| |polarCoordinates| |doubleResultant| |whatInfinity| + |subresultantSequence| |nilFactor| |rightRemainder| |constant| + |wreath| |identitySquareMatrix| |supDimElseRittWu?| |difference| + |Frobenius| |lowerCase?| |s17agf| |front| |arity| |coordinate| + |sizePascalTriangle| |squareFreePart| |rightUnit| |shuffle| |e02ajf| + |f02awf| |henselFact| |perfectNthPower?| |s20adf| |exprToGenUPS| + |routines| |optional| |outputFloating| |makingStats?| |paren| + |polygamma| |iicsch| |definingInequation| |erf| |leftUnit| |setTex!| + |scale| |elRow2!| |mightHaveRoots| |dequeue!| |viewSizeDefault| + |e02bcf| |floor| |external?| |scaleRoots| |index| |finite?| + |atrapezoidal| |remove!| |trace2PowMod| |closed?| |mdeg| + |coefficients| |nary?| |iilog| |nextSublist| |c06frf| |sech2cosh| + |cyclePartition| |nextsubResultant2| |drawToScale| |imagE| |dilog| + |point| |numberOfComputedEntries| |lazyPrem| |iFTable| |bracket| + |insertionSort!| |extract!| |expIfCan| |presub| |triangular?| + |decimal| |sin| |edf2df| |search| |createNormalPrimitivePoly| |pair| + |idealiser| |rational| |stop| |refine| |lambert| |yellow| + |constantKernel| |cos| |tubePlot| |e04dgf| |leftFactorIfCan| + |mainCharacterization| |characteristicSet| |\\/| |iisqrt3| + |structuralConstants| |multiset| |iteratedInitials| |tan| |series| + |leviCivitaSymbol| |checkForZero| |gcdcofactprim| |cycleSplit!| + |certainlySubVariety?| |powerAssociative?| |recip| |integralMatrix| + |f04mbf| |cot| |leftOne| |operators| |factorsOfCyclicGroupSize| + |cAcoth| |connect| |mapUnivariateIfCan| |diagonals| |vectorise| + |subspace| |sec| |fortranLiteralLine| |addmod| |orOperands| + |explicitlyEmpty?| |aQuadratic| |goodPoint| |pquo| |edf2efi| + |directSum| |csc| |numer| |identification| |maxColIndex| |equiv| + |roughBasicSet| |returns| |cTanh| |eulerE| |probablyZeroDim?| |min| + |asin| |denom| |c02aff| |KrullNumber| |andOperands| |mapSolve| + |write!| |s19acf| |sizeMultiplication| |gcdPolynomial| |acos| + |createMultiplicationTable| |constant?| |mulmod| |e02bdf| + |numericalIntegration| |status| |ipow| |LiePolyIfCan| + |OMconnOutDevice| |elements| |atan| |message| |pi| |factorByRecursion| + |redpps| |d02kef| |round| |airyAi| |RittWuCompare| |Beta| |iicoth| + |rewriteIdealWithQuasiMonicGenerators| |acot| |infinity| |rightTrim| + |factorGroebnerBasis| |gcdcofact| |d01bbf| |trivialIdeal?| + |unitsColorDefault| |selectOptimizationRoutines| |less?| + |multiEuclideanTree| |gethi| |asec| |obj| |leftTrim| |makeCrit| |frst| + |areEquivalent?| |truncate| |bag| |figureUnits| |drawCurves| + |rightRegularRepresentation| |c02agf| |acsc| |plusInfinity| |cache| + |iiacsc| |resultantnaif| |iitanh| |flexible?| |associatorDependence| + |fibonacci| |monicModulo| |degreePartition| + |selectIntegrationRoutines| |sinh| |compdegd| |minusInfinity| + |generators| |name| |plotPolar| |cosSinInfo| |flagFactor| |shiftRoots| + |monic?| |functionIsFracPolynomial?| |getGoodPrime| |cosh| |dom| + |df2fi| |jacobiIdentity?| |tryFunctionalDecomposition?| + |stosePrepareSubResAlgo| |ranges| |nextPrimitiveNormalPoly| |elem?| + |An| |label| |thetaCoord| |tanh| |kernel| |inf| |mainVariable| + |increasePrecision| |d01gaf| |ricDsolve| |rangeIsFinite| + |OMputEndAttr| |unitNormal| |s13adf| |coth| |draw| |headRemainder| + |pseudoRemainder| |sinhIfCan| |wholeRagits| |quasiMonicPolynomials| + |s18dcf| |viewPosDefault| |testModulus| |d01alf| |sech| |in?| |pdct| + |ScanArabic| |traverse| |consnewpol| |alternatingGroup| |lyndon| + |realEigenvectors| |headReduced?| |initials| |imagK| |cubic| |iExquo| + |s20acf| |romberg| |low| |basisOfRightAnnihilator| |singleFactorBound| + |cartesian| |parabolic| |diag| |OMgetInteger| |numberOfComponents| + |conditionP| |title| |makeObject| |inc| |child?| |quotedOperators| + |wrregime| |mainVariables| |keys| |unitVector| |monicDivide| + |OMputEndBVar| |getOperator| |e| |seriesSolve| + |semiResultantEuclidean2| |increment| |check| |error| |jacobi| + |setMinPoints| |solid| |Si| |coef| |c05adf| |resultantEuclideannaif| + |setLegalFortranSourceExtensions| |pastel| |monicLeftDivide| |assert| + |getButtonValue| |df2mf| |OMgetEndAtp| |clikeUniv| |complexRoots| + |uniform01| |prod| |sturmVariationsOf| |alphabetic?| |fill!| + |monicRightFactorIfCan| |edf2ef| |e04gcf| |notOperand| |extractIfCan| + |knownInfBasis| |palglimint| |e01bgf| |palginfieldint| + |infiniteProduct| |e04naf| |isAbsolutelyIrreducible?| |equality| |cup| + |alphanumeric| |discriminant| |debug| |cot2trig| |select!| |unravel| + |cPower| |inGroundField?| |option| |dimensionsOf| |magnitude| + |charpol| |factorial| |e02bef| |SFunction| |mathieu24| |e02ahf| + |changeName| |univariatePolynomials| |mkAnswer| |monicRightDivide| + |primaryDecomp| |splitLinear| |localReal?| |currentSubProgram| + |nextItem| |subresultantVector| |jordanAdmissible?| |node| |stirling1| + |acotIfCan| |dimensionOfIrreducibleRepresentation| + |toseLastSubResultant| |irreducibleRepresentation| |numFunEvals| + |rotatey| |extendedint| |prindINFO| |kmax| |s19adf| |entry| + |lazyPseudoDivide| |resultant| |stoseIntegralLastSubResultant| + |inRadical?| |dec| |removeSinhSq| |mapdiv| |colorDef| |c06eaf| + |taylor| |solveid| |fixedPoints| ** |cardinality| |prepareSubResAlgo| + |quasiComponent| |expintegrate| |taylorIfCan| |infRittWu?| |laurent| + |supRittWu?| |enterInCache| |float| |lazyEvaluate| |fixedDivisor| + |outlineRender| |augment| |intensity| |redPo| |puiseux| |double?| + |enumerate| |pow| |failed| |f01qcf| |lflimitedint| EQ |chebyshevT| + |graphState| |normalize| |transpose| |modifyPoint| |extendedIntegrate| + |integral| |infinite?| |complexElementary| |reorder| + |normalizedAssociate| |asecIfCan| |inv| |rootPoly| |exprToXXP| + |OMreadStr| |df2st| |omError| |powern| |rst| |definingEquations| + |reduceLODE| |ground?| |prolateSpheroidal| |changeBase| |extractIndex| + |startStats!| |d03faf| |removeSquaresIfCan| |prinpolINFO| |resize| + |s13aaf| |ground| |fixPredicate| |ravel| |directory| + |complexEigenvalues| |atom?| |var2StepsDefault| |resetVariableOrder| + |makeViewport2D| |triangSolve| |leadingMonomial| |mvar| + |binaryTournament| |eq?| |halfExtendedResultant1| |dequeue| |reshape| + |iisqrt2| |useSingleFactorBound?| |satisfy?| |leadingCoefficient| + |hessian| |lazyPquo| |removeSinSq| |zerosOf| |c06gbf| |copy!| |rowEch| + UP2UTS |primitiveMonomials| |badNum| |identity| GE |maxrank| + |OMParseError?| |stFuncN| |cschIfCan| |reductum| |prem| |minPoly| GT + |OMgetEndAttr| |subResultantsChain| |contours| |middle| |children| + |pile| |rank| |shufflein| |oddlambert| LE |e04mbf| |beauzamyBound| + |prinshINFO| |startPolynomial| |bipolarCylindrical| |showTheIFTable| + |mainValue| |createZechTable| LT |rightDivide| |uniform| |mpsode| + |update| |scan| |bfEntry| |repeatUntilLoop| |complexZeros| + |leftFactor| |subTriSet?| |represents| |GospersMethod| |zCoord| + |elementary| |f02bjf| |shellSort| |eq| |topPredicate| |eigenvectors| + |alternative?| |car| |pol| |univcase| |se2rfi| |d01aqf| |d01gbf| + |iter| |lastSubResultantElseSplit| |findCycle| |lifting1| |OMgetApp| + |cdr| |screenResolution| |completeSmith| |power| |sort| |iCompose| + |internalLastSubResultant| |credPol| |getMatch| |fortranDoubleComplex| + |aspFilename| |pushup| |complexForm| |wordInStrongGenerators| + |showTheRoutinesTable| |autoReduced?| |tab1| |returnTypeOf| + |OMsupportsSymbol?| |clipWithRanges| |chineseRemainder| + |mainMonomials| |summation| |separant| |selectNonFiniteRoutines| + |position| |nonQsign| |systemSizeIF| |midpoint| |SturmHabichtSequence| + |karatsubaDivide| |countRealRootsMultiple| |exp1| + |selectMultiDimensionalRoutines| |weight| |li| + |createLowComplexityNormalBasis| |stoseInvertibleSetreg| |mix| |trim| + |f04jgf| |randnum| |f01brf| |random| |cross| |listOfLists| |generic?| + |topFortranOutputStack| |physicalLength| |createRandomElement| + |OMconnInDevice| |isExpt| |inverseIntegralMatrixAtInfinity| + |exponentialOrder| |exp| |cot2tan| |optional?| |pushdterm| + |printStats!| |sturmSequence| |doubleRank| |critMTonD1| + |semiSubResultantGcdEuclidean1| |diff| |generalTwoFactor| + |mainCoefficients| |resetBadValues| |solve| |clipPointsDefault| + |antisymmetricTensors| |complexNumericIfCan| + |halfExtendedSubResultantGcd2| |iomode| |dihedral| |rk4qc| |cSinh| + |modularGcdPrimitive| |reverse!| |OMmakeConn| |printTypes| |s17dhf| + |generalizedContinuumHypothesisAssumed| |logical?| |s15aef| + |clearTable!| |smith| |lazyPremWithDefault| |rules| |primitive?| + |radix| |musserTrials| |prologue| |changeMeasure| |subst| |negative?| + |reopen!| |factorSquareFree| |asinhIfCan| |stoseInvertible?sqfreg| + |qfactor| |OMgetObject| |digits| |mainForm| |radPoly| |makeTerm| + |evaluateInverse| |useSingleFactorBound| |lieAdmissible?| + |solveLinearPolynomialEquationByRecursion| |fortranTypeOf| |besselK| + UTS2UP |setOrder| |datalist| |d02raf| |reducedContinuedFraction| + |chiSquare| |exprToUPS| |numberOfFactors| |trailingCoefficient| + |makeViewport3D| |mapUp!| |primeFactor| |binding| |lyndonIfCan| + |pointLists| |contains?| |implies| |insertTop!| |janko2| |iiacot| + |supersub| |computeCycleEntry| |objects| |semiDiscriminantEuclidean| + |blankSeparate| |complexLimit| |xor| |cAtan| |putGraph| |getlo| + |OMsupportsCD?| |newSubProgram| |base| |algebraicCoefficients?| + |mantissa| |d01apf| |overlabel| |OMbindTCP| |insertRoot!| + |linearAssociatedOrder| |unrankImproperPartitions1| |critpOrder| + |iiasech| |printHeader| |impliesOperands| |nextsousResultant2| + |double| |reduced?| |leftTraceMatrix| |invmultisect| |cAsin| + |scanOneDimSubspaces| |prefix| |vspace| |deleteProperty!| + |prepareDecompose| |useEisensteinCriterion?| + |characteristicPolynomial| |imaginary| |multiplyExponents| |getOrder| + |positiveSolve| |outputMeasure| |denomLODE| |representationType| + |solveInField| |rewriteSetWithReduction| |merge| |isPower| |brace| + |ratDsolve| |crest| |updatF| |outputArgs| |selectODEIVPRoutines| + |squareFreePrim| |zero?| |typeLists| |test| + |unprotectedRemoveRedundantFactors| |direction| |tableau| + |evenInfiniteProduct| |aQuartic| |sub| |getCode| |algebraicVariables| + |partialDenominators| |currentCategoryFrame| |color| + |factorSFBRlcUnit| |shallowExpand| |tanIfCan| |swapRows!| |inR?| + |d01asf| |leftScalarTimes!| |setRow!| |branchIfCan| |shrinkable| + |anticoord| |getBadValues| |setScreenResolution3D| |declare!| + |inconsistent?| |univariateSolve| |divideIfCan!| |measure2Result| + |s21bcf| |getPickedPoints| |initiallyReduce| |coord| |value| + |exteriorDifferential| |definingPolynomial| |basisOfLeftNucloid| + |realEigenvalues| |cons| |leftNorm| |calcRanges| |numberOfHues| + |findBinding| |LagrangeInterpolation| |solveLinearlyOverQ| + |externalList| |cAsec| |copyInto!| |selectsecond| |complexIntegrate| + |createPrimitiveNormalPoly| |sylvesterMatrix| |UP2ifCan| |option?| + |rspace| |limit| |freeOf?| |pushucoef| |makeEq| |messagePrint| |seed| + |previous| |phiCoord| |extendedResultant| |diagonalProduct| + |linkToFortran| |pToHdmp| |upDateBranches| |listRepresentation| + |rightScalarTimes!| |sparsityIF| |rur| |tree| |irreducible?| + |inrootof| |rewriteIdealWithHeadRemainder| + |genericRightMinimalPolynomial| |#| |changeWeightLevel| + |patternVariable| |besselY| |zero| |reciprocalPolynomial| |iidsum| + |outputAsTex| |perfectSquare?| |reducedDiscriminant| |delete!| + |duplicates| |order| |squareFreeFactors| |lazyIntegrate| |nthFactor| + |iiGamma| |block| |adjoint| |And| |extractSplittingLeaf| |notelem| + |createPrimitivePoly| |components| |antiAssociative?| |s15adf| + |genericRightDiscriminant| |Or| |char| |rischDE| |goodnessOfFit| ^ + |primintegrate| |genus| |rightQuotient| |simpson| |roughSubIdeal?| + |roughEqualIdeals?| |Not| |sum| |cAsinh| |binaryTree| |approxNthRoot| + |eulerPhi| |limitPlus| |diagonalMatrix| |groebSolve| + |ScanFloatIgnoreSpaces| |overlap| + |generalizedContinuumHypothesisAssumed?| |ParCond| |rootKerSimp| + |repeating| |domainOf| |indicialEquation| |toseSquareFreePart| |mat| + |acosIfCan| |rationalPoint?| |dmpToHdmp| |lastSubResultantEuclidean| + |retractable?| |createNormalElement| |laguerreL| |computeCycleLength| + |lastSubResultant| |removeRedundantFactors| |RemainderList| + |makeSketch| |purelyAlgebraicLeadingMonomial?| |rk4| |setMinPoints3D| + |elliptic| |log10| |setFieldInfo| |sqfree| |lazyPseudoQuotient| + |diophantineSystem| |permutation| |radicalEigenvector| |quadraticNorm| + |moduleSum| |denomRicDE| |deref| |Zero| |extractTop!| |btwFact| + |internalIntegrate0| |region| |randomLC| |members| |critMonD1| + |getOperands| |stirling2| |One| |monomial?| |LyndonWordsList1| + |OMclose| |internalInfRittWu?| |genericLeftTraceForm| |term?| + |normalElement| |irreducibleFactors| |iiacsch| |exponents| + |moreAlgebraic?| |curveColor| |arrayStack| |comp| |padicallyExpand| + |lhs| |digit?| |drawStyle| |submod| |ScanFloatIgnoreSpacesIfCan| + |decompose| |leadingIdeal| |numberOfOperations| |raisePolynomial| + |rhs| |branchPointAtInfinity?| |upperCase!| |stoseInvertibleSet| + |subset?| |ode2| |constructorName| |rCoord| |genericPosition| |hcrf| + |conical| |numericalOptimization| |leftMinimalPolynomial| |e01sbf| + |expressIdealMember| |semiResultantEuclidean1| |BasicMethod| + |showAllElements| |s14aaf| |next| |computeBasis| |delay| |trunc| + |bringDown| |monomialIntPoly| |setref| |listLoops| |radicalRoots| + |bipolar| |qelt| |OMsetEncoding| |semiLastSubResultantEuclidean| + |primPartElseUnitCanonical| |modularFactor| |viewThetaDefault| + |bitCoef| |listBranches| |cyclic| |systemCommand| |safeFloor| |one?| + |pToDmp| |divisorCascade| |lifting| |f04arf| |cyclicSubmodule| + |neglist| |e01baf| |component| |FormatArabic| |firstNumer| |iiasinh| + |cLog| |associative?| |setTopPredicate| |minimumExponent| |atanhIfCan| + |f01qdf| |factors| |randomR| |maxPoints3D| |normal| |innerSolve| + |discreteLog| |companionBlocks| |nonLinearPart| |tablePow| + |normalDenom| |var1StepsDefault| |minordet| |palgint0| |interReduce| + |setOfMinN| |viewpoint| |partition| |maximumExponent| |f04mcf| + |setleaves!| |iicos| |append| |s18aff| |patternMatchTimes| |twist| + |collectUpper| |factorset| |null?| |absolutelyIrreducible?| + |algebraicSort| |processTemplate| |SturmHabicht| |sylvesterSequence| + |nlde| |linearMatrix| NOT |internalAugment| |coshIfCan| + |integralAtInfinity?| |delete| |iiabs| |coth2trigh| |doubleComplex?| + |linearlyDependentOverZ?| |squareTop| |ode| |pureLex| |qqq| OR |terms| + |decomposeFunc| |fi2df| |surface| |particularSolution| |argscript| + |skewSFunction| |rroot| |rename| |oblateSpheroidal| + |rewriteSetByReducingWithParticularGenerators| AND |bombieriNorm| + |real?| |basisOfLeftNucleus| |sncndn| |integerIfCan| + |createThreeSpace| |isTimes| |singularAtInfinity?| |allRootsOf| + |nextPrimitivePoly| |leftRankPolynomial| |divisors| |leftDivide| + |OMputAttr| |square?| |htrigs| |viewport3D| |find| + |linearAssociatedExp| |schema| |totalfract| |nextPartition| |presuper| + |substring?| |weakBiRank| |symbolIfCan| |isobaric?| |nthRoot| + |OMgetEndApp| |removeSuperfluousQuasiComponents| |var1Steps| + |kroneckerDelta| |leftTrace| |variationOfParameters| |mapCoef| + |quotientByP| |cyclotomicFactorization| |abelianGroup| |c06fqf| + |internalZeroSetSplit| |quickSort| |numberOfComposites| + |complementaryBasis| |rootProduct| |showTheFTable| |Ei| + |rationalIfCan| |hclf| |suffix?| |someBasis| |OMputAtp| + |bandedHessian| |qroot| |minimalPolynomial| |s18def| |hMonic| + |mergeFactors| |changeThreshhold| |csch2sinh| |sortConstraints| + |diagonal?| |closedCurve?| |f07fdf| |s21bbf| |outputFixed| + |ParCondList| |dmp2rfi| |partialNumerators| |cTan| + |derivationCoordinates| |reverseLex| |aLinear| |prefix?| |xRange| + |setColumn!| |extractPoint| |cAcosh| |UpTriBddDenomInv| + |euclideanSize| |unit?| |evenlambert| |init| |printingInfo?| |reindex| + |unmakeSUP| |eigenvalues| |att2Result| |yRange| |schwerpunkt| + |generalPosition| |qPot| |integralBasis| |choosemon| |subCase?| |isOp| + |factorAndSplit| |permanent| |sh| |matrixDimensions| |basicSet| + |zRange| |integralBasisAtInfinity| |lazyResidueClass| |readable?| + |permutationGroup| |s17akf| |symFunc| |numberOfNormalPoly| |sin2csc| + |s17ahf| |lists| |eisensteinIrreducible?| |OMwrite| |returnType!| + |tail| |parts| |subMatrix| |map!| * |modTree| |leastAffineMultiple| + |leadingSupport| |elColumn2!| |key?| |powers| |socf2socdf| |sPol| + |lift| |readLineIfCan!| |fprindINFO| |build| |totalDifferential| + |swapColumns!| |qsetelt!| |leftExtendedGcd| |shanksDiscLogAlgorithm| + |quotient| |discriminantEuclidean| |product| |s17aff| |flatten| + |symmetricProduct| |plus!| |reduce| |constantLeft| |c06ebf| |s21baf| + |lazyIrreducibleFactors| |biRank| |slex| |mergeDifference| |laguerre| + |standardBasisOfCyclicSubmodule| |child| |infix| |OMputBVar| + |movedPoints| |removeRoughlyRedundantFactorsInContents| |maxdeg| + |algDsolve| |infix?| |interpretString| |f01mcf| |optpair| + |showArrayValues| |leftQuotient| |minset| |getExplanations| + |radicalSimplify| |mkcomm| |arguments| |clearFortranOutputStack| + |algSplitSimple| |d01ajf| |mask| |OMgetAttr| |vertConcat| + |approximate| |mainMonomial| |shade| |ODESolve| |leftLcm| + |stoseInvertibleSetsqfreg| |oddInfiniteProduct| |e01bef| |e02adf| + |minPoints| |aCubic| |stFunc1| |complex| |accuracyIF| |makeMulti| + |power!| |sequences| |buildSyntax| |ode1| |rightTrace| + |radicalOfLeftTraceForm| |endSubProgram| |push| |primextintfrac| + |asinIfCan| |mr| |acsch| |createNormalPoly| |drawComplex| + |setVariableOrder| |createPrimitiveElement| |odd?| |fmecg| |addPoint| + |lexTriangular| |operator| |bsolve| |dominantTerm| |cap| + |complexSolve| |swap!| |rename!| |roman| |triangularSystems| |reset| + |cfirst| |fintegrate| |combineFeatureCompatibility| + |radicalEigenvalues| |functionIsContinuousAtEndPoints| |geometric| + |f02abf| |distdfact| |separateFactors| |OMconnectTCP| |writeLine!| + |updatD| |coercePreimagesImages| |outerProduct| |viewZoomDefault| + |rightAlternative?| |cycle| |principal?| |mesh?| |rotatez| + |removeRedundantFactorsInPols| |linearAssociatedLog| + |zeroSetSplitIntoTriangularSystems| |froot| |algebraicDecompose| + |LowTriBddDenomInv| |write| |sayLength| |bezoutMatrix| |modulus| + |antiCommutator| |OMUnknownCD?| |constantOperator| |pointColor| + |antiCommutative?| |rightNorm| |cCsc| |stack| |integer?| |scripted?| + |save| |imagj| |gramschmidt| |simpleBounds?| |ramifiedAtInfinity?| + |saturate| |ridHack1| |extractBottom!| |currentEnv| |subSet| FG2F + |maxIndex| |OMencodingXML| |badValues| |sumSquares| |nullSpace| |or| + |internalSubPolSet?| |leadingExponent| |s17ajf| + |regularRepresentation| |lookup| |predicate| |nor| + |drawComplexVectorField| |logGamma| |bumptab1| |d01fcf| |epilogue| + |s18adf| |purelyTranscendental?| |and| |transcendenceDegree| + |chainSubResultants| |abs| |is?| |rowEchelon| |binary| |setRealSteps| + |fortranLogical| |clearTheIFTable| |pop!| |positiveRemainder| + |OMgetEndBVar| |sumOfKthPowerDivisors| |radicalEigenvectors| |latex| + |applyRules| |setStatus!| |rangePascalTriangle| |f02bbf| |OMgetString| + |initializeGroupForWordProblem| |solveRetract| |besselJ| |constDsolve| + |rubiksGroup| |coerceImages| |nextNormalPrimitivePoly| |inHallBasis?| + |expt| |cos2sec| |quadratic?| |lp| |univariatePolynomial| |dn| + |monomial| |bivariate?| |separate| |tracePowMod| |wronskianMatrix| F + |solveLinearPolynomialEquation| |c05nbf| |makeop| |tValues| |getCurve| + |bumptab| |genericRightTrace| |univariate?| |lowerPolynomial| |pade| + |varselect| |trueEqual| |universe| |countRealRoots| + |firstUncouplingMatrix| |mainVariable?| |frobenius| |asechIfCan| + |multivariate| |quasiMonic?| |isQuotient| |stopTableGcd!| + |setClipValue| |fortranDouble| |createIrreduciblePoly| + |bezoutResultant| |solid?| |implies?| |arg1| |showAll?| + |addMatchRestricted| |clipSurface| |partialQuotients| |OMputSymbol| + |exprHasAlgebraicWeight| |variables| |pair?| |mindegTerm| + |getMultiplicationTable| |critM| |rightTraceMatrix| |decrease| |ksec| + |root| |arg2| |e04fdf| |startTableInvSet!| |compose| + |pointColorPalette| |repeating?| |s19abf| |varList| |computePowers| + |dot| |mapMatrixIfCan| |mapBivariate| |firstDenom| |deepCopy| + |halfExtendedSubResultantGcd1| |loopPoints| |complement| |palgextint0| + |brillhartIrreducible?| |sinIfCan| |central?| |leftExactQuotient| + |complexNormalize| |largest| |complexExpand| F2FG |normalForm| + |constantRight| |c06ecf| |quoted?| |f04axf| |conditions| |whileLoop| + |subResultantGcd| |showFortranOutputStack| |deriv| |aromberg| + |prevPrime| |typeList| |twoFactor| |quadratic| |insert!| |ignore?| + |zeroSetSplit| |leftRegularRepresentation| |sqfrFactor| |makeprod| + |isPlus| |nodeOf?| |match| |adaptive| |subQuasiComponent?| |hash| + |showClipRegion| |isMult| |controlPanel| |LyndonWordsList| |height| + |cSin| |inverseColeman| |fortranCarriageReturn| |ratDenom| |totolex| + |plot| |defineProperty| |concat| |numberOfVariables| |deepExpand| + |merge!| |count| |high| |numberOfChildren| |unexpand| |quote| + |replaceKthElement| |cExp| |s17dlf| |makeUnit| |setPosition| + |operation| |baseRDE| |OMUnknownSymbol?| |shiftRight| |evaluate| + |curve?| |setprevious!| |currentScope| |inverseLaplace| |e02dcf| + |e01daf| |lex| |numFunEvals3D| |closedCurve| |trapezoidal| + |normalized?| |exQuo| |cSech| |cosh2sech| |physicalLength!| |pole?| + |bfKeys| |iiasin| |vedf2vef| |viewWriteAvailable| |highCommonTerms| + |chiSquare1| |primextendedint| |orbit| |fortranCharacter| + |solveLinear| |outputSpacing| |nextLatticePermutation| + |fortranComplex| |e02gaf| |listConjugateBases| |viewPhiDefault| + |factorOfDegree| |generalizedInverse| |bit?| + |factorSquareFreeByRecursion| |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) ((-482 |#2| |#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) ((-589 |#2|) -3703 (|has| |#2| (-970)) (|has| |#2| (-337)) (|has| |#2| (-157))) ((-589 $) -3703 (|has| |#2| (-970)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-583 (-521)) -12 (|has| |#2| (-583 (-521))) (|has| |#2| (-970))) ((-583 |#2|) |has| |#2| (-970)) ((-654 |#2|) -3703 (|has| |#2| (-337)) (|has| |#2| (-157))) ((-663) -3703 (|has| |#2| (-970)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-727) |has| |#2| (-782)) ((-728) -3703 (|has| |#2| (-782)) (|has| |#2| (-729))) ((-729) |has| |#2| (-729)) ((-730) -3703 (|has| |#2| (-782)) (|has| |#2| (-729))) ((-732) -3703 (|has| |#2| (-782)) (|has| |#2| (-729))) ((-782) |has| |#2| (-782)) ((-784) -3703 (|has| |#2| (-782)) (|has| |#2| (-729))) ((-829 (-1084)) -12 (|has| |#2| (-829 (-1084))) (|has| |#2| (-970))) ((-961 (-381 (-521))) -12 (|has| |#2| (-961 (-381 (-521)))) (|has| |#2| (-1013))) ((-961 (-521)) -12 (|has| |#2| (-961 (-521))) (|has| |#2| (-1013))) ((-961 |#2|) |has| |#2| (-1013)) ((-976 |#2|) -3703 (|has| |#2| (-970)) (|has| |#2| (-337)) (|has| |#2| (-157))) ((-976 $) |has| |#2| (-157)) ((-970) -3703 (|has| |#2| (-970)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-977) -3703 (|has| |#2| (-970)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-1025) -3703 (|has| |#2| (-970)) (|has| |#2| (-782)) (|has| |#2| (-157))) ((-1013) -3703 (|has| |#2| (-1013)) (|has| |#2| (-970)) (|has| |#2| (-782)) (|has| |#2| (-729)) (|has| |#2| (-342)) (|has| |#2| (-337)) (|has| |#2| (-157)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-1119) . T) ((-1172 |#2|) |has| |#2| (-337))) -((-3126 (((-217 |#1| |#3|) (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|) 21)) (-3859 ((|#3| (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|) 23)) (-1390 (((-217 |#1| |#3|) (-1 |#3| |#2|) (-217 |#1| |#2|)) 18))) -(((-216 |#1| |#2| |#3|) (-10 -7 (-15 -3126 ((-217 |#1| |#3|) (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|)) (-15 -3859 (|#3| (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|)) (-15 -1390 ((-217 |#1| |#3|) (-1 |#3| |#2|) (-217 |#1| |#2|)))) (-707) (-1119) (-1119)) (T -216)) -((-1390 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-217 *5 *6)) (-14 *5 (-707)) (-4 *6 (-1119)) (-4 *7 (-1119)) (-5 *2 (-217 *5 *7)) (-5 *1 (-216 *5 *6 *7)))) (-3859 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-217 *5 *6)) (-14 *5 (-707)) (-4 *6 (-1119)) (-4 *2 (-1119)) (-5 *1 (-216 *5 *6 *2)))) (-3126 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-217 *6 *7)) (-14 *6 (-707)) (-4 *7 (-1119)) (-4 *5 (-1119)) (-5 *2 (-217 *6 *5)) (-5 *1 (-216 *6 *7 *5))))) -(-10 -7 (-15 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|#2|)) NIL (|has| |#2| (-970)))) (-4163 (((-707) (-1 (-108) |#2|) $) NIL (|has| $ (-6 -4233))) (((-707) |#2| $) NIL (-12 (|has| $ (-6 -4233)) (|has| |#2| (-1013))))) (-2404 (($ $) NIL)) (-2189 (((-1165 |#2|) $) 10) (($ (-521)) NIL (-3703 (-12 (|has| |#2| (-961 (-521))) (|has| |#2| (-1013))) (|has| |#2| (-970)))) (($ (-381 (-521))) NIL (-12 (|has| |#2| (-961 (-381 (-521)))) (|has| |#2| (-1013)))) (($ |#2|) 13 (|has| |#2| (-1013))) (((-792) $) NIL (|has| |#2| (-561 (-792))))) (-3846 (((-707)) NIL (|has| |#2| (-970)))) (-3049 (((-108) (-1 (-108) |#2|) $) NIL (|has| $ (-6 -4233)))) (-3304 (($ $) NIL (|has| |#2| (-782)))) (-3505 (($ $ (-707)) NIL (|has| |#2| (-970))) (($ $ (-850)) NIL (|has| |#2| (-970)))) (-3561 (($) 35 (|has| |#2| (-124)) CONST)) (-3572 (($) 38 (|has| |#2| (-970)) CONST)) (-2212 (($ $) NIL (-12 (|has| |#2| (-210)) (|has| |#2| (-970)))) (($ $ (-707)) NIL (-12 (|has| |#2| (-210)) (|has| |#2| (-970)))) (($ $ (-1084)) NIL (-12 (|has| |#2| (-829 (-1084))) (|has| |#2| (-970)))) 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(|has| |#2| (-970))) (($ $ |#2|) 42 (|has| |#2| (-663))) (($ |#2| $) 43 (|has| |#2| (-663))) (($ (-707) $) NIL (|has| |#2| (-124))) (($ (-850) $) NIL (|has| |#2| (-25)))) (-3475 (((-707) $) NIL (|has| $ (-6 -4233))))) +((-2015 (*1 *1 *2) (-12 (-5 *2 (-1165 *4)) (-4 *4 (-1119)) (-4 *1 (-215 *3 *4)))) (-2965 (*1 *1 *2) (-12 (-5 *2 (-849)) (-4 *1 (-215 *3 *4)) (-4 *4 (-970)) (-4 *4 (-1119)))) (-4103 (*1 *2 *1 *1) (-12 (-4 *1 (-215 *3 *2)) (-4 *2 (-1119)) (-4 *2 (-970)))) (* (*1 *1 *1 *2) (-12 (-4 *1 (-215 *3 *2)) (-4 *2 (-1119)) (-4 *2 (-663)))) (* (*1 *1 *2 *1) (-12 (-4 *1 (-215 *3 *2)) (-4 *2 (-1119)) (-4 *2 (-663))))) +(-13 (-554 (-521) |t#2|) (-561 (-1165 |t#2|)) (-10 -8 (-6 -4233) (-15 -2015 ($ (-1165 |t#2|))) (IF (|has| |t#2| (-1013)) (-6 (-385 |t#2|)) |%noBranch|) (IF (|has| |t#2| (-970)) (PROGN (-6 (-107 |t#2| |t#2|)) (-6 (-208 |t#2|)) (-6 (-351 |t#2|)) (-15 -2965 ($ (-849))) (-15 -4103 (|t#2| $ $))) |%noBranch|) (IF (|has| |t#2| (-25)) (-6 (-25)) |%noBranch|) (IF (|has| |t#2| (-124)) (-6 (-124)) |%noBranch|) (IF (|has| |t#2| (-663)) (PROGN (-15 * ($ |t#2| $)) (-15 * ($ $ |t#2|))) |%noBranch|) (IF (|has| |t#2| (-342)) (-6 (-342)) |%noBranch|) (IF (|has| |t#2| (-157)) (PROGN (-6 (-37 |t#2|)) (-6 (-157))) |%noBranch|) (IF (|has| |t#2| (-6 -4230)) (-6 -4230) |%noBranch|) (IF (|has| |t#2| (-781)) (-6 (-781)) |%noBranch|) (IF (|has| |t#2| (-729)) (-6 (-729)) |%noBranch|) (IF (|has| |t#2| (-337)) (-6 (-1172 |t#2|)) |%noBranch|))) +(((-21) -3703 (|has| |#2| (-970)) (|has| |#2| (-781)) (|has| |#2| (-337)) (|has| |#2| (-157))) ((-23) -3703 (|has| |#2| (-970)) (|has| |#2| (-781)) (|has| |#2| (-729)) (|has| |#2| (-337)) (|has| |#2| (-157)) (|has| |#2| (-124))) ((-25) -3703 (|has| |#2| (-970)) (|has| |#2| (-781)) (|has| |#2| (-729)) (|has| |#2| (-337)) (|has| |#2| (-157)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-33) . T) ((-37 |#2|) |has| |#2| (-157)) ((-97) -3703 (|has| |#2| (-1013)) (|has| |#2| (-970)) (|has| |#2| (-781)) (|has| |#2| (-729)) (|has| |#2| (-342)) (|has| |#2| (-337)) (|has| |#2| (-157)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3703 (|has| |#2| (-970)) (|has| |#2| (-337)) (|has| |#2| (-157))) ((-107 $ $) |has| |#2| (-157)) ((-124) -3703 (|has| |#2| (-970)) (|has| |#2| (-781)) (|has| |#2| (-729)) (|has| |#2| (-337)) (|has| |#2| (-157)) (|has| |#2| (-124))) ((-561 (-791)) -3703 (|has| |#2| (-1013)) (|has| |#2| (-970)) (|has| |#2| (-781)) (|has| |#2| (-729)) (|has| |#2| (-342)) (|has| |#2| (-337)) (|has| |#2| (-157)) (|has| |#2| (-561 (-791))) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-561 (-1165 |#2|)) . T) ((-157) |has| |#2| (-157)) ((-208 |#2|) |has| |#2| (-970)) ((-210) -12 (|has| |#2| (-210)) (|has| |#2| (-970))) ((-261 #0=(-521) |#2|) . T) ((-263 #0# |#2|) . T) ((-284 |#2|) -12 (|has| |#2| (-284 |#2|)) (|has| |#2| (-1013))) ((-342) |has| |#2| (-342)) ((-351 |#2|) |has| |#2| (-970)) ((-385 |#2|) |has| |#2| (-1013)) ((-460 |#2|) . T) ((-554 #0# |#2|) . 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T) ((-1172 |#2|) |has| |#2| (-337))) +((-3184 (((-217 |#1| |#3|) (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|) 21)) (-3859 ((|#3| (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|) 23)) (-1393 (((-217 |#1| |#3|) (-1 |#3| |#2|) (-217 |#1| |#2|)) 18))) +(((-216 |#1| |#2| |#3|) (-10 -7 (-15 -3184 ((-217 |#1| |#3|) (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|)) (-15 -3859 (|#3| (-1 |#3| |#2| |#3|) (-217 |#1| |#2|) |#3|)) (-15 -1393 ((-217 |#1| |#3|) (-1 |#3| |#2|) (-217 |#1| |#2|)))) (-707) (-1119) (-1119)) (T -216)) +((-1393 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-217 *5 *6)) (-14 *5 (-707)) (-4 *6 (-1119)) (-4 *7 (-1119)) (-5 *2 (-217 *5 *7)) (-5 *1 (-216 *5 *6 *7)))) (-3859 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-217 *5 *6)) (-14 *5 (-707)) (-4 *6 (-1119)) (-4 *2 (-1119)) (-5 *1 (-216 *5 *6 *2)))) (-3184 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-217 *6 *7)) (-14 *6 (-707)) (-4 *7 (-1119)) (-4 *5 (-1119)) (-5 *2 (-217 *6 *5)) (-5 *1 (-216 *6 *7 *5))))) +(-10 -7 (-15 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|#1|)) (-15 -2006 ((-108) (-1 (-108) |#2|) |#1|)) (-15 -3478 ((-707) |#1|))) (-460 |#2|) (-1119)) (T -459)) +NIL +(-10 -8 (-15 -2223 ((-791) |#1|)) (-15 -1549 ((-108) |#1| |#1|)) (-15 -2313 (|#1| |#1| (-587 |#2|) (-587 |#2|))) (-15 -2313 (|#1| |#1| |#2| |#2|)) (-15 -2313 (|#1| |#1| (-269 |#2|))) (-15 -2313 (|#1| |#1| (-587 (-269 |#2|)))) (-15 -1785 ((-108) |#2| |#1|)) (-15 -4163 ((-707) |#2| |#1|)) (-15 -3568 ((-587 |#2|) |#1|)) (-15 -4163 ((-707) (-1 (-108) |#2|) |#1|)) (-15 -1936 ((-108) (-1 (-108) |#2|) |#1|)) (-15 -2006 ((-108) (-1 (-108) |#2|) |#1|)) (-15 -3478 ((-707) |#1|))) +((-1422 (((-108) $ $) 19 (|has| |#1| (-1013)))) (-1269 (((-108) $ (-707)) 8)) (-2231 (($) 7 T CONST)) (-3831 (((-587 |#1|) $) 30 (|has| $ (-6 -4233)))) (-1513 (((-108) $ (-707)) 9)) (-3568 (((-587 |#1|) $) 29 (|has| $ (-6 -4233)))) (-1785 (((-108) |#1| $) 27 (-12 (|has| |#1| (-1013)) (|has| $ (-6 -4233))))) (-3833 (($ (-1 |#1| |#1|) $) 34 (|has| $ (-6 -4234)))) (-1393 (($ (-1 |#1| |#1|) $) 35)) (-2859 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T) ((-97) |has| |#1| (-1013)) ((-561 (-792)) -3703 (|has| |#1| (-1013)) (|has| |#1| (-561 (-792)))) ((-284 |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013))) ((-482 |#1| |#1|) -12 (|has| |#1| (-284 |#1|)) (|has| |#1| (-1013))) ((-1013) |has| |#1| (-1013)) ((-1119) . 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2959064 2959107 "UPOLYC" 2961185 NIL UPOLYC (NIL T) -9 NIL 2962405) (-1140 2942460 2944864 2947989 "UPOLYC-" 2947994 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1139 2942091 2942134 2942265 "UPOLYC2" 2942411 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1138 2933550 2941660 2941797 "UP" 2942001 NIL UP (NIL NIL T) -8 NIL NIL) (-1137 2932893 2933000 2933163 "UPMP" 2933439 NIL UPMP (NIL T T) -7 NIL NIL) (-1136 2932446 2932527 2932666 "UPDIVP" 2932806 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1135 2931014 2931263 2931579 "UPDECOMP" 2932195 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1134 2930249 2930361 2930546 "UPCDEN" 2930898 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1133 2929772 2929841 2929988 "UP2" 2930174 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1132 2928289 2928976 2929253 "UNISEG" 2929530 NIL UNISEG (NIL T) -8 NIL NIL) (-1131 2927504 2927631 2927836 "UNISEG2" 2928132 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1130 2926564 2926744 2926970 "UNIFACT" 2927320 NIL UNIFACT (NIL T) -7 NIL NIL) (-1129 2910463 2925745 2925995 "ULS" 2926371 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1128 2898431 2910368 2910439 "ULSCONS" 2910444 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1127 2881184 2893194 2893256 "ULSCCAT" 2893968 NIL ULSCCAT (NIL T T) -9 NIL 2894264) (-1126 2880235 2880480 2880867 "ULSCCAT-" 2880872 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1125 2870228 2876742 2876785 "ULSCAT" 2877641 NIL ULSCAT (NIL T) -9 NIL 2878371) (-1124 2869662 2869741 2869918 "ULS2" 2870143 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1123 2868059 2869026 2869057 "UFD" 2869269 T UFD (NIL) -9 NIL 2869383) (-1122 2867853 2867899 2867994 "UFD-" 2867999 NIL UFD- (NIL T) -8 NIL NIL) (-1121 2866935 2867118 2867334 "UDVO" 2867659 T UDVO (NIL) -7 NIL NIL) (-1120 2864751 2865160 2865631 "UDPO" 2866499 NIL UDPO (NIL T) -7 NIL NIL) (-1119 2864683 2864688 2864719 "TYPE" 2864724 T TYPE (NIL) -9 NIL NIL) (-1118 2863654 2863856 2864096 "TWOFACT" 2864477 NIL TWOFACT (NIL T) -7 NIL NIL) (-1117 2862592 2862929 2863192 "TUPLE" 2863426 NIL TUPLE (NIL T) -8 NIL NIL) (-1116 2860283 2860802 2861341 "TUBETOOL" 2862075 T TUBETOOL (NIL) -7 NIL NIL) (-1115 2859132 2859337 2859578 "TUBE" 2860076 NIL TUBE (NIL T) -8 NIL NIL) (-1114 2853856 2858110 2858392 "TS" 2858884 NIL TS (NIL T) -8 NIL NIL) (-1113 2842559 2846651 2846748 "TSETCAT" 2851982 NIL TSETCAT (NIL T T T T) -9 NIL 2853513) (-1112 2837294 2838892 2840782 "TSETCAT-" 2840787 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1111 2831557 2832403 2833345 "TRMANIP" 2836430 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1110 2830998 2831061 2831224 "TRIMAT" 2831489 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1109 2828804 2829041 2829404 "TRIGMNIP" 2830747 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1108 2828323 2828436 2828467 "TRIGCAT" 2828680 T TRIGCAT (NIL) -9 NIL NIL) (-1107 2827992 2828071 2828212 "TRIGCAT-" 2828217 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1106 2824891 2826852 2827132 "TREE" 2827747 NIL TREE (NIL T) -8 NIL NIL) (-1105 2824164 2824692 2824723 "TRANFUN" 2824758 T TRANFUN (NIL) -9 NIL 2824824) (-1104 2823443 2823634 2823914 "TRANFUN-" 2823919 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1103 2823247 2823279 2823340 "TOPSP" 2823404 T TOPSP (NIL) -7 NIL NIL) (-1102 2822599 2822714 2822867 "TOOLSIGN" 2823128 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1101 2821260 2821776 2822015 "TEXTFILE" 2822382 T TEXTFILE (NIL) -8 NIL NIL) (-1100 2819125 2819639 2820077 "TEX" 2820844 T TEX (NIL) -8 NIL NIL) (-1099 2818906 2818937 2819009 "TEX1" 2819088 NIL TEX1 (NIL T) -7 NIL NIL) (-1098 2818554 2818617 2818707 "TEMUTL" 2818838 T TEMUTL (NIL) -7 NIL NIL) (-1097 2816708 2816988 2817313 "TBCMPPK" 2818277 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1096 2808596 2814868 2814925 "TBAGG" 2815325 NIL TBAGG (NIL T T) -9 NIL 2815536) (-1095 2803666 2805154 2806908 "TBAGG-" 2806913 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1094 2803050 2803157 2803302 "TANEXP" 2803555 NIL TANEXP (NIL T) -7 NIL NIL) (-1093 2796551 2802907 2803000 "TABLE" 2803005 NIL TABLE (NIL T T) -8 NIL NIL) (-1092 2795964 2796062 2796200 "TABLEAU" 2796448 NIL TABLEAU (NIL T) -8 NIL NIL) (-1091 2790572 2791792 2793040 "TABLBUMP" 2794750 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1090 2787035 2787730 2788513 "SYSSOLP" 2789823 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1089 2783419 2784022 2784762 "SYNTAX" 2786317 T SYNTAX (NIL) -8 NIL NIL) (-1088 2780553 2781161 2781799 "SYMTAB" 2782803 T SYMTAB (NIL) -8 NIL NIL) (-1087 2775802 2776704 2777687 "SYMS" 2779592 T SYMS (NIL) -8 NIL NIL) (-1086 2773035 2775262 2775491 "SYMPOLY" 2775607 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1085 2772555 2772630 2772752 "SYMFUNC" 2772947 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1084 2768533 2769792 2770614 "SYMBOL" 2771755 T SYMBOL (NIL) -8 NIL NIL) (-1083 2762072 2763761 2765481 "SWITCH" 2766835 T SWITCH (NIL) -8 NIL NIL) (-1082 2755305 2760899 2761201 "SUTS" 2761827 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1081 2747198 2754426 2754706 "SUPXS" 2755082 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1080 2738730 2746819 2746944 "SUP" 2747107 NIL SUP (NIL T) -8 NIL NIL) (-1079 2737889 2738016 2738233 "SUPFRACF" 2738598 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1078 2737514 2737573 2737684 "SUP2" 2737824 NIL SUP2 (NIL T T) -7 NIL NIL) (-1077 2735932 2736206 2736568 "SUMRF" 2737213 NIL SUMRF (NIL T) -7 NIL NIL) (-1076 2735249 2735315 2735513 "SUMFS" 2735853 NIL SUMFS (NIL T T) -7 NIL NIL) (-1075 2719188 2734430 2734680 "SULS" 2735056 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1074 2718510 2718713 2718853 "SUCH" 2719096 NIL SUCH (NIL T T) -8 NIL NIL) (-1073 2712437 2713449 2714407 "SUBSPACE" 2717598 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1072 2711867 2711957 2712121 "SUBRESP" 2712325 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1071 2705236 2706532 2707843 "STTF" 2710603 NIL STTF (NIL T) -7 NIL NIL) (-1070 2699409 2700529 2701676 "STTFNC" 2704136 NIL STTFNC (NIL T) -7 NIL NIL) (-1069 2690760 2692627 2694420 "STTAYLOR" 2697650 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1068 2684004 2690624 2690707 "STRTBL" 2690712 NIL STRTBL (NIL T) -8 NIL NIL) (-1067 2679395 2683959 2683990 "STRING" 2683995 T STRING (NIL) -8 NIL NIL) (-1066 2674283 2678768 2678799 "STRICAT" 2678858 T STRICAT (NIL) -9 NIL 2678920) (-1065 2666999 2671806 2672426 "STREAM" 2673698 NIL STREAM (NIL T) -8 NIL NIL) (-1064 2666509 2666586 2666730 "STREAM3" 2666916 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1063 2665491 2665674 2665909 "STREAM2" 2666322 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1062 2665179 2665231 2665324 "STREAM1" 2665433 NIL STREAM1 (NIL T) -7 NIL NIL) (-1061 2664195 2664376 2664607 "STINPROD" 2664995 NIL STINPROD (NIL T) -7 NIL NIL) (-1060 2663773 2663957 2663988 "STEP" 2664068 T STEP (NIL) -9 NIL 2664146) (-1059 2657316 2663672 2663749 "STBL" 2663754 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1058 2652491 2656538 2656582 "STAGG" 2656735 NIL STAGG (NIL T) -9 NIL 2656824) (-1057 2650193 2650795 2651667 "STAGG-" 2651672 NIL STAGG- (NIL T T) -8 NIL NIL) (-1056 2648388 2649963 2650055 "STACK" 2650136 NIL STACK (NIL T) -8 NIL NIL) (-1055 2641119 2646535 2646990 "SREGSET" 2648018 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1054 2633559 2634927 2636439 "SRDCMPK" 2639725 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1053 2626526 2630999 2631030 "SRAGG" 2632333 T SRAGG (NIL) -9 NIL 2632941) (-1052 2625543 2625798 2626177 "SRAGG-" 2626182 NIL SRAGG- (NIL T) -8 NIL NIL) (-1051 2619992 2624462 2624889 "SQMATRIX" 2625162 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1050 2613744 2616712 2617438 "SPLTREE" 2619338 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1049 2609734 2610400 2611046 "SPLNODE" 2613170 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1048 2608780 2609013 2609044 "SPFCAT" 2609488 T SPFCAT (NIL) -9 NIL NIL) (-1047 2607517 2607727 2607991 "SPECOUT" 2608538 T SPECOUT (NIL) -7 NIL NIL) (-1046 2607278 2607318 2607387 "SPADPRSR" 2607470 T SPADPRSR (NIL) -7 NIL NIL) (-1045 2599300 2601047 2601090 "SPACEC" 2605413 NIL SPACEC (NIL T) -9 NIL 2607229) (-1044 2597472 2599233 2599281 "SPACE3" 2599286 NIL SPACE3 (NIL T) -8 NIL NIL) (-1043 2596224 2596395 2596686 "SORTPAK" 2597277 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1042 2594280 2594583 2595001 "SOLVETRA" 2595888 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1041 2593291 2593513 2593787 "SOLVESER" 2594053 NIL SOLVESER (NIL T) -7 NIL NIL) (-1040 2588511 2589392 2590394 "SOLVERAD" 2592343 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1039 2584326 2584935 2585664 "SOLVEFOR" 2587878 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1038 2578625 2583677 2583774 "SNTSCAT" 2583779 NIL SNTSCAT (NIL T T T T) -9 NIL 2583849) (-1037 2572730 2576956 2577346 "SMTS" 2578315 NIL SMTS (NIL T T T) -8 NIL NIL) (-1036 2567141 2572619 2572695 "SMP" 2572700 NIL SMP (NIL T T) -8 NIL NIL) (-1035 2565300 2565601 2565999 "SMITH" 2566838 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1034 2558264 2562460 2562563 "SMATCAT" 2563903 NIL SMATCAT (NIL NIL T T T) -9 NIL 2564452) (-1033 2555205 2556028 2557205 "SMATCAT-" 2557210 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1032 2552918 2554441 2554485 "SKAGG" 2554746 NIL SKAGG (NIL T) -9 NIL 2554881) (-1031 2548976 2552022 2552300 "SINT" 2552662 T SINT (NIL) -8 NIL NIL) (-1030 2548748 2548786 2548852 "SIMPAN" 2548932 T SIMPAN (NIL) -7 NIL NIL) (-1029 2547586 2547807 2548082 "SIGNRF" 2548507 NIL SIGNRF (NIL T) -7 NIL NIL) (-1028 2546395 2546546 2546836 "SIGNEF" 2547415 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1027 2544085 2544539 2545045 "SHP" 2545936 NIL SHP (NIL T NIL) -7 NIL NIL) (-1026 2537938 2543986 2544062 "SHDP" 2544067 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1025 2537427 2537619 2537650 "SGROUP" 2537802 T SGROUP (NIL) -9 NIL 2537889) (-1024 2537197 2537249 2537353 "SGROUP-" 2537358 NIL SGROUP- (NIL T) -8 NIL NIL) (-1023 2534033 2534730 2535453 "SGCF" 2536496 T SGCF (NIL) -7 NIL NIL) (-1022 2528431 2533483 2533580 "SFRTCAT" 2533585 NIL SFRTCAT (NIL T T T T) -9 NIL 2533623) (-1021 2521891 2522906 2524040 "SFRGCD" 2527414 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1020 2515057 2516128 2517312 "SFQCMPK" 2520824 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1019 2514679 2514768 2514878 "SFORT" 2514998 NIL SFORT (NIL T T) -8 NIL NIL) (-1018 2513824 2514519 2514640 "SEXOF" 2514645 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1017 2512958 2513705 2513773 "SEX" 2513778 T SEX (NIL) -8 NIL NIL) (-1016 2507734 2508423 2508519 "SEXCAT" 2512290 NIL SEXCAT (NIL T T T T T) -9 NIL 2512909) (-1015 2504914 2507668 2507716 "SET" 2507721 NIL SET (NIL T) -8 NIL NIL) (-1014 2503165 2503627 2503932 "SETMN" 2504655 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1013 2502772 2502898 2502929 "SETCAT" 2503046 T SETCAT (NIL) -9 NIL 2503130) (-1012 2502552 2502604 2502703 "SETCAT-" 2502708 NIL SETCAT- (NIL T) -8 NIL NIL) (-1011 2498939 2501013 2501057 "SETAGG" 2501927 NIL SETAGG (NIL T) -9 NIL 2502267) (-1010 2498397 2498513 2498750 "SETAGG-" 2498755 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1009 2497600 2497893 2497955 "SEGXCAT" 2498241 NIL SEGXCAT (NIL T T) -9 NIL 2498361) (-1008 2496656 2497266 2497448 "SEG" 2497453 NIL SEG (NIL T) -8 NIL NIL) (-1007 2495562 2495775 2495819 "SEGCAT" 2496401 NIL SEGCAT (NIL T) -9 NIL 2496639) (-1006 2494611 2494941 2495141 "SEGBIND" 2495397 NIL SEGBIND (NIL T) -8 NIL NIL) (-1005 2494232 2494291 2494404 "SEGBIND2" 2494546 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1004 2493451 2493577 2493781 "SEG2" 2494076 NIL SEG2 (NIL T T) -7 NIL NIL) (-1003 2492888 2493386 2493433 "SDVAR" 2493438 NIL SDVAR (NIL T) -8 NIL NIL) (-1002 2485140 2492661 2492789 "SDPOL" 2492794 NIL SDPOL (NIL T) -8 NIL NIL) (-1001 2483733 2483999 2484318 "SCPKG" 2484855 NIL SCPKG (NIL T) -7 NIL NIL) (-1000 2482870 2483049 2483249 "SCOPE" 2483555 T SCOPE (NIL) -8 NIL NIL) (-999 2482097 2482230 2482407 "SCACHE" 2482725 NIL SCACHE (NIL T) -7 NIL NIL) (-998 2481540 2481861 2481944 "SAOS" 2482034 T SAOS (NIL) -8 NIL NIL) (-997 2481108 2481143 2481314 "SAERFFC" 2481499 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-996 2475004 2481007 2481085 "SAE" 2481090 NIL SAE (NIL T T NIL) -8 NIL NIL) (-995 2474600 2474635 2474792 "SAEFACT" 2474963 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-994 2472926 2473240 2473639 "RURPK" 2474266 NIL RURPK (NIL T NIL) -7 NIL NIL) (-993 2471579 2471856 2472163 "RULESET" 2472762 NIL RULESET (NIL T T T) -8 NIL NIL) (-992 2468787 2469290 2469751 "RULE" 2471261 NIL RULE (NIL T T T) -8 NIL NIL) (-991 2468429 2468584 2468665 "RULECOLD" 2468739 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-990 2463321 2464115 2465031 "RSETGCD" 2467628 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-989 2452635 2457687 2457782 "RSETCAT" 2461847 NIL RSETCAT (NIL T T T T) -9 NIL 2462944) (-988 2450566 2451105 2451925 "RSETCAT-" 2451930 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-987 2442996 2444371 2445887 "RSDCMPK" 2449165 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-986 2441013 2441454 2441527 "RRCC" 2442603 NIL RRCC (NIL T T) -9 NIL 2442947) (-985 2440367 2440541 2440817 "RRCC-" 2440822 NIL RRCC- (NIL T T T) -8 NIL NIL) (-984 2414733 2424358 2424423 "RPOLCAT" 2434925 NIL RPOLCAT (NIL T T T) -9 NIL 2438083) (-983 2406237 2408575 2411693 "RPOLCAT-" 2411698 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-982 2397303 2404467 2404947 "ROUTINE" 2405777 T ROUTINE (NIL) -8 NIL NIL) (-981 2394008 2396859 2397006 "ROMAN" 2397176 T ROMAN (NIL) -8 NIL NIL) (-980 2392294 2392879 2393136 "ROIRC" 2393814 NIL ROIRC (NIL T T) -8 NIL NIL) (-979 2388698 2391002 2391031 "RNS" 2391327 T RNS (NIL) -9 NIL 2391597) (-978 2387212 2387595 2388126 "RNS-" 2388199 NIL RNS- (NIL T) -8 NIL NIL) (-977 2386637 2387045 2387074 "RNG" 2387079 T RNG (NIL) -9 NIL 2387100) (-976 2386034 2386396 2386437 "RMODULE" 2386497 NIL RMODULE (NIL T) -9 NIL 2386539) (-975 2384886 2384980 2385310 "RMCAT2" 2385935 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-974 2381600 2384069 2384390 "RMATRIX" 2384621 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-973 2374596 2376830 2376943 "RMATCAT" 2380252 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2381234) (-972 2373975 2374122 2374425 "RMATCAT-" 2374430 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-971 2373545 2373620 2373746 "RINTERP" 2373894 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-970 2372595 2373159 2373188 "RING" 2373298 T RING (NIL) -9 NIL 2373392) (-969 2372390 2372434 2372528 "RING-" 2372533 NIL RING- (NIL T) -8 NIL NIL) (-968 2371238 2371475 2371731 "RIDIST" 2372154 T RIDIST (NIL) -7 NIL NIL) (-967 2362560 2370712 2370915 "RGCHAIN" 2371087 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-966 2359565 2360179 2360847 "RF" 2361924 NIL RF (NIL T) -7 NIL NIL) (-965 2359214 2359277 2359378 "RFFACTOR" 2359496 NIL RFFACTOR (NIL T) -7 NIL NIL) (-964 2358942 2358977 2359072 "RFFACT" 2359173 NIL RFFACT (NIL T) -7 NIL NIL) (-963 2357072 2357436 2357816 "RFDIST" 2358582 T RFDIST (NIL) -7 NIL NIL) (-962 2356530 2356622 2356782 "RETSOL" 2356974 NIL RETSOL (NIL T T) -7 NIL NIL) (-961 2356122 2356202 2356244 "RETRACT" 2356434 NIL RETRACT (NIL T) -9 NIL NIL) (-960 2355974 2355999 2356083 "RETRACT-" 2356088 NIL RETRACT- (NIL T T) -8 NIL NIL) (-959 2348832 2355631 2355756 "RESULT" 2355869 T RESULT (NIL) -8 NIL NIL) (-958 2347417 2348106 2348303 "RESRING" 2348735 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-957 2347057 2347106 2347202 "RESLATC" 2347354 NIL RESLATC (NIL T) -7 NIL NIL) (-956 2346766 2346800 2346905 "REPSQ" 2347016 NIL REPSQ (NIL T) -7 NIL NIL) (-955 2344197 2344777 2345377 "REP" 2346186 T REP (NIL) -7 NIL NIL) (-954 2343898 2343932 2344041 "REPDB" 2344156 NIL REPDB (NIL T) -7 NIL NIL) (-953 2337843 2339222 2340442 "REP2" 2342710 NIL REP2 (NIL T) -7 NIL NIL) (-952 2334249 2334930 2335735 "REP1" 2337070 NIL REP1 (NIL T) -7 NIL NIL) (-951 2326995 2332410 2332862 "REGSET" 2333880 NIL REGSET (NIL T T T T) -8 NIL NIL) (-950 2325816 2326151 2326399 "REF" 2326780 NIL REF (NIL T) -8 NIL NIL) (-949 2325197 2325300 2325465 "REDORDER" 2325700 NIL REDORDER (NIL T T) -7 NIL NIL) (-948 2321166 2324431 2324652 "RECLOS" 2325028 NIL RECLOS (NIL T) -8 NIL NIL) (-947 2320223 2320404 2320617 "REALSOLV" 2320973 T REALSOLV (NIL) -7 NIL NIL) (-946 2320070 2320111 2320140 "REAL" 2320145 T REAL (NIL) -9 NIL 2320180) (-945 2316561 2317363 2318245 "REAL0Q" 2319235 NIL REAL0Q (NIL T) -7 NIL NIL) (-944 2312172 2313160 2314219 "REAL0" 2315542 NIL REAL0 (NIL T) -7 NIL NIL) (-943 2311580 2311652 2311857 "RDIV" 2312094 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-942 2310653 2310827 2311038 "RDIST" 2311402 NIL RDIST (NIL T) -7 NIL NIL) (-941 2309257 2309544 2309913 "RDETRS" 2310361 NIL RDETRS (NIL T T) -7 NIL NIL) (-940 2307078 2307532 2308067 "RDETR" 2308799 NIL RDETR (NIL T T) -7 NIL NIL) (-939 2305694 2305972 2306373 "RDEEFS" 2306794 NIL RDEEFS (NIL T T) -7 NIL NIL) (-938 2304194 2304500 2304929 "RDEEF" 2305382 NIL RDEEF (NIL T T) -7 NIL NIL) (-937 2298478 2301410 2301439 "RCFIELD" 2302716 T RCFIELD (NIL) -9 NIL 2303446) (-936 2296547 2297051 2297744 "RCFIELD-" 2297817 NIL RCFIELD- (NIL T) -8 NIL NIL) (-935 2292878 2294663 2294705 "RCAGG" 2295776 NIL RCAGG (NIL T) -9 NIL 2296241) (-934 2292509 2292603 2292763 "RCAGG-" 2292768 NIL RCAGG- (NIL T T) -8 NIL NIL) (-933 2291854 2291965 2292127 "RATRET" 2292393 NIL RATRET (NIL T) -7 NIL NIL) (-932 2291411 2291478 2291597 "RATFACT" 2291782 NIL RATFACT (NIL T) -7 NIL NIL) (-931 2290726 2290846 2290996 "RANDSRC" 2291281 T RANDSRC (NIL) -7 NIL NIL) (-930 2290463 2290507 2290578 "RADUTIL" 2290675 T RADUTIL (NIL) -7 NIL NIL) (-929 2283470 2289206 2289523 "RADIX" 2290178 NIL RADIX (NIL NIL) -8 NIL NIL) (-928 2275040 2283314 2283442 "RADFF" 2283447 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-927 2274691 2274766 2274795 "RADCAT" 2274952 T RADCAT (NIL) -9 NIL NIL) (-926 2274476 2274524 2274621 "RADCAT-" 2274626 NIL RADCAT- (NIL T) -8 NIL NIL) (-925 2272627 2274251 2274340 "QUEUE" 2274420 NIL QUEUE (NIL T) -8 NIL NIL) (-924 2269124 2272564 2272609 "QUAT" 2272614 NIL QUAT (NIL T) -8 NIL NIL) (-923 2268762 2268805 2268932 "QUATCT2" 2269075 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-922 2262555 2265935 2265976 "QUATCAT" 2266755 NIL QUATCAT (NIL T) -9 NIL 2267520) (-921 2258699 2259736 2261123 "QUATCAT-" 2261217 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-920 2256219 2257783 2257825 "QUAGG" 2258200 NIL QUAGG (NIL T) -9 NIL 2258375) (-919 2255144 2255617 2255789 "QFORM" 2256091 NIL QFORM (NIL NIL T) -8 NIL NIL) (-918 2246440 2251698 2251739 "QFCAT" 2252397 NIL QFCAT (NIL T) -9 NIL 2253390) (-917 2242012 2243213 2244804 "QFCAT-" 2244898 NIL QFCAT- (NIL T T) -8 NIL NIL) (-916 2241650 2241693 2241820 "QFCAT2" 2241963 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-915 2241110 2241220 2241350 "QEQUAT" 2241540 T QEQUAT (NIL) -8 NIL NIL) (-914 2234296 2235367 2236549 "QCMPACK" 2240043 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-913 2231872 2232293 2232721 "QALGSET" 2233951 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-912 2231117 2231291 2231523 "QALGSET2" 2231692 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-911 2229808 2230031 2230348 "PWFFINTB" 2230890 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-910 2227996 2228164 2228517 "PUSHVAR" 2229622 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-909 2223913 2224967 2225009 "PTRANFN" 2226893 NIL PTRANFN (NIL T) -9 NIL NIL) (-908 2222325 2222616 2222937 "PTPACK" 2223624 NIL PTPACK (NIL T) -7 NIL NIL) (-907 2221961 2222018 2222125 "PTFUNC2" 2222262 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-906 2216437 2220778 2220819 "PTCAT" 2221187 NIL PTCAT (NIL T) -9 NIL 2221349) (-905 2216095 2216130 2216254 "PSQFR" 2216396 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-904 2214690 2214988 2215322 "PSEUDLIN" 2215793 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-903 2201498 2203862 2206185 "PSETPK" 2212450 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-902 2194584 2197298 2197393 "PSETCAT" 2200374 NIL PSETCAT (NIL T T T T) -9 NIL 2201188) (-901 2192422 2193056 2193875 "PSETCAT-" 2193880 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-900 2191770 2191935 2191964 "PSCURVE" 2192232 T PSCURVE (NIL) -9 NIL 2192399) (-899 2188221 2189747 2189812 "PSCAT" 2190648 NIL PSCAT (NIL T T T) -9 NIL 2190888) (-898 2187285 2187501 2187900 "PSCAT-" 2187905 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-897 2185938 2186570 2186784 "PRTITION" 2187091 T PRTITION (NIL) -8 NIL NIL) (-896 2175036 2177242 2179430 "PRS" 2183800 NIL PRS (NIL T T) -7 NIL NIL) (-895 2172894 2174386 2174427 "PRQAGG" 2174610 NIL PRQAGG (NIL T) -9 NIL 2174712) (-894 2172464 2172566 2172595 "PROPLOG" 2172780 T PROPLOG (NIL) -9 NIL NIL) (-893 2169587 2170152 2170679 "PROPFRML" 2171969 NIL PROPFRML (NIL T) -8 NIL NIL) (-892 2163361 2167753 2168573 "PRODUCT" 2168813 NIL PRODUCT (NIL T T) -8 NIL NIL) (-891 2160637 2162821 2163054 "PR" 2163172 NIL PR (NIL T T) -8 NIL NIL) (-890 2160433 2160465 2160524 "PRINT" 2160598 T PRINT (NIL) -7 NIL NIL) (-889 2159773 2159890 2160042 "PRIMES" 2160313 NIL PRIMES (NIL T) -7 NIL NIL) (-888 2157838 2158239 2158705 "PRIMELT" 2159352 NIL PRIMELT (NIL T) -7 NIL NIL) (-887 2157566 2157615 2157644 "PRIMCAT" 2157768 T PRIMCAT (NIL) -9 NIL NIL) (-886 2153727 2157504 2157549 "PRIMARR" 2157554 NIL PRIMARR (NIL T) -8 NIL NIL) (-885 2152734 2152912 2153140 "PRIMARR2" 2153545 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-884 2152377 2152433 2152544 "PREASSOC" 2152672 NIL PREASSOC (NIL T T) -7 NIL NIL) (-883 2151851 2151984 2152013 "PPCURVE" 2152218 T PPCURVE (NIL) -9 NIL 2152354) (-882 2149210 2149609 2150201 "POLYROOT" 2151432 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-881 2143116 2148816 2148975 "POLY" 2149083 NIL POLY (NIL T) -8 NIL NIL) (-880 2142501 2142559 2142792 "POLYLIFT" 2143052 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-879 2138786 2139235 2139863 "POLYCATQ" 2142046 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-878 2125826 2131223 2131288 "POLYCAT" 2134773 NIL POLYCAT (NIL T T T) -9 NIL 2136700) (-877 2119277 2121138 2123521 "POLYCAT-" 2123526 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-876 2118866 2118934 2119053 "POLY2UP" 2119203 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-875 2118502 2118559 2118666 "POLY2" 2118803 NIL POLY2 (NIL T T) -7 NIL NIL) (-874 2117187 2117426 2117702 "POLUTIL" 2118276 NIL POLUTIL (NIL T T) -7 NIL NIL) (-873 2115549 2115826 2116156 "POLTOPOL" 2116909 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-872 2111072 2115486 2115531 "POINT" 2115536 NIL POINT (NIL T) -8 NIL NIL) (-871 2109259 2109616 2109991 "PNTHEORY" 2110717 T PNTHEORY (NIL) -7 NIL NIL) (-870 2107687 2107984 2108393 "PMTOOLS" 2108957 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-869 2107280 2107358 2107475 "PMSYM" 2107603 NIL PMSYM (NIL T) -7 NIL NIL) (-868 2106790 2106859 2107033 "PMQFCAT" 2107205 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-867 2106145 2106255 2106411 "PMPRED" 2106667 NIL PMPRED (NIL T) -7 NIL NIL) (-866 2105541 2105627 2105788 "PMPREDFS" 2106046 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-865 2104187 2104395 2104779 "PMPLCAT" 2105303 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-864 2103719 2103798 2103950 "PMLSAGG" 2104102 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-863 2103196 2103272 2103452 "PMKERNEL" 2103637 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-862 2102813 2102888 2103001 "PMINS" 2103115 NIL PMINS (NIL T) -7 NIL NIL) (-861 2102243 2102312 2102527 "PMFS" 2102738 NIL PMFS (NIL T T T) -7 NIL NIL) (-860 2101474 2101592 2101796 "PMDOWN" 2102120 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-859 2100637 2100796 2100978 "PMASS" 2101312 T PMASS (NIL) -7 NIL NIL) (-858 2099911 2100022 2100185 "PMASSFS" 2100523 NIL PMASSFS (NIL T T) -7 NIL NIL) (-857 2099566 2099634 2099728 "PLOTTOOL" 2099837 T PLOTTOOL (NIL) -7 NIL NIL) (-856 2094188 2095377 2096525 "PLOT" 2098438 T PLOT (NIL) -8 NIL NIL) (-855 2090002 2091036 2091957 "PLOT3D" 2093287 T PLOT3D (NIL) -8 NIL NIL) (-854 2088914 2089091 2089326 "PLOT1" 2089806 NIL PLOT1 (NIL T) -7 NIL NIL) (-853 2064309 2068980 2073831 "PLEQN" 2084180 NIL PLEQN (NIL T T T T) -7 NIL NIL) (-852 2063627 2063749 2063929 "PINTERP" 2064174 NIL PINTERP (NIL NIL T) -7 NIL NIL) (-851 2063320 2063367 2063470 "PINTERPA" 2063574 NIL PINTERPA (NIL T T) -7 NIL NIL) (-850 2062547 2063114 2063207 "PI" 2063247 T PI (NIL) -8 NIL NIL) (-849 2060938 2061923 2061952 "PID" 2062134 T PID (NIL) -9 NIL 2062268) (-848 2060663 2060700 2060788 "PICOERCE" 2060895 NIL PICOERCE (NIL T) -7 NIL NIL) (-847 2059984 2060122 2060298 "PGROEB" 2060519 NIL PGROEB (NIL T) -7 NIL NIL) (-846 2055571 2056385 2057290 "PGE" 2059099 T PGE (NIL) -7 NIL NIL) (-845 2053695 2053941 2054307 "PGCD" 2055288 NIL PGCD (NIL T T T T) -7 NIL NIL) (-844 2053033 2053136 2053297 "PFRPAC" 2053579 NIL PFRPAC (NIL T) -7 NIL NIL) (-843 2049648 2051581 2051934 "PFR" 2052712 NIL PFR (NIL T) -8 NIL NIL) (-842 2048037 2048281 2048606 "PFOTOOLS" 2049395 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-841 2046570 2046809 2047160 "PFOQ" 2047794 NIL PFOQ (NIL T T T) -7 NIL NIL) (-840 2045047 2045259 2045621 "PFO" 2046354 NIL PFO (NIL T T T T T) -7 NIL NIL) (-839 2041570 2044936 2045005 "PF" 2045010 NIL PF (NIL NIL) -8 NIL NIL) (-838 2038998 2040279 2040308 "PFECAT" 2040893 T PFECAT (NIL) -9 NIL 2041277) (-837 2038443 2038597 2038811 "PFECAT-" 2038816 NIL PFECAT- (NIL T) -8 NIL NIL) (-836 2037047 2037298 2037599 "PFBRU" 2038192 NIL PFBRU (NIL T T) -7 NIL NIL) (-835 2034914 2035265 2035697 "PFBR" 2036698 NIL PFBR (NIL T T T T) -7 NIL NIL) (-834 2030766 2032290 2032966 "PERM" 2034271 NIL PERM (NIL T) -8 NIL NIL) (-833 2026032 2026973 2027843 "PERMGRP" 2029929 NIL PERMGRP (NIL T) -8 NIL NIL) (-832 2024102 2025095 2025137 "PERMCAT" 2025583 NIL PERMCAT (NIL T) -9 NIL 2025888) (-831 2023757 2023798 2023921 "PERMAN" 2024055 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-830 2021197 2023326 2023457 "PENDTREE" 2023659 NIL PENDTREE (NIL T) -8 NIL NIL) (-829 2019269 2020047 2020089 "PDRING" 2020746 NIL PDRING (NIL T) -9 NIL 2021031) (-828 2018372 2018590 2018952 "PDRING-" 2018957 NIL PDRING- (NIL T T) -8 NIL NIL) (-827 2015514 2016264 2016955 "PDEPROB" 2017701 T PDEPROB (NIL) -8 NIL NIL) (-826 2013085 2013581 2014130 "PDEPACK" 2014985 T PDEPACK (NIL) -7 NIL NIL) (-825 2011997 2012187 2012438 "PDECOMP" 2012884 NIL PDECOMP (NIL T T) -7 NIL NIL) (-824 2009608 2010423 2010452 "PDECAT" 2011237 T PDECAT (NIL) -9 NIL 2011948) (-823 2009361 2009394 2009483 "PCOMP" 2009569 NIL PCOMP (NIL T T) -7 NIL NIL) (-822 2007568 2008164 2008460 "PBWLB" 2009091 NIL PBWLB (NIL T) -8 NIL NIL) (-821 2000077 2001645 2002981 "PATTERN" 2006253 NIL PATTERN (NIL T) -8 NIL NIL) (-820 1999709 1999766 1999875 "PATTERN2" 2000014 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-819 1997466 1997854 1998311 "PATTERN1" 1999298 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-818 1994861 1995415 1995896 "PATRES" 1997031 NIL PATRES (NIL T T) -8 NIL NIL) (-817 1994425 1994492 1994624 "PATRES2" 1994788 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-816 1992322 1992722 1993127 "PATMATCH" 1994094 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-815 1991858 1992041 1992083 "PATMAB" 1992190 NIL PATMAB (NIL T) -9 NIL 1992273) (-814 1990403 1990712 1990970 "PATLRES" 1991663 NIL PATLRES (NIL T T T) -8 NIL NIL) (-813 1989948 1990071 1990113 "PATAB" 1990118 NIL PATAB (NIL T) -9 NIL 1990290) (-812 1987429 1987961 1988534 "PARTPERM" 1989395 T PARTPERM (NIL) -7 NIL NIL) (-811 1987050 1987113 1987215 "PARSURF" 1987360 NIL PARSURF (NIL T) -8 NIL NIL) (-810 1986682 1986739 1986848 "PARSU2" 1986987 NIL PARSU2 (NIL T T) -7 NIL NIL) (-809 1986446 1986486 1986553 "PARSER" 1986635 T PARSER (NIL) -7 NIL NIL) (-808 1986067 1986130 1986232 "PARSCURV" 1986377 NIL PARSCURV (NIL T) -8 NIL NIL) (-807 1985699 1985756 1985865 "PARSC2" 1986004 NIL PARSC2 (NIL T T) -7 NIL NIL) (-806 1985338 1985396 1985493 "PARPCURV" 1985635 NIL PARPCURV (NIL T) -8 NIL NIL) (-805 1984970 1985027 1985136 "PARPC2" 1985275 NIL PARPC2 (NIL T T) -7 NIL NIL) (-804 1984490 1984576 1984695 "PAN2EXPR" 1984871 T PAN2EXPR (NIL) -7 NIL NIL) (-803 1983296 1983611 1983839 "PALETTE" 1984282 T PALETTE (NIL) -8 NIL NIL) (-802 1981764 1982301 1982661 "PAIR" 1982982 NIL PAIR (NIL T T) -8 NIL NIL) (-801 1975614 1981023 1981217 "PADICRC" 1981619 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-800 1968822 1974960 1975144 "PADICRAT" 1975462 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-799 1967126 1968759 1968804 "PADIC" 1968809 NIL PADIC (NIL NIL) -8 NIL NIL) (-798 1964330 1965904 1965945 "PADICCT" 1966526 NIL PADICCT (NIL NIL) -9 NIL 1966808) (-797 1963287 1963487 1963755 "PADEPAC" 1964117 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-796 1962499 1962632 1962838 "PADE" 1963149 NIL PADE (NIL T T T) -7 NIL NIL) (-795 1960510 1961342 1961657 "OWP" 1962267 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-794 1959619 1960115 1960287 "OVAR" 1960378 NIL OVAR (NIL NIL) -8 NIL NIL) (-793 1958883 1959004 1959165 "OUT" 1959478 T OUT (NIL) -7 NIL NIL) (-792 1947929 1950108 1952278 "OUTFORM" 1956733 T OUTFORM (NIL) -8 NIL NIL) (-791 1947337 1947658 1947747 "OSI" 1947860 T OSI (NIL) -8 NIL NIL) (-790 1946082 1946309 1946594 "ORTHPOL" 1947084 NIL ORTHPOL (NIL T) -7 NIL NIL) (-789 1943453 1945743 1945881 "OREUP" 1946025 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-788 1940849 1943146 1943272 "ORESUP" 1943395 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-787 1938384 1938884 1939444 "OREPCTO" 1940338 NIL OREPCTO (NIL T T) -7 NIL NIL) (-786 1932293 1934499 1934540 "OREPCAT" 1936861 NIL OREPCAT (NIL T) -9 NIL 1937964) (-785 1929441 1930223 1931280 "OREPCAT-" 1931285 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-784 1928618 1928890 1928919 "ORDSET" 1929228 T ORDSET (NIL) -9 NIL 1929392) (-783 1928137 1928259 1928452 "ORDSET-" 1928457 NIL ORDSET- (NIL T) -8 NIL NIL) (-782 1926750 1927551 1927580 "ORDRING" 1927782 T ORDRING (NIL) -9 NIL 1927906) (-781 1926395 1926489 1926633 "ORDRING-" 1926638 NIL ORDRING- (NIL T) -8 NIL NIL) (-780 1925770 1926251 1926280 "ORDMON" 1926285 T ORDMON (NIL) -9 NIL 1926306) (-779 1924932 1925079 1925274 "ORDFUNS" 1925619 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-778 1924443 1924802 1924831 "ORDFIN" 1924836 T ORDFIN (NIL) -9 NIL 1924857) (-777 1920955 1923029 1923438 "ORDCOMP" 1924067 NIL ORDCOMP (NIL T) -8 NIL NIL) (-776 1920221 1920348 1920534 "ORDCOMP2" 1920815 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-775 1916729 1917611 1918448 "OPTPROB" 1919404 T OPTPROB (NIL) -8 NIL NIL) (-774 1913571 1914200 1914894 "OPTPACK" 1916055 T OPTPACK (NIL) -7 NIL NIL) (-773 1911296 1912032 1912061 "OPTCAT" 1912876 T OPTCAT (NIL) -9 NIL 1913522) (-772 1911064 1911103 1911169 "OPQUERY" 1911250 T OPQUERY (NIL) -7 NIL NIL) (-771 1908200 1909391 1909891 "OP" 1910596 NIL OP (NIL T) -8 NIL NIL) (-770 1904965 1906997 1907366 "ONECOMP" 1907864 NIL ONECOMP (NIL T) -8 NIL NIL) (-769 1904270 1904385 1904559 "ONECOMP2" 1904837 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-768 1903689 1903795 1903925 "OMSERVER" 1904160 T OMSERVER (NIL) -7 NIL NIL) (-767 1900577 1903129 1903170 "OMSAGG" 1903231 NIL OMSAGG (NIL T) -9 NIL 1903295) (-766 1899200 1899463 1899745 "OMPKG" 1900315 T OMPKG (NIL) -7 NIL NIL) (-765 1898629 1898732 1898761 "OM" 1899060 T OM (NIL) -9 NIL NIL) (-764 1897168 1898181 1898349 "OMLO" 1898510 NIL OMLO (NIL T T) -8 NIL NIL) (-763 1896098 1896245 1896471 "OMEXPR" 1896994 NIL OMEXPR (NIL T) -7 NIL NIL) (-762 1895416 1895644 1895780 "OMERR" 1895982 T OMERR (NIL) -8 NIL NIL) (-761 1894594 1894837 1894997 "OMERRK" 1895276 T OMERRK (NIL) -8 NIL NIL) (-760 1894072 1894271 1894379 "OMENC" 1894506 T OMENC (NIL) -8 NIL NIL) (-759 1887967 1889152 1890323 "OMDEV" 1892921 T OMDEV (NIL) -8 NIL NIL) (-758 1887036 1887207 1887401 "OMCONN" 1887793 T OMCONN (NIL) -8 NIL NIL) (-757 1885651 1886637 1886666 "OINTDOM" 1886671 T OINTDOM (NIL) -9 NIL 1886692) (-756 1881413 1882643 1883358 "OFMONOID" 1884968 NIL OFMONOID (NIL T) -8 NIL NIL) (-755 1880851 1881350 1881395 "ODVAR" 1881400 NIL ODVAR (NIL T) -8 NIL NIL) (-754 1877976 1880348 1880533 "ODR" 1880726 NIL ODR (NIL T T NIL) -8 NIL NIL) (-753 1870282 1877755 1877879 "ODPOL" 1877884 NIL ODPOL (NIL T) -8 NIL NIL) (-752 1864105 1870154 1870259 "ODP" 1870264 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-751 1862871 1863086 1863361 "ODETOOLS" 1863879 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-750 1859840 1860496 1861212 "ODESYS" 1862204 NIL ODESYS (NIL T T) -7 NIL NIL) (-749 1854744 1855652 1856675 "ODERTRIC" 1858915 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-748 1854170 1854252 1854446 "ODERED" 1854656 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-747 1851072 1851620 1852295 "ODERAT" 1853593 NIL ODERAT (NIL T T) -7 NIL NIL) (-746 1848040 1848504 1849100 "ODEPRRIC" 1850601 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-745 1845911 1846478 1846987 "ODEPROB" 1847551 T ODEPROB (NIL) -8 NIL NIL) (-744 1842443 1842926 1843572 "ODEPRIM" 1845390 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-743 1841696 1841798 1842056 "ODEPAL" 1842335 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-742 1837898 1838679 1839533 "ODEPACK" 1840862 T ODEPACK (NIL) -7 NIL NIL) (-741 1836935 1837042 1837270 "ODEINT" 1837787 NIL ODEINT (NIL T T) -7 NIL NIL) (-740 1831036 1832461 1833908 "ODEIFTBL" 1835508 T ODEIFTBL (NIL) -8 NIL NIL) (-739 1826380 1827166 1828124 "ODEEF" 1830195 NIL ODEEF (NIL T T) -7 NIL NIL) (-738 1825717 1825806 1826035 "ODECONST" 1826285 NIL ODECONST (NIL T T T) -7 NIL NIL) (-737 1823874 1824507 1824536 "ODECAT" 1825139 T ODECAT (NIL) -9 NIL 1825668) (-736 1820746 1823586 1823705 "OCT" 1823787 NIL OCT (NIL T) -8 NIL NIL) (-735 1820384 1820427 1820554 "OCTCT2" 1820697 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-734 1815217 1817655 1817696 "OC" 1818792 NIL OC (NIL T) -9 NIL 1819649) (-733 1812444 1813192 1814182 "OC-" 1814276 NIL OC- (NIL T T) -8 NIL NIL) (-732 1811822 1812264 1812293 "OCAMON" 1812298 T OCAMON (NIL) -9 NIL 1812319) (-731 1811282 1811392 1811522 "OBJPROP" 1811712 T OBJPROP (NIL) -8 NIL NIL) (-730 1810735 1811142 1811171 "OASGP" 1811176 T OASGP (NIL) -9 NIL 1811196) (-729 1810022 1810485 1810514 "OAMONS" 1810554 T OAMONS (NIL) -9 NIL 1810597) (-728 1809462 1809869 1809898 "OAMON" 1809903 T OAMON (NIL) -9 NIL 1809923) (-727 1808766 1809258 1809287 "OAGROUP" 1809292 T OAGROUP (NIL) -9 NIL 1809312) (-726 1808456 1808506 1808594 "NUMTUBE" 1808710 NIL NUMTUBE (NIL T) -7 NIL NIL) (-725 1802029 1803547 1805083 "NUMQUAD" 1806940 T NUMQUAD (NIL) -7 NIL NIL) (-724 1797785 1798773 1799798 "NUMODE" 1801024 T NUMODE (NIL) -7 NIL NIL) (-723 1795188 1796034 1796063 "NUMINT" 1796980 T NUMINT (NIL) -9 NIL 1797736) (-722 1794136 1794333 1794551 "NUMFMT" 1794990 T NUMFMT (NIL) -7 NIL NIL) (-721 1780518 1783452 1785982 "NUMERIC" 1791645 NIL NUMERIC (NIL T) -7 NIL NIL) (-720 1774918 1779970 1780065 "NTSCAT" 1780070 NIL NTSCAT (NIL T T T T) -9 NIL 1780108) (-719 1774112 1774277 1774470 "NTPOLFN" 1774757 NIL NTPOLFN (NIL T) -7 NIL NIL) (-718 1761968 1770954 1771764 "NSUP" 1773334 NIL NSUP (NIL T) -8 NIL NIL) (-717 1761604 1761661 1761768 "NSUP2" 1761905 NIL NSUP2 (NIL T T) -7 NIL NIL) (-716 1751566 1761383 1761513 "NSMP" 1761518 NIL NSMP (NIL T T) -8 NIL NIL) (-715 1749998 1750299 1750656 "NREP" 1751254 NIL NREP (NIL T) -7 NIL NIL) (-714 1748589 1748841 1749199 "NPCOEF" 1749741 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-713 1747655 1747770 1747986 "NORMRETR" 1748470 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-712 1745708 1745998 1746405 "NORMPK" 1747363 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-711 1745393 1745421 1745545 "NORMMA" 1745674 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-710 1745220 1745350 1745379 "NONE" 1745384 T NONE (NIL) -8 NIL NIL) (-709 1745009 1745038 1745107 "NONE1" 1745184 NIL NONE1 (NIL T) -7 NIL NIL) (-708 1744494 1744556 1744741 "NODE1" 1744941 NIL NODE1 (NIL T T) -7 NIL NIL) (-707 1742787 1743657 1743912 "NNI" 1744259 T NNI (NIL) -8 NIL NIL) (-706 1741207 1741520 1741884 "NLINSOL" 1742455 NIL NLINSOL (NIL T) -7 NIL NIL) (-705 1737375 1738342 1739264 "NIPROB" 1740305 T NIPROB (NIL) -8 NIL NIL) (-704 1736132 1736366 1736668 "NFINTBAS" 1737137 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-703 1734840 1735071 1735352 "NCODIV" 1735900 NIL NCODIV (NIL T T) -7 NIL NIL) (-702 1734602 1734639 1734714 "NCNTFRAC" 1734797 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-701 1732782 1733146 1733566 "NCEP" 1734227 NIL NCEP (NIL T) -7 NIL NIL) (-700 1731693 1732432 1732461 "NASRING" 1732571 T NASRING (NIL) -9 NIL 1732645) (-699 1731488 1731532 1731626 "NASRING-" 1731631 NIL NASRING- (NIL T) -8 NIL NIL) (-698 1730641 1731140 1731169 "NARNG" 1731286 T NARNG (NIL) -9 NIL 1731377) (-697 1730333 1730400 1730534 "NARNG-" 1730539 NIL NARNG- (NIL T) -8 NIL NIL) (-696 1729212 1729419 1729654 "NAGSP" 1730118 T NAGSP (NIL) -7 NIL NIL) (-695 1720636 1722282 1723917 "NAGS" 1727597 T NAGS (NIL) -7 NIL NIL) (-694 1719200 1719504 1719831 "NAGF07" 1720329 T NAGF07 (NIL) -7 NIL NIL) (-693 1713782 1715062 1716358 "NAGF04" 1717924 T NAGF04 (NIL) -7 NIL NIL) (-692 1706814 1708412 1710029 "NAGF02" 1712185 T NAGF02 (NIL) -7 NIL NIL) (-691 1702078 1703168 1704275 "NAGF01" 1705727 T NAGF01 (NIL) -7 NIL NIL) (-690 1695738 1697296 1698873 "NAGE04" 1700521 T NAGE04 (NIL) -7 NIL NIL) (-689 1686979 1689082 1691194 "NAGE02" 1693646 T NAGE02 (NIL) -7 NIL NIL) (-688 1682972 1683909 1684863 "NAGE01" 1686045 T NAGE01 (NIL) -7 NIL NIL) (-687 1680779 1681310 1681865 "NAGD03" 1682437 T NAGD03 (NIL) -7 NIL NIL) (-686 1672565 1674484 1676429 "NAGD02" 1678854 T NAGD02 (NIL) -7 NIL NIL) (-685 1666424 1667837 1669265 "NAGD01" 1671157 T NAGD01 (NIL) -7 NIL NIL) (-684 1662681 1663491 1664316 "NAGC06" 1665619 T NAGC06 (NIL) -7 NIL NIL) (-683 1661158 1661487 1661840 "NAGC05" 1662348 T NAGC05 (NIL) -7 NIL NIL) (-682 1660542 1660659 1660801 "NAGC02" 1661036 T NAGC02 (NIL) -7 NIL NIL) (-681 1659603 1660160 1660201 "NAALG" 1660280 NIL NAALG (NIL T) -9 NIL 1660341) (-680 1659438 1659467 1659557 "NAALG-" 1659562 NIL NAALG- (NIL T T) -8 NIL NIL) (-679 1653388 1654496 1655683 "MULTSQFR" 1658334 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-678 1652707 1652782 1652966 "MULTFACT" 1653300 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-677 1645900 1649811 1649864 "MTSCAT" 1650924 NIL MTSCAT (NIL T T) -9 NIL 1651438) (-676 1645612 1645666 1645758 "MTHING" 1645840 NIL MTHING (NIL T) -7 NIL NIL) (-675 1645404 1645437 1645497 "MSYSCMD" 1645572 T MSYSCMD (NIL) -7 NIL NIL) (-674 1641516 1644159 1644479 "MSET" 1645117 NIL MSET (NIL T) -8 NIL NIL) (-673 1638611 1641077 1641119 "MSETAGG" 1641124 NIL MSETAGG (NIL T) -9 NIL 1641158) (-672 1634467 1636009 1636750 "MRING" 1637914 NIL MRING (NIL T T) -8 NIL NIL) (-671 1634037 1634104 1634233 "MRF2" 1634394 NIL MRF2 (NIL T T T) -7 NIL NIL) (-670 1633655 1633690 1633834 "MRATFAC" 1633996 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-669 1631267 1631562 1631993 "MPRFF" 1633360 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-668 1625287 1631122 1631218 "MPOLY" 1631223 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-667 1624777 1624812 1625020 "MPCPF" 1625246 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-666 1624293 1624336 1624519 "MPC3" 1624728 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-665 1623494 1623575 1623794 "MPC2" 1624208 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-664 1621795 1622132 1622522 "MONOTOOL" 1623154 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-663 1620919 1621254 1621283 "MONOID" 1621560 T MONOID (NIL) -9 NIL 1621732) (-662 1620297 1620460 1620703 "MONOID-" 1620708 NIL MONOID- (NIL T) -8 NIL NIL) (-661 1611277 1617263 1617323 "MONOGEN" 1617997 NIL MONOGEN (NIL T T) -9 NIL 1618453) (-660 1608495 1609230 1610230 "MONOGEN-" 1610349 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-659 1607354 1607774 1607803 "MONADWU" 1608195 T MONADWU (NIL) -9 NIL 1608433) (-658 1606726 1606885 1607133 "MONADWU-" 1607138 NIL MONADWU- (NIL T) -8 NIL NIL) (-657 1606111 1606329 1606358 "MONAD" 1606565 T MONAD (NIL) -9 NIL 1606677) (-656 1605796 1605874 1606006 "MONAD-" 1606011 NIL MONAD- (NIL T) -8 NIL NIL) (-655 1604047 1604709 1604988 "MOEBIUS" 1605549 NIL MOEBIUS (NIL T) -8 NIL NIL) (-654 1603440 1603818 1603859 "MODULE" 1603864 NIL MODULE (NIL T) -9 NIL 1603890) (-653 1603008 1603104 1603294 "MODULE-" 1603299 NIL MODULE- (NIL T T) -8 NIL NIL) (-652 1600679 1601374 1601700 "MODRING" 1602833 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-651 1597635 1598800 1599317 "MODOP" 1600211 NIL MODOP (NIL T T) -8 NIL NIL) (-650 1595822 1596274 1596615 "MODMONOM" 1597434 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-649 1585540 1594026 1594448 "MODMON" 1595450 NIL MODMON (NIL T T) -8 NIL NIL) (-648 1582666 1584384 1584660 "MODFIELD" 1585415 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1582192 1582235 1582414 "MMAP" 1582617 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-646 1580428 1581205 1581246 "MLO" 1581663 NIL MLO (NIL T) -9 NIL 1581904) (-645 1577795 1578310 1578912 "MLIFT" 1579909 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-644 1577186 1577270 1577424 "MKUCFUNC" 1577706 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-643 1576785 1576855 1576978 "MKRECORD" 1577109 NIL MKRECORD (NIL T T) -7 NIL NIL) (-642 1575833 1575994 1576222 "MKFUNC" 1576596 NIL MKFUNC (NIL T) -7 NIL NIL) (-641 1575221 1575325 1575481 "MKFLCFN" 1575716 NIL MKFLCFN (NIL T) -7 NIL NIL) (-640 1574647 1575014 1575103 "MKCHSET" 1575165 NIL MKCHSET (NIL T) -8 NIL NIL) (-639 1573924 1574026 1574211 "MKBCFUNC" 1574540 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-638 1570608 1573478 1573614 "MINT" 1573808 T MINT (NIL) -8 NIL NIL) (-637 1569420 1569663 1569940 "MHROWRED" 1570363 NIL MHROWRED (NIL T) -7 NIL NIL) (-636 1564691 1567865 1568289 "MFLOAT" 1569016 T MFLOAT (NIL) -8 NIL NIL) (-635 1564048 1564124 1564295 "MFINFACT" 1564603 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-634 1560363 1561211 1562095 "MESH" 1563184 T MESH (NIL) -7 NIL NIL) (-633 1558753 1559065 1559418 "MDDFACT" 1560050 NIL MDDFACT (NIL T) -7 NIL NIL) (-632 1555595 1557912 1557954 "MDAGG" 1558209 NIL MDAGG (NIL T) -9 NIL 1558352) (-631 1545293 1554888 1555095 "MCMPLX" 1555408 T MCMPLX (NIL) -8 NIL NIL) (-630 1544434 1544580 1544780 "MCDEN" 1545142 NIL MCDEN (NIL T T) -7 NIL NIL) (-629 1542324 1542594 1542974 "MCALCFN" 1544164 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-628 1539946 1540469 1541030 "MATSTOR" 1541795 NIL MATSTOR (NIL T) -7 NIL NIL) (-627 1535954 1539321 1539568 "MATRIX" 1539731 NIL MATRIX (NIL T) -8 NIL NIL) (-626 1531724 1532427 1533163 "MATLIN" 1535311 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-625 1521921 1525059 1525136 "MATCAT" 1529974 NIL MATCAT (NIL T T T) -9 NIL 1531391) (-624 1518286 1519299 1520654 "MATCAT-" 1520659 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-623 1516888 1517041 1517372 "MATCAT2" 1518121 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-622 1515000 1515324 1515708 "MAPPKG3" 1516563 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-621 1513981 1514154 1514376 "MAPPKG2" 1514824 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-620 1512480 1512764 1513091 "MAPPKG1" 1513687 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-619 1512091 1512149 1512272 "MAPHACK3" 1512416 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-618 1511683 1511744 1511858 "MAPHACK2" 1512023 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-617 1511121 1511224 1511366 "MAPHACK1" 1511574 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-616 1509229 1509823 1510126 "MAGMA" 1510850 NIL MAGMA (NIL T) -8 NIL NIL) (-615 1505703 1507473 1507933 "M3D" 1508802 NIL M3D (NIL T) -8 NIL NIL) (-614 1499858 1504073 1504115 "LZSTAGG" 1504897 NIL LZSTAGG (NIL T) -9 NIL 1505192) (-613 1495831 1496989 1498446 "LZSTAGG-" 1498451 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-612 1492947 1493724 1494210 "LWORD" 1495377 NIL LWORD (NIL T) -8 NIL NIL) (-611 1486107 1492718 1492852 "LSQM" 1492857 NIL LSQM (NIL NIL T) -8 NIL NIL) (-610 1485331 1485470 1485698 "LSPP" 1485962 NIL LSPP (NIL T T T T) -7 NIL NIL) (-609 1483143 1483444 1483900 "LSMP" 1485020 NIL LSMP (NIL T T T T) -7 NIL NIL) (-608 1479922 1480596 1481326 "LSMP1" 1482445 NIL LSMP1 (NIL T) -7 NIL NIL) (-607 1473848 1479090 1479132 "LSAGG" 1479194 NIL LSAGG (NIL T) -9 NIL 1479272) (-606 1470543 1471467 1472680 "LSAGG-" 1472685 NIL LSAGG- (NIL T T) -8 NIL NIL) (-605 1468169 1469687 1469936 "LPOLY" 1470338 NIL LPOLY (NIL T T) -8 NIL NIL) (-604 1467751 1467836 1467959 "LPEFRAC" 1468078 NIL LPEFRAC (NIL T) -7 NIL NIL) (-603 1466098 1466845 1467098 "LO" 1467583 NIL LO (NIL T T T) -8 NIL NIL) (-602 1465751 1465863 1465892 "LOGIC" 1466003 T LOGIC (NIL) -9 NIL 1466083) (-601 1465613 1465636 1465707 "LOGIC-" 1465712 NIL LOGIC- (NIL T) -8 NIL NIL) (-600 1464806 1464946 1465139 "LODOOPS" 1465469 NIL LODOOPS (NIL T T) -7 NIL NIL) (-599 1462224 1464723 1464788 "LODO" 1464793 NIL LODO (NIL T NIL) -8 NIL NIL) (-598 1460770 1461005 1461356 "LODOF" 1461971 NIL LODOF (NIL T T) -7 NIL NIL) (-597 1457189 1459625 1459666 "LODOCAT" 1460098 NIL LODOCAT (NIL T) -9 NIL 1460309) (-596 1456923 1456981 1457107 "LODOCAT-" 1457112 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-595 1454237 1456764 1456882 "LODO2" 1456887 NIL LODO2 (NIL T T) -8 NIL NIL) (-594 1451666 1454174 1454219 "LODO1" 1454224 NIL LODO1 (NIL T) -8 NIL NIL) (-593 1450529 1450694 1451005 "LODEEF" 1451489 NIL LODEEF (NIL T T T) -7 NIL NIL) (-592 1445815 1448659 1448701 "LNAGG" 1449648 NIL LNAGG (NIL T) -9 NIL 1450092) (-591 1444962 1445176 1445518 "LNAGG-" 1445523 NIL LNAGG- (NIL T T) -8 NIL NIL) (-590 1441127 1441889 1442527 "LMOPS" 1444378 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-589 1440524 1440886 1440927 "LMODULE" 1440987 NIL LMODULE (NIL T) -9 NIL 1441029) (-588 1437770 1440169 1440292 "LMDICT" 1440434 NIL LMDICT (NIL T) -8 NIL NIL) (-587 1430997 1436716 1437014 "LIST" 1437505 NIL LIST (NIL T) -8 NIL NIL) (-586 1430522 1430596 1430735 "LIST3" 1430917 NIL LIST3 (NIL T T T) -7 NIL NIL) (-585 1429529 1429707 1429935 "LIST2" 1430340 NIL LIST2 (NIL T T) -7 NIL NIL) (-584 1427663 1427975 1428374 "LIST2MAP" 1429176 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-583 1426375 1427055 1427096 "LINEXP" 1427349 NIL LINEXP (NIL T) -9 NIL 1427497) (-582 1425022 1425282 1425579 "LINDEP" 1426127 NIL LINDEP (NIL T T) -7 NIL NIL) (-581 1421789 1422508 1423285 "LIMITRF" 1424277 NIL LIMITRF (NIL T) -7 NIL NIL) (-580 1420069 1420364 1420779 "LIMITPS" 1421484 NIL LIMITPS (NIL T T) -7 NIL NIL) (-579 1414524 1419580 1419808 "LIE" 1419890 NIL LIE (NIL T T) -8 NIL NIL) (-578 1413574 1414017 1414058 "LIECAT" 1414198 NIL LIECAT (NIL T) -9 NIL 1414349) (-577 1413415 1413442 1413530 "LIECAT-" 1413535 NIL LIECAT- (NIL T T) -8 NIL NIL) (-576 1406027 1412864 1413029 "LIB" 1413270 T LIB (NIL) -8 NIL NIL) (-575 1401664 1402545 1403480 "LGROBP" 1405144 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-574 1399530 1399804 1400166 "LF" 1401385 NIL LF (NIL T T) -7 NIL NIL) (-573 1398369 1399061 1399090 "LFCAT" 1399297 T LFCAT (NIL) -9 NIL 1399436) (-572 1395281 1395907 1396593 "LEXTRIPK" 1397735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-571 1391987 1392851 1393354 "LEXP" 1394861 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-570 1390385 1390698 1391099 "LEADCDET" 1391669 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-569 1389581 1389655 1389882 "LAZM3PK" 1390306 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-568 1384497 1387660 1388197 "LAUPOL" 1389094 NIL LAUPOL (NIL T T) -8 NIL NIL) (-567 1384064 1384108 1384275 "LAPLACE" 1384447 NIL LAPLACE (NIL T T) -7 NIL NIL) (-566 1381992 1383165 1383416 "LA" 1383897 NIL LA (NIL T T T) -8 NIL NIL) (-565 1381054 1381648 1381689 "LALG" 1381750 NIL LALG (NIL T) -9 NIL 1381808) (-564 1380769 1380828 1380963 "LALG-" 1380968 NIL LALG- (NIL T T) -8 NIL NIL) (-563 1379679 1379866 1380163 "KOVACIC" 1380569 NIL KOVACIC (NIL T T) -7 NIL NIL) (-562 1379513 1379537 1379579 "KONVERT" 1379641 NIL KONVERT (NIL T) -9 NIL NIL) (-561 1379347 1379371 1379413 "KOERCE" 1379475 NIL KOERCE (NIL T) -9 NIL NIL) (-560 1377081 1377841 1378234 "KERNEL" 1378986 NIL KERNEL (NIL T) -8 NIL NIL) (-559 1376583 1376664 1376794 "KERNEL2" 1376995 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-558 1370434 1375122 1375177 "KDAGG" 1375554 NIL KDAGG (NIL T T) -9 NIL 1375760) (-557 1369963 1370087 1370292 "KDAGG-" 1370297 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-556 1363138 1369624 1369779 "KAFILE" 1369841 NIL KAFILE (NIL T) -8 NIL NIL) (-555 1357593 1362649 1362877 "JORDAN" 1362959 NIL JORDAN (NIL T T) -8 NIL NIL) (-554 1353892 1355798 1355853 "IXAGG" 1356782 NIL IXAGG (NIL T T) -9 NIL 1357241) (-553 1352811 1353117 1353536 "IXAGG-" 1353541 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-552 1348396 1352733 1352792 "IVECTOR" 1352797 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-551 1347162 1347399 1347665 "ITUPLE" 1348163 NIL ITUPLE (NIL T) -8 NIL NIL) (-550 1345598 1345775 1346081 "ITRIGMNP" 1346984 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-549 1344343 1344547 1344830 "ITFUN3" 1345374 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-548 1343975 1344032 1344141 "ITFUN2" 1344280 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-547 1341777 1342848 1343145 "ITAYLOR" 1343710 NIL ITAYLOR (NIL T) -8 NIL NIL) (-546 1330768 1335963 1337122 "ISUPS" 1340650 NIL ISUPS (NIL T) -8 NIL NIL) (-545 1329872 1330012 1330248 "ISUMP" 1330615 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-544 1325136 1329673 1329752 "ISTRING" 1329825 NIL ISTRING (NIL NIL) -8 NIL NIL) (-543 1324349 1324430 1324645 "IRURPK" 1325050 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-542 1323285 1323486 1323726 "IRSN" 1324129 T IRSN (NIL) -7 NIL NIL) (-541 1321320 1321675 1322110 "IRRF2F" 1322923 NIL IRRF2F (NIL T) -7 NIL NIL) (-540 1321067 1321105 1321181 "IRREDFFX" 1321276 NIL IRREDFFX (NIL T) -7 NIL NIL) (-539 1319682 1319941 1320240 "IROOT" 1320800 NIL IROOT (NIL T) -7 NIL NIL) (-538 1316320 1317371 1318061 "IR" 1319024 NIL IR (NIL T) -8 NIL NIL) (-537 1313933 1314428 1314994 "IR2" 1315798 NIL IR2 (NIL T T) -7 NIL NIL) (-536 1313009 1313122 1313342 "IR2F" 1313816 NIL IR2F (NIL T T) -7 NIL NIL) (-535 1312800 1312834 1312894 "IPRNTPK" 1312969 T IPRNTPK (NIL) -7 NIL NIL) (-534 1309354 1312689 1312758 "IPF" 1312763 NIL IPF (NIL NIL) -8 NIL NIL) (-533 1307671 1309279 1309336 "IPADIC" 1309341 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-532 1307170 1307228 1307417 "INVLAPLA" 1307607 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-531 1296819 1299172 1301558 "INTTR" 1304834 NIL INTTR (NIL T T) -7 NIL NIL) (-530 1293167 1293908 1294771 "INTTOOLS" 1296005 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-529 1292753 1292844 1292961 "INTSLPE" 1293070 T INTSLPE (NIL) -7 NIL NIL) (-528 1290703 1292676 1292735 "INTRVL" 1292740 NIL INTRVL (NIL T) -8 NIL NIL) (-527 1288310 1288822 1289396 "INTRF" 1290188 NIL INTRF (NIL T) -7 NIL NIL) (-526 1287725 1287822 1287963 "INTRET" 1288208 NIL INTRET (NIL T) -7 NIL NIL) (-525 1285727 1286116 1286585 "INTRAT" 1287333 NIL INTRAT (NIL T T) -7 NIL NIL) (-524 1282960 1283543 1284168 "INTPM" 1285212 NIL INTPM (NIL T T) -7 NIL NIL) (-523 1279669 1280268 1281012 "INTPAF" 1282346 NIL INTPAF (NIL T T T) -7 NIL NIL) (-522 1274912 1275858 1276893 "INTPACK" 1278654 T INTPACK (NIL) -7 NIL NIL) (-521 1271766 1274641 1274768 "INT" 1274805 T INT (NIL) -8 NIL NIL) (-520 1271018 1271170 1271378 "INTHERTR" 1271608 NIL INTHERTR (NIL T T) -7 NIL NIL) (-519 1270457 1270537 1270725 "INTHERAL" 1270932 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-518 1268303 1268746 1269203 "INTHEORY" 1270020 T INTHEORY (NIL) -7 NIL NIL) (-517 1259626 1261246 1263024 "INTG0" 1266655 NIL INTG0 (NIL T T T) -7 NIL NIL) (-516 1240199 1244989 1249799 "INTFTBL" 1254836 T INTFTBL (NIL) -8 NIL NIL) (-515 1239448 1239586 1239759 "INTFACT" 1240058 NIL INTFACT (NIL T) -7 NIL NIL) (-514 1236839 1237285 1237848 "INTEF" 1239002 NIL INTEF (NIL T T) -7 NIL NIL) (-513 1235300 1236049 1236078 "INTDOM" 1236379 T INTDOM (NIL) -9 NIL 1236586) (-512 1234669 1234843 1235085 "INTDOM-" 1235090 NIL INTDOM- (NIL T) -8 NIL NIL) (-511 1231161 1233093 1233148 "INTCAT" 1233947 NIL INTCAT (NIL T) -9 NIL 1234266) (-510 1230634 1230736 1230864 "INTBIT" 1231053 T INTBIT (NIL) -7 NIL NIL) (-509 1229309 1229463 1229776 "INTALG" 1230479 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-508 1228766 1228856 1229026 "INTAF" 1229213 NIL INTAF (NIL T T) -7 NIL NIL) (-507 1222220 1228576 1228716 "INTABL" 1228721 NIL INTABL (NIL T T T) -8 NIL NIL) (-506 1217170 1219899 1219928 "INS" 1220896 T INS (NIL) -9 NIL 1221577) (-505 1214410 1215181 1216155 "INS-" 1216228 NIL INS- (NIL T) -8 NIL NIL) (-504 1213189 1213416 1213713 "INPSIGN" 1214163 NIL INPSIGN (NIL T T) -7 NIL NIL) (-503 1212307 1212424 1212621 "INPRODPF" 1213069 NIL INPRODPF (NIL T T) -7 NIL NIL) (-502 1211201 1211318 1211555 "INPRODFF" 1212187 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-501 1210201 1210353 1210613 "INNMFACT" 1211037 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-500 1209398 1209495 1209683 "INMODGCD" 1210100 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-499 1207907 1208151 1208475 "INFSP" 1209143 NIL INFSP (NIL T T T) -7 NIL NIL) (-498 1207091 1207208 1207391 "INFPROD0" 1207787 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-497 1204101 1205260 1205751 "INFORM" 1206608 T INFORM (NIL) -8 NIL NIL) (-496 1203711 1203771 1203869 "INFORM1" 1204036 NIL INFORM1 (NIL T) -7 NIL NIL) (-495 1203234 1203323 1203437 "INFINITY" 1203617 T INFINITY (NIL) -7 NIL NIL) (-494 1201852 1202100 1202421 "INEP" 1202982 NIL INEP (NIL T T T) -7 NIL NIL) (-493 1201128 1201749 1201814 "INDE" 1201819 NIL INDE (NIL T) -8 NIL NIL) (-492 1200692 1200760 1200877 "INCRMAPS" 1201055 NIL INCRMAPS (NIL T) -7 NIL NIL) (-491 1196003 1196928 1197872 "INBFF" 1199780 NIL INBFF (NIL T) -7 NIL NIL) (-490 1192498 1195848 1195951 "IMATRIX" 1195956 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-489 1191210 1191333 1191648 "IMATQF" 1192354 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-488 1189430 1189657 1189994 "IMATLIN" 1190966 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-487 1184056 1189354 1189412 "ILIST" 1189417 NIL ILIST (NIL T NIL) -8 NIL NIL) (-486 1182009 1183916 1184029 "IIARRAY2" 1184034 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-485 1177377 1181920 1181984 "IFF" 1181989 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-484 1172420 1176669 1176857 "IFARRAY" 1177234 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-483 1171627 1172324 1172397 "IFAMON" 1172402 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-482 1171210 1171275 1171330 "IEVALAB" 1171537 NIL IEVALAB (NIL T T) -9 NIL NIL) (-481 1170885 1170953 1171113 "IEVALAB-" 1171118 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-480 1170543 1170799 1170862 "IDPO" 1170867 NIL IDPO (NIL T T) -8 NIL NIL) (-479 1169820 1170432 1170507 "IDPOAMS" 1170512 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-478 1169154 1169709 1169784 "IDPOAM" 1169789 NIL IDPOAM (NIL T T) -8 NIL NIL) (-477 1168239 1168489 1168543 "IDPC" 1168956 NIL IDPC (NIL T T) -9 NIL 1169105) (-476 1167735 1168131 1168204 "IDPAM" 1168209 NIL IDPAM (NIL T T) -8 NIL NIL) (-475 1167138 1167627 1167700 "IDPAG" 1167705 NIL IDPAG (NIL T T) -8 NIL NIL) (-474 1163393 1164241 1165136 "IDECOMP" 1166295 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-473 1156267 1157316 1158363 "IDEAL" 1162429 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-472 1155431 1155543 1155742 "ICDEN" 1156151 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-471 1154530 1154911 1155058 "ICARD" 1155304 T ICARD (NIL) -8 NIL NIL) (-470 1152602 1152915 1153318 "IBPTOOLS" 1154207 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-469 1148216 1152222 1152335 "IBITS" 1152521 NIL IBITS (NIL NIL) -8 NIL NIL) (-468 1144939 1145515 1146210 "IBATOOL" 1147633 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-467 1142719 1143180 1143713 "IBACHIN" 1144474 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-466 1140596 1142565 1142668 "IARRAY2" 1142673 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-465 1136749 1140522 1140579 "IARRAY1" 1140584 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-464 1130688 1135167 1135645 "IAN" 1136291 T IAN (NIL) -8 NIL NIL) (-463 1130199 1130256 1130429 "IALGFACT" 1130625 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-462 1129726 1129839 1129868 "HYPCAT" 1130075 T HYPCAT (NIL) -9 NIL NIL) (-461 1129264 1129381 1129567 "HYPCAT-" 1129572 NIL HYPCAT- (NIL T) -8 NIL NIL) (-460 1125943 1127274 1127316 "HOAGG" 1128297 NIL HOAGG (NIL T) -9 NIL 1128976) (-459 1124537 1124936 1125462 "HOAGG-" 1125467 NIL HOAGG- (NIL T T) -8 NIL NIL) (-458 1118368 1123978 1124144 "HEXADEC" 1124391 T HEXADEC (NIL) -8 NIL NIL) (-457 1117116 1117338 1117601 "HEUGCD" 1118145 NIL HEUGCD (NIL T) -7 NIL NIL) (-456 1116219 1116953 1117083 "HELLFDIV" 1117088 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-455 1114447 1115996 1116084 "HEAP" 1116163 NIL HEAP (NIL T) -8 NIL NIL) (-454 1108314 1114362 1114424 "HDP" 1114429 NIL HDP (NIL NIL T) -8 NIL NIL) (-453 1102026 1107951 1108102 "HDMP" 1108215 NIL HDMP (NIL NIL T) -8 NIL NIL) (-452 1101351 1101490 1101654 "HB" 1101882 T HB (NIL) -7 NIL NIL) (-451 1094848 1101197 1101301 "HASHTBL" 1101306 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-450 1092601 1094476 1094655 "HACKPI" 1094689 T HACKPI (NIL) -8 NIL NIL) (-449 1088297 1092455 1092567 "GTSET" 1092572 NIL GTSET (NIL T T T T) -8 NIL NIL) (-448 1081823 1088175 1088273 "GSTBL" 1088278 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-447 1074059 1080859 1081123 "GSERIES" 1081614 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-446 1073081 1073534 1073563 "GROUP" 1073824 T GROUP (NIL) -9 NIL 1073983) (-445 1072197 1072420 1072764 "GROUP-" 1072769 NIL GROUP- (NIL T) -8 NIL NIL) (-444 1070566 1070885 1071272 "GROEBSOL" 1071874 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-443 1069506 1069768 1069820 "GRMOD" 1070349 NIL GRMOD (NIL T T) -9 NIL 1070517) (-442 1069274 1069310 1069438 "GRMOD-" 1069443 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-441 1064602 1065628 1066628 "GRIMAGE" 1068294 T GRIMAGE (NIL) -8 NIL NIL) (-440 1063069 1063329 1063653 "GRDEF" 1064298 T GRDEF (NIL) -7 NIL NIL) (-439 1062513 1062629 1062770 "GRAY" 1062948 T GRAY (NIL) -7 NIL NIL) (-438 1061746 1062126 1062178 "GRALG" 1062331 NIL GRALG (NIL T T) -9 NIL 1062423) (-437 1061407 1061480 1061643 "GRALG-" 1061648 NIL GRALG- (NIL T T T) -8 NIL NIL) (-436 1058215 1060996 1061172 "GPOLSET" 1061314 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-435 1057571 1057628 1057885 "GOSPER" 1058152 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-434 1053330 1054009 1054535 "GMODPOL" 1057270 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-433 1052335 1052519 1052757 "GHENSEL" 1053142 NIL GHENSEL (NIL T T) -7 NIL NIL) (-432 1046401 1047244 1048270 "GENUPS" 1051419 NIL GENUPS (NIL T T) -7 NIL NIL) (-431 1046098 1046149 1046238 "GENUFACT" 1046344 NIL GENUFACT (NIL T) -7 NIL NIL) (-430 1045510 1045587 1045752 "GENPGCD" 1046016 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-429 1044984 1045019 1045232 "GENMFACT" 1045469 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-428 1043552 1043807 1044114 "GENEEZ" 1044727 NIL GENEEZ (NIL T T) -7 NIL NIL) (-427 1037426 1043165 1043326 "GDMP" 1043475 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-426 1026808 1031197 1032303 "GCNAALG" 1036409 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-425 1025229 1026101 1026130 "GCDDOM" 1026385 T GCDDOM (NIL) -9 NIL 1026542) (-424 1024699 1024826 1025041 "GCDDOM-" 1025046 NIL GCDDOM- (NIL T) -8 NIL NIL) (-423 1023371 1023556 1023860 "GB" 1024478 NIL GB (NIL T T T T) -7 NIL NIL) (-422 1011991 1014317 1016709 "GBINTERN" 1021062 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-421 1009828 1010120 1010541 "GBF" 1011666 NIL GBF (NIL T T T T) -7 NIL NIL) (-420 1008609 1008774 1009041 "GBEUCLID" 1009644 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-419 1007958 1008083 1008232 "GAUSSFAC" 1008480 T GAUSSFAC (NIL) -7 NIL NIL) (-418 1006335 1006637 1006950 "GALUTIL" 1007677 NIL GALUTIL (NIL T) -7 NIL NIL) (-417 1004652 1004926 1005249 "GALPOLYU" 1006062 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-416 1002041 1002331 1002736 "GALFACTU" 1004349 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-415 993847 995346 996954 "GALFACT" 1000473 NIL GALFACT (NIL T) -7 NIL NIL) (-414 991234 991892 991921 "FVFUN" 993077 T FVFUN (NIL) -9 NIL 993797) (-413 990499 990681 990710 "FVC" 991001 T FVC (NIL) -9 NIL 991184) (-412 990141 990296 990377 "FUNCTION" 990451 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-411 987811 988362 988851 "FT" 989672 T FT (NIL) -8 NIL NIL) (-410 986629 987112 987315 "FTEM" 987628 T FTEM (NIL) -8 NIL NIL) (-409 984894 985182 985584 "FSUPFACT" 986321 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-408 983291 983580 983912 "FST" 984582 T FST (NIL) -8 NIL NIL) (-407 982466 982572 982766 "FSRED" 983173 NIL FSRED (NIL T T) -7 NIL NIL) (-406 981145 981400 981754 "FSPRMELT" 982181 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-405 978230 978668 979167 "FSPECF" 980708 NIL FSPECF (NIL T T) -7 NIL NIL) (-404 960603 969160 969201 "FS" 973039 NIL FS (NIL T) -9 NIL 975321) (-403 949253 952243 956299 "FS-" 956596 NIL FS- (NIL T T) -8 NIL NIL) (-402 948769 948823 948999 "FSINT" 949194 NIL FSINT (NIL T T) -7 NIL NIL) (-401 947050 947762 948065 "FSERIES" 948548 NIL FSERIES (NIL T T) -8 NIL NIL) (-400 946068 946184 946414 "FSCINT" 946930 NIL FSCINT (NIL T T) -7 NIL NIL) (-399 942302 945012 945054 "FSAGG" 945424 NIL FSAGG (NIL T) -9 NIL 945683) (-398 940064 940665 941461 "FSAGG-" 941556 NIL FSAGG- (NIL T T) -8 NIL NIL) (-397 939106 939249 939476 "FSAGG2" 939917 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-396 936765 937044 937597 "FS2UPS" 938824 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-395 936351 936394 936547 "FS2" 936716 NIL FS2 (NIL T T T T) -7 NIL NIL) (-394 935211 935382 935690 "FS2EXPXP" 936176 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-393 934637 934752 934904 "FRUTIL" 935091 NIL FRUTIL (NIL T) -7 NIL NIL) (-392 926058 930136 931492 "FR" 933313 NIL FR (NIL T) -8 NIL NIL) (-391 921134 923777 923818 "FRNAALG" 925214 NIL FRNAALG (NIL T) -9 NIL 925821) (-390 916813 917883 919158 "FRNAALG-" 919908 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-389 916451 916494 916621 "FRNAAF2" 916764 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-388 914816 915308 915602 "FRMOD" 916264 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-387 912539 913207 913523 "FRIDEAL" 914607 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-386 911738 911825 912112 "FRIDEAL2" 912446 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-385 910995 911403 911445 "FRETRCT" 911450 NIL FRETRCT (NIL T) -9 NIL 911621) (-384 910107 910338 910689 "FRETRCT-" 910694 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-383 907316 908536 908596 "FRAMALG" 909478 NIL FRAMALG (NIL T T) -9 NIL 909770) (-382 905449 905905 906535 "FRAMALG-" 906758 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-381 899351 904924 905200 "FRAC" 905205 NIL FRAC (NIL T) -8 NIL NIL) (-380 898987 899044 899151 "FRAC2" 899288 NIL FRAC2 (NIL T T) -7 NIL NIL) (-379 898623 898680 898787 "FR2" 898924 NIL FR2 (NIL T T) -7 NIL NIL) (-378 893296 896209 896238 "FPS" 897357 T FPS (NIL) -9 NIL 897913) (-377 892745 892854 893018 "FPS-" 893164 NIL FPS- (NIL T) -8 NIL NIL) (-376 890193 891890 891919 "FPC" 892144 T FPC (NIL) -9 NIL 892286) (-375 889986 890026 890123 "FPC-" 890128 NIL FPC- (NIL T) -8 NIL NIL) (-374 888864 889474 889516 "FPATMAB" 889521 NIL FPATMAB (NIL T) -9 NIL 889673) (-373 886564 887040 887466 "FPARFRAC" 888501 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-372 881959 882456 883138 "FORTRAN" 885996 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-371 879675 880175 880714 "FORT" 881440 T FORT (NIL) -7 NIL NIL) (-370 877350 877912 877941 "FORTFN" 879001 T FORTFN (NIL) -9 NIL 879625) (-369 877113 877163 877192 "FORTCAT" 877251 T FORTCAT (NIL) -9 NIL 877313) (-368 875173 875656 876055 "FORMULA" 876734 T FORMULA (NIL) -8 NIL NIL) (-367 874961 874991 875060 "FORMULA1" 875137 NIL FORMULA1 (NIL T) -7 NIL NIL) (-366 874484 874536 874709 "FORDER" 874903 NIL FORDER (NIL T T T T) -7 NIL NIL) (-365 873580 873744 873937 "FOP" 874311 T FOP (NIL) -7 NIL NIL) (-364 872188 872860 873034 "FNLA" 873462 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-363 870856 871245 871274 "FNCAT" 871846 T FNCAT (NIL) -9 NIL 872139) (-362 870422 870815 870843 "FNAME" 870848 T FNAME (NIL) -8 NIL NIL) (-361 869081 870054 870083 "FMTC" 870088 T FMTC (NIL) -9 NIL 870123) (-360 865399 866606 867234 "FMONOID" 868486 NIL FMONOID (NIL T) -8 NIL NIL) (-359 864619 865142 865290 "FM" 865295 NIL FM (NIL T T) -8 NIL NIL) (-358 862042 862688 862717 "FMFUN" 863861 T FMFUN (NIL) -9 NIL 864569) (-357 861310 861491 861520 "FMC" 861810 T FMC (NIL) -9 NIL 861992) (-356 858539 859373 859427 "FMCAT" 860609 NIL FMCAT (NIL T T) -9 NIL 861103) (-355 857434 858307 858406 "FM1" 858484 NIL FM1 (NIL T T) -8 NIL NIL) (-354 855208 855624 856118 "FLOATRP" 856985 NIL FLOATRP (NIL T) -7 NIL NIL) (-353 848694 852864 853494 "FLOAT" 854598 T FLOAT (NIL) -8 NIL NIL) (-352 846132 846632 847210 "FLOATCP" 848161 NIL FLOATCP (NIL T) -7 NIL NIL) (-351 844920 845768 845809 "FLINEXP" 845814 NIL FLINEXP (NIL T) -9 NIL 845907) (-350 844075 844310 844637 "FLINEXP-" 844642 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-349 843151 843295 843519 "FLASORT" 843927 NIL FLASORT (NIL T T) -7 NIL NIL) (-348 840369 841211 841264 "FLALG" 842491 NIL FLALG (NIL T T) -9 NIL 842958) (-347 834153 837855 837897 "FLAGG" 839159 NIL FLAGG (NIL T) -9 NIL 839811) (-346 832879 833218 833708 "FLAGG-" 833713 NIL FLAGG- (NIL T T) -8 NIL NIL) (-345 831921 832064 832291 "FLAGG2" 832732 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-344 828893 829911 829971 "FINRALG" 831099 NIL FINRALG (NIL T T) -9 NIL 831607) (-343 828053 828282 828621 "FINRALG-" 828626 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-342 827459 827672 827701 "FINITE" 827897 T FINITE (NIL) -9 NIL 828004) (-341 819918 822079 822120 "FINAALG" 825787 NIL FINAALG (NIL T) -9 NIL 827240) (-340 815259 816300 817444 "FINAALG-" 818823 NIL FINAALG- (NIL T T) -8 NIL NIL) (-339 814654 815014 815117 "FILE" 815189 NIL FILE (NIL T) -8 NIL NIL) (-338 813338 813650 813705 "FILECAT" 814389 NIL FILECAT (NIL T T) -9 NIL 814605) (-337 811200 812756 812785 "FIELD" 812825 T FIELD (NIL) -9 NIL 812905) (-336 809820 810205 810716 "FIELD-" 810721 NIL FIELD- (NIL T) -8 NIL NIL) (-335 807635 808457 808803 "FGROUP" 809507 NIL FGROUP (NIL T) -8 NIL NIL) (-334 806725 806889 807109 "FGLMICPK" 807467 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-333 802527 806650 806707 "FFX" 806712 NIL FFX (NIL T NIL) -8 NIL NIL) (-332 802128 802189 802324 "FFSLPE" 802460 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-331 798123 798900 799696 "FFPOLY" 801364 NIL FFPOLY (NIL T) -7 NIL NIL) (-330 797627 797663 797872 "FFPOLY2" 798081 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-329 793449 797546 797609 "FFP" 797614 NIL FFP (NIL T NIL) -8 NIL NIL) (-328 788817 793360 793424 "FF" 793429 NIL FF (NIL NIL NIL) -8 NIL NIL) (-327 783913 788160 788350 "FFNBX" 788671 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-326 778823 783048 783306 "FFNBP" 783767 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-325 773426 778107 778318 "FFNB" 778656 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-324 772258 772456 772771 "FFINTBAS" 773223 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-323 768481 770721 770750 "FFIELDC" 771370 T FFIELDC (NIL) -9 NIL 771746) (-322 767144 767514 768011 "FFIELDC-" 768016 NIL FFIELDC- (NIL T) -8 NIL NIL) (-321 766714 766759 766883 "FFHOM" 767086 NIL FFHOM (NIL T T T) -7 NIL NIL) (-320 764412 764896 765413 "FFF" 766229 NIL FFF (NIL T) -7 NIL NIL) (-319 760000 764154 764255 "FFCGX" 764355 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-318 755602 759732 759839 "FFCGP" 759943 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-317 750755 755329 755437 "FFCG" 755538 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-316 732700 741823 741910 "FFCAT" 747075 NIL FFCAT (NIL T T T) -9 NIL 748562) (-315 727898 728945 730259 "FFCAT-" 731489 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-314 727309 727352 727587 "FFCAT2" 727849 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-313 716509 720299 721516 "FEXPR" 726164 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-312 715508 715943 715985 "FEVALAB" 716069 NIL FEVALAB (NIL T) -9 NIL 716330) (-311 714667 714877 715215 "FEVALAB-" 715220 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-310 713260 714050 714253 "FDIV" 714566 NIL FDIV (NIL T T T T) -8 NIL NIL) (-309 710326 711041 711157 "FDIVCAT" 712725 NIL FDIVCAT (NIL T T T T) -9 NIL 713162) (-308 710088 710115 710285 "FDIVCAT-" 710290 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-307 709308 709395 709672 "FDIV2" 709995 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-306 707994 708253 708542 "FCPAK1" 709039 T FCPAK1 (NIL) -7 NIL NIL) (-305 707122 707494 707635 "FCOMP" 707885 NIL FCOMP (NIL T) -8 NIL NIL) (-304 690750 694165 697728 "FC" 703579 T FC (NIL) -8 NIL NIL) (-303 683345 687391 687432 "FAXF" 689234 NIL FAXF (NIL T) -9 NIL 689925) (-302 680624 681279 682104 "FAXF-" 682569 NIL FAXF- (NIL T T) -8 NIL NIL) (-301 675724 680000 680176 "FARRAY" 680481 NIL FARRAY (NIL T) -8 NIL NIL) (-300 671114 673185 673238 "FAMR" 674250 NIL FAMR (NIL T T) -9 NIL 674710) (-299 670005 670307 670741 "FAMR-" 670746 NIL FAMR- (NIL T T T) -8 NIL NIL) (-298 669201 669927 669980 "FAMONOID" 669985 NIL FAMONOID (NIL T) -8 NIL NIL) (-297 667033 667717 667771 "FAMONC" 668712 NIL FAMONC (NIL T T) -9 NIL 669097) (-296 665725 666787 666924 "FAGROUP" 666929 NIL FAGROUP (NIL T) -8 NIL NIL) (-295 663528 663847 664249 "FACUTIL" 665406 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-294 662627 662812 663034 "FACTFUNC" 663338 NIL FACTFUNC (NIL T) -7 NIL NIL) (-293 654950 661878 662090 "EXPUPXS" 662483 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-292 652433 652973 653559 "EXPRTUBE" 654384 T EXPRTUBE (NIL) -7 NIL NIL) (-291 648627 649219 649956 "EXPRODE" 651772 NIL EXPRODE (NIL T T) -7 NIL NIL) (-290 633786 647286 647712 "EXPR" 648233 NIL EXPR (NIL T) -8 NIL NIL) (-289 628214 628801 629613 "EXPR2UPS" 633084 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-288 627850 627907 628014 "EXPR2" 628151 NIL EXPR2 (NIL T T) -7 NIL NIL) (-287 619204 626987 627282 "EXPEXPAN" 627688 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-286 619031 619161 619190 "EXIT" 619195 T EXIT (NIL) -8 NIL NIL) (-285 618658 618720 618833 "EVALCYC" 618963 NIL EVALCYC (NIL T) -7 NIL NIL) (-284 618198 618316 618358 "EVALAB" 618528 NIL EVALAB (NIL T) -9 NIL 618632) (-283 617679 617801 618022 "EVALAB-" 618027 NIL EVALAB- (NIL T T) -8 NIL NIL) (-282 615141 616453 616482 "EUCDOM" 617037 T EUCDOM (NIL) -9 NIL 617387) (-281 613546 613988 614578 "EUCDOM-" 614583 NIL EUCDOM- (NIL T) -8 NIL NIL) (-280 601124 603872 606612 "ESTOOLS" 610826 T ESTOOLS (NIL) -7 NIL NIL) (-279 600760 600817 600924 "ESTOOLS2" 601061 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-278 600511 600553 600633 "ESTOOLS1" 600712 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-277 594448 596172 596201 "ES" 598965 T ES (NIL) -9 NIL 600371) (-276 589396 590682 592499 "ES-" 592663 NIL ES- (NIL T) -8 NIL NIL) (-275 585771 586531 587311 "ESCONT" 588636 T ESCONT (NIL) -7 NIL NIL) (-274 585516 585548 585630 "ESCONT1" 585733 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-273 585191 585241 585341 "ES2" 585460 NIL ES2 (NIL T T) -7 NIL NIL) (-272 584821 584879 584988 "ES1" 585127 NIL ES1 (NIL T T) -7 NIL NIL) (-271 584037 584166 584342 "ERROR" 584665 T ERROR (NIL) -7 NIL NIL) (-270 577540 583896 583987 "EQTBL" 583992 NIL EQTBL (NIL T T) -8 NIL NIL) (-269 569977 572858 574305 "EQ" 576126 NIL -3082 (NIL T) -8 NIL NIL) (-268 569609 569666 569775 "EQ2" 569914 NIL EQ2 (NIL T T) -7 NIL NIL) (-267 564901 565947 567040 "EP" 568548 NIL EP (NIL T) -7 NIL NIL) (-266 563484 563784 564101 "ENV" 564604 T ENV (NIL) -8 NIL NIL) (-265 562643 563207 563236 "ENTIRER" 563241 T ENTIRER (NIL) -9 NIL 563286) (-264 559099 560598 560968 "EMR" 562442 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-263 558242 558427 558482 "ELTAGG" 558862 NIL ELTAGG (NIL T T) -9 NIL 559073) (-262 557961 558023 558164 "ELTAGG-" 558169 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-261 557749 557778 557833 "ELTAB" 557917 NIL ELTAB (NIL T T) -9 NIL NIL) (-260 556875 557021 557220 "ELFUTS" 557600 NIL ELFUTS (NIL T T) -7 NIL NIL) (-259 556616 556672 556701 "ELEMFUN" 556806 T ELEMFUN (NIL) -9 NIL NIL) (-258 556486 556507 556575 "ELEMFUN-" 556580 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-257 551377 554586 554628 "ELAGG" 555568 NIL ELAGG (NIL T) -9 NIL 556031) (-256 549662 550096 550759 "ELAGG-" 550764 NIL ELAGG- (NIL T T) -8 NIL NIL) (-255 542530 544329 545156 "EFUPXS" 548938 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-254 535980 537781 538591 "EFULS" 541806 NIL EFULS (NIL T T T) -8 NIL NIL) (-253 533411 533769 534247 "EFSTRUC" 535612 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-252 522483 524048 525608 "EF" 531926 NIL EF (NIL T T) -7 NIL NIL) (-251 521584 521968 522117 "EAB" 522354 T EAB (NIL) -8 NIL NIL) (-250 520797 521543 521571 "E04UCFA" 521576 T E04UCFA (NIL) -8 NIL NIL) (-249 520010 520756 520784 "E04NAFA" 520789 T E04NAFA (NIL) -8 NIL NIL) (-248 519223 519969 519997 "E04MBFA" 520002 T E04MBFA (NIL) -8 NIL NIL) (-247 518436 519182 519210 "E04JAFA" 519215 T E04JAFA (NIL) -8 NIL NIL) (-246 517651 518395 518423 "E04GCFA" 518428 T E04GCFA (NIL) -8 NIL NIL) (-245 516866 517610 517638 "E04FDFA" 517643 T E04FDFA (NIL) -8 NIL NIL) (-244 516079 516825 516853 "E04DGFA" 516858 T E04DGFA (NIL) -8 NIL NIL) (-243 510264 511609 512971 "E04AGNT" 514737 T E04AGNT (NIL) -7 NIL NIL) (-242 508990 509470 509511 "DVARCAT" 509986 NIL DVARCAT (NIL T) -9 NIL 510184) (-241 508194 508406 508720 "DVARCAT-" 508725 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-240 501056 507996 508123 "DSMP" 508128 NIL DSMP (NIL T T T) -8 NIL NIL) (-239 495866 497001 498069 "DROPT" 500008 T DROPT (NIL) -8 NIL NIL) (-238 495531 495590 495688 "DROPT1" 495801 NIL DROPT1 (NIL T) -7 NIL NIL) (-237 490646 491772 492909 "DROPT0" 494414 T DROPT0 (NIL) -7 NIL NIL) (-236 488991 489316 489702 "DRAWPT" 490280 T DRAWPT (NIL) -7 NIL NIL) (-235 483578 484501 485580 "DRAW" 487965 NIL DRAW (NIL T) -7 NIL NIL) (-234 483211 483264 483382 "DRAWHACK" 483519 NIL DRAWHACK (NIL T) -7 NIL NIL) (-233 481942 482211 482502 "DRAWCX" 482940 T DRAWCX (NIL) -7 NIL NIL) (-232 481460 481528 481678 "DRAWCURV" 481868 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-231 471932 473890 476005 "DRAWCFUN" 479365 T DRAWCFUN (NIL) -7 NIL NIL) (-230 468745 470627 470669 "DQAGG" 471298 NIL DQAGG (NIL T) -9 NIL 471571) (-229 457251 463989 464072 "DPOLCAT" 465910 NIL DPOLCAT (NIL T T T T) -9 NIL 466454) (-228 452091 453437 455394 "DPOLCAT-" 455399 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-227 446175 451953 452050 "DPMO" 452055 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-226 440162 445956 446122 "DPMM" 446127 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-225 439675 439773 439893 "DOMAIN" 440062 T DOMAIN (NIL) -8 NIL NIL) (-224 433387 439312 439463 "DMP" 439576 NIL DMP (NIL NIL T) -8 NIL NIL) (-223 432987 433043 433187 "DLP" 433325 NIL DLP (NIL T) -7 NIL NIL) (-222 426631 432088 432315 "DLIST" 432792 NIL DLIST (NIL T) -8 NIL NIL) (-221 423477 425486 425528 "DLAGG" 426078 NIL DLAGG (NIL T) -9 NIL 426307) (-220 422186 422878 422907 "DIVRING" 423057 T DIVRING (NIL) -9 NIL 423165) (-219 421174 421427 421820 "DIVRING-" 421825 NIL DIVRING- (NIL T) -8 NIL NIL) (-218 419276 419633 420039 "DISPLAY" 420788 T DISPLAY (NIL) -7 NIL NIL) (-217 413165 419190 419253 "DIRPROD" 419258 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-216 412013 412216 412481 "DIRPROD2" 412958 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-215 401643 407648 407702 "DIRPCAT" 408110 NIL DIRPCAT (NIL NIL T) -9 NIL 408937) (-214 398969 399611 400492 "DIRPCAT-" 400829 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-213 398256 398416 398602 "DIOSP" 398803 T DIOSP (NIL) -7 NIL NIL) (-212 394958 397168 397210 "DIOPS" 397644 NIL DIOPS (NIL T) -9 NIL 397873) (-211 394507 394621 394812 "DIOPS-" 394817 NIL DIOPS- (NIL T T) -8 NIL NIL) (-210 393378 394016 394045 "DIFRING" 394232 T DIFRING (NIL) -9 NIL 394341) (-209 393024 393101 393253 "DIFRING-" 393258 NIL DIFRING- (NIL T) -8 NIL NIL) (-208 390813 392095 392136 "DIFEXT" 392495 NIL DIFEXT (NIL T) -9 NIL 392788) (-207 389099 389527 390192 "DIFEXT-" 390197 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-206 386421 388631 388673 "DIAGG" 388678 NIL DIAGG (NIL T) -9 NIL 388698) (-205 385805 385962 386214 "DIAGG-" 386219 NIL DIAGG- (NIL T T) -8 NIL NIL) (-204 381270 384764 385041 "DHMATRIX" 385574 NIL DHMATRIX (NIL T) -8 NIL NIL) (-203 376882 377791 378801 "DFSFUN" 380280 T DFSFUN (NIL) -7 NIL NIL) (-202 371668 375596 375961 "DFLOAT" 376537 T DFLOAT (NIL) -8 NIL NIL) (-201 369901 370182 370577 "DFINTTLS" 371376 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-200 366934 367936 368334 "DERHAM" 369568 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-199 364783 366709 366798 "DEQUEUE" 366878 NIL DEQUEUE (NIL T) -8 NIL NIL) (-198 364001 364134 364329 "DEGRED" 364645 NIL DEGRED (NIL T T) -7 NIL NIL) (-197 360401 361146 361998 "DEFINTRF" 363229 NIL DEFINTRF (NIL T) -7 NIL NIL) (-196 357932 358401 358999 "DEFINTEF" 359920 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-195 351763 357373 357539 "DECIMAL" 357786 T DECIMAL (NIL) -8 NIL NIL) (-194 349275 349733 350239 "DDFACT" 351307 NIL DDFACT (NIL T T) -7 NIL NIL) (-193 348871 348914 349065 "DBLRESP" 349226 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-192 346581 346915 347284 "DBASE" 348629 NIL DBASE (NIL T) -8 NIL NIL) (-191 345716 346540 346568 "D03FAFA" 346573 T D03FAFA (NIL) -8 NIL NIL) (-190 344852 345675 345703 "D03EEFA" 345708 T D03EEFA (NIL) -8 NIL NIL) (-189 342802 343268 343757 "D03AGNT" 344383 T D03AGNT (NIL) -7 NIL NIL) (-188 342120 342761 342789 "D02EJFA" 342794 T D02EJFA (NIL) -8 NIL NIL) (-187 341438 342079 342107 "D02CJFA" 342112 T D02CJFA (NIL) -8 NIL NIL) (-186 340756 341397 341425 "D02BHFA" 341430 T D02BHFA (NIL) -8 NIL NIL) (-185 340074 340715 340743 "D02BBFA" 340748 T D02BBFA (NIL) -8 NIL NIL) (-184 333272 334860 336466 "D02AGNT" 338488 T D02AGNT (NIL) -7 NIL NIL) (-183 331041 331563 332109 "D01WGTS" 332746 T D01WGTS (NIL) -7 NIL NIL) (-182 330144 331000 331028 "D01TRNS" 331033 T D01TRNS (NIL) -8 NIL NIL) (-181 329247 330103 330131 "D01GBFA" 330136 T D01GBFA (NIL) -8 NIL NIL) (-180 328350 329206 329234 "D01FCFA" 329239 T D01FCFA (NIL) -8 NIL NIL) (-179 327453 328309 328337 "D01ASFA" 328342 T D01ASFA (NIL) -8 NIL NIL) (-178 326556 327412 327440 "D01AQFA" 327445 T D01AQFA (NIL) -8 NIL NIL) (-177 325659 326515 326543 "D01APFA" 326548 T D01APFA (NIL) -8 NIL NIL) (-176 324762 325618 325646 "D01ANFA" 325651 T D01ANFA (NIL) -8 NIL NIL) (-175 323865 324721 324749 "D01AMFA" 324754 T D01AMFA (NIL) -8 NIL NIL) (-174 322968 323824 323852 "D01ALFA" 323857 T D01ALFA (NIL) -8 NIL NIL) (-173 322071 322927 322955 "D01AKFA" 322960 T D01AKFA (NIL) -8 NIL NIL) (-172 321174 322030 322058 "D01AJFA" 322063 T D01AJFA (NIL) -8 NIL NIL) (-171 314478 316027 317586 "D01AGNT" 319635 T D01AGNT (NIL) -7 NIL NIL) (-170 313815 313943 314095 "CYCLOTOM" 314346 T CYCLOTOM (NIL) -7 NIL NIL) (-169 310550 311263 311990 "CYCLES" 313108 T CYCLES (NIL) -7 NIL NIL) (-168 309862 309996 310167 "CVMP" 310411 NIL CVMP (NIL T) -7 NIL NIL) (-167 307644 307901 308276 "CTRIGMNP" 309590 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-166 307249 307332 307437 "CTORCALL" 307559 T CTORCALL (NIL) -8 NIL NIL) (-165 306623 306722 306875 "CSTTOOLS" 307146 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-164 302422 303079 303837 "CRFP" 305935 NIL CRFP (NIL T T) -7 NIL NIL) (-163 301469 301654 301882 "CRAPACK" 302226 NIL CRAPACK (NIL T) -7 NIL NIL) (-162 300853 300954 301158 "CPMATCH" 301345 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-161 300578 300606 300712 "CPIMA" 300819 NIL CPIMA (NIL T T T) -7 NIL NIL) (-160 296942 297614 298332 "COORDSYS" 299913 NIL COORDSYS (NIL T) -7 NIL NIL) (-159 296326 296455 296605 "CONTOUR" 296812 T CONTOUR (NIL) -8 NIL NIL) (-158 292187 294329 294821 "CONTFRAC" 295866 NIL CONTFRAC (NIL T) -8 NIL NIL) (-157 291340 291904 291933 "COMRING" 291938 T COMRING (NIL) -9 NIL 291989) (-156 290421 290698 290882 "COMPPROP" 291176 T COMPPROP (NIL) -8 NIL NIL) (-155 290082 290117 290245 "COMPLPAT" 290380 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-154 280063 289891 290000 "COMPLEX" 290005 NIL COMPLEX (NIL T) -8 NIL NIL) (-153 279699 279756 279863 "COMPLEX2" 280000 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-152 279417 279452 279550 "COMPFACT" 279658 NIL COMPFACT (NIL T T) -7 NIL NIL) (-151 263751 274045 274086 "COMPCAT" 275088 NIL COMPCAT (NIL T) -9 NIL 276481) (-150 253266 256190 259817 "COMPCAT-" 260173 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-149 252997 253025 253127 "COMMUPC" 253232 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-148 252792 252825 252884 "COMMONOP" 252958 T COMMONOP (NIL) -7 NIL NIL) (-147 252375 252543 252630 "COMM" 252725 T COMM (NIL) -8 NIL NIL) (-146 251623 251817 251846 "COMBOPC" 252184 T COMBOPC (NIL) -9 NIL 252359) (-145 250519 250729 250971 "COMBINAT" 251413 NIL COMBINAT (NIL T) -7 NIL NIL) (-144 246717 247290 247930 "COMBF" 249941 NIL COMBF (NIL T T) -7 NIL NIL) (-143 245503 245833 246068 "COLOR" 246502 T COLOR (NIL) -8 NIL NIL) (-142 245143 245190 245315 "CMPLXRT" 245450 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-141 240645 241673 242753 "CLIP" 244083 T CLIP (NIL) -7 NIL NIL) (-140 238983 239753 239991 "CLIF" 240473 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-139 235205 237129 237171 "CLAGG" 238100 NIL CLAGG (NIL T) -9 NIL 238636) (-138 233627 234084 234667 "CLAGG-" 234672 NIL CLAGG- (NIL T T) -8 NIL NIL) (-137 233171 233256 233396 "CINTSLPE" 233536 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-136 230672 231143 231691 "CHVAR" 232699 NIL CHVAR (NIL T T T) -7 NIL NIL) (-135 229894 230458 230487 "CHARZ" 230492 T CHARZ (NIL) -9 NIL 230506) (-134 229648 229688 229766 "CHARPOL" 229848 NIL CHARPOL (NIL T) -7 NIL NIL) (-133 228754 229351 229380 "CHARNZ" 229427 T CHARNZ (NIL) -9 NIL 229482) (-132 226777 227444 227779 "CHAR" 228439 T CHAR (NIL) -8 NIL NIL) (-131 226502 226563 226592 "CFCAT" 226703 T CFCAT (NIL) -9 NIL NIL) (-130 225747 225858 226040 "CDEN" 226386 NIL CDEN (NIL T T T) -7 NIL NIL) (-129 221739 224900 225180 "CCLASS" 225487 T CCLASS (NIL) -8 NIL NIL) (-128 216792 217768 218521 "CARTEN" 221042 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-127 215900 216048 216269 "CARTEN2" 216639 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 214197 215052 215308 "CARD" 215664 T CARD (NIL) -8 NIL NIL) (-125 213569 213897 213926 "CACHSET" 214058 T CACHSET (NIL) -9 NIL 214135) (-124 213065 213361 213390 "CABMON" 213440 T CABMON (NIL) -9 NIL 213496) (-123 210622 212757 212864 "BTREE" 212991 NIL BTREE (NIL T) -8 NIL NIL) (-122 208120 210270 210392 "BTOURN" 210532 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205538 207591 207633 "BTCAT" 207701 NIL BTCAT (NIL T) -9 NIL 207778) (-120 205205 205285 205434 "BTCAT-" 205439 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200425 204296 204325 "BTAGG" 204581 T BTAGG (NIL) -9 NIL 204760) (-118 199848 199992 200222 "BTAGG-" 200227 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 196892 199126 199341 "BSTREE" 199665 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196030 196156 196340 "BRILL" 196748 NIL BRILL (NIL T) -7 NIL NIL) (-115 192731 194758 194800 "BRAGG" 195449 NIL BRAGG (NIL T) -9 NIL 195706) (-114 191260 191666 192221 "BRAGG-" 192226 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184468 190606 190790 "BPADICRT" 191108 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 182772 184405 184450 "BPADIC" 184455 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182472 182502 182615 "BOUNDZRO" 182736 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 177987 179078 179945 "BOP" 181625 T BOP (NIL) -8 NIL NIL) (-109 175608 176052 176572 "BOP1" 177500 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174227 174938 175161 "BOOLEAN" 175405 T BOOLEAN (NIL) -8 NIL NIL) (-107 173593 173971 174024 "BMODULE" 174029 NIL BMODULE (NIL T T) -9 NIL 174093) (-106 169403 173391 173464 "BITS" 173540 T BITS (NIL) -8 NIL NIL) (-105 168500 168935 169087 "BINFILE" 169271 T BINFILE (NIL) -8 NIL NIL) (-104 167912 168034 168176 "BINDING" 168378 T BINDING (NIL) -8 NIL NIL) (-103 161747 167356 167521 "BINARY" 167767 T BINARY (NIL) -8 NIL NIL) (-102 159574 161002 161044 "BGAGG" 161304 NIL BGAGG (NIL T) -9 NIL 161441) (-101 159405 159437 159528 "BGAGG-" 159533 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158503 158789 158994 "BFUNCT" 159220 T BFUNCT (NIL) -8 NIL NIL) (-99 157204 157382 157667 "BEZOUT" 158327 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 153729 156064 156392 "BBTREE" 156907 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153466 153519 153546 "BASTYPE" 153663 T BASTYPE (NIL) -9 NIL NIL) (-96 153321 153350 153420 "BASTYPE-" 153425 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 152759 152835 152985 "BALFACT" 153232 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151581 152178 152363 "AUTOMOR" 152604 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151306 151311 151338 "ATTREG" 151343 T ATTREG (NIL) -9 NIL NIL) (-92 149585 150003 150355 "ATTRBUT" 150972 T ATTRBUT (NIL) -8 NIL NIL) (-91 149120 149233 149260 "ATRIG" 149461 T ATRIG (NIL) -9 NIL NIL) (-90 148929 148970 149057 "ATRIG-" 149062 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147126 148705 148793 "ASTACK" 148872 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145631 145928 146293 "ASSOCEQ" 146808 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144663 145290 145414 "ASP9" 145538 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144427 144611 144650 "ASP8" 144655 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143297 144032 144174 "ASP80" 144316 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142196 142932 143064 "ASP7" 143196 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141152 141873 141991 "ASP78" 142109 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140123 140832 140949 "ASP77" 141066 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139038 139761 139892 "ASP74" 140023 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 137939 138673 138805 "ASP73" 138937 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 136894 137616 137734 "ASP6" 137852 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 135843 136571 136689 "ASP55" 136807 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 134793 135517 135636 "ASP50" 135755 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 133881 134494 134604 "ASP4" 134714 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 132969 133582 133692 "ASP49" 133802 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 131754 132508 132676 "ASP42" 132858 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130532 131287 131457 "ASP41" 131641 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129484 130209 130327 "ASP35" 130445 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129249 129432 129471 "ASP34" 129476 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 128986 129053 129129 "ASP33" 129204 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 127882 128621 128753 "ASP31" 128885 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127647 127830 127869 "ASP30" 127874 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127382 127451 127527 "ASP29" 127602 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127147 127330 127369 "ASP28" 127374 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 126912 127095 127134 "ASP27" 127139 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 125996 126610 126721 "ASP24" 126832 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 124913 125637 125767 "ASP20" 125897 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124001 124614 124724 "ASP1" 124834 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 122945 123675 123794 "ASP19" 123913 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122682 122749 122825 "ASP12" 122900 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121535 122281 122425 "ASP10" 122569 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119434 121379 121470 "ARRAY2" 121475 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115250 119082 119196 "ARRAY1" 119351 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114282 114455 114676 "ARRAY12" 115073 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108641 110512 110588 "ARR2CAT" 113218 NIL ARR2CAT (NIL T T T) -9 NIL 113976) (-54 106075 106819 107773 "ARR2CAT-" 107778 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 104835 104985 105288 "APPRULE" 105913 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104488 104536 104654 "APPLYORE" 104781 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103462 103753 103948 "ANY" 104311 T ANY (NIL) -8 NIL NIL) (-50 102740 102863 103020 "ANY1" 103336 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100272 101190 101515 "ANTISYM" 102465 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100099 100231 100258 "ANON" 100263 T ANON (NIL) -8 NIL NIL) (-47 94176 98644 99095 "AN" 99666 T AN (NIL) -8 NIL NIL) (-46 90529 91927 91978 "AMR" 92717 NIL AMR (NIL T T) -9 NIL 93316) (-45 89642 89863 90225 "AMR-" 90230 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74192 89559 89620 "ALIST" 89625 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71029 73786 73955 "ALGSC" 74110 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67585 68139 68746 "ALGPKG" 70469 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66862 66963 67147 "ALGMFACT" 67471 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62612 63292 63946 "ALGMANIP" 66386 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53931 62238 62388 "ALGFF" 62545 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53127 53258 53437 "ALGFACT" 53789 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52117 52727 52766 "ALGEBRA" 52826 NIL ALGEBRA (NIL T) -9 NIL 52884) (-36 51835 51894 52026 "ALGEBRA-" 52031 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34095 49838 49891 "ALAGG" 50027 NIL ALAGG (NIL T T) -9 NIL 50188) (-34 33630 33743 33770 "AHYP" 33971 T AHYP (NIL) -9 NIL NIL) (-33 32560 32808 32835 "AGG" 33334 T AGG (NIL) -9 NIL 33613) (-32 31994 32156 32370 "AGG-" 32375 NIL AGG- (NIL T) -8 NIL NIL) (-31 29681 30099 30516 "AF" 31637 NIL AF (NIL T T) -7 NIL NIL) (-30 28950 29208 29364 "ACPLOT" 29543 T ACPLOT (NIL) -8 NIL NIL) (-29 18416 26362 26414 "ACFS" 27125 NIL ACFS (NIL T) -9 NIL 27364) (-28 16430 16920 17695 "ACFS-" 17700 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12697 14653 14680 "ACF" 15559 T ACF (NIL) -9 NIL 15971) (-26 11401 11735 12228 "ACF-" 12233 NIL ACF- (NIL T) -8 NIL NIL) (-25 10999 11168 11195 "ABELSG" 11287 T ABELSG (NIL) -9 NIL 11352) (-24 10866 10891 10957 "ABELSG-" 10962 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10235 10496 10523 "ABELMON" 10693 T ABELMON (NIL) -9 NIL 10805) (-22 9899 9983 10121 "ABELMON-" 10126 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9233 9579 9606 "ABELGRP" 9731 T ABELGRP (NIL) -9 NIL 9813) (-20 8696 8825 9041 "ABELGRP-" 9046 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8075 "A1AGG" 8080 NIL A1AGG (NIL T) -9 NIL 8120) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-1196 3136367 3136372 3136377 "NIL" NIL T NIL (NIL) NIL NIL NIL) (-3 3136352 3136357 3136362 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-2 3136337 3136342 3136347 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1 3136322 3136327 3136332 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (0 3136307 3136312 3136317 "NIL" NIL NIL NIL (NIL) -8 NIL NIL) (-1191 3135437 3136182 3136259 "ZMOD" 3136264 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1190 3134547 3134711 3134920 "ZLINDEP" 3135269 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1189 3123951 3125696 3127648 "ZDSOLVE" 3132696 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1188 3123197 3123338 3123527 "YSTREAM" 3123797 NIL YSTREAM (NIL T) -7 NIL NIL) (-1187 3120965 3122502 3122705 "XRPOLY" 3123040 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1186 3117427 3118756 3119338 "XPR" 3120429 NIL XPR (NIL T T) -8 NIL NIL) (-1185 3115141 3116762 3116965 "XPOLY" 3117258 NIL XPOLY (NIL T) -8 NIL NIL) (-1184 3112954 3114332 3114387 "XPOLYC" 3114672 NIL XPOLYC (NIL T T) -9 NIL 3114785) (-1183 3109326 3111471 3111859 "XPBWPOLY" 3112612 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1182 3105253 3107566 3107609 "XF" 3108230 NIL XF (NIL T) -9 NIL 3108629) (-1181 3104874 3104962 3105131 "XF-" 3105136 NIL XF- (NIL T T) -8 NIL NIL) (-1180 3100253 3101552 3101607 "XFALG" 3103755 NIL XFALG (NIL T T) -9 NIL 3104542) (-1179 3099390 3099494 3099698 "XEXPPKG" 3100145 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1178 3097488 3099241 3099336 "XDPOLY" 3099341 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1177 3096366 3096976 3097019 "XALG" 3097081 NIL XALG (NIL T) -9 NIL 3097200) (-1176 3089842 3094350 3094843 "WUTSET" 3095958 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1175 3087654 3088461 3088812 "WP" 3089624 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1174 3086540 3086738 3087033 "WFFINTBS" 3087451 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1173 3084444 3084871 3085333 "WEIER" 3086112 NIL WEIER (NIL T) -7 NIL NIL) (-1172 3083592 3084016 3084059 "VSPACE" 3084195 NIL VSPACE (NIL T) -9 NIL 3084269) (-1171 3083430 3083457 3083548 "VSPACE-" 3083553 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1170 3083176 3083219 3083290 "VOID" 3083381 T VOID (NIL) -8 NIL NIL) (-1169 3081312 3081671 3082077 "VIEW" 3082792 T VIEW (NIL) -7 NIL NIL) (-1168 3077737 3078375 3079112 "VIEWDEF" 3080597 T VIEWDEF (NIL) -7 NIL NIL) (-1167 3067076 3069285 3071458 "VIEW3D" 3075586 T VIEW3D (NIL) -8 NIL NIL) (-1166 3059358 3060987 3062566 "VIEW2D" 3065519 T VIEW2D (NIL) -8 NIL NIL) (-1165 3054767 3059128 3059220 "VECTOR" 3059301 NIL VECTOR (NIL T) -8 NIL NIL) (-1164 3053344 3053603 3053921 "VECTOR2" 3054497 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1163 3046883 3051135 3051179 "VECTCAT" 3052167 NIL VECTCAT (NIL T) -9 NIL 3052751) (-1162 3045897 3046151 3046541 "VECTCAT-" 3046546 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1161 3045378 3045548 3045668 "VARIABLE" 3045812 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1160 3045310 3045315 3045346 "UTYPE" 3045351 T UTYPE (NIL) -9 NIL NIL) (-1159 3044145 3044299 3044560 "UTSODETL" 3045136 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1158 3041585 3042045 3042569 "UTSODE" 3043686 NIL UTSODE (NIL T T) -7 NIL NIL) (-1157 3033432 3039225 3039713 "UTS" 3041154 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1156 3024780 3030142 3030185 "UTSCAT" 3031286 NIL UTSCAT (NIL T) -9 NIL 3032043) (-1155 3022136 3022851 3023839 "UTSCAT-" 3023844 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1154 3021767 3021810 3021941 "UTS2" 3022087 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1153 3016042 3018607 3018651 "URAGG" 3020721 NIL URAGG (NIL T) -9 NIL 3021443) (-1152 3012981 3013844 3014967 "URAGG-" 3014972 NIL URAGG- (NIL T T) -8 NIL NIL) (-1151 3008667 3011598 3012069 "UPXSSING" 3012645 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1150 3000561 3007788 3008068 "UPXS" 3008444 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1149 2993593 3000466 3000537 "UPXSCONS" 3000542 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1148 2983885 2990712 2990774 "UPXSCCA" 2991423 NIL UPXSCCA (NIL T T) -9 NIL 2991664) (-1147 2983524 2983609 2983782 "UPXSCCA-" 2983787 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1146 2973738 2980338 2980381 "UPXSCAT" 2981024 NIL UPXSCAT (NIL T) -9 NIL 2981632) (-1145 2973172 2973251 2973428 "UPXS2" 2973653 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1144 2971826 2972079 2972430 "UPSQFREE" 2972915 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1143 2965721 2968773 2968828 "UPSCAT" 2969977 NIL UPSCAT (NIL T T) -9 NIL 2970750) (-1142 2964935 2965139 2965462 "UPSCAT-" 2965467 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1141 2951067 2959064 2959107 "UPOLYC" 2961185 NIL UPOLYC (NIL T) -9 NIL 2962405) (-1140 2942460 2944864 2947989 "UPOLYC-" 2947994 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1139 2942091 2942134 2942265 "UPOLYC2" 2942411 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1138 2933550 2941660 2941797 "UP" 2942001 NIL UP (NIL NIL T) -8 NIL NIL) (-1137 2932893 2933000 2933163 "UPMP" 2933439 NIL UPMP (NIL T T) -7 NIL NIL) (-1136 2932446 2932527 2932666 "UPDIVP" 2932806 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1135 2931014 2931263 2931579 "UPDECOMP" 2932195 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1134 2930249 2930361 2930546 "UPCDEN" 2930898 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1133 2929772 2929841 2929988 "UP2" 2930174 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1132 2928289 2928976 2929253 "UNISEG" 2929530 NIL UNISEG (NIL T) -8 NIL NIL) (-1131 2927504 2927631 2927836 "UNISEG2" 2928132 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1130 2926564 2926744 2926970 "UNIFACT" 2927320 NIL UNIFACT (NIL T) -7 NIL NIL) (-1129 2910463 2925745 2925995 "ULS" 2926371 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1128 2898431 2910368 2910439 "ULSCONS" 2910444 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1127 2881184 2893194 2893256 "ULSCCAT" 2893968 NIL ULSCCAT (NIL T T) -9 NIL 2894264) (-1126 2880235 2880480 2880867 "ULSCCAT-" 2880872 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1125 2870228 2876742 2876785 "ULSCAT" 2877641 NIL ULSCAT (NIL T) -9 NIL 2878371) (-1124 2869662 2869741 2869918 "ULS2" 2870143 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1123 2868059 2869026 2869057 "UFD" 2869269 T UFD (NIL) -9 NIL 2869383) (-1122 2867853 2867899 2867994 "UFD-" 2867999 NIL UFD- (NIL T) -8 NIL NIL) (-1121 2866935 2867118 2867334 "UDVO" 2867659 T UDVO (NIL) -7 NIL NIL) (-1120 2864751 2865160 2865631 "UDPO" 2866499 NIL UDPO (NIL T) -7 NIL NIL) (-1119 2864683 2864688 2864719 "TYPE" 2864724 T TYPE (NIL) -9 NIL NIL) (-1118 2863654 2863856 2864096 "TWOFACT" 2864477 NIL TWOFACT (NIL T) -7 NIL NIL) (-1117 2862592 2862929 2863192 "TUPLE" 2863426 NIL TUPLE (NIL T) -8 NIL NIL) (-1116 2860283 2860802 2861341 "TUBETOOL" 2862075 T TUBETOOL (NIL) -7 NIL NIL) (-1115 2859132 2859337 2859578 "TUBE" 2860076 NIL TUBE (NIL T) -8 NIL NIL) (-1114 2853856 2858110 2858392 "TS" 2858884 NIL TS (NIL T) -8 NIL NIL) (-1113 2842559 2846651 2846748 "TSETCAT" 2851982 NIL TSETCAT (NIL T T T T) -9 NIL 2853513) (-1112 2837294 2838892 2840782 "TSETCAT-" 2840787 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1111 2831557 2832403 2833345 "TRMANIP" 2836430 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1110 2830998 2831061 2831224 "TRIMAT" 2831489 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1109 2828804 2829041 2829404 "TRIGMNIP" 2830747 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1108 2828323 2828436 2828467 "TRIGCAT" 2828680 T TRIGCAT (NIL) -9 NIL NIL) (-1107 2827992 2828071 2828212 "TRIGCAT-" 2828217 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1106 2824891 2826852 2827132 "TREE" 2827747 NIL TREE (NIL T) -8 NIL NIL) (-1105 2824164 2824692 2824723 "TRANFUN" 2824758 T TRANFUN (NIL) -9 NIL 2824824) (-1104 2823443 2823634 2823914 "TRANFUN-" 2823919 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1103 2823247 2823279 2823340 "TOPSP" 2823404 T TOPSP (NIL) -7 NIL NIL) (-1102 2822599 2822714 2822867 "TOOLSIGN" 2823128 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1101 2821260 2821776 2822015 "TEXTFILE" 2822382 T TEXTFILE (NIL) -8 NIL NIL) (-1100 2819125 2819639 2820077 "TEX" 2820844 T TEX (NIL) -8 NIL NIL) (-1099 2818906 2818937 2819009 "TEX1" 2819088 NIL TEX1 (NIL T) -7 NIL NIL) (-1098 2818554 2818617 2818707 "TEMUTL" 2818838 T TEMUTL (NIL) -7 NIL NIL) (-1097 2816708 2816988 2817313 "TBCMPPK" 2818277 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1096 2808596 2814868 2814925 "TBAGG" 2815325 NIL TBAGG (NIL T T) -9 NIL 2815536) (-1095 2803666 2805154 2806908 "TBAGG-" 2806913 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1094 2803050 2803157 2803302 "TANEXP" 2803555 NIL TANEXP (NIL T) -7 NIL NIL) (-1093 2796551 2802907 2803000 "TABLE" 2803005 NIL TABLE (NIL T T) -8 NIL NIL) (-1092 2795964 2796062 2796200 "TABLEAU" 2796448 NIL TABLEAU (NIL T) -8 NIL NIL) (-1091 2790572 2791792 2793040 "TABLBUMP" 2794750 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1090 2787035 2787730 2788513 "SYSSOLP" 2789823 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1089 2783419 2784022 2784762 "SYNTAX" 2786317 T SYNTAX (NIL) -8 NIL NIL) (-1088 2780553 2781161 2781799 "SYMTAB" 2782803 T SYMTAB (NIL) -8 NIL NIL) (-1087 2775802 2776704 2777687 "SYMS" 2779592 T SYMS (NIL) -8 NIL NIL) (-1086 2773035 2775262 2775491 "SYMPOLY" 2775607 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1085 2772555 2772630 2772752 "SYMFUNC" 2772947 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1084 2768533 2769792 2770614 "SYMBOL" 2771755 T SYMBOL (NIL) -8 NIL NIL) (-1083 2762072 2763761 2765481 "SWITCH" 2766835 T SWITCH (NIL) -8 NIL NIL) (-1082 2755305 2760899 2761201 "SUTS" 2761827 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1081 2747198 2754426 2754706 "SUPXS" 2755082 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1080 2738730 2746819 2746944 "SUP" 2747107 NIL SUP (NIL T) -8 NIL NIL) (-1079 2737889 2738016 2738233 "SUPFRACF" 2738598 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1078 2737514 2737573 2737684 "SUP2" 2737824 NIL SUP2 (NIL T T) -7 NIL NIL) (-1077 2735932 2736206 2736568 "SUMRF" 2737213 NIL SUMRF (NIL T) -7 NIL NIL) (-1076 2735249 2735315 2735513 "SUMFS" 2735853 NIL SUMFS (NIL T T) -7 NIL NIL) (-1075 2719188 2734430 2734680 "SULS" 2735056 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1074 2718510 2718713 2718853 "SUCH" 2719096 NIL SUCH (NIL T T) -8 NIL NIL) (-1073 2712437 2713449 2714407 "SUBSPACE" 2717598 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1072 2711867 2711957 2712121 "SUBRESP" 2712325 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1071 2705236 2706532 2707843 "STTF" 2710603 NIL STTF (NIL T) -7 NIL NIL) (-1070 2699409 2700529 2701676 "STTFNC" 2704136 NIL STTFNC (NIL T) -7 NIL NIL) (-1069 2690760 2692627 2694420 "STTAYLOR" 2697650 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1068 2684004 2690624 2690707 "STRTBL" 2690712 NIL STRTBL (NIL T) -8 NIL NIL) (-1067 2679395 2683959 2683990 "STRING" 2683995 T STRING (NIL) -8 NIL NIL) (-1066 2674283 2678768 2678799 "STRICAT" 2678858 T STRICAT (NIL) -9 NIL 2678920) (-1065 2666999 2671806 2672426 "STREAM" 2673698 NIL STREAM (NIL T) -8 NIL NIL) (-1064 2666509 2666586 2666730 "STREAM3" 2666916 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1063 2665491 2665674 2665909 "STREAM2" 2666322 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1062 2665179 2665231 2665324 "STREAM1" 2665433 NIL STREAM1 (NIL T) -7 NIL NIL) (-1061 2664195 2664376 2664607 "STINPROD" 2664995 NIL STINPROD (NIL T) -7 NIL NIL) (-1060 2663773 2663957 2663988 "STEP" 2664068 T STEP (NIL) -9 NIL 2664146) (-1059 2657316 2663672 2663749 "STBL" 2663754 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1058 2652491 2656538 2656582 "STAGG" 2656735 NIL STAGG (NIL T) -9 NIL 2656824) (-1057 2650193 2650795 2651667 "STAGG-" 2651672 NIL STAGG- (NIL T T) -8 NIL NIL) (-1056 2648388 2649963 2650055 "STACK" 2650136 NIL STACK (NIL T) -8 NIL NIL) (-1055 2641119 2646535 2646990 "SREGSET" 2648018 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1054 2633559 2634927 2636439 "SRDCMPK" 2639725 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1053 2626526 2630999 2631030 "SRAGG" 2632333 T SRAGG (NIL) -9 NIL 2632941) (-1052 2625543 2625798 2626177 "SRAGG-" 2626182 NIL SRAGG- (NIL T) -8 NIL NIL) (-1051 2619992 2624462 2624889 "SQMATRIX" 2625162 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1050 2613744 2616712 2617438 "SPLTREE" 2619338 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1049 2609734 2610400 2611046 "SPLNODE" 2613170 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1048 2608780 2609013 2609044 "SPFCAT" 2609488 T SPFCAT (NIL) -9 NIL NIL) (-1047 2607517 2607727 2607991 "SPECOUT" 2608538 T SPECOUT (NIL) -7 NIL NIL) (-1046 2607278 2607318 2607387 "SPADPRSR" 2607470 T SPADPRSR (NIL) -7 NIL NIL) (-1045 2599300 2601047 2601090 "SPACEC" 2605413 NIL SPACEC (NIL T) -9 NIL 2607229) (-1044 2597472 2599233 2599281 "SPACE3" 2599286 NIL SPACE3 (NIL T) -8 NIL NIL) (-1043 2596224 2596395 2596686 "SORTPAK" 2597277 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1042 2594280 2594583 2595001 "SOLVETRA" 2595888 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1041 2593291 2593513 2593787 "SOLVESER" 2594053 NIL SOLVESER (NIL T) -7 NIL NIL) (-1040 2588511 2589392 2590394 "SOLVERAD" 2592343 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1039 2584326 2584935 2585664 "SOLVEFOR" 2587878 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1038 2578625 2583677 2583774 "SNTSCAT" 2583779 NIL SNTSCAT (NIL T T T T) -9 NIL 2583849) (-1037 2572730 2576956 2577346 "SMTS" 2578315 NIL SMTS (NIL T T T) -8 NIL NIL) (-1036 2567141 2572619 2572695 "SMP" 2572700 NIL SMP (NIL T T) -8 NIL NIL) (-1035 2565300 2565601 2565999 "SMITH" 2566838 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1034 2558264 2562460 2562563 "SMATCAT" 2563903 NIL SMATCAT (NIL NIL T T T) -9 NIL 2564452) (-1033 2555205 2556028 2557205 "SMATCAT-" 2557210 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1032 2552918 2554441 2554485 "SKAGG" 2554746 NIL SKAGG (NIL T) -9 NIL 2554881) (-1031 2548976 2552022 2552300 "SINT" 2552662 T SINT (NIL) -8 NIL NIL) (-1030 2548748 2548786 2548852 "SIMPAN" 2548932 T SIMPAN (NIL) -7 NIL NIL) (-1029 2547586 2547807 2548082 "SIGNRF" 2548507 NIL SIGNRF (NIL T) -7 NIL NIL) (-1028 2546395 2546546 2546836 "SIGNEF" 2547415 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1027 2544085 2544539 2545045 "SHP" 2545936 NIL SHP (NIL T NIL) -7 NIL NIL) (-1026 2537938 2543986 2544062 "SHDP" 2544067 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1025 2537427 2537619 2537650 "SGROUP" 2537802 T SGROUP (NIL) -9 NIL 2537889) (-1024 2537197 2537249 2537353 "SGROUP-" 2537358 NIL SGROUP- (NIL T) -8 NIL NIL) (-1023 2534033 2534730 2535453 "SGCF" 2536496 T SGCF (NIL) -7 NIL NIL) (-1022 2528431 2533483 2533580 "SFRTCAT" 2533585 NIL SFRTCAT (NIL T T T T) -9 NIL 2533623) (-1021 2521891 2522906 2524040 "SFRGCD" 2527414 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1020 2515057 2516128 2517312 "SFQCMPK" 2520824 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1019 2514679 2514768 2514878 "SFORT" 2514998 NIL SFORT (NIL T T) -8 NIL NIL) (-1018 2513824 2514519 2514640 "SEXOF" 2514645 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1017 2512958 2513705 2513773 "SEX" 2513778 T SEX (NIL) -8 NIL NIL) (-1016 2507734 2508423 2508519 "SEXCAT" 2512290 NIL SEXCAT (NIL T T T T T) -9 NIL 2512909) (-1015 2504914 2507668 2507716 "SET" 2507721 NIL SET (NIL T) -8 NIL NIL) (-1014 2503165 2503627 2503932 "SETMN" 2504655 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1013 2502772 2502898 2502929 "SETCAT" 2503046 T SETCAT (NIL) -9 NIL 2503130) (-1012 2502552 2502604 2502703 "SETCAT-" 2502708 NIL SETCAT- (NIL T) -8 NIL NIL) (-1011 2498939 2501013 2501057 "SETAGG" 2501927 NIL SETAGG (NIL T) -9 NIL 2502267) (-1010 2498397 2498513 2498750 "SETAGG-" 2498755 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1009 2497600 2497893 2497955 "SEGXCAT" 2498241 NIL SEGXCAT (NIL T T) -9 NIL 2498361) (-1008 2496656 2497266 2497448 "SEG" 2497453 NIL SEG (NIL T) -8 NIL NIL) (-1007 2495562 2495775 2495819 "SEGCAT" 2496401 NIL SEGCAT (NIL T) -9 NIL 2496639) (-1006 2494611 2494941 2495141 "SEGBIND" 2495397 NIL SEGBIND (NIL T) -8 NIL NIL) (-1005 2494232 2494291 2494404 "SEGBIND2" 2494546 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1004 2493451 2493577 2493781 "SEG2" 2494076 NIL SEG2 (NIL T T) -7 NIL NIL) (-1003 2492888 2493386 2493433 "SDVAR" 2493438 NIL SDVAR (NIL T) -8 NIL NIL) (-1002 2485140 2492661 2492789 "SDPOL" 2492794 NIL SDPOL (NIL T) -8 NIL NIL) (-1001 2483733 2483999 2484318 "SCPKG" 2484855 NIL SCPKG (NIL T) -7 NIL NIL) (-1000 2482870 2483049 2483249 "SCOPE" 2483555 T SCOPE (NIL) -8 NIL NIL) (-999 2482097 2482230 2482407 "SCACHE" 2482725 NIL SCACHE (NIL T) -7 NIL NIL) (-998 2481540 2481861 2481944 "SAOS" 2482034 T SAOS (NIL) -8 NIL NIL) (-997 2481108 2481143 2481314 "SAERFFC" 2481499 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-996 2475004 2481007 2481085 "SAE" 2481090 NIL SAE (NIL T T NIL) -8 NIL NIL) (-995 2474600 2474635 2474792 "SAEFACT" 2474963 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-994 2472926 2473240 2473639 "RURPK" 2474266 NIL RURPK (NIL T NIL) -7 NIL NIL) (-993 2471579 2471856 2472163 "RULESET" 2472762 NIL RULESET (NIL T T T) -8 NIL NIL) (-992 2468787 2469290 2469751 "RULE" 2471261 NIL RULE (NIL T T T) -8 NIL NIL) (-991 2468429 2468584 2468665 "RULECOLD" 2468739 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-990 2463321 2464115 2465031 "RSETGCD" 2467628 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-989 2452635 2457687 2457782 "RSETCAT" 2461847 NIL RSETCAT (NIL T T T T) -9 NIL 2462944) (-988 2450566 2451105 2451925 "RSETCAT-" 2451930 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-987 2442996 2444371 2445887 "RSDCMPK" 2449165 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-986 2441013 2441454 2441527 "RRCC" 2442603 NIL RRCC (NIL T T) -9 NIL 2442947) (-985 2440367 2440541 2440817 "RRCC-" 2440822 NIL RRCC- (NIL T T T) -8 NIL NIL) (-984 2414733 2424358 2424423 "RPOLCAT" 2434925 NIL RPOLCAT (NIL T T T) -9 NIL 2438083) (-983 2406237 2408575 2411693 "RPOLCAT-" 2411698 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-982 2397303 2404467 2404947 "ROUTINE" 2405777 T ROUTINE (NIL) -8 NIL NIL) (-981 2394008 2396859 2397006 "ROMAN" 2397176 T ROMAN (NIL) -8 NIL NIL) (-980 2392294 2392879 2393136 "ROIRC" 2393814 NIL ROIRC (NIL T T) -8 NIL NIL) (-979 2388698 2391002 2391031 "RNS" 2391327 T RNS (NIL) -9 NIL 2391597) (-978 2387212 2387595 2388126 "RNS-" 2388199 NIL RNS- (NIL T) -8 NIL NIL) (-977 2386637 2387045 2387074 "RNG" 2387079 T RNG (NIL) -9 NIL 2387100) (-976 2386034 2386396 2386437 "RMODULE" 2386497 NIL RMODULE (NIL T) -9 NIL 2386539) (-975 2384886 2384980 2385310 "RMCAT2" 2385935 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-974 2381600 2384069 2384390 "RMATRIX" 2384621 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-973 2374596 2376830 2376943 "RMATCAT" 2380252 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2381234) (-972 2373975 2374122 2374425 "RMATCAT-" 2374430 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-971 2373545 2373620 2373746 "RINTERP" 2373894 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-970 2372595 2373159 2373188 "RING" 2373298 T RING (NIL) -9 NIL 2373392) (-969 2372390 2372434 2372528 "RING-" 2372533 NIL RING- (NIL T) -8 NIL NIL) (-968 2371238 2371475 2371731 "RIDIST" 2372154 T RIDIST (NIL) -7 NIL NIL) (-967 2362560 2370712 2370915 "RGCHAIN" 2371087 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-966 2359565 2360179 2360847 "RF" 2361924 NIL RF (NIL T) -7 NIL NIL) (-965 2359214 2359277 2359378 "RFFACTOR" 2359496 NIL RFFACTOR (NIL T) -7 NIL NIL) (-964 2358942 2358977 2359072 "RFFACT" 2359173 NIL RFFACT (NIL T) -7 NIL NIL) (-963 2357072 2357436 2357816 "RFDIST" 2358582 T RFDIST (NIL) -7 NIL NIL) (-962 2356530 2356622 2356782 "RETSOL" 2356974 NIL RETSOL (NIL T T) -7 NIL NIL) (-961 2356122 2356202 2356244 "RETRACT" 2356434 NIL RETRACT (NIL T) -9 NIL NIL) (-960 2355974 2355999 2356083 "RETRACT-" 2356088 NIL RETRACT- (NIL T T) -8 NIL NIL) (-959 2348832 2355631 2355756 "RESULT" 2355869 T RESULT (NIL) -8 NIL NIL) (-958 2347417 2348106 2348303 "RESRING" 2348735 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-957 2347057 2347106 2347202 "RESLATC" 2347354 NIL RESLATC (NIL T) -7 NIL NIL) (-956 2346766 2346800 2346905 "REPSQ" 2347016 NIL REPSQ (NIL T) -7 NIL NIL) (-955 2344197 2344777 2345377 "REP" 2346186 T REP (NIL) -7 NIL NIL) (-954 2343898 2343932 2344041 "REPDB" 2344156 NIL REPDB (NIL T) -7 NIL NIL) (-953 2337843 2339222 2340442 "REP2" 2342710 NIL REP2 (NIL T) -7 NIL NIL) (-952 2334249 2334930 2335735 "REP1" 2337070 NIL REP1 (NIL T) -7 NIL NIL) (-951 2326995 2332410 2332862 "REGSET" 2333880 NIL REGSET (NIL T T T T) -8 NIL NIL) (-950 2325816 2326151 2326399 "REF" 2326780 NIL REF (NIL T) -8 NIL NIL) (-949 2325197 2325300 2325465 "REDORDER" 2325700 NIL REDORDER (NIL T T) -7 NIL NIL) (-948 2321166 2324431 2324652 "RECLOS" 2325028 NIL RECLOS (NIL T) -8 NIL NIL) (-947 2320223 2320404 2320617 "REALSOLV" 2320973 T REALSOLV (NIL) -7 NIL NIL) (-946 2320070 2320111 2320140 "REAL" 2320145 T REAL (NIL) -9 NIL 2320180) (-945 2316561 2317363 2318245 "REAL0Q" 2319235 NIL REAL0Q (NIL T) -7 NIL NIL) (-944 2312172 2313160 2314219 "REAL0" 2315542 NIL REAL0 (NIL T) -7 NIL NIL) (-943 2311580 2311652 2311857 "RDIV" 2312094 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-942 2310653 2310827 2311038 "RDIST" 2311402 NIL RDIST (NIL T) -7 NIL NIL) (-941 2309257 2309544 2309913 "RDETRS" 2310361 NIL RDETRS (NIL T T) -7 NIL NIL) (-940 2307078 2307532 2308067 "RDETR" 2308799 NIL RDETR (NIL T T) -7 NIL NIL) (-939 2305694 2305972 2306373 "RDEEFS" 2306794 NIL RDEEFS (NIL T T) -7 NIL NIL) (-938 2304194 2304500 2304929 "RDEEF" 2305382 NIL RDEEF (NIL T T) -7 NIL NIL) (-937 2298478 2301410 2301439 "RCFIELD" 2302716 T RCFIELD (NIL) -9 NIL 2303446) (-936 2296547 2297051 2297744 "RCFIELD-" 2297817 NIL RCFIELD- (NIL T) -8 NIL NIL) (-935 2292878 2294663 2294705 "RCAGG" 2295776 NIL RCAGG (NIL T) -9 NIL 2296241) (-934 2292509 2292603 2292763 "RCAGG-" 2292768 NIL RCAGG- (NIL T T) -8 NIL NIL) (-933 2291854 2291965 2292127 "RATRET" 2292393 NIL RATRET (NIL T) -7 NIL NIL) (-932 2291411 2291478 2291597 "RATFACT" 2291782 NIL RATFACT (NIL T) -7 NIL NIL) (-931 2290726 2290846 2290996 "RANDSRC" 2291281 T RANDSRC (NIL) -7 NIL NIL) (-930 2290463 2290507 2290578 "RADUTIL" 2290675 T RADUTIL (NIL) -7 NIL NIL) (-929 2283470 2289206 2289523 "RADIX" 2290178 NIL RADIX (NIL NIL) -8 NIL NIL) (-928 2275040 2283314 2283442 "RADFF" 2283447 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-927 2274691 2274766 2274795 "RADCAT" 2274952 T RADCAT (NIL) -9 NIL NIL) (-926 2274476 2274524 2274621 "RADCAT-" 2274626 NIL RADCAT- (NIL T) -8 NIL NIL) (-925 2272627 2274251 2274340 "QUEUE" 2274420 NIL QUEUE (NIL T) -8 NIL NIL) (-924 2269124 2272564 2272609 "QUAT" 2272614 NIL QUAT (NIL T) -8 NIL NIL) (-923 2268762 2268805 2268932 "QUATCT2" 2269075 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-922 2262555 2265935 2265976 "QUATCAT" 2266755 NIL QUATCAT (NIL T) -9 NIL 2267520) (-921 2258699 2259736 2261123 "QUATCAT-" 2261217 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-920 2256219 2257783 2257825 "QUAGG" 2258200 NIL QUAGG (NIL T) -9 NIL 2258375) (-919 2255144 2255617 2255789 "QFORM" 2256091 NIL QFORM (NIL NIL T) -8 NIL NIL) (-918 2246440 2251698 2251739 "QFCAT" 2252397 NIL QFCAT (NIL T) -9 NIL 2253390) (-917 2242012 2243213 2244804 "QFCAT-" 2244898 NIL QFCAT- (NIL T T) -8 NIL NIL) (-916 2241650 2241693 2241820 "QFCAT2" 2241963 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-915 2241110 2241220 2241350 "QEQUAT" 2241540 T QEQUAT (NIL) -8 NIL NIL) (-914 2234296 2235367 2236549 "QCMPACK" 2240043 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-913 2231872 2232293 2232721 "QALGSET" 2233951 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-912 2231117 2231291 2231523 "QALGSET2" 2231692 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-911 2229808 2230031 2230348 "PWFFINTB" 2230890 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-910 2227996 2228164 2228517 "PUSHVAR" 2229622 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-909 2223913 2224967 2225009 "PTRANFN" 2226893 NIL PTRANFN (NIL T) -9 NIL NIL) (-908 2222325 2222616 2222937 "PTPACK" 2223624 NIL PTPACK (NIL T) -7 NIL NIL) (-907 2221961 2222018 2222125 "PTFUNC2" 2222262 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-906 2216437 2220778 2220819 "PTCAT" 2221187 NIL PTCAT (NIL T) -9 NIL 2221349) (-905 2216095 2216130 2216254 "PSQFR" 2216396 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-904 2214690 2214988 2215322 "PSEUDLIN" 2215793 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-903 2201498 2203862 2206185 "PSETPK" 2212450 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-902 2194584 2197298 2197393 "PSETCAT" 2200374 NIL PSETCAT (NIL T T T T) -9 NIL 2201188) (-901 2192422 2193056 2193875 "PSETCAT-" 2193880 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-900 2191770 2191935 2191964 "PSCURVE" 2192232 T PSCURVE (NIL) -9 NIL 2192399) (-899 2188221 2189747 2189812 "PSCAT" 2190648 NIL PSCAT (NIL T T T) -9 NIL 2190888) (-898 2187285 2187501 2187900 "PSCAT-" 2187905 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-897 2185938 2186570 2186784 "PRTITION" 2187091 T PRTITION (NIL) -8 NIL NIL) (-896 2175036 2177242 2179430 "PRS" 2183800 NIL PRS (NIL T T) -7 NIL NIL) (-895 2172894 2174386 2174427 "PRQAGG" 2174610 NIL PRQAGG (NIL T) -9 NIL 2174712) (-894 2172464 2172566 2172595 "PROPLOG" 2172780 T PROPLOG (NIL) -9 NIL NIL) (-893 2169587 2170152 2170679 "PROPFRML" 2171969 NIL PROPFRML (NIL T) -8 NIL NIL) (-892 2169047 2169157 2169287 "PROPERTY" 2169477 T PROPERTY (NIL) -8 NIL NIL) (-891 2162821 2167213 2168033 "PRODUCT" 2168273 NIL PRODUCT (NIL T T) -8 NIL NIL) (-890 2160097 2162281 2162514 "PR" 2162632 NIL PR (NIL T T) -8 NIL NIL) (-889 2159893 2159925 2159984 "PRINT" 2160058 T PRINT (NIL) -7 NIL NIL) (-888 2159233 2159350 2159502 "PRIMES" 2159773 NIL PRIMES (NIL T) -7 NIL NIL) (-887 2157298 2157699 2158165 "PRIMELT" 2158812 NIL PRIMELT (NIL T) -7 NIL NIL) (-886 2157026 2157075 2157104 "PRIMCAT" 2157228 T PRIMCAT (NIL) -9 NIL NIL) (-885 2153187 2156964 2157009 "PRIMARR" 2157014 NIL PRIMARR (NIL T) -8 NIL NIL) (-884 2152194 2152372 2152600 "PRIMARR2" 2153005 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-883 2151837 2151893 2152004 "PREASSOC" 2152132 NIL PREASSOC (NIL T T) -7 NIL NIL) (-882 2151311 2151444 2151473 "PPCURVE" 2151678 T PPCURVE (NIL) -9 NIL 2151814) (-881 2148670 2149069 2149661 "POLYROOT" 2150892 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-880 2142576 2148276 2148435 "POLY" 2148543 NIL POLY (NIL T) -8 NIL NIL) (-879 2141961 2142019 2142252 "POLYLIFT" 2142512 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-878 2138246 2138695 2139323 "POLYCATQ" 2141506 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-877 2125286 2130683 2130748 "POLYCAT" 2134233 NIL POLYCAT (NIL T T T) -9 NIL 2136160) (-876 2118737 2120598 2122981 "POLYCAT-" 2122986 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-875 2118326 2118394 2118513 "POLY2UP" 2118663 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-874 2117962 2118019 2118126 "POLY2" 2118263 NIL POLY2 (NIL T T) -7 NIL NIL) (-873 2116647 2116886 2117162 "POLUTIL" 2117736 NIL POLUTIL (NIL T T) -7 NIL NIL) (-872 2115009 2115286 2115616 "POLTOPOL" 2116369 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-871 2110532 2114946 2114991 "POINT" 2114996 NIL POINT (NIL T) -8 NIL NIL) (-870 2108719 2109076 2109451 "PNTHEORY" 2110177 T PNTHEORY (NIL) -7 NIL NIL) (-869 2107147 2107444 2107853 "PMTOOLS" 2108417 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-868 2106740 2106818 2106935 "PMSYM" 2107063 NIL PMSYM (NIL T) -7 NIL NIL) (-867 2106250 2106319 2106493 "PMQFCAT" 2106665 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-866 2105605 2105715 2105871 "PMPRED" 2106127 NIL PMPRED (NIL T) -7 NIL NIL) (-865 2105001 2105087 2105248 "PMPREDFS" 2105506 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-864 2103647 2103855 2104239 "PMPLCAT" 2104763 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-863 2103179 2103258 2103410 "PMLSAGG" 2103562 NIL PMLSAGG (NIL T T 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2063034 NIL PINTERPA (NIL T T) -7 NIL NIL) (-849 2062007 2062574 2062667 "PI" 2062707 T PI (NIL) -8 NIL NIL) (-848 2060398 2061383 2061412 "PID" 2061594 T PID (NIL) -9 NIL 2061728) (-847 2060123 2060160 2060248 "PICOERCE" 2060355 NIL PICOERCE (NIL T) -7 NIL NIL) (-846 2059444 2059582 2059758 "PGROEB" 2059979 NIL PGROEB (NIL T) -7 NIL NIL) (-845 2055031 2055845 2056750 "PGE" 2058559 T PGE (NIL) -7 NIL NIL) (-844 2053155 2053401 2053767 "PGCD" 2054748 NIL PGCD (NIL T T T T) -7 NIL NIL) (-843 2052493 2052596 2052757 "PFRPAC" 2053039 NIL PFRPAC (NIL T) -7 NIL NIL) (-842 2049108 2051041 2051394 "PFR" 2052172 NIL PFR (NIL T) -8 NIL NIL) (-841 2047497 2047741 2048066 "PFOTOOLS" 2048855 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-840 2046030 2046269 2046620 "PFOQ" 2047254 NIL PFOQ (NIL T T T) -7 NIL NIL) (-839 2044507 2044719 2045081 "PFO" 2045814 NIL PFO (NIL T T T T T) -7 NIL NIL) (-838 2041030 2044396 2044465 "PF" 2044470 NIL PF (NIL NIL) -8 NIL NIL) (-837 2038458 2039739 2039768 "PFECAT" 2040353 T PFECAT (NIL) -9 NIL 2040737) (-836 2037903 2038057 2038271 "PFECAT-" 2038276 NIL PFECAT- (NIL T) -8 NIL NIL) (-835 2036507 2036758 2037059 "PFBRU" 2037652 NIL PFBRU (NIL T T) -7 NIL NIL) (-834 2034374 2034725 2035157 "PFBR" 2036158 NIL PFBR (NIL T T T T) -7 NIL NIL) (-833 2030226 2031750 2032426 "PERM" 2033731 NIL PERM (NIL T) -8 NIL NIL) (-832 2025492 2026433 2027303 "PERMGRP" 2029389 NIL PERMGRP (NIL T) -8 NIL NIL) (-831 2023562 2024555 2024597 "PERMCAT" 2025043 NIL PERMCAT (NIL T) -9 NIL 2025348) (-830 2023217 2023258 2023381 "PERMAN" 2023515 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-829 2020657 2022786 2022917 "PENDTREE" 2023119 NIL PENDTREE (NIL T) -8 NIL NIL) (-828 2018729 2019507 2019549 "PDRING" 2020206 NIL PDRING (NIL T) -9 NIL 2020491) (-827 2017832 2018050 2018412 "PDRING-" 2018417 NIL PDRING- (NIL T T) -8 NIL NIL) (-826 2014974 2015724 2016415 "PDEPROB" 2017161 T PDEPROB (NIL) -8 NIL NIL) (-825 2012545 2013041 2013590 "PDEPACK" 2014445 T PDEPACK (NIL) -7 NIL NIL) (-824 2011457 2011647 2011898 "PDECOMP" 2012344 NIL PDECOMP (NIL T T) -7 NIL NIL) (-823 2009068 2009883 2009912 "PDECAT" 2010697 T PDECAT (NIL) -9 NIL 2011408) (-822 2008821 2008854 2008943 "PCOMP" 2009029 NIL PCOMP (NIL T T) -7 NIL NIL) (-821 2007028 2007624 2007920 "PBWLB" 2008551 NIL PBWLB (NIL T) -8 NIL NIL) (-820 1999537 2001105 2002441 "PATTERN" 2005713 NIL PATTERN (NIL T) -8 NIL NIL) (-819 1999169 1999226 1999335 "PATTERN2" 1999474 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-818 1996926 1997314 1997771 "PATTERN1" 1998758 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-817 1994321 1994875 1995356 "PATRES" 1996491 NIL PATRES (NIL T T) -8 NIL NIL) (-816 1993885 1993952 1994084 "PATRES2" 1994248 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-815 1991782 1992182 1992587 "PATMATCH" 1993554 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-814 1991318 1991501 1991543 "PATMAB" 1991650 NIL PATMAB (NIL T) -9 NIL 1991733) (-813 1989863 1990172 1990430 "PATLRES" 1991123 NIL PATLRES (NIL T T T) -8 NIL NIL) (-812 1989408 1989531 1989573 "PATAB" 1989578 NIL PATAB (NIL T) -9 NIL 1989750) (-811 1986889 1987421 1987994 "PARTPERM" 1988855 T PARTPERM (NIL) -7 NIL NIL) (-810 1986510 1986573 1986675 "PARSURF" 1986820 NIL PARSURF (NIL T) -8 NIL NIL) (-809 1986142 1986199 1986308 "PARSU2" 1986447 NIL PARSU2 (NIL T T) -7 NIL NIL) (-808 1985906 1985946 1986013 "PARSER" 1986095 T PARSER (NIL) -7 NIL NIL) (-807 1985527 1985590 1985692 "PARSCURV" 1985837 NIL PARSCURV (NIL T) -8 NIL NIL) (-806 1985159 1985216 1985325 "PARSC2" 1985464 NIL PARSC2 (NIL T T) -7 NIL NIL) (-805 1984798 1984856 1984953 "PARPCURV" 1985095 NIL PARPCURV (NIL T) -8 NIL NIL) (-804 1984430 1984487 1984596 "PARPC2" 1984735 NIL PARPC2 (NIL T T) -7 NIL NIL) (-803 1983950 1984036 1984155 "PAN2EXPR" 1984331 T PAN2EXPR (NIL) -7 NIL NIL) (-802 1982756 1983071 1983299 "PALETTE" 1983742 T PALETTE (NIL) -8 NIL NIL) (-801 1981224 1981761 1982121 "PAIR" 1982442 NIL PAIR (NIL T T) -8 NIL NIL) (-800 1975074 1980483 1980677 "PADICRC" 1981079 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-799 1968282 1974420 1974604 "PADICRAT" 1974922 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-798 1966586 1968219 1968264 "PADIC" 1968269 NIL PADIC (NIL NIL) -8 NIL NIL) (-797 1963790 1965364 1965405 "PADICCT" 1965986 NIL PADICCT (NIL NIL) -9 NIL 1966268) (-796 1962747 1962947 1963215 "PADEPAC" 1963577 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-795 1961959 1962092 1962298 "PADE" 1962609 NIL PADE (NIL T T T) -7 NIL NIL) (-794 1959970 1960802 1961117 "OWP" 1961727 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-793 1959079 1959575 1959747 "OVAR" 1959838 NIL OVAR (NIL NIL) -8 NIL NIL) (-792 1958343 1958464 1958625 "OUT" 1958938 T OUT (NIL) -7 NIL NIL) (-791 1947389 1949568 1951738 "OUTFORM" 1956193 T OUTFORM (NIL) -8 NIL NIL) (-790 1946797 1947118 1947207 "OSI" 1947320 T OSI (NIL) -8 NIL NIL) (-789 1945542 1945769 1946054 "ORTHPOL" 1946544 NIL ORTHPOL (NIL T) -7 NIL NIL) (-788 1942913 1945203 1945341 "OREUP" 1945485 NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL) (-787 1940309 1942606 1942732 "ORESUP" 1942855 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-786 1937844 1938344 1938904 "OREPCTO" 1939798 NIL OREPCTO (NIL T T) -7 NIL NIL) (-785 1931753 1933959 1934000 "OREPCAT" 1936321 NIL OREPCAT (NIL T) -9 NIL 1937424) (-784 1928901 1929683 1930740 "OREPCAT-" 1930745 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-783 1928078 1928350 1928379 "ORDSET" 1928688 T ORDSET (NIL) -9 NIL 1928852) (-782 1927597 1927719 1927912 "ORDSET-" 1927917 NIL ORDSET- (NIL T) -8 NIL NIL) (-781 1926210 1927011 1927040 "ORDRING" 1927242 T ORDRING (NIL) -9 NIL 1927366) (-780 1925855 1925949 1926093 "ORDRING-" 1926098 NIL ORDRING- (NIL T) -8 NIL NIL) (-779 1925230 1925711 1925740 "ORDMON" 1925745 T ORDMON (NIL) -9 NIL 1925766) (-778 1924392 1924539 1924734 "ORDFUNS" 1925079 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-777 1923903 1924262 1924291 "ORDFIN" 1924296 T ORDFIN (NIL) -9 NIL 1924317) (-776 1920415 1922489 1922898 "ORDCOMP" 1923527 NIL ORDCOMP (NIL T) -8 NIL NIL) (-775 1919681 1919808 1919994 "ORDCOMP2" 1920275 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-774 1916189 1917071 1917908 "OPTPROB" 1918864 T OPTPROB (NIL) -8 NIL NIL) (-773 1913031 1913660 1914354 "OPTPACK" 1915515 T OPTPACK (NIL) -7 NIL NIL) (-772 1910756 1911492 1911521 "OPTCAT" 1912336 T OPTCAT (NIL) -9 NIL 1912982) (-771 1910524 1910563 1910629 "OPQUERY" 1910710 T OPQUERY (NIL) -7 NIL NIL) (-770 1907660 1908851 1909351 "OP" 1910056 NIL OP (NIL T) -8 NIL NIL) (-769 1904425 1906457 1906826 "ONECOMP" 1907324 NIL ONECOMP (NIL T) -8 NIL NIL) (-768 1903730 1903845 1904019 "ONECOMP2" 1904297 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-767 1903149 1903255 1903385 "OMSERVER" 1903620 T OMSERVER (NIL) -7 NIL NIL) (-766 1900037 1902589 1902630 "OMSAGG" 1902691 NIL OMSAGG (NIL T) -9 NIL 1902755) (-765 1898660 1898923 1899205 "OMPKG" 1899775 T OMPKG (NIL) -7 NIL NIL) (-764 1898089 1898192 1898221 "OM" 1898520 T OM (NIL) -9 NIL NIL) (-763 1896628 1897641 1897809 "OMLO" 1897970 NIL OMLO (NIL T T) -8 NIL NIL) (-762 1895558 1895705 1895931 "OMEXPR" 1896454 NIL OMEXPR (NIL T) -7 NIL NIL) (-761 1894876 1895104 1895240 "OMERR" 1895442 T OMERR (NIL) -8 NIL NIL) (-760 1894054 1894297 1894457 "OMERRK" 1894736 T OMERRK (NIL) -8 NIL NIL) (-759 1893532 1893731 1893839 "OMENC" 1893966 T OMENC (NIL) -8 NIL NIL) (-758 1887427 1888612 1889783 "OMDEV" 1892381 T OMDEV (NIL) -8 NIL NIL) (-757 1886496 1886667 1886861 "OMCONN" 1887253 T OMCONN (NIL) -8 NIL NIL) (-756 1885111 1886097 1886126 "OINTDOM" 1886131 T OINTDOM (NIL) -9 NIL 1886152) (-755 1880873 1882103 1882818 "OFMONOID" 1884428 NIL OFMONOID (NIL T) -8 NIL NIL) (-754 1880311 1880810 1880855 "ODVAR" 1880860 NIL ODVAR (NIL T) -8 NIL NIL) (-753 1877436 1879808 1879993 "ODR" 1880186 NIL ODR (NIL T T NIL) -8 NIL NIL) (-752 1869742 1877215 1877339 "ODPOL" 1877344 NIL ODPOL (NIL T) -8 NIL NIL) (-751 1863565 1869614 1869719 "ODP" 1869724 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-750 1862331 1862546 1862821 "ODETOOLS" 1863339 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-749 1859300 1859956 1860672 "ODESYS" 1861664 NIL ODESYS (NIL T T) -7 NIL NIL) (-748 1854204 1855112 1856135 "ODERTRIC" 1858375 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-747 1853630 1853712 1853906 "ODERED" 1854116 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-746 1850532 1851080 1851755 "ODERAT" 1853053 NIL ODERAT (NIL T T) -7 NIL NIL) (-745 1847500 1847964 1848560 "ODEPRRIC" 1850061 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-744 1845371 1845938 1846447 "ODEPROB" 1847011 T ODEPROB (NIL) -8 NIL NIL) (-743 1841903 1842386 1843032 "ODEPRIM" 1844850 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-742 1841156 1841258 1841516 "ODEPAL" 1841795 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-741 1837358 1838139 1838993 "ODEPACK" 1840322 T ODEPACK (NIL) -7 NIL NIL) (-740 1836395 1836502 1836730 "ODEINT" 1837247 NIL ODEINT (NIL T T) -7 NIL NIL) (-739 1830496 1831921 1833368 "ODEIFTBL" 1834968 T ODEIFTBL (NIL) -8 NIL NIL) (-738 1825840 1826626 1827584 "ODEEF" 1829655 NIL ODEEF (NIL T T) -7 NIL NIL) (-737 1825177 1825266 1825495 "ODECONST" 1825745 NIL ODECONST (NIL T T T) -7 NIL NIL) (-736 1823334 1823967 1823996 "ODECAT" 1824599 T ODECAT (NIL) -9 NIL 1825128) (-735 1820206 1823046 1823165 "OCT" 1823247 NIL OCT (NIL T) -8 NIL NIL) (-734 1819844 1819887 1820014 "OCTCT2" 1820157 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-733 1814677 1817115 1817156 "OC" 1818252 NIL OC (NIL T) -9 NIL 1819109) (-732 1811904 1812652 1813642 "OC-" 1813736 NIL OC- (NIL T T) -8 NIL NIL) (-731 1811282 1811724 1811753 "OCAMON" 1811758 T OCAMON (NIL) -9 NIL 1811779) (-730 1810735 1811142 1811171 "OASGP" 1811176 T OASGP (NIL) -9 NIL 1811196) (-729 1810022 1810485 1810514 "OAMONS" 1810554 T OAMONS (NIL) -9 NIL 1810597) (-728 1809462 1809869 1809898 "OAMON" 1809903 T OAMON (NIL) -9 NIL 1809923) (-727 1808766 1809258 1809287 "OAGROUP" 1809292 T OAGROUP (NIL) -9 NIL 1809312) (-726 1808456 1808506 1808594 "NUMTUBE" 1808710 NIL NUMTUBE (NIL T) -7 NIL NIL) (-725 1802029 1803547 1805083 "NUMQUAD" 1806940 T NUMQUAD (NIL) -7 NIL NIL) (-724 1797785 1798773 1799798 "NUMODE" 1801024 T NUMODE (NIL) -7 NIL NIL) (-723 1795188 1796034 1796063 "NUMINT" 1796980 T NUMINT (NIL) -9 NIL 1797736) (-722 1794136 1794333 1794551 "NUMFMT" 1794990 T NUMFMT (NIL) -7 NIL NIL) (-721 1780518 1783452 1785982 "NUMERIC" 1791645 NIL NUMERIC (NIL T) -7 NIL NIL) (-720 1774918 1779970 1780065 "NTSCAT" 1780070 NIL NTSCAT (NIL T T T T) -9 NIL 1780108) (-719 1774112 1774277 1774470 "NTPOLFN" 1774757 NIL NTPOLFN (NIL T) -7 NIL NIL) (-718 1761968 1770954 1771764 "NSUP" 1773334 NIL NSUP (NIL T) -8 NIL NIL) (-717 1761604 1761661 1761768 "NSUP2" 1761905 NIL NSUP2 (NIL T T) -7 NIL NIL) (-716 1751566 1761383 1761513 "NSMP" 1761518 NIL NSMP (NIL T T) -8 NIL NIL) (-715 1749998 1750299 1750656 "NREP" 1751254 NIL NREP (NIL T) -7 NIL NIL) (-714 1748589 1748841 1749199 "NPCOEF" 1749741 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-713 1747655 1747770 1747986 "NORMRETR" 1748470 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-712 1745708 1745998 1746405 "NORMPK" 1747363 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-711 1745393 1745421 1745545 "NORMMA" 1745674 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-710 1745220 1745350 1745379 "NONE" 1745384 T NONE (NIL) -8 NIL NIL) (-709 1745009 1745038 1745107 "NONE1" 1745184 NIL NONE1 (NIL T) -7 NIL NIL) (-708 1744494 1744556 1744741 "NODE1" 1744941 NIL NODE1 (NIL T T) -7 NIL NIL) (-707 1742787 1743657 1743912 "NNI" 1744259 T NNI (NIL) -8 NIL NIL) (-706 1741207 1741520 1741884 "NLINSOL" 1742455 NIL NLINSOL (NIL T) -7 NIL NIL) (-705 1737375 1738342 1739264 "NIPROB" 1740305 T NIPROB (NIL) -8 NIL NIL) (-704 1736132 1736366 1736668 "NFINTBAS" 1737137 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-703 1734840 1735071 1735352 "NCODIV" 1735900 NIL NCODIV (NIL T T) -7 NIL NIL) (-702 1734602 1734639 1734714 "NCNTFRAC" 1734797 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-701 1732782 1733146 1733566 "NCEP" 1734227 NIL NCEP (NIL T) -7 NIL NIL) (-700 1731693 1732432 1732461 "NASRING" 1732571 T NASRING (NIL) -9 NIL 1732645) (-699 1731488 1731532 1731626 "NASRING-" 1731631 NIL NASRING- (NIL T) -8 NIL NIL) (-698 1730641 1731140 1731169 "NARNG" 1731286 T NARNG (NIL) -9 NIL 1731377) (-697 1730333 1730400 1730534 "NARNG-" 1730539 NIL NARNG- (NIL T) -8 NIL NIL) (-696 1729212 1729419 1729654 "NAGSP" 1730118 T NAGSP (NIL) -7 NIL NIL) (-695 1720636 1722282 1723917 "NAGS" 1727597 T NAGS (NIL) -7 NIL NIL) (-694 1719200 1719504 1719831 "NAGF07" 1720329 T NAGF07 (NIL) -7 NIL NIL) (-693 1713782 1715062 1716358 "NAGF04" 1717924 T NAGF04 (NIL) -7 NIL NIL) (-692 1706814 1708412 1710029 "NAGF02" 1712185 T NAGF02 (NIL) -7 NIL NIL) (-691 1702078 1703168 1704275 "NAGF01" 1705727 T NAGF01 (NIL) -7 NIL NIL) (-690 1695738 1697296 1698873 "NAGE04" 1700521 T NAGE04 (NIL) -7 NIL NIL) (-689 1686979 1689082 1691194 "NAGE02" 1693646 T NAGE02 (NIL) -7 NIL NIL) (-688 1682972 1683909 1684863 "NAGE01" 1686045 T NAGE01 (NIL) -7 NIL NIL) (-687 1680779 1681310 1681865 "NAGD03" 1682437 T NAGD03 (NIL) -7 NIL NIL) (-686 1672565 1674484 1676429 "NAGD02" 1678854 T NAGD02 (NIL) -7 NIL NIL) (-685 1666424 1667837 1669265 "NAGD01" 1671157 T NAGD01 (NIL) -7 NIL NIL) (-684 1662681 1663491 1664316 "NAGC06" 1665619 T NAGC06 (NIL) -7 NIL NIL) (-683 1661158 1661487 1661840 "NAGC05" 1662348 T NAGC05 (NIL) -7 NIL NIL) (-682 1660542 1660659 1660801 "NAGC02" 1661036 T NAGC02 (NIL) -7 NIL NIL) (-681 1659603 1660160 1660201 "NAALG" 1660280 NIL NAALG (NIL T) -9 NIL 1660341) (-680 1659438 1659467 1659557 "NAALG-" 1659562 NIL NAALG- (NIL T T) -8 NIL NIL) (-679 1653388 1654496 1655683 "MULTSQFR" 1658334 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-678 1652707 1652782 1652966 "MULTFACT" 1653300 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-677 1645900 1649811 1649864 "MTSCAT" 1650924 NIL MTSCAT (NIL T T) -9 NIL 1651438) (-676 1645612 1645666 1645758 "MTHING" 1645840 NIL MTHING (NIL T) -7 NIL NIL) (-675 1645404 1645437 1645497 "MSYSCMD" 1645572 T MSYSCMD (NIL) -7 NIL NIL) (-674 1641516 1644159 1644479 "MSET" 1645117 NIL MSET (NIL T) -8 NIL NIL) (-673 1638611 1641077 1641119 "MSETAGG" 1641124 NIL MSETAGG (NIL T) -9 NIL 1641158) (-672 1634467 1636009 1636750 "MRING" 1637914 NIL MRING (NIL T T) -8 NIL NIL) (-671 1634037 1634104 1634233 "MRF2" 1634394 NIL MRF2 (NIL T T T) -7 NIL NIL) (-670 1633655 1633690 1633834 "MRATFAC" 1633996 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-669 1631267 1631562 1631993 "MPRFF" 1633360 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-668 1625287 1631122 1631218 "MPOLY" 1631223 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-667 1624777 1624812 1625020 "MPCPF" 1625246 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-666 1624293 1624336 1624519 "MPC3" 1624728 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-665 1623494 1623575 1623794 "MPC2" 1624208 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-664 1621795 1622132 1622522 "MONOTOOL" 1623154 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-663 1620919 1621254 1621283 "MONOID" 1621560 T MONOID (NIL) -9 NIL 1621732) (-662 1620297 1620460 1620703 "MONOID-" 1620708 NIL MONOID- (NIL T) -8 NIL NIL) (-661 1611277 1617263 1617323 "MONOGEN" 1617997 NIL MONOGEN (NIL T T) -9 NIL 1618453) (-660 1608495 1609230 1610230 "MONOGEN-" 1610349 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-659 1607354 1607774 1607803 "MONADWU" 1608195 T MONADWU (NIL) -9 NIL 1608433) (-658 1606726 1606885 1607133 "MONADWU-" 1607138 NIL MONADWU- (NIL T) -8 NIL NIL) (-657 1606111 1606329 1606358 "MONAD" 1606565 T MONAD (NIL) -9 NIL 1606677) (-656 1605796 1605874 1606006 "MONAD-" 1606011 NIL MONAD- (NIL T) -8 NIL NIL) (-655 1604047 1604709 1604988 "MOEBIUS" 1605549 NIL MOEBIUS (NIL T) -8 NIL NIL) (-654 1603440 1603818 1603859 "MODULE" 1603864 NIL MODULE (NIL T) -9 NIL 1603890) (-653 1603008 1603104 1603294 "MODULE-" 1603299 NIL MODULE- (NIL T T) -8 NIL NIL) (-652 1600679 1601374 1601700 "MODRING" 1602833 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-651 1597635 1598800 1599317 "MODOP" 1600211 NIL MODOP (NIL T T) -8 NIL NIL) (-650 1595822 1596274 1596615 "MODMONOM" 1597434 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-649 1585540 1594026 1594448 "MODMON" 1595450 NIL MODMON (NIL T T) -8 NIL NIL) (-648 1582666 1584384 1584660 "MODFIELD" 1585415 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-647 1582192 1582235 1582414 "MMAP" 1582617 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-646 1580428 1581205 1581246 "MLO" 1581663 NIL MLO (NIL T) -9 NIL 1581904) (-645 1577795 1578310 1578912 "MLIFT" 1579909 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-644 1577186 1577270 1577424 "MKUCFUNC" 1577706 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-643 1576785 1576855 1576978 "MKRECORD" 1577109 NIL MKRECORD (NIL T T) -7 NIL NIL) (-642 1575833 1575994 1576222 "MKFUNC" 1576596 NIL MKFUNC (NIL T) -7 NIL NIL) (-641 1575221 1575325 1575481 "MKFLCFN" 1575716 NIL MKFLCFN (NIL T) -7 NIL NIL) (-640 1574647 1575014 1575103 "MKCHSET" 1575165 NIL MKCHSET (NIL T) -8 NIL NIL) (-639 1573924 1574026 1574211 "MKBCFUNC" 1574540 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-638 1570608 1573478 1573614 "MINT" 1573808 T MINT (NIL) -8 NIL NIL) (-637 1569420 1569663 1569940 "MHROWRED" 1570363 NIL MHROWRED (NIL T) -7 NIL NIL) (-636 1564691 1567865 1568289 "MFLOAT" 1569016 T MFLOAT (NIL) -8 NIL NIL) (-635 1564048 1564124 1564295 "MFINFACT" 1564603 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-634 1560363 1561211 1562095 "MESH" 1563184 T MESH (NIL) -7 NIL NIL) (-633 1558753 1559065 1559418 "MDDFACT" 1560050 NIL MDDFACT (NIL T) -7 NIL NIL) (-632 1555595 1557912 1557954 "MDAGG" 1558209 NIL MDAGG (NIL T) -9 NIL 1558352) (-631 1545293 1554888 1555095 "MCMPLX" 1555408 T MCMPLX (NIL) -8 NIL NIL) (-630 1544434 1544580 1544780 "MCDEN" 1545142 NIL MCDEN (NIL T T) -7 NIL NIL) (-629 1542324 1542594 1542974 "MCALCFN" 1544164 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-628 1539946 1540469 1541030 "MATSTOR" 1541795 NIL MATSTOR (NIL T) -7 NIL NIL) (-627 1535954 1539321 1539568 "MATRIX" 1539731 NIL MATRIX (NIL T) -8 NIL NIL) (-626 1531724 1532427 1533163 "MATLIN" 1535311 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-625 1521921 1525059 1525136 "MATCAT" 1529974 NIL MATCAT (NIL T T T) -9 NIL 1531391) (-624 1518286 1519299 1520654 "MATCAT-" 1520659 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-623 1516888 1517041 1517372 "MATCAT2" 1518121 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-622 1515000 1515324 1515708 "MAPPKG3" 1516563 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-621 1513981 1514154 1514376 "MAPPKG2" 1514824 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-620 1512480 1512764 1513091 "MAPPKG1" 1513687 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-619 1512091 1512149 1512272 "MAPHACK3" 1512416 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-618 1511683 1511744 1511858 "MAPHACK2" 1512023 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-617 1511121 1511224 1511366 "MAPHACK1" 1511574 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-616 1509229 1509823 1510126 "MAGMA" 1510850 NIL MAGMA (NIL T) -8 NIL NIL) (-615 1505703 1507473 1507933 "M3D" 1508802 NIL M3D (NIL T) -8 NIL NIL) (-614 1499858 1504073 1504115 "LZSTAGG" 1504897 NIL LZSTAGG (NIL T) -9 NIL 1505192) (-613 1495831 1496989 1498446 "LZSTAGG-" 1498451 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-612 1492947 1493724 1494210 "LWORD" 1495377 NIL LWORD (NIL T) -8 NIL NIL) (-611 1486107 1492718 1492852 "LSQM" 1492857 NIL LSQM (NIL NIL T) -8 NIL NIL) (-610 1485331 1485470 1485698 "LSPP" 1485962 NIL LSPP (NIL T T T T) -7 NIL NIL) (-609 1483143 1483444 1483900 "LSMP" 1485020 NIL LSMP (NIL T T T T) -7 NIL NIL) (-608 1479922 1480596 1481326 "LSMP1" 1482445 NIL LSMP1 (NIL T) -7 NIL NIL) (-607 1473848 1479090 1479132 "LSAGG" 1479194 NIL LSAGG (NIL T) -9 NIL 1479272) (-606 1470543 1471467 1472680 "LSAGG-" 1472685 NIL LSAGG- (NIL T T) -8 NIL NIL) (-605 1468169 1469687 1469936 "LPOLY" 1470338 NIL LPOLY (NIL T T) -8 NIL NIL) (-604 1467751 1467836 1467959 "LPEFRAC" 1468078 NIL LPEFRAC (NIL T) -7 NIL NIL) (-603 1466098 1466845 1467098 "LO" 1467583 NIL LO (NIL T T T) -8 NIL NIL) (-602 1465751 1465863 1465892 "LOGIC" 1466003 T LOGIC (NIL) -9 NIL 1466083) (-601 1465613 1465636 1465707 "LOGIC-" 1465712 NIL LOGIC- (NIL T) -8 NIL NIL) (-600 1464806 1464946 1465139 "LODOOPS" 1465469 NIL LODOOPS (NIL T T) -7 NIL NIL) (-599 1462224 1464723 1464788 "LODO" 1464793 NIL LODO (NIL T NIL) -8 NIL NIL) (-598 1460770 1461005 1461356 "LODOF" 1461971 NIL LODOF (NIL T T) -7 NIL NIL) (-597 1457189 1459625 1459666 "LODOCAT" 1460098 NIL LODOCAT (NIL T) -9 NIL 1460309) (-596 1456923 1456981 1457107 "LODOCAT-" 1457112 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-595 1454237 1456764 1456882 "LODO2" 1456887 NIL LODO2 (NIL T T) -8 NIL NIL) (-594 1451666 1454174 1454219 "LODO1" 1454224 NIL LODO1 (NIL T) -8 NIL NIL) (-593 1450529 1450694 1451005 "LODEEF" 1451489 NIL LODEEF (NIL T T T) -7 NIL NIL) (-592 1445815 1448659 1448701 "LNAGG" 1449648 NIL LNAGG (NIL T) -9 NIL 1450092) (-591 1444962 1445176 1445518 "LNAGG-" 1445523 NIL LNAGG- (NIL T T) -8 NIL NIL) (-590 1441127 1441889 1442527 "LMOPS" 1444378 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-589 1440524 1440886 1440927 "LMODULE" 1440987 NIL LMODULE (NIL T) -9 NIL 1441029) (-588 1437770 1440169 1440292 "LMDICT" 1440434 NIL LMDICT (NIL T) -8 NIL NIL) (-587 1430997 1436716 1437014 "LIST" 1437505 NIL LIST (NIL T) -8 NIL NIL) (-586 1430522 1430596 1430735 "LIST3" 1430917 NIL LIST3 (NIL T T T) -7 NIL NIL) (-585 1429529 1429707 1429935 "LIST2" 1430340 NIL LIST2 (NIL T T) -7 NIL NIL) (-584 1427663 1427975 1428374 "LIST2MAP" 1429176 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-583 1426375 1427055 1427096 "LINEXP" 1427349 NIL LINEXP (NIL T) -9 NIL 1427497) (-582 1425022 1425282 1425579 "LINDEP" 1426127 NIL LINDEP (NIL T T) -7 NIL NIL) (-581 1421789 1422508 1423285 "LIMITRF" 1424277 NIL LIMITRF (NIL T) -7 NIL NIL) (-580 1420069 1420364 1420779 "LIMITPS" 1421484 NIL LIMITPS (NIL T T) -7 NIL NIL) (-579 1414524 1419580 1419808 "LIE" 1419890 NIL LIE (NIL T T) -8 NIL NIL) (-578 1413574 1414017 1414058 "LIECAT" 1414198 NIL LIECAT (NIL T) -9 NIL 1414349) (-577 1413415 1413442 1413530 "LIECAT-" 1413535 NIL LIECAT- (NIL T T) -8 NIL NIL) (-576 1406027 1412864 1413029 "LIB" 1413270 T LIB (NIL) -8 NIL NIL) (-575 1401664 1402545 1403480 "LGROBP" 1405144 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-574 1399530 1399804 1400166 "LF" 1401385 NIL LF (NIL T T) -7 NIL NIL) (-573 1398369 1399061 1399090 "LFCAT" 1399297 T LFCAT (NIL) -9 NIL 1399436) (-572 1395281 1395907 1396593 "LEXTRIPK" 1397735 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-571 1391987 1392851 1393354 "LEXP" 1394861 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-570 1390385 1390698 1391099 "LEADCDET" 1391669 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-569 1389581 1389655 1389882 "LAZM3PK" 1390306 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-568 1384497 1387660 1388197 "LAUPOL" 1389094 NIL LAUPOL (NIL T T) -8 NIL NIL) (-567 1384064 1384108 1384275 "LAPLACE" 1384447 NIL LAPLACE (NIL T T) -7 NIL NIL) (-566 1381992 1383165 1383416 "LA" 1383897 NIL LA (NIL T T T) -8 NIL NIL) (-565 1381054 1381648 1381689 "LALG" 1381750 NIL LALG (NIL T) -9 NIL 1381808) (-564 1380769 1380828 1380963 "LALG-" 1380968 NIL LALG- (NIL T T) -8 NIL NIL) (-563 1379679 1379866 1380163 "KOVACIC" 1380569 NIL KOVACIC (NIL T T) -7 NIL NIL) (-562 1379513 1379537 1379579 "KONVERT" 1379641 NIL KONVERT (NIL T) -9 NIL NIL) (-561 1379347 1379371 1379413 "KOERCE" 1379475 NIL KOERCE (NIL T) -9 NIL NIL) (-560 1377081 1377841 1378234 "KERNEL" 1378986 NIL KERNEL (NIL T) -8 NIL NIL) (-559 1376583 1376664 1376794 "KERNEL2" 1376995 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-558 1370434 1375122 1375177 "KDAGG" 1375554 NIL KDAGG (NIL T T) -9 NIL 1375760) (-557 1369963 1370087 1370292 "KDAGG-" 1370297 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-556 1363138 1369624 1369779 "KAFILE" 1369841 NIL KAFILE (NIL T) -8 NIL NIL) (-555 1357593 1362649 1362877 "JORDAN" 1362959 NIL JORDAN (NIL T T) -8 NIL NIL) (-554 1353892 1355798 1355853 "IXAGG" 1356782 NIL IXAGG (NIL T T) -9 NIL 1357241) (-553 1352811 1353117 1353536 "IXAGG-" 1353541 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-552 1348396 1352733 1352792 "IVECTOR" 1352797 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-551 1347162 1347399 1347665 "ITUPLE" 1348163 NIL ITUPLE (NIL T) -8 NIL NIL) (-550 1345598 1345775 1346081 "ITRIGMNP" 1346984 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-549 1344343 1344547 1344830 "ITFUN3" 1345374 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-548 1343975 1344032 1344141 "ITFUN2" 1344280 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-547 1341777 1342848 1343145 "ITAYLOR" 1343710 NIL ITAYLOR (NIL T) -8 NIL NIL) (-546 1330768 1335963 1337122 "ISUPS" 1340650 NIL ISUPS (NIL T) -8 NIL NIL) (-545 1329872 1330012 1330248 "ISUMP" 1330615 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-544 1325136 1329673 1329752 "ISTRING" 1329825 NIL ISTRING (NIL NIL) -8 NIL NIL) (-543 1324349 1324430 1324645 "IRURPK" 1325050 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-542 1323285 1323486 1323726 "IRSN" 1324129 T IRSN (NIL) -7 NIL NIL) (-541 1321320 1321675 1322110 "IRRF2F" 1322923 NIL IRRF2F (NIL T) -7 NIL NIL) (-540 1321067 1321105 1321181 "IRREDFFX" 1321276 NIL IRREDFFX (NIL T) -7 NIL NIL) (-539 1319682 1319941 1320240 "IROOT" 1320800 NIL IROOT (NIL T) -7 NIL NIL) (-538 1316320 1317371 1318061 "IR" 1319024 NIL IR (NIL T) -8 NIL NIL) (-537 1313933 1314428 1314994 "IR2" 1315798 NIL IR2 (NIL T T) -7 NIL NIL) (-536 1313009 1313122 1313342 "IR2F" 1313816 NIL IR2F (NIL T T) -7 NIL NIL) (-535 1312800 1312834 1312894 "IPRNTPK" 1312969 T IPRNTPK (NIL) -7 NIL NIL) (-534 1309354 1312689 1312758 "IPF" 1312763 NIL IPF (NIL NIL) -8 NIL NIL) (-533 1307671 1309279 1309336 "IPADIC" 1309341 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-532 1307170 1307228 1307417 "INVLAPLA" 1307607 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-531 1296819 1299172 1301558 "INTTR" 1304834 NIL INTTR (NIL T T) -7 NIL NIL) (-530 1293167 1293908 1294771 "INTTOOLS" 1296005 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-529 1292753 1292844 1292961 "INTSLPE" 1293070 T INTSLPE (NIL) -7 NIL NIL) (-528 1290703 1292676 1292735 "INTRVL" 1292740 NIL INTRVL (NIL T) -8 NIL NIL) (-527 1288310 1288822 1289396 "INTRF" 1290188 NIL INTRF (NIL T) -7 NIL NIL) (-526 1287725 1287822 1287963 "INTRET" 1288208 NIL INTRET (NIL T) -7 NIL NIL) (-525 1285727 1286116 1286585 "INTRAT" 1287333 NIL INTRAT (NIL T T) -7 NIL NIL) (-524 1282960 1283543 1284168 "INTPM" 1285212 NIL INTPM (NIL T T) -7 NIL NIL) (-523 1279669 1280268 1281012 "INTPAF" 1282346 NIL INTPAF (NIL T T T) -7 NIL NIL) (-522 1274912 1275858 1276893 "INTPACK" 1278654 T INTPACK (NIL) -7 NIL NIL) (-521 1271766 1274641 1274768 "INT" 1274805 T INT (NIL) -8 NIL NIL) (-520 1271018 1271170 1271378 "INTHERTR" 1271608 NIL INTHERTR (NIL T T) -7 NIL NIL) (-519 1270457 1270537 1270725 "INTHERAL" 1270932 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-518 1268303 1268746 1269203 "INTHEORY" 1270020 T INTHEORY (NIL) -7 NIL NIL) (-517 1259626 1261246 1263024 "INTG0" 1266655 NIL INTG0 (NIL T T T) -7 NIL NIL) (-516 1240199 1244989 1249799 "INTFTBL" 1254836 T INTFTBL (NIL) -8 NIL NIL) (-515 1239448 1239586 1239759 "INTFACT" 1240058 NIL INTFACT (NIL T) -7 NIL NIL) (-514 1236839 1237285 1237848 "INTEF" 1239002 NIL INTEF (NIL T T) -7 NIL NIL) (-513 1235300 1236049 1236078 "INTDOM" 1236379 T INTDOM (NIL) -9 NIL 1236586) (-512 1234669 1234843 1235085 "INTDOM-" 1235090 NIL INTDOM- (NIL T) -8 NIL NIL) (-511 1231161 1233093 1233148 "INTCAT" 1233947 NIL INTCAT (NIL T) -9 NIL 1234266) (-510 1230634 1230736 1230864 "INTBIT" 1231053 T INTBIT (NIL) -7 NIL NIL) (-509 1229309 1229463 1229776 "INTALG" 1230479 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-508 1228766 1228856 1229026 "INTAF" 1229213 NIL INTAF (NIL T T) -7 NIL NIL) (-507 1222220 1228576 1228716 "INTABL" 1228721 NIL INTABL (NIL T T T) -8 NIL NIL) (-506 1217170 1219899 1219928 "INS" 1220896 T INS (NIL) -9 NIL 1221577) (-505 1214410 1215181 1216155 "INS-" 1216228 NIL INS- (NIL T) -8 NIL NIL) (-504 1213189 1213416 1213713 "INPSIGN" 1214163 NIL INPSIGN (NIL T T) -7 NIL NIL) (-503 1212307 1212424 1212621 "INPRODPF" 1213069 NIL INPRODPF (NIL T T) -7 NIL NIL) (-502 1211201 1211318 1211555 "INPRODFF" 1212187 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-501 1210201 1210353 1210613 "INNMFACT" 1211037 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-500 1209398 1209495 1209683 "INMODGCD" 1210100 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-499 1207907 1208151 1208475 "INFSP" 1209143 NIL INFSP (NIL T T T) -7 NIL NIL) (-498 1207091 1207208 1207391 "INFPROD0" 1207787 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-497 1204101 1205260 1205751 "INFORM" 1206608 T INFORM (NIL) -8 NIL NIL) (-496 1203711 1203771 1203869 "INFORM1" 1204036 NIL INFORM1 (NIL T) -7 NIL NIL) (-495 1203234 1203323 1203437 "INFINITY" 1203617 T INFINITY (NIL) -7 NIL NIL) (-494 1201852 1202100 1202421 "INEP" 1202982 NIL INEP (NIL T T T) -7 NIL NIL) (-493 1201128 1201749 1201814 "INDE" 1201819 NIL INDE (NIL T) -8 NIL NIL) (-492 1200692 1200760 1200877 "INCRMAPS" 1201055 NIL INCRMAPS (NIL T) -7 NIL NIL) (-491 1196003 1196928 1197872 "INBFF" 1199780 NIL INBFF (NIL T) -7 NIL NIL) (-490 1192498 1195848 1195951 "IMATRIX" 1195956 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-489 1191210 1191333 1191648 "IMATQF" 1192354 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-488 1189430 1189657 1189994 "IMATLIN" 1190966 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-487 1184056 1189354 1189412 "ILIST" 1189417 NIL ILIST (NIL T NIL) -8 NIL NIL) (-486 1182009 1183916 1184029 "IIARRAY2" 1184034 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-485 1177377 1181920 1181984 "IFF" 1181989 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-484 1172420 1176669 1176857 "IFARRAY" 1177234 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-483 1171627 1172324 1172397 "IFAMON" 1172402 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-482 1171210 1171275 1171330 "IEVALAB" 1171537 NIL IEVALAB (NIL T T) -9 NIL NIL) (-481 1170885 1170953 1171113 "IEVALAB-" 1171118 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-480 1170543 1170799 1170862 "IDPO" 1170867 NIL IDPO (NIL T T) -8 NIL NIL) (-479 1169820 1170432 1170507 "IDPOAMS" 1170512 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-478 1169154 1169709 1169784 "IDPOAM" 1169789 NIL IDPOAM (NIL T T) -8 NIL NIL) (-477 1168239 1168489 1168543 "IDPC" 1168956 NIL IDPC (NIL T T) -9 NIL 1169105) (-476 1167735 1168131 1168204 "IDPAM" 1168209 NIL IDPAM (NIL T T) -8 NIL NIL) (-475 1167138 1167627 1167700 "IDPAG" 1167705 NIL IDPAG (NIL T T) -8 NIL NIL) (-474 1163393 1164241 1165136 "IDECOMP" 1166295 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-473 1156267 1157316 1158363 "IDEAL" 1162429 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-472 1155431 1155543 1155742 "ICDEN" 1156151 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-471 1154530 1154911 1155058 "ICARD" 1155304 T ICARD (NIL) -8 NIL NIL) (-470 1152602 1152915 1153318 "IBPTOOLS" 1154207 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-469 1148216 1152222 1152335 "IBITS" 1152521 NIL IBITS (NIL NIL) -8 NIL NIL) (-468 1144939 1145515 1146210 "IBATOOL" 1147633 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-467 1142719 1143180 1143713 "IBACHIN" 1144474 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-466 1140596 1142565 1142668 "IARRAY2" 1142673 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-465 1136749 1140522 1140579 "IARRAY1" 1140584 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-464 1130688 1135167 1135645 "IAN" 1136291 T IAN (NIL) -8 NIL NIL) (-463 1130199 1130256 1130429 "IALGFACT" 1130625 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-462 1129726 1129839 1129868 "HYPCAT" 1130075 T HYPCAT (NIL) -9 NIL NIL) (-461 1129264 1129381 1129567 "HYPCAT-" 1129572 NIL HYPCAT- (NIL T) -8 NIL NIL) (-460 1125943 1127274 1127316 "HOAGG" 1128297 NIL HOAGG (NIL T) -9 NIL 1128976) (-459 1124537 1124936 1125462 "HOAGG-" 1125467 NIL HOAGG- (NIL T T) -8 NIL NIL) (-458 1118368 1123978 1124144 "HEXADEC" 1124391 T HEXADEC (NIL) -8 NIL NIL) (-457 1117116 1117338 1117601 "HEUGCD" 1118145 NIL HEUGCD (NIL T) -7 NIL NIL) (-456 1116219 1116953 1117083 "HELLFDIV" 1117088 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-455 1114447 1115996 1116084 "HEAP" 1116163 NIL HEAP (NIL T) -8 NIL NIL) (-454 1108314 1114362 1114424 "HDP" 1114429 NIL HDP (NIL NIL T) -8 NIL NIL) (-453 1102026 1107951 1108102 "HDMP" 1108215 NIL HDMP (NIL NIL T) -8 NIL NIL) (-452 1101351 1101490 1101654 "HB" 1101882 T HB (NIL) -7 NIL NIL) (-451 1094848 1101197 1101301 "HASHTBL" 1101306 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-450 1092601 1094476 1094655 "HACKPI" 1094689 T HACKPI (NIL) -8 NIL NIL) (-449 1088297 1092455 1092567 "GTSET" 1092572 NIL GTSET (NIL T T T T) -8 NIL NIL) (-448 1081823 1088175 1088273 "GSTBL" 1088278 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-447 1074059 1080859 1081123 "GSERIES" 1081614 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-446 1073081 1073534 1073563 "GROUP" 1073824 T GROUP (NIL) -9 NIL 1073983) (-445 1072197 1072420 1072764 "GROUP-" 1072769 NIL GROUP- (NIL T) -8 NIL NIL) (-444 1070566 1070885 1071272 "GROEBSOL" 1071874 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-443 1069506 1069768 1069820 "GRMOD" 1070349 NIL GRMOD (NIL T T) -9 NIL 1070517) (-442 1069274 1069310 1069438 "GRMOD-" 1069443 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-441 1064602 1065628 1066628 "GRIMAGE" 1068294 T GRIMAGE (NIL) -8 NIL NIL) (-440 1063069 1063329 1063653 "GRDEF" 1064298 T GRDEF (NIL) -7 NIL NIL) (-439 1062513 1062629 1062770 "GRAY" 1062948 T GRAY (NIL) -7 NIL NIL) (-438 1061746 1062126 1062178 "GRALG" 1062331 NIL GRALG (NIL T T) -9 NIL 1062423) (-437 1061407 1061480 1061643 "GRALG-" 1061648 NIL GRALG- (NIL T T T) -8 NIL NIL) (-436 1058215 1060996 1061172 "GPOLSET" 1061314 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-435 1057571 1057628 1057885 "GOSPER" 1058152 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-434 1053330 1054009 1054535 "GMODPOL" 1057270 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-433 1052335 1052519 1052757 "GHENSEL" 1053142 NIL GHENSEL (NIL T T) -7 NIL NIL) (-432 1046401 1047244 1048270 "GENUPS" 1051419 NIL GENUPS (NIL T T) -7 NIL NIL) (-431 1046098 1046149 1046238 "GENUFACT" 1046344 NIL GENUFACT (NIL T) -7 NIL NIL) (-430 1045510 1045587 1045752 "GENPGCD" 1046016 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-429 1044984 1045019 1045232 "GENMFACT" 1045469 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-428 1043552 1043807 1044114 "GENEEZ" 1044727 NIL GENEEZ (NIL T T) -7 NIL NIL) (-427 1037426 1043165 1043326 "GDMP" 1043475 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-426 1026808 1031197 1032303 "GCNAALG" 1036409 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-425 1025229 1026101 1026130 "GCDDOM" 1026385 T GCDDOM (NIL) -9 NIL 1026542) (-424 1024699 1024826 1025041 "GCDDOM-" 1025046 NIL GCDDOM- (NIL T) -8 NIL NIL) (-423 1023371 1023556 1023860 "GB" 1024478 NIL GB (NIL T T T T) -7 NIL NIL) (-422 1011991 1014317 1016709 "GBINTERN" 1021062 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-421 1009828 1010120 1010541 "GBF" 1011666 NIL GBF (NIL T T T T) -7 NIL NIL) (-420 1008609 1008774 1009041 "GBEUCLID" 1009644 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-419 1007958 1008083 1008232 "GAUSSFAC" 1008480 T GAUSSFAC (NIL) -7 NIL NIL) (-418 1006335 1006637 1006950 "GALUTIL" 1007677 NIL GALUTIL (NIL T) -7 NIL NIL) (-417 1004652 1004926 1005249 "GALPOLYU" 1006062 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-416 1002041 1002331 1002736 "GALFACTU" 1004349 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-415 993847 995346 996954 "GALFACT" 1000473 NIL GALFACT (NIL T) -7 NIL NIL) (-414 991234 991892 991921 "FVFUN" 993077 T FVFUN (NIL) -9 NIL 993797) (-413 990499 990681 990710 "FVC" 991001 T FVC (NIL) -9 NIL 991184) (-412 990141 990296 990377 "FUNCTION" 990451 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-411 987811 988362 988851 "FT" 989672 T FT (NIL) -8 NIL NIL) (-410 986629 987112 987315 "FTEM" 987628 T FTEM (NIL) -8 NIL NIL) (-409 984894 985182 985584 "FSUPFACT" 986321 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-408 983291 983580 983912 "FST" 984582 T FST (NIL) -8 NIL NIL) (-407 982466 982572 982766 "FSRED" 983173 NIL FSRED (NIL T T) -7 NIL NIL) (-406 981145 981400 981754 "FSPRMELT" 982181 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-405 978230 978668 979167 "FSPECF" 980708 NIL FSPECF (NIL T T) -7 NIL NIL) (-404 960603 969160 969201 "FS" 973039 NIL FS (NIL T) -9 NIL 975321) (-403 949253 952243 956299 "FS-" 956596 NIL FS- (NIL T T) -8 NIL NIL) (-402 948769 948823 948999 "FSINT" 949194 NIL FSINT (NIL T T) -7 NIL NIL) (-401 947050 947762 948065 "FSERIES" 948548 NIL FSERIES (NIL T T) -8 NIL NIL) (-400 946068 946184 946414 "FSCINT" 946930 NIL FSCINT (NIL T T) -7 NIL NIL) (-399 942302 945012 945054 "FSAGG" 945424 NIL FSAGG (NIL T) -9 NIL 945683) (-398 940064 940665 941461 "FSAGG-" 941556 NIL FSAGG- (NIL T T) -8 NIL NIL) (-397 939106 939249 939476 "FSAGG2" 939917 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-396 936765 937044 937597 "FS2UPS" 938824 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-395 936351 936394 936547 "FS2" 936716 NIL FS2 (NIL T T T T) -7 NIL NIL) (-394 935211 935382 935690 "FS2EXPXP" 936176 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-393 934637 934752 934904 "FRUTIL" 935091 NIL FRUTIL (NIL T) -7 NIL NIL) (-392 926058 930136 931492 "FR" 933313 NIL FR (NIL T) -8 NIL NIL) (-391 921134 923777 923818 "FRNAALG" 925214 NIL FRNAALG (NIL T) -9 NIL 925821) (-390 916813 917883 919158 "FRNAALG-" 919908 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-389 916451 916494 916621 "FRNAAF2" 916764 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-388 914816 915308 915602 "FRMOD" 916264 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-387 912539 913207 913523 "FRIDEAL" 914607 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-386 911738 911825 912112 "FRIDEAL2" 912446 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-385 910995 911403 911445 "FRETRCT" 911450 NIL FRETRCT (NIL T) -9 NIL 911621) (-384 910107 910338 910689 "FRETRCT-" 910694 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-383 907316 908536 908596 "FRAMALG" 909478 NIL FRAMALG (NIL T T) -9 NIL 909770) (-382 905449 905905 906535 "FRAMALG-" 906758 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-381 899351 904924 905200 "FRAC" 905205 NIL FRAC (NIL T) -8 NIL NIL) (-380 898987 899044 899151 "FRAC2" 899288 NIL FRAC2 (NIL T T) -7 NIL NIL) (-379 898623 898680 898787 "FR2" 898924 NIL FR2 (NIL T T) -7 NIL NIL) (-378 893296 896209 896238 "FPS" 897357 T FPS (NIL) -9 NIL 897913) (-377 892745 892854 893018 "FPS-" 893164 NIL FPS- (NIL T) -8 NIL NIL) (-376 890193 891890 891919 "FPC" 892144 T FPC (NIL) -9 NIL 892286) (-375 889986 890026 890123 "FPC-" 890128 NIL FPC- (NIL T) -8 NIL NIL) (-374 888864 889474 889516 "FPATMAB" 889521 NIL FPATMAB (NIL T) -9 NIL 889673) (-373 886564 887040 887466 "FPARFRAC" 888501 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-372 881959 882456 883138 "FORTRAN" 885996 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-371 879675 880175 880714 "FORT" 881440 T FORT (NIL) -7 NIL NIL) (-370 877350 877912 877941 "FORTFN" 879001 T FORTFN (NIL) -9 NIL 879625) (-369 877113 877163 877192 "FORTCAT" 877251 T FORTCAT (NIL) -9 NIL 877313) (-368 875173 875656 876055 "FORMULA" 876734 T FORMULA (NIL) -8 NIL NIL) (-367 874961 874991 875060 "FORMULA1" 875137 NIL FORMULA1 (NIL T) -7 NIL NIL) (-366 874484 874536 874709 "FORDER" 874903 NIL FORDER (NIL T T T T) -7 NIL NIL) (-365 873580 873744 873937 "FOP" 874311 T FOP (NIL) -7 NIL NIL) (-364 872188 872860 873034 "FNLA" 873462 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-363 870856 871245 871274 "FNCAT" 871846 T FNCAT (NIL) -9 NIL 872139) (-362 870422 870815 870843 "FNAME" 870848 T FNAME (NIL) -8 NIL NIL) (-361 869081 870054 870083 "FMTC" 870088 T FMTC (NIL) -9 NIL 870123) (-360 865399 866606 867234 "FMONOID" 868486 NIL FMONOID (NIL T) -8 NIL NIL) (-359 864619 865142 865290 "FM" 865295 NIL FM (NIL T T) -8 NIL NIL) (-358 862042 862688 862717 "FMFUN" 863861 T FMFUN (NIL) -9 NIL 864569) (-357 861310 861491 861520 "FMC" 861810 T FMC (NIL) -9 NIL 861992) (-356 858539 859373 859427 "FMCAT" 860609 NIL FMCAT (NIL T T) -9 NIL 861103) (-355 857434 858307 858406 "FM1" 858484 NIL FM1 (NIL T T) -8 NIL NIL) (-354 855208 855624 856118 "FLOATRP" 856985 NIL FLOATRP (NIL T) -7 NIL NIL) (-353 848694 852864 853494 "FLOAT" 854598 T FLOAT (NIL) -8 NIL NIL) (-352 846132 846632 847210 "FLOATCP" 848161 NIL FLOATCP (NIL T) -7 NIL NIL) (-351 844920 845768 845809 "FLINEXP" 845814 NIL FLINEXP (NIL T) -9 NIL 845907) (-350 844075 844310 844637 "FLINEXP-" 844642 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-349 843151 843295 843519 "FLASORT" 843927 NIL FLASORT (NIL T T) -7 NIL NIL) (-348 840369 841211 841264 "FLALG" 842491 NIL FLALG (NIL T T) -9 NIL 842958) (-347 834153 837855 837897 "FLAGG" 839159 NIL FLAGG (NIL T) -9 NIL 839811) (-346 832879 833218 833708 "FLAGG-" 833713 NIL FLAGG- (NIL T T) -8 NIL NIL) (-345 831921 832064 832291 "FLAGG2" 832732 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-344 828893 829911 829971 "FINRALG" 831099 NIL FINRALG (NIL T T) -9 NIL 831607) (-343 828053 828282 828621 "FINRALG-" 828626 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-342 827459 827672 827701 "FINITE" 827897 T FINITE (NIL) -9 NIL 828004) (-341 819918 822079 822120 "FINAALG" 825787 NIL FINAALG (NIL T) -9 NIL 827240) (-340 815259 816300 817444 "FINAALG-" 818823 NIL FINAALG- (NIL T T) -8 NIL NIL) (-339 814654 815014 815117 "FILE" 815189 NIL FILE (NIL T) -8 NIL NIL) (-338 813338 813650 813705 "FILECAT" 814389 NIL FILECAT (NIL T T) -9 NIL 814605) (-337 811200 812756 812785 "FIELD" 812825 T FIELD (NIL) -9 NIL 812905) (-336 809820 810205 810716 "FIELD-" 810721 NIL FIELD- (NIL T) -8 NIL NIL) (-335 807635 808457 808803 "FGROUP" 809507 NIL FGROUP (NIL T) -8 NIL NIL) (-334 806725 806889 807109 "FGLMICPK" 807467 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-333 802527 806650 806707 "FFX" 806712 NIL FFX (NIL T NIL) -8 NIL NIL) (-332 802128 802189 802324 "FFSLPE" 802460 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-331 798123 798900 799696 "FFPOLY" 801364 NIL FFPOLY (NIL T) -7 NIL NIL) (-330 797627 797663 797872 "FFPOLY2" 798081 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-329 793449 797546 797609 "FFP" 797614 NIL FFP (NIL T NIL) -8 NIL NIL) (-328 788817 793360 793424 "FF" 793429 NIL FF (NIL NIL NIL) -8 NIL NIL) (-327 783913 788160 788350 "FFNBX" 788671 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-326 778823 783048 783306 "FFNBP" 783767 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-325 773426 778107 778318 "FFNB" 778656 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-324 772258 772456 772771 "FFINTBAS" 773223 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-323 768481 770721 770750 "FFIELDC" 771370 T FFIELDC (NIL) -9 NIL 771746) (-322 767144 767514 768011 "FFIELDC-" 768016 NIL FFIELDC- (NIL T) -8 NIL NIL) (-321 766714 766759 766883 "FFHOM" 767086 NIL FFHOM (NIL T T T) -7 NIL NIL) (-320 764412 764896 765413 "FFF" 766229 NIL FFF (NIL T) -7 NIL NIL) (-319 760000 764154 764255 "FFCGX" 764355 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-318 755602 759732 759839 "FFCGP" 759943 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-317 750755 755329 755437 "FFCG" 755538 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-316 732700 741823 741910 "FFCAT" 747075 NIL FFCAT (NIL T T T) -9 NIL 748562) (-315 727898 728945 730259 "FFCAT-" 731489 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-314 727309 727352 727587 "FFCAT2" 727849 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-313 716509 720299 721516 "FEXPR" 726164 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-312 715508 715943 715985 "FEVALAB" 716069 NIL FEVALAB (NIL T) -9 NIL 716330) (-311 714667 714877 715215 "FEVALAB-" 715220 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-310 713260 714050 714253 "FDIV" 714566 NIL FDIV (NIL T T T T) -8 NIL NIL) (-309 710326 711041 711157 "FDIVCAT" 712725 NIL FDIVCAT (NIL T T T T) -9 NIL 713162) (-308 710088 710115 710285 "FDIVCAT-" 710290 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-307 709308 709395 709672 "FDIV2" 709995 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-306 707994 708253 708542 "FCPAK1" 709039 T FCPAK1 (NIL) -7 NIL NIL) (-305 707122 707494 707635 "FCOMP" 707885 NIL FCOMP (NIL T) -8 NIL NIL) (-304 690750 694165 697728 "FC" 703579 T FC (NIL) -8 NIL NIL) (-303 683345 687391 687432 "FAXF" 689234 NIL FAXF (NIL T) -9 NIL 689925) (-302 680624 681279 682104 "FAXF-" 682569 NIL FAXF- (NIL T T) -8 NIL NIL) (-301 675724 680000 680176 "FARRAY" 680481 NIL FARRAY (NIL T) -8 NIL NIL) (-300 671114 673185 673238 "FAMR" 674250 NIL FAMR (NIL T T) -9 NIL 674710) (-299 670005 670307 670741 "FAMR-" 670746 NIL FAMR- (NIL T T T) -8 NIL NIL) (-298 669201 669927 669980 "FAMONOID" 669985 NIL FAMONOID (NIL T) -8 NIL NIL) (-297 667033 667717 667771 "FAMONC" 668712 NIL FAMONC (NIL T T) -9 NIL 669097) (-296 665725 666787 666924 "FAGROUP" 666929 NIL FAGROUP (NIL T) -8 NIL NIL) (-295 663528 663847 664249 "FACUTIL" 665406 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-294 662627 662812 663034 "FACTFUNC" 663338 NIL FACTFUNC (NIL T) -7 NIL NIL) (-293 654950 661878 662090 "EXPUPXS" 662483 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-292 652433 652973 653559 "EXPRTUBE" 654384 T EXPRTUBE (NIL) -7 NIL NIL) (-291 648627 649219 649956 "EXPRODE" 651772 NIL EXPRODE (NIL T T) -7 NIL NIL) (-290 633786 647286 647712 "EXPR" 648233 NIL EXPR (NIL T) -8 NIL NIL) (-289 628214 628801 629613 "EXPR2UPS" 633084 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-288 627850 627907 628014 "EXPR2" 628151 NIL EXPR2 (NIL T T) -7 NIL NIL) (-287 619204 626987 627282 "EXPEXPAN" 627688 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-286 619031 619161 619190 "EXIT" 619195 T EXIT (NIL) -8 NIL NIL) (-285 618658 618720 618833 "EVALCYC" 618963 NIL EVALCYC (NIL T) -7 NIL NIL) (-284 618198 618316 618358 "EVALAB" 618528 NIL EVALAB (NIL T) -9 NIL 618632) (-283 617679 617801 618022 "EVALAB-" 618027 NIL EVALAB- (NIL T T) -8 NIL NIL) (-282 615141 616453 616482 "EUCDOM" 617037 T EUCDOM (NIL) -9 NIL 617387) (-281 613546 613988 614578 "EUCDOM-" 614583 NIL EUCDOM- (NIL T) -8 NIL NIL) (-280 601124 603872 606612 "ESTOOLS" 610826 T ESTOOLS (NIL) -7 NIL NIL) (-279 600760 600817 600924 "ESTOOLS2" 601061 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-278 600511 600553 600633 "ESTOOLS1" 600712 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-277 594448 596172 596201 "ES" 598965 T ES (NIL) -9 NIL 600371) (-276 589396 590682 592499 "ES-" 592663 NIL ES- (NIL T) -8 NIL NIL) (-275 585771 586531 587311 "ESCONT" 588636 T ESCONT (NIL) -7 NIL NIL) (-274 585516 585548 585630 "ESCONT1" 585733 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-273 585191 585241 585341 "ES2" 585460 NIL ES2 (NIL T T) -7 NIL NIL) (-272 584821 584879 584988 "ES1" 585127 NIL ES1 (NIL T T) -7 NIL NIL) (-271 584037 584166 584342 "ERROR" 584665 T ERROR (NIL) -7 NIL NIL) (-270 577540 583896 583987 "EQTBL" 583992 NIL EQTBL (NIL T T) -8 NIL NIL) (-269 569977 572858 574305 "EQ" 576126 NIL -3087 (NIL T) -8 NIL NIL) (-268 569609 569666 569775 "EQ2" 569914 NIL EQ2 (NIL T T) -7 NIL NIL) (-267 564901 565947 567040 "EP" 568548 NIL EP (NIL T) -7 NIL NIL) (-266 563484 563784 564101 "ENV" 564604 T ENV (NIL) -8 NIL NIL) (-265 562643 563207 563236 "ENTIRER" 563241 T ENTIRER (NIL) -9 NIL 563286) (-264 559099 560598 560968 "EMR" 562442 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-263 558242 558427 558482 "ELTAGG" 558862 NIL ELTAGG (NIL T T) -9 NIL 559073) (-262 557961 558023 558164 "ELTAGG-" 558169 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-261 557749 557778 557833 "ELTAB" 557917 NIL ELTAB (NIL T T) -9 NIL NIL) (-260 556875 557021 557220 "ELFUTS" 557600 NIL ELFUTS (NIL T T) -7 NIL NIL) (-259 556616 556672 556701 "ELEMFUN" 556806 T ELEMFUN (NIL) -9 NIL NIL) (-258 556486 556507 556575 "ELEMFUN-" 556580 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-257 551377 554586 554628 "ELAGG" 555568 NIL ELAGG (NIL T) -9 NIL 556031) (-256 549662 550096 550759 "ELAGG-" 550764 NIL ELAGG- (NIL T T) -8 NIL NIL) (-255 542530 544329 545156 "EFUPXS" 548938 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-254 535980 537781 538591 "EFULS" 541806 NIL EFULS (NIL T T T) -8 NIL NIL) (-253 533411 533769 534247 "EFSTRUC" 535612 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-252 522483 524048 525608 "EF" 531926 NIL EF (NIL T T) -7 NIL NIL) (-251 521584 521968 522117 "EAB" 522354 T EAB (NIL) -8 NIL NIL) (-250 520797 521543 521571 "E04UCFA" 521576 T E04UCFA (NIL) -8 NIL NIL) (-249 520010 520756 520784 "E04NAFA" 520789 T E04NAFA (NIL) -8 NIL NIL) (-248 519223 519969 519997 "E04MBFA" 520002 T E04MBFA (NIL) -8 NIL NIL) (-247 518436 519182 519210 "E04JAFA" 519215 T E04JAFA (NIL) -8 NIL NIL) (-246 517651 518395 518423 "E04GCFA" 518428 T E04GCFA (NIL) -8 NIL NIL) (-245 516866 517610 517638 "E04FDFA" 517643 T E04FDFA (NIL) -8 NIL NIL) (-244 516079 516825 516853 "E04DGFA" 516858 T E04DGFA (NIL) -8 NIL NIL) (-243 510264 511609 512971 "E04AGNT" 514737 T E04AGNT (NIL) -7 NIL NIL) (-242 508990 509470 509511 "DVARCAT" 509986 NIL DVARCAT (NIL T) -9 NIL 510184) (-241 508194 508406 508720 "DVARCAT-" 508725 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-240 501056 507996 508123 "DSMP" 508128 NIL DSMP (NIL T T T) -8 NIL NIL) (-239 495866 497001 498069 "DROPT" 500008 T DROPT (NIL) -8 NIL NIL) (-238 495531 495590 495688 "DROPT1" 495801 NIL DROPT1 (NIL T) -7 NIL NIL) (-237 490646 491772 492909 "DROPT0" 494414 T DROPT0 (NIL) -7 NIL NIL) (-236 488991 489316 489702 "DRAWPT" 490280 T DRAWPT (NIL) -7 NIL NIL) (-235 483578 484501 485580 "DRAW" 487965 NIL DRAW (NIL T) -7 NIL NIL) (-234 483211 483264 483382 "DRAWHACK" 483519 NIL DRAWHACK (NIL T) -7 NIL NIL) (-233 481942 482211 482502 "DRAWCX" 482940 T DRAWCX (NIL) -7 NIL NIL) (-232 481460 481528 481678 "DRAWCURV" 481868 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-231 471932 473890 476005 "DRAWCFUN" 479365 T DRAWCFUN (NIL) -7 NIL NIL) (-230 468745 470627 470669 "DQAGG" 471298 NIL DQAGG (NIL T) -9 NIL 471571) (-229 457251 463989 464072 "DPOLCAT" 465910 NIL DPOLCAT (NIL T T T T) -9 NIL 466454) (-228 452091 453437 455394 "DPOLCAT-" 455399 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-227 446175 451953 452050 "DPMO" 452055 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-226 440162 445956 446122 "DPMM" 446127 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-225 439675 439773 439893 "DOMAIN" 440062 T DOMAIN (NIL) -8 NIL NIL) (-224 433387 439312 439463 "DMP" 439576 NIL DMP (NIL NIL T) -8 NIL NIL) (-223 432987 433043 433187 "DLP" 433325 NIL DLP (NIL T) -7 NIL NIL) (-222 426631 432088 432315 "DLIST" 432792 NIL DLIST (NIL T) -8 NIL NIL) (-221 423477 425486 425528 "DLAGG" 426078 NIL DLAGG (NIL T) -9 NIL 426307) (-220 422186 422878 422907 "DIVRING" 423057 T DIVRING (NIL) -9 NIL 423165) (-219 421174 421427 421820 "DIVRING-" 421825 NIL DIVRING- (NIL T) -8 NIL NIL) (-218 419276 419633 420039 "DISPLAY" 420788 T DISPLAY (NIL) -7 NIL NIL) (-217 413165 419190 419253 "DIRPROD" 419258 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-216 412013 412216 412481 "DIRPROD2" 412958 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-215 401643 407648 407702 "DIRPCAT" 408110 NIL DIRPCAT (NIL NIL T) -9 NIL 408937) (-214 398969 399611 400492 "DIRPCAT-" 400829 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-213 398256 398416 398602 "DIOSP" 398803 T DIOSP (NIL) -7 NIL NIL) (-212 394958 397168 397210 "DIOPS" 397644 NIL DIOPS (NIL T) -9 NIL 397873) (-211 394507 394621 394812 "DIOPS-" 394817 NIL DIOPS- (NIL T T) -8 NIL NIL) (-210 393378 394016 394045 "DIFRING" 394232 T DIFRING (NIL) -9 NIL 394341) (-209 393024 393101 393253 "DIFRING-" 393258 NIL DIFRING- (NIL T) -8 NIL NIL) (-208 390813 392095 392136 "DIFEXT" 392495 NIL DIFEXT (NIL T) -9 NIL 392788) (-207 389099 389527 390192 "DIFEXT-" 390197 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-206 386421 388631 388673 "DIAGG" 388678 NIL DIAGG (NIL T) -9 NIL 388698) (-205 385805 385962 386214 "DIAGG-" 386219 NIL DIAGG- (NIL T T) -8 NIL NIL) (-204 381270 384764 385041 "DHMATRIX" 385574 NIL DHMATRIX (NIL T) -8 NIL NIL) (-203 376882 377791 378801 "DFSFUN" 380280 T DFSFUN (NIL) -7 NIL NIL) (-202 371668 375596 375961 "DFLOAT" 376537 T DFLOAT (NIL) -8 NIL NIL) (-201 369901 370182 370577 "DFINTTLS" 371376 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-200 366934 367936 368334 "DERHAM" 369568 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-199 364783 366709 366798 "DEQUEUE" 366878 NIL DEQUEUE (NIL T) -8 NIL NIL) (-198 364001 364134 364329 "DEGRED" 364645 NIL DEGRED (NIL T T) -7 NIL NIL) (-197 360401 361146 361998 "DEFINTRF" 363229 NIL DEFINTRF (NIL T) -7 NIL NIL) (-196 357932 358401 358999 "DEFINTEF" 359920 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-195 351763 357373 357539 "DECIMAL" 357786 T DECIMAL (NIL) -8 NIL NIL) (-194 349275 349733 350239 "DDFACT" 351307 NIL DDFACT (NIL T T) -7 NIL NIL) (-193 348871 348914 349065 "DBLRESP" 349226 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-192 346581 346915 347284 "DBASE" 348629 NIL DBASE (NIL T) -8 NIL NIL) (-191 345716 346540 346568 "D03FAFA" 346573 T D03FAFA (NIL) -8 NIL NIL) (-190 344852 345675 345703 "D03EEFA" 345708 T D03EEFA (NIL) -8 NIL NIL) (-189 342802 343268 343757 "D03AGNT" 344383 T D03AGNT (NIL) -7 NIL NIL) (-188 342120 342761 342789 "D02EJFA" 342794 T D02EJFA (NIL) -8 NIL NIL) (-187 341438 342079 342107 "D02CJFA" 342112 T D02CJFA (NIL) -8 NIL NIL) (-186 340756 341397 341425 "D02BHFA" 341430 T D02BHFA (NIL) -8 NIL NIL) (-185 340074 340715 340743 "D02BBFA" 340748 T D02BBFA (NIL) -8 NIL NIL) (-184 333272 334860 336466 "D02AGNT" 338488 T D02AGNT (NIL) -7 NIL NIL) (-183 331041 331563 332109 "D01WGTS" 332746 T D01WGTS (NIL) -7 NIL NIL) (-182 330144 331000 331028 "D01TRNS" 331033 T D01TRNS (NIL) -8 NIL NIL) (-181 329247 330103 330131 "D01GBFA" 330136 T D01GBFA (NIL) -8 NIL NIL) (-180 328350 329206 329234 "D01FCFA" 329239 T D01FCFA (NIL) -8 NIL NIL) (-179 327453 328309 328337 "D01ASFA" 328342 T D01ASFA (NIL) -8 NIL NIL) (-178 326556 327412 327440 "D01AQFA" 327445 T D01AQFA (NIL) -8 NIL NIL) (-177 325659 326515 326543 "D01APFA" 326548 T D01APFA (NIL) -8 NIL NIL) (-176 324762 325618 325646 "D01ANFA" 325651 T D01ANFA (NIL) -8 NIL NIL) (-175 323865 324721 324749 "D01AMFA" 324754 T D01AMFA (NIL) -8 NIL NIL) (-174 322968 323824 323852 "D01ALFA" 323857 T D01ALFA (NIL) -8 NIL NIL) (-173 322071 322927 322955 "D01AKFA" 322960 T D01AKFA 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(-4 *5 (-1119)) @@ -1725,8 +1740,8 @@ (-4 *2 (-1119)))) ((*1 *2 *3) (-12 (-4 *4 (-970)) - (-5 *2 (-2 (|:| -3736 (-1080 *4)) (|:| |deg| (-850)))) - (-5 *1 (-198 *4 *5)) (-5 *3 (-1080 *4)) (-4 *5 (-13 (-513) (-784))))) + (-5 *2 (-2 (|:| -3201 (-1080 *4)) (|:| |deg| (-849)))) + (-5 *1 (-198 *4 *5)) (-5 *3 (-1080 *4)) (-4 *5 (-13 (-513) (-783))))) ((*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-217 *5 *6)) (-14 *5 (-707)) (-4 *6 (-1119)) (-4 *2 (-1119)) (-5 *1 (-216 *5 *6 *2)))) @@ -1735,7 +1750,7 @@ (-4 *2 (-1141 *4)) (-4 *3 (-23)) (-14 *5 (-1 *2 *2 *3)) (-14 *6 (-1 (-3 *3 "failed") *3 *3)) (-14 *7 (-1 (-3 *2 "failed") *2 *2 *3)))) - ((*1 *1 *1) (-12 (-5 *1 (-290 *2)) (-4 *2 (-513)) (-4 *2 (-784)))) + ((*1 *1 *1) (-12 (-5 *1 (-290 *2)) (-4 *2 (-513)) (-4 *2 (-783)))) ((*1 *1 *1) (-12 (-4 *1 (-309 *2 *3 *4 *5)) (-4 *2 (-337)) (-4 *3 (-1141 *2)) (-4 *4 (-1141 (-381 *3))) (-4 *5 (-316 *2 *3 *4)))) @@ -1770,11 +1785,11 @@ ((*1 *1 *2) (-12 (-4 *3 (-157)) (-4 *1 (-661 *3 *2)) (-4 *2 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(-12 (-5 *2 (-850)) (-5 *1 (-143)))) + ((*1 *1 *2 *1) (-12 (-5 *2 (-849)) (-5 *1 (-143)))) ((*1 *2 *1 *2) - (-12 (-5 *2 (-872 *3)) (-4 *3 (-13 (-337) (-1105))) + (-12 (-5 *2 (-871 *3)) (-4 *3 (-13 (-337) (-1105))) (-5 *1 (-204 *3)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-215 *3 *2)) (-4 *2 (-1119)) (-4 *2 (-663)))) @@ -1970,26 +1944,26 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-335 *2)) (-4 *2 (-1013)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-335 *2)) (-4 *2 (-1013)))) ((*1 *1 *2 *3) - (-12 (-5 *1 (-355 *3 *2)) (-4 *3 (-970)) (-4 *2 (-784)))) + (-12 (-5 *1 (-355 *3 *2)) (-4 *3 (-970)) (-4 *2 (-783)))) ((*1 *1 *2 *3) (-12 (-4 *1 (-356 *2 *3)) (-4 *2 (-970)) (-4 *3 (-1013)))) ((*1 *1 *1 *2) (-12 (-5 *1 (-360 *2)) (-4 *2 (-1013)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-360 *2)) (-4 *2 (-1013)))) ((*1 *1 *2 *1) (-12 (-14 *3 (-587 (-1084))) (-4 *4 (-157)) - (-4 *6 (-215 (-3475 *3) (-707))) + (-4 *6 (-215 (-3478 *3) (-707))) (-14 *7 - (-1 (-108) (-2 (|:| -2716 *5) (|:| -2997 *6)) - (-2 (|:| -2716 *5) (|:| -2997 *6)))) - (-5 *1 (-434 *3 *4 *5 *6 *7 *2)) (-4 *5 (-784)) - (-4 *2 (-878 *4 *6 (-794 *3))))) + (-1 (-108) (-2 (|:| -2723 *5) (|:| -2246 *6)) + (-2 (|:| -2723 *5) (|:| -2246 *6)))) + (-5 *1 (-434 *3 *4 *5 *6 *7 *2)) (-4 *5 (-783)) + (-4 *2 (-877 *4 *6 (-793 *3))))) ((*1 *1 *1 *2) (-12 (-4 *1 (-443 *2 *3)) (-4 *2 (-157)) (-4 *3 (-23)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-443 *2 *3)) (-4 *2 (-157)) (-4 *3 (-23)))) ((*1 *1 *1 *1) - (-12 (-4 *2 (-337)) (-4 *3 (-729)) (-4 *4 (-784)) - (-5 *1 (-473 *2 *3 *4 *5)) (-4 *5 (-878 *2 *3 *4)))) + (-12 (-4 *2 (-337)) (-4 *3 (-729)) (-4 *4 (-783)) + (-5 *1 (-473 *2 *3 *4 *5)) (-4 *5 (-877 *2 *3 *4)))) ((*1 *2 *2 *2) (-12 (-5 *2 (-1165 *3)) (-4 *3 (-323)) (-5 *1 (-491 *3)))) ((*1 *1 *1 *1) (-5 *1 (-497))) @@ -1997,7 +1971,7 @@ ((*1 *1 *1 *2) (-12 (-5 *1 (-547 *2)) (-4 *2 (-970)))) ((*1 *1 *2 *1) (-12 (-5 *1 (-547 *2)) (-4 *2 (-970)))) ((*1 *1 *2 *1) (-12 (-4 *1 (-589 *2)) (-4 *2 (-977)))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-616 *2)) (-4 *2 (-784)))) + ((*1 *1 *1 *1) (-12 (-5 *1 (-616 *2)) (-4 *2 (-783)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-1 *6 *5)) (-4 *5 (-1013)) (-4 *6 (-1013)) (-4 *7 (-1013)) (-5 *2 (-1 *7 *5)) @@ -2021,10 +1995,10 @@ (-12 (-4 *1 (-625 *2 *3 *4)) (-4 *2 (-970)) (-4 *3 (-347 *2)) (-4 *4 (-347 *2)))) ((*1 *1 *1 *1) (-4 *1 (-657))) - ((*1 *1 *1 *2) (-12 (-5 *1 (-756 *2)) (-4 *2 (-784)))) - ((*1 *1 *2 *1) (-12 (-5 *1 (-756 *2)) (-4 *2 (-784)))) - ((*1 *1 *1 *1) (-5 *1 (-792))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-821 *2)) (-4 *2 (-1013)))) + ((*1 *1 *1 *2) (-12 (-5 *1 (-755 *2)) (-4 *2 (-783)))) + ((*1 *1 *2 *1) (-12 (-5 *1 (-755 *2)) (-4 *2 (-783)))) + ((*1 *1 *1 *1) (-5 *1 (-791))) + ((*1 *1 *1 *1) (-12 (-5 *1 (-820 *2)) (-4 *2 (-1013)))) ((*1 *2 *3 *2) (-12 (-5 *2 (-1165 *4)) (-4 *4 (-1141 *3)) (-4 *3 (-513)) (-5 *1 (-896 *3 *4)))) @@ -2037,8 +2011,8 @@ (-12 (-4 *1 (-1034 *3 *4 *5 *2)) (-4 *4 (-970)) (-4 *5 (-215 *3 *4)) (-4 *2 (-215 *3 *4)))) ((*1 *1 *2 *1) - (-12 (-4 *3 (-970)) (-4 *4 (-784)) (-5 *1 (-1037 *3 *4 *2)) - (-4 *2 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(-707))) (-5 *1 (-1073 *3 *4)) (-14 *3 (-849)) + (-4 *4 (-970))))) +(((*1 *2 *3) (-12 (-5 *3 (-1067)) (-5 *2 (-849)) (-5 *1 (-722))))) +(((*1 *2 *1) (-12 (-5 *2 (-521)) (-5 *1 (-897))))) +(((*1 *2 *3) + (-12 (-5 *3 (-202)) (-5 *2 (-108)) (-5 *1 (-274 *4 *5)) (-14 *4 *3) + (-14 *5 *3))) ((*1 *2 *3 *4) - (-12 (-4 *5 (-425)) (-4 *6 (-729)) (-4 *7 (-784)) - (-4 *3 (-984 *5 *6 *7)) - (-5 *2 - (-2 (|:| |done| (-587 *4)) - (|:| |todo| (-587 (-2 (|:| |val| (-587 *3)) (|:| -1884 *4)))))) - (-5 *1 (-1054 *5 *6 *7 *3 *4)) (-4 *4 (-1022 *5 *6 *7 *3))))) -(((*1 *2) - (-12 (-4 *3 (-513)) (-5 *2 (-587 *4)) (-5 *1 (-42 *3 *4)) - (-4 *4 (-391 *3))))) + (-12 (-5 *4 (-1008 (-776 (-202)))) (-5 *3 (-202)) (-5 *2 (-108)) + (-5 *1 (-280)))) + ((*1 *2 *1 *1) + (-12 (-4 *3 (-337)) (-4 *4 (-729)) (-4 *5 (-783)) (-5 *2 (-108)) + (-5 *1 (-473 *3 *4 *5 *6)) (-4 *6 (-877 *3 *4 *5))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-513))) (-5 *1 (-252 *3 *2)) + (-12 (-4 *3 (-13 (-783) (-513))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-404 *3) (-927))))) ((*1 *2 *2) (-12 (-4 *3 (-37 (-381 (-521)))) (-4 *4 (-1156 *3)) @@ -6894,41 +6795,31 @@ ((*1 *2 *2) (-12 (-5 *2 (-1065 *3)) (-4 *3 (-37 (-381 (-521)))) (-5 *1 (-1071 *3))))) -(((*1 *2 *3 *2) - (-12 (-5 *2 (-587 (-1008 (-353)))) (-5 *3 (-587 (-239))) - (-5 *1 (-237)))) - ((*1 *1 *2) (-12 (-5 *2 (-587 (-1008 (-353)))) (-5 *1 (-239)))) - ((*1 *2 *1 *2) (-12 (-5 *2 (-587 (-1008 (-353)))) (-5 *1 (-441)))) - ((*1 *2 *1) (-12 (-5 *2 (-587 (-1008 (-353)))) (-5 *1 (-441))))) -(((*1 *2 *3) - (-12 - (-5 *3 - (-2 (|:| |xinit| (-202)) (|:| |xend| (-202)) - (|:| |fn| (-1165 (-290 (-202)))) (|:| |yinit| (-587 (-202))) - (|:| |intvals| (-587 (-202))) (|:| |g| (-290 (-202))) - (|:| |abserr| (-202)) (|:| |relerr| (-202)))) - (-5 *2 (-353)) (-5 *1 (-184))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-760)) (-5 *2 (-1170)) (-5 *1 (-759))))) -(((*1 *1 *1 *1 *1) (-4 *1 (-698)))) +(((*1 *2 *3 *3 *4 *5 *3 *3 *4 *4 *4 *6) + (-12 (-5 *4 (-521)) (-5 *5 (-627 (-202))) + (-5 *6 (-3 (|:| |fn| (-362)) (|:| |fp| (-62 -4049)))) (-5 *3 (-202)) + (-5 *2 (-959)) (-5 *1 (-685))))) (((*1 *2 *3 *4) - (-12 (-5 *3 (-1165 (-290 (-202)))) (-5 *4 (-587 (-1084))) - (-5 *2 (-627 (-290 (-202)))) (-5 *1 (-184)))) - ((*1 *2 *3 *4) - (-12 (-4 *5 (-1013)) (-4 *6 (-829 *5)) (-5 *2 (-627 *6)) - (-5 *1 (-629 *5 *6 *3 *4)) (-4 *3 (-347 *6)) - (-4 *4 (-13 (-347 *5) (-10 -7 (-6 -4233))))))) -(((*1 *2 *1) - (-12 (-5 *2 (-792)) (-5 *1 (-364 *3 *4 *5)) (-14 *3 (-707)) - (-14 *4 (-707)) (-4 *5 (-157))))) -(((*1 *1 *2) (-12 (-5 *2 (-707)) (-5 *1 (-126))))) -(((*1 *2 *1 *3) (-12 (-5 *3 (-1067)) (-5 *2 (-1170)) (-5 *1 (-1167))))) + (-12 (-5 *4 (-587 *5)) (-4 *5 (-1141 *3)) (-4 *3 (-282)) + (-5 *2 (-108)) (-5 *1 (-428 *3 *5))))) +(((*1 *2) (-12 (-5 *2 (-587 (-707))) (-5 *1 (-1168)))) + ((*1 *2 *2) (-12 (-5 *2 (-587 (-707))) (-5 *1 (-1168))))) +(((*1 *2 *3 *4 *5 *6 *5) + (-12 (-5 *4 (-154 (-202))) (-5 *5 (-521)) (-5 *6 (-1067)) + (-5 *3 (-202)) (-5 *2 (-959)) (-5 *1 (-695))))) (((*1 *2 *3) - (-12 (-4 *4 (-838)) (-4 *5 (-729)) (-4 *6 (-784)) - (-4 *7 (-878 *4 *5 *6)) (-5 *2 (-392 (-1080 *7))) - (-5 *1 (-835 *4 *5 *6 *7)) (-5 *3 (-1080 *7)))) - ((*1 *2 *3) - (-12 (-4 *4 (-838)) (-4 *5 (-1141 *4)) (-5 *2 (-392 (-1080 *5))) - (-5 *1 (-836 *4 *5)) (-5 *3 (-1080 *5))))) + (-12 (-4 *4 (-513)) (-4 *5 (-729)) (-4 *6 (-783)) + (-4 *7 (-984 *4 *5 *6)) + (-5 *2 (-2 (|:| |goodPols| (-587 *7)) (|:| |badPols| (-587 *7)))) + (-5 *1 (-903 *4 *5 *6 *7)) (-5 *3 (-587 *7))))) +(((*1 *2 *1) + (-12 (-5 *2 (-587 (-521))) (-5 *1 (-929 *3)) (-14 *3 (-521))))) +(((*1 *2 *2) (|partial| -12 (-4 *1 (-909 *2)) (-4 *2 (-1105))))) +(((*1 *1 *1 *1) (-12 (-4 *1 (-1141 *2)) (-4 *2 (-970))))) +(((*1 *2 *3 *1) + (-12 (-4 *1 (-902 *4 *5 *6 *3)) (-4 *4 (-970)) (-4 *5 (-729)) + (-4 *6 (-783)) (-4 *3 (-984 *4 *5 *6)) (-4 *4 (-513)) + (-5 *2 (-2 (|:| |num| *3) (|:| |den| *4)))))) (((*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 (-202) (-202))) (-5 *4 (-1008 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1166)) (-5 *1 (-231)))) @@ -6936,22 +6827,22 @@ (-12 (-5 *3 (-1 (-202) (-202))) (-5 *4 (-1008 (-353))) (-5 *2 (-1166)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-806 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-805 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1166)) (-5 *1 (-231)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-806 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-805 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) (-5 *2 (-1166)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-808 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-807 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-808 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-807 (-1 (-202) (-202)))) (-5 *4 (-1008 (-353))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-1 (-872 (-202)) (-202))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-1 (-871 (-202)) (-202))) (-5 *4 (-1008 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 (-872 (-202)) (-202))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-1 (-871 (-202)) (-202))) (-5 *4 (-1008 (-353))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *4 *5) (-12 (-5 *3 (-1 (-202) (-202) (-202))) (-5 *4 (-1008 (-353))) @@ -6960,20 +6851,20 @@ (-12 (-5 *3 (-1 (-202) (-202) (-202))) (-5 *4 (-1008 (-353))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-1 (-872 (-202)) (-202) (-202))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-1 (-871 (-202)) (-202) (-202))) (-5 *4 (-1008 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-1 (-872 (-202)) (-202) (-202))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-1 (-871 (-202)) (-202) (-202))) (-5 *4 (-1008 (-353))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-811 (-1 (-202) (-202) (-202)))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-810 (-1 (-202) (-202) (-202)))) (-5 *4 (-1008 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-811 (-1 (-202) (-202) (-202)))) (-5 *4 (-1008 (-353))) + (-12 (-5 *3 (-810 (-1 (-202) (-202) (-202)))) (-5 *4 (-1008 (-353))) (-5 *2 (-1167)) (-5 *1 (-231)))) ((*1 *2 *3 *4 *4 *5) (-12 (-5 *3 (-269 *7)) (-5 *4 (-1084)) (-5 *5 (-587 (-239))) - (-4 *7 (-404 *6)) (-4 *6 (-13 (-513) (-784) (-961 (-521)))) + (-4 *7 (-404 *6)) (-4 *6 (-13 (-513) (-783) (-961 (-521)))) (-5 *2 (-1166)) (-5 *1 (-232 *6 *7)))) ((*1 *2 *3 *4 *5) (-12 (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) (-5 *2 (-1166)) @@ -6982,19 +6873,19 @@ (-12 (-5 *4 (-1006 (-353))) (-5 *2 (-1166)) (-5 *1 (-235 *3)) (-4 *3 (-13 (-562 (-497)) (-1013))))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-806 *6)) (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) + (-12 (-5 *3 (-805 *6)) (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) (-4 *6 (-13 (-562 (-497)) (-1013))) (-5 *2 (-1166)) (-5 *1 (-235 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-806 *5)) (-5 *4 (-1006 (-353))) + (-12 (-5 *3 (-805 *5)) (-5 *4 (-1006 (-353))) (-4 *5 (-13 (-562 (-497)) (-1013))) (-5 *2 (-1166)) (-5 *1 (-235 *5)))) ((*1 *2 *3 *4 *5) - (-12 (-5 *3 (-808 *6)) (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) + (-12 (-5 *3 (-807 *6)) (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) (-4 *6 (-13 (-562 (-497)) (-1013))) (-5 *2 (-1167)) (-5 *1 (-235 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-808 *5)) (-5 *4 (-1006 (-353))) + (-12 (-5 *3 (-807 *5)) (-5 *4 (-1006 (-353))) (-4 *5 (-13 (-562 (-497)) (-1013))) (-5 *2 (-1167)) (-5 *1 (-235 *5)))) ((*1 *2 *3 *4 *4 *5) @@ -7004,11 +6895,11 @@ (-12 (-5 *4 (-1006 (-353))) (-5 *2 (-1167)) (-5 *1 (-235 *3)) (-4 *3 (-13 (-562 (-497)) (-1013))))) ((*1 *2 *3 *4 *4 *5) - (-12 (-5 *3 (-811 *6)) (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) + (-12 (-5 *3 (-810 *6)) (-5 *4 (-1006 (-353))) (-5 *5 (-587 (-239))) (-4 *6 (-13 (-562 (-497)) (-1013))) (-5 *2 (-1167)) (-5 *1 (-235 *6)))) ((*1 *2 *3 *4 *4) - (-12 (-5 *3 (-811 *5)) (-5 *4 (-1006 (-353))) + (-12 (-5 *3 (-810 *5)) (-5 *4 (-1006 (-353))) (-4 *5 (-13 (-562 (-497)) (-1013))) (-5 *2 (-1167)) (-5 *1 (-235 *5)))) ((*1 *2 *3 *3) @@ -7017,9 +6908,9 @@ (-12 (-5 *3 (-587 (-202))) (-5 *4 (-587 (-239))) (-5 *2 (-1166)) (-5 *1 (-236)))) ((*1 *2 *3) - (-12 (-5 *3 (-587 (-872 (-202)))) (-5 *2 (-1166)) (-5 *1 (-236)))) + (-12 (-5 *3 (-587 (-871 (-202)))) (-5 *2 (-1166)) (-5 *1 (-236)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-587 (-872 (-202)))) (-5 *4 (-587 (-239))) + (-12 (-5 *3 (-587 (-871 (-202)))) (-5 *4 (-587 (-239))) (-5 *2 (-1166)) (-5 *1 (-236)))) ((*1 *2 *3 *3 *3) (-12 (-5 *3 (-587 (-202))) (-5 *2 (-1167)) (-5 *1 (-236)))) @@ -7027,7 +6918,7 @@ (-12 (-5 *3 (-587 (-202))) (-5 *4 (-587 (-239))) (-5 *2 (-1167)) (-5 *1 (-236))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-513))) (-5 *1 (-252 *3 *2)) + (-12 (-4 *3 (-13 (-783) (-513))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-404 *3) (-927))))) ((*1 *2 *2) (-12 (-4 *3 (-37 (-381 (-521)))) (-4 *4 (-1156 *3)) @@ -7042,44 +6933,89 @@ ((*1 *2 *2) (-12 (-5 *2 (-1065 *3)) (-4 *3 (-37 (-381 (-521)))) (-5 *1 (-1071 *3))))) -(((*1 *2 *1 *3 *3) - (-12 (-5 *3 (-521)) (-4 *1 (-1125 *4)) (-4 *4 (-970)) (-4 *4 (-513)) - (-5 *2 (-381 (-881 *4))))) - ((*1 *2 *1 *3) - (-12 (-5 *3 (-521)) (-4 *1 (-1125 *4)) (-4 *4 (-970)) (-4 *4 (-513)) - (-5 *2 (-381 (-881 *4)))))) -(((*1 *2 *3) - (-12 (-5 *2 (-1086 (-381 (-521)))) (-5 *1 (-169)) (-5 *3 (-521))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-202)) (-5 *4 (-521)) (-5 *2 (-959)) (-5 *1 (-695))))) (((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| |cd| (-1067)) (|:| -2884 (-1067)))) - (-5 *1 (-759))))) -(((*1 *2 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-202)) (-5 *4 (-521)) - (-5 *5 (-3 (|:| |fn| (-362)) (|:| |fp| (-62 -4049)))) (-5 *2 (-959)) - (-5 *1 (-685))))) -(((*1 *2 *1) (-12 (-5 *1 (-1115 *2)) (-4 *2 (-900))))) + (-12 (-5 *2 (-2 (|:| -1493 *1) (|:| -4220 *1) (|:| |associate| *1))) + (-4 *1 (-513))))) +(((*1 *2 *1) (-12 (-5 *2 (-1170)) (-5 *1 (-758))))) +(((*1 *2 *3) + (-12 + (-5 *3 + (-2 (|:| |var| (-1084)) (|:| |fn| (-290 (-202))) + (|:| -1403 (-1008 (-776 (-202)))) (|:| |abserr| (-202)) + (|:| |relerr| (-202)))) + (-5 *2 + (-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 (-171))))) (((*1 *2 *3 *4) - (-12 (-4 *5 (-425)) (-4 *6 (-729)) (-4 *7 (-784)) - (-4 *3 (-984 *5 *6 *7)) - (-5 *2 (-587 (-2 (|:| |val| *3) (|:| -1884 *4)))) - (-5 *1 (-990 *5 *6 *7 *3 *4)) (-4 *4 (-989 *5 *6 *7 *3))))) -(((*1 *2 *3 *4 *4 *3) - (-12 (-5 *3 (-521)) (-5 *4 (-627 (-202))) (-5 *2 (-959)) - (-5 *1 (-689))))) + (-12 (-5 *3 (-594 (-381 *6))) (-5 *4 (-1 (-587 *5) *6)) + (-4 *5 (-13 (-337) (-135) (-961 (-521)) (-961 (-381 (-521))))) + (-4 *6 (-1141 *5)) (-5 *2 (-587 (-381 *6))) (-5 *1 (-748 *5 *6)))) + ((*1 *2 *3 *4 *5) + (-12 (-5 *3 (-594 (-381 *7))) (-5 *4 (-1 (-587 *6) *7)) + (-5 *5 (-1 (-392 *7) *7)) + (-4 *6 (-13 (-337) 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*3 *4) (-12 (-5 *4 (-1 *5 *5)) (-4 *5 (-13 (-337) (-10 -8 (-15 ** ($ $ (-381 (-521))))))) @@ -7547,12 +7487,26 @@ (-2 (|:| |solns| (-587 *5)) (|:| |maps| (-587 (-2 (|:| |arg| *5) (|:| |res| *5)))))) (-5 *1 (-1039 *3 *5)) (-4 *3 (-1141 *5))))) +(((*1 *2 *1) + (-12 (-5 *2 (-801 (-893 *3) (-893 *3))) (-5 *1 (-893 *3)) + (-4 *3 (-894))))) +(((*1 *2 *3 *4) + (-12 (-5 *3 (-587 *8)) (-5 *4 (-587 *9)) (-4 *8 (-984 *5 *6 *7)) + (-4 *9 (-989 *5 *6 *7 *8)) (-4 *5 (-425)) (-4 *6 (-729)) + (-4 *7 (-783)) (-5 *2 (-707)) (-5 *1 (-987 *5 *6 *7 *8 *9)))) + ((*1 *2 *3 *4) + (-12 (-5 *3 (-587 *8)) (-5 *4 (-587 *9)) (-4 *8 (-984 *5 *6 *7)) + (-4 *9 (-1022 *5 *6 *7 *8)) (-4 *5 (-425)) (-4 *6 (-729)) + (-4 *7 (-783)) (-5 *2 (-707)) (-5 *1 (-1054 *5 *6 *7 *8 *9))))) +(((*1 *2 *3 *4 *5 *4) + (-12 (-5 *3 (-627 (-202))) (-5 *4 (-521)) (-5 *5 (-108)) + (-5 *2 (-959)) (-5 *1 (-682))))) (((*1 *2 *1) (-12 (-5 *2 (-1036 (-521) (-560 (-47)))) (-5 *1 (-47)))) ((*1 *2 *1) (-12 (-4 *3 (-918 *2)) (-4 *4 (-1141 *3)) (-4 *2 (-282)) (-5 *1 (-387 *2 *3 *4 *5)) (-4 *5 (-13 (-383 *3 *4) (-961 *3))))) ((*1 *2 *1) - (-12 (-4 *3 (-513)) (-4 *3 (-784)) (-5 *2 (-1036 *3 (-560 *1))) + (-12 (-4 *3 (-513)) (-4 *3 (-783)) (-5 *2 (-1036 *3 (-560 *1))) (-4 *1 (-404 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-1036 (-521) (-560 (-464)))) (-5 *1 (-464)))) ((*1 *2 *1) @@ -7564,7 +7518,7 @@ ((*1 *2 *1) (-12 (-4 *1 (-918 *2)) (-4 *2 (-513))))) (((*1 *1 *1) (-4 *1 (-91))) ((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-513))) (-5 *1 (-252 *3 *2)) + (-12 (-4 *3 (-13 (-783) (-513))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-404 *3) (-927))))) ((*1 *2 *2) (-12 (-4 *3 (-37 (-381 (-521)))) (-4 *4 (-1156 *3)) @@ -7582,53 +7536,49 @@ (-12 (-5 *2 (-1065 *3)) (-4 *3 (-37 (-381 (-521)))) (-5 *1 (-1071 *3))))) (((*1 *1) - (-12 (-4 *1 (-378)) (-2400 (|has| *1 (-6 -4224))) - (-2400 (|has| *1 (-6 -4216))))) - ((*1 *2 *1) (-12 (-4 *1 (-399 *2)) (-4 *2 (-1013)) (-4 *2 (-784)))) - ((*1 *2 *1) (-12 (-4 *1 (-767 *2)) (-4 *2 (-784)))) - ((*1 *1 *1 *1) (-4 *1 (-784))) 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(-5 *2 (-587 (-269 *4))) (-5 *1 (-571 *3 *4 *5)) (-4 *3 (-783)) + (-4 *4 (-13 (-157) (-654 (-381 (-521))))) (-14 *5 (-849))))) (((*1 *2 *1) (-12 (-5 *2 (-1036 (-521) (-560 (-47)))) (-5 *1 (-47)))) ((*1 *2 *1) (-12 (-4 *3 (-282)) (-4 *4 (-918 *3)) (-4 *5 (-1141 *4)) (-5 *2 (-1165 *6)) (-5 *1 (-387 *3 *4 *5 *6)) (-4 *6 (-13 (-383 *4 *5) (-961 *4))))) ((*1 *2 *1) - (-12 (-4 *3 (-970)) (-4 *3 (-784)) (-5 *2 (-1036 *3 (-560 *1))) + (-12 (-4 *3 (-970)) (-4 *3 (-783)) (-5 *2 (-1036 *3 (-560 *1))) (-4 *1 (-404 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-1036 (-521) (-560 (-464)))) (-5 *1 (-464)))) ((*1 *2 *1) @@ -7639,7 +7589,7 @@ (-4 *4 (|SubsetCategory| (-663) *3)))) ((*1 *2 *1) (-12 (-4 *1 (-918 *2)) (-4 *2 (-513))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-513))) (-5 *1 (-252 *3 *2)) + (-12 (-4 *3 (-13 (-783) (-513))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-404 *3) (-927))))) ((*1 *2 *2) (-12 (-4 *3 (-37 (-381 (-521)))) (-4 *4 (-1156 *3)) @@ -7654,27 +7604,33 @@ (-12 (-5 *2 (-1065 *3)) (-4 *3 (-37 (-381 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(-1123)) (-5 *1 (-136 *2 *4 *3)) + (-4 *3 (-1141 (-381 *4)))))) +(((*1 *2 *2 *2 *2) + (-12 (-4 *2 (-13 (-337) (-10 -8 (-15 ** ($ $ (-381 (-521))))))) + (-5 *1 (-1039 *3 *2)) (-4 *3 (-1141 *2))))) +(((*1 *2 *1) (-12 (-4 *1 (-614 *3)) (-4 *3 (-1119)) (-5 *2 (-108))))) (((*1 *2 *1) - (-12 (-5 *2 (-792)) (-5 *1 (-364 *3 *4 *5)) (-14 *3 (-707)) - (-14 *4 (-707)) (-4 *5 (-157))))) -(((*1 *2 *2 *1) (-12 (-4 *1 (-230 *2)) (-4 *2 (-1119))))) -(((*1 *2) (-12 (-5 *2 (-521)) (-5 *1 (-440)))) - ((*1 *2 *2) (-12 (-5 *2 (-521)) (-5 *1 (-440)))) - ((*1 *2) (-12 (-5 *2 (-521)) (-5 *1 (-856))))) -(((*1 *1 *2 *3) - (-12 (-5 *2 (-761)) (-5 *3 (-587 (-1084))) (-5 *1 (-762))))) -(((*1 *2 *3 *3 *2) (-12 (-5 *2 (-959)) (-5 *3 (-1084)) (-5 *1 (-171))))) + (-12 (-5 *2 (-801 (-893 *3) (-893 *3))) (-5 *1 (-893 *3)) + (-4 *3 (-894))))) +(((*1 *1 *1 *1 *1) (-4 *1 (-506)))) +(((*1 *2 *3) (-12 (-5 *3 (-1067)) (-5 *2 (-1170)) (-5 *1 (-410))))) (((*1 *2 *2) - (-12 (-4 *3 (-13 (-784) (-513))) (-5 *1 (-252 *3 *2)) + (-12 (-4 *3 (-13 (-783) (-513))) (-5 *1 (-252 *3 *2)) (-4 *2 (-13 (-404 *3) (-927))))) ((*1 *2 *2) (-12 (-4 *3 (-37 (-381 (-521)))) (-4 *4 (-1156 *3)) @@ -7689,41 +7645,31 @@ (-12 (-5 *2 (-1065 *3)) (-4 *3 (-37 (-381 (-521)))) (-5 *1 (-1071 *3)))) ((*1 *1 *1) (-4 *1 (-1108)))) -(((*1 *2 *3) - (-12 (-5 *3 (-310 *5 *6 *7 *8)) (-4 *5 (-404 *4)) (-4 *6 (-1141 *5)) - (-4 *7 (-1141 (-381 *6))) (-4 *8 (-316 *5 *6 *7)) - (-4 *4 (-13 (-784) (-513) (-961 (-521)))) (-5 *2 (-108)) - (-5 *1 (-840 *4 *5 *6 *7 *8)))) - ((*1 *2 *3) - (-12 (-5 *3 (-310 (-381 (-521)) *4 *5 *6)) - (-4 *4 (-1141 (-381 (-521)))) (-4 *5 (-1141 (-381 *4))) - (-4 *6 (-316 (-381 (-521)) *4 *5)) (-5 *2 (-108)) - (-5 *1 (-841 *4 *5 *6))))) -(((*1 *2 *3 *3 *3 *3 *4 *5) - (-12 (-5 *3 (-202)) (-5 *4 (-521)) - (-5 *5 (-3 (|:| |fn| (-362)) (|:| |fp| (-62 -4049)))) (-5 *2 (-959)) - (-5 *1 (-683))))) -(((*1 *2 *3) (-12 (-5 *2 (-392 *3)) (-5 *1 (-515 *3)) (-4 *3 (-506))))) -(((*1 *1) (-5 *1 (-132)))) -(((*1 *2 *3 *3) - (-12 (-5 *3 (-1067)) (-5 *2 (-1170)) (-5 *1 (-1097 *4 *5)) - (-4 *4 (-1013)) (-4 *5 (-1013))))) -(((*1 *2 *3) - (-12 (-4 *4 (-729)) - (-4 *5 (-13 (-784) (-10 -8 (-15 -1430 ((-1084) $))))) (-4 *6 (-513)) - (-5 *2 (-2 (|:| -2641 (-881 *6)) (|:| -2618 (-881 *6)))) - (-5 *1 (-669 *4 *5 *6 *3)) (-4 *3 (-878 (-381 (-881 *6)) *4 *5))))) -(((*1 *1 *2) - (-12 (-5 *2 (-587 (-850))) (-5 *1 (-1014 *3 *4)) (-14 *3 (-850)) - (-14 *4 (-850))))) -(((*1 *2 *3) - (-12 (-5 *3 (-224 *4 *5)) (-14 *4 (-587 (-1084))) (-4 *5 (-970)) - (-5 *2 (-453 *4 *5)) (-5 *1 (-873 *4 *5))))) -(((*1 *2 *3 *1) - (-12 (-4 *1 (-558 *3 *4)) (-4 *3 (-1013)) (-4 *4 (-1013)) - (-5 *2 (-108))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1045 *3)) (-4 *3 (-970)) (-5 *2 (-1073 3 *3)))) + ((*1 *1) (-12 (-5 *1 (-1073 *2 *3)) (-14 *2 (-849)) (-4 *3 (-970)))) + ((*1 *1 *1 *2) (-12 (-5 *2 (-1044 (-202))) (-5 *1 (-1167)))) + ((*1 *2 *1) (-12 (-5 *2 (-1044 (-202))) (-5 *1 (-1167))))) +(((*1 *2 *1 *3) + (-12 (-5 *3 (-707)) (-4 *1 (-1141 *4)) (-4 *4 (-970)) + (-5 *2 (-1165 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(-5 *3 (-1165 (-627 *4))) (-4 *4 (-157)) - (-5 *2 (-1165 (-627 (-381 (-881 *4))))) (-5 *1 (-168 *4)))) + (-5 *2 (-1165 (-627 (-381 (-880 *4))))) (-5 *1 (-168 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-587 *3)) (-4 *3 - (-13 (-784) - (-10 -8 (-15 -2544 ((-1067) $ (-1084))) (-15 -1678 ((-1170) $)) - (-15 -3971 ((-1170) $))))) + (-13 (-783) + (-10 -8 (-15 -2550 ((-1067) $ (-1084))) (-15 -1718 ((-1170) $)) + (-15 -2084 ((-1170) $))))) (-5 *1 (-192 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-929 10)) (-5 *1 (-195)))) ((*1 *2 *1) (-12 (-5 *2 (-381 (-521))) (-5 *1 (-195)))) - ((*1 *2 *1) (-12 (-5 *2 (-587 *3)) (-5 *1 (-222 *3)) (-4 *3 (-784)))) - ((*1 *1 *2) (-12 (-5 *2 (-587 *3)) (-4 *3 (-784)) (-5 *1 (-222 *3)))) + ((*1 *2 *1) (-12 (-5 *2 (-587 *3)) (-5 *1 (-222 *3)) (-4 *3 (-783)))) + ((*1 *1 *2) (-12 (-5 *2 (-587 *3)) (-4 *3 (-783)) (-5 *1 (-222 *3)))) ((*1 *2 *3) (-12 (-5 *3 (-1006 (-290 *4))) - (-4 *4 (-13 (-784) (-513) (-562 (-353)))) (-5 *2 (-1006 (-353))) + (-4 *4 (-13 (-783) (-513) (-562 (-353)))) (-5 *2 (-1006 (-353))) (-5 *1 (-234 *4)))) - ((*1 *1 *2) (-12 (-4 *1 (-242 *2)) (-4 *2 (-784)))) + ((*1 *1 *2) (-12 (-4 *1 (-242 *2)) (-4 *2 (-783)))) ((*1 *1 *2) (-12 (-5 *2 (-587 (-521))) (-5 *1 (-251)))) ((*1 *2 *1) (-12 (-4 *2 (-1141 *3)) (-5 *1 (-264 *3 *2 *4 *5 *6 *7)) @@ -10990,9 +10972,9 @@ ((*1 *1 *2) (-12 (-5 *2 (-1150 *4 *5 *6)) (-4 *4 (-13 (-27) (-1105) (-404 *3))) (-14 *5 (-1084)) (-14 *6 *4) - (-4 *3 (-13 (-784) (-961 (-521)) (-583 (-521)) (-425))) + (-4 *3 (-13 (-783) (-961 (-521)) (-583 (-521)) (-425))) (-5 *1 (-287 *3 *4 *5 *6)))) - ((*1 *2 *1) (-12 (-5 *2 (-792)) (-5 *1 (-304)))) + ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-304)))) ((*1 *2 *1) (-12 (-5 *2 (-290 *5)) (-5 *1 (-313 *3 *4 *5)) (-14 *3 (-587 (-1084))) (-14 *4 (-587 (-1084))) (-4 *5 (-361)))) @@ -11003,32 +10985,32 @@ (-12 (-4 *4 (-323)) (-4 *2 (-303 *4)) (-5 *1 (-321 *2 *4 *3)) (-4 *3 (-303 *4)))) ((*1 *2 *1) - (-12 (-4 *1 (-348 *3 *4)) (-4 *3 (-784)) (-4 *4 (-157)) + (-12 (-4 *1 (-348 *3 *4)) (-4 *3 (-783)) (-4 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(-4 *3 (-783)))) ((*1 *2 *1) - (-12 (-5 *2 (-886 (-886 (-886 *3)))) (-5 *1 (-615 *3)) + (-12 (-5 *2 (-885 (-885 (-885 *3)))) (-5 *1 (-615 *3)) (-4 *3 (-1013)))) ((*1 *1 *2) - (-12 (-5 *2 (-886 (-886 (-886 *3)))) (-4 *3 (-1013)) + (-12 (-5 *2 (-885 (-885 (-885 *3)))) (-4 *3 (-1013)) (-5 *1 (-615 *3)))) - ((*1 *2 *1) (-12 (-5 *2 (-756 *3)) (-5 *1 (-616 *3)) (-4 *3 (-784)))) + ((*1 *2 *1) (-12 (-5 *2 (-755 *3)) (-5 *1 (-616 *3)) (-4 *3 (-783)))) ((*1 *2 *3) (-12 (-5 *2 (-1 *3)) (-5 *1 (-620 *3)) (-4 *3 (-1013)))) ((*1 *1 *2) (-12 (-4 *3 (-970)) (-4 *1 (-625 *3 *4 *2)) (-4 *4 (-347 *3)) @@ -11192,18 +11174,18 @@ ((*1 *1 *2) (-12 (-4 *3 (-970)) (-5 *1 (-649 *3 *2)) (-4 *2 (-1141 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -2716 *3) (|:| -2997 *4))) - (-5 *1 (-650 *3 *4 *5)) (-4 *3 (-784)) (-4 *4 (-1013)) + (-12 (-5 *2 (-2 (|:| -2723 *3) (|:| -2246 *4))) + (-5 *1 (-650 *3 *4 *5)) (-4 *3 (-783)) (-4 *4 (-1013)) (-14 *5 (-1 (-108) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -2716 *3) (|:| -2997 *4))) (-4 *3 (-784)) + (-12 (-5 *2 (-2 (|:| -2723 *3) (|:| -2246 *4))) (-4 *3 (-783)) (-4 *4 (-1013)) (-5 *1 (-650 *3 *4 *5)) (-14 *5 (-1 (-108) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-157)) (-5 *1 (-652 *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 (-587 (-2 (|:| -2973 *3) (|:| -2517 *4)))) (-4 *3 (-970)) + (-12 (-5 *2 (-587 (-2 (|:| -2979 *3) (|:| -2523 *4)))) (-4 *3 (-970)) (-4 *4 (-663)) (-5 *1 (-672 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-521)) (-4 *1 (-700)))) ((*1 *1 *2) @@ -11212,28 +11194,28 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1084)) (|:| |fn| (-290 (-202))) - (|:| -2442 (-1008 (-777 (-202)))) (|:| |abserr| (-202)) + (|:| -1403 (-1008 (-776 (-202)))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (|:| |mdnia| (-2 (|:| |fn| (-290 (-202))) - (|:| -2442 (-587 (-1008 (-777 (-202))))) + (|:| -1403 (-587 (-1008 (-776 (-202))))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))))) (-5 *1 (-705)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-290 (-202))) - (|:| -2442 (-587 (-1008 (-777 (-202))))) (|:| |abserr| (-202)) + (|:| -1403 (-587 (-1008 (-776 (-202))))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (-5 *1 (-705)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1084)) (|:| |fn| (-290 (-202))) - (|:| -2442 (-1008 (-777 (-202)))) (|:| |abserr| (-202)) + (|:| -1403 (-1008 (-776 (-202)))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) (-5 *1 (-705)))) - ((*1 *2 *1) (-12 (-5 *2 (-792)) (-5 *1 (-705)))) + ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-705)))) ((*1 *2 *3) (-12 (-5 *2 (-710)) (-5 *1 (-709 *3)) (-4 *3 (-1119)))) ((*1 *1 *2) (-12 @@ -11242,59 +11224,59 @@ (|:| |fn| (-1165 (-290 (-202)))) (|:| |yinit| (-587 (-202))) (|:| |intvals| (-587 (-202))) (|:| |g| (-290 (-202))) (|:| |abserr| (-202)) (|:| |relerr| (-202)))) - (-5 *1 (-745)))) - ((*1 *2 *1) (-12 (-5 *2 (-792)) (-5 *1 (-745)))) + (-5 *1 (-744)))) + ((*1 *2 *1) (-12 (-5 *2 (-791)) (-5 *1 (-744)))) ((*1 *2 *1) - (-12 (-4 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singularities not yet evaluated"))) - (|:| -2442 - (-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 (-516))))) -(((*1 *2 *1) - (-12 (-5 *2 (-1015 (-1015 *3))) (-5 *1 (-833 *3)) (-4 *3 (-1013))))) -(((*1 *2 *2) (-12 (-5 *2 (-521)) (-5 *1 (-518))))) -(((*1 *2 *3 *4 *3 *5) - (-12 (-5 *3 (-1067)) (-5 *4 (-154 (-202))) (-5 *5 (-521)) - (-5 *2 (-959)) (-5 *1 (-695))))) -(((*1 *2 *3 *3 *4) - (-12 (-5 *3 (-587 (-453 *5 *6))) (-5 *4 (-794 *5)) - (-14 *5 (-587 (-1084))) (-5 *2 (-453 *5 *6)) (-5 *1 (-575 *5 *6)) - (-4 *6 (-425)))) + (-12 (-5 *3 (-1165 (-290 (-202)))) (-5 *4 (-587 (-1084))) + (-5 *2 (-627 (-290 (-202)))) (-5 *1 (-184)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-587 (-453 *5 *6))) (-5 *4 (-794 *5)) - (-14 *5 (-587 (-1084))) (-5 *2 (-453 *5 *6)) (-5 *1 (-575 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(-6 -4233)) (-4 *1 (-139 *3)) (-4 *3 (-1119)))) @@ -14637,38 +14480,35 @@ (-12 (-5 *2 (-1 (-108) *3)) (-4 *1 (-614 *3)) (-4 *3 (-1119)))) ((*1 *2 *1 *3) (|partial| -12 (-4 *1 (-1113 *4 *5 *3 *2)) (-4 *4 (-513)) - (-4 *5 (-729)) (-4 *3 (-784)) (-4 *2 (-984 *4 *5 *3)))) + (-4 *5 (-729)) (-4 *3 (-783)) (-4 *2 (-984 *4 *5 *3)))) ((*1 *2 *1 *3) (-12 (-5 *3 (-707)) (-5 *1 (-1117 *2)) (-4 *2 (-1119))))) -(((*1 *2 *3 *3 *3 *4 *4 *4 *4 *4 *5 *3 *3 *3 *6 *4 *3) - (-12 (-5 *4 (-627 (-202))) (-5 *5 (-627 (-521))) (-5 *6 (-202)) - (-5 *3 (-521)) (-5 *2 (-959)) (-5 *1 (-689))))) -(((*1 *2 *2) - (-12 (-5 *2 (-587 (-587 *3))) (-4 *3 (-784)) (-5 *1 (-1091 *3))))) -(((*1 *2 *3 *4 *5) - (|partial| -12 (-5 *3 (-707)) (-4 *4 (-282)) (-4 *6 (-1141 *4)) - (-5 *2 (-1165 (-587 *6))) (-5 *1 (-428 *4 *6)) (-5 *5 (-587 *6))))) -(((*1 *2 *2 *2) - (-12 (-5 *2 (-587 *6)) (-4 *6 (-984 *3 *4 *5)) (-4 *3 (-135)) - (-4 *3 (-282)) (-4 *3 (-513)) (-4 *4 (-729)) (-4 *5 (-784)) - (-5 *1 (-903 *3 *4 *5 *6))))) -(((*1 *2 *3 *4 *5 *5 *6) - (-12 (-5 *5 (-560 *4)) (-5 *6 (-1084)) - (-4 *4 (-13 (-404 *7) (-27) (-1105))) - (-4 *7 (-13 (-425) (-961 (-521)) (-784) (-135) (-583 (-521)))) - (-5 *2 - (-2 (|:| |particular| (-3 *4 "failed")) (|:| -2470 (-587 *4)))) - (-5 *1 (-523 *7 *4 *3)) (-4 *3 (-597 *4)) (-4 *3 (-1013))))) +(((*1 *2 *1 *3) (-12 (-5 *3 (-1067)) (-5 *2 (-1170)) (-5 *1 (-758))))) +(((*1 *2 *1) (|partial| -12 (-5 *2 (-560 *1)) (-4 *1 (-277))))) +(((*1 *2 *2) (-12 (-5 *2 (-353)) (-5 *1 (-1167)))) + ((*1 *2) (-12 (-5 *2 (-353)) (-5 *1 (-1167))))) +(((*1 *2 *3 *3 *4) + (-12 (-4 *5 (-425)) (-4 *6 (-729)) (-4 *7 (-783)) + (-4 *3 (-984 *5 *6 *7)) + (-5 *2 (-587 (-2 (|:| |val| *3) (|:| -1946 *4)))) + (-5 *1 (-990 *5 *6 *7 *3 *4)) (-4 *4 (-989 *5 *6 *7 *3))))) +(((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-521))) (-4 *3 (-970)) (-5 *1 (-546 *3)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-521))) (-4 *1 (-1125 *3)) (-4 *3 (-970)))) + ((*1 *1 *2 *1) + (-12 (-5 *2 (-1 *3 (-521))) (-4 *1 (-1156 *3)) (-4 *3 (-970))))) +(((*1 *2 *1) (-12 (-5 *2 (-108)) (-5 *1 (-1089))))) (((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-108) *3)) (-4 *3 (-1119)) (-5 *1 (-551 *3)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 (-108) *3)) (-4 *3 (-1119)) (-5 *1 (-1065 *3))))) (((*1 *1 *1) - (-12 (|has| *1 (-6 -4234)) (-4 *1 (-347 *2)) (-4 *2 (-1119)) - (-4 *2 (-784)))) - ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-108) *3 *3)) (|has| *1 (-6 -4234)) - (-4 *1 (-347 *3)) (-4 *3 (-1119))))) + (-12 (-5 *1 (-546 *2)) (-4 *2 (-37 (-381 (-521)))) (-4 *2 (-970))))) +(((*1 *2 *3 *4 *5 *6) + (-12 (-5 *6 (-849)) (-4 *5 (-282)) (-4 *3 (-1141 *5)) + (-5 *2 (-2 (|:| |plist| (-587 *3)) (|:| |modulo| *5))) + (-5 *1 (-433 *5 *3)) (-5 *4 (-587 *3))))) (((*1 *1 *1 *2) (-12 (-4 *1 (-46 *2 *3)) (-4 *2 (-970)) (-4 *3 (-728)) (-4 *2 (-337)))) @@ -14679,7 +14519,7 @@ ((*1 *1 *1 *1) (-4 *1 (-337))) ((*1 *1 *1 *2) (-12 (-5 *2 (-521)) (-5 *1 (-353)))) ((*1 *1 *2 *2) - (-12 (-5 *2 (-1036 *3 (-560 *1))) (-4 *3 (-513)) (-4 *3 (-784)) + (-12 (-5 *2 (-1036 *3 (-560 *1))) (-4 *3 (-513)) (-4 *3 (-783)) (-4 *1 (-404 *3)))) ((*1 *1 *1 *1) (-4 *1 (-446))) ((*1 *2 *2 *2) @@ -14701,12 +14541,12 @@ ((*1 *1 *1 *2) (-12 (-4 *1 (-625 *2 *3 *4)) (-4 *2 (-970)) (-4 *3 (-347 *2)) (-4 *4 (-347 *2)) (-4 *2 (-337)))) - ((*1 *1 *1 *1) (-5 *1 (-792))) + ((*1 *1 *1 *1) (-5 *1 (-791))) ((*1 *1 *1 *1) - (|partial| -12 (-5 *1 (-795 *2 *3 *4 *5)) (-4 *2 (-337)) + (|partial| -12 (-5 *1 (-794 *2 *3 *4 *5)) (-4 *2 (-337)) (-4 *2 (-970)) (-14 *3 (-587 (-1084))) (-14 *4 (-587 (-707))) (-14 *5 (-707)))) - ((*1 *1 *1 *1) (-12 (-5 *1 (-821 *2)) (-4 *2 (-1013)))) + ((*1 *1 *1 *1) (-12 (-5 *1 (-820 *2)) (-4 *2 (-1013)))) ((*1 *1 *2 *2) (-12 (-4 *1 (-918 *2)) (-4 *2 (-513)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-973 *3 *4 *2 *5 *6)) (-4 *2 (-970)) @@ -14715,70 +14555,52 @@ (-12 (-5 *2 (-1065 *3)) (-4 *3 (-970)) (-5 *1 (-1069 *3)))) ((*1 *1 *1 *2) (-12 (-4 *1 (-1172 *2)) (-4 *2 (-337)))) ((*1 *1 *1 *1) - (|partial| -12 (-4 *2 (-337)) (-4 *2 (-970)) (-4 *3 (-784)) + (|partial| -12 (-4 *2 (-337)) (-4 *2 (-970)) 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*3)) (-4 *3 (-970)) (-5 *1 (-1069 *3)))) - ((*1 *2 *2 *2) (-12 (-5 *2 (-872 (-202))) (-5 *1 (-1116)))) + ((*1 *2 *2 *2) (-12 (-5 *2 (-871 (-202))) (-5 *1 (-1116)))) ((*1 *1 *1 *1) (-12 (-4 *1 (-1163 *2)) (-4 *2 (-1119)) (-4 *2 (-21)))) ((*1 *1 *1) (-12 (-4 *1 (-1163 *2)) (-4 *2 (-1119)) (-4 *2 (-21))))) -(((*1 *2 *1) (-12 (-4 *1 (-242 *2)) (-4 *2 (-784)))) +(((*1 *2 *1) (-12 (-4 *1 (-242 *2)) (-4 *2 (-783)))) ((*1 *1 *2) - (|partial| -12 (-5 *2 (-1084)) (-5 *1 (-794 *3)) (-14 *3 (-587 *2)))) + (|partial| -12 (-5 *2 (-1084)) (-5 *1 (-793 *3)) (-14 *3 (-587 *2)))) ((*1 *2 *1) (-12 (-5 *2 (-1084)) (-5 *1 (-893 *3)) (-4 *3 (-894)))) ((*1 *2 *1) (-12 (-5 *2 (-1084)) (-5 *1 (-915)))) ((*1 *2 *1) (-12 (-5 *2 (-1084)) (-5 *1 (-1006 *3)) (-4 *3 (-1119)))) @@ -14808,86 +14630,86 @@ (-12 (-4 *1 (-1143 *3 *4)) (-4 *3 (-970)) (-4 *4 (-728)) (-5 *2 (-1084)))) ((*1 *2) (-12 (-5 *2 (-1084)) (-5 *1 (-1161 *3)) (-14 *3 *2)))) +(((*1 *2 *3 *3) + (-12 (-4 *4 (-513)) (-5 *2 (-2 (|:| |coef2| *3) (|:| -3052 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*5)) (-4 *5 (-157)) (-4 *6 (-157)) (-5 *2 (-154 *6)) (-5 *1 (-153 *5 *6)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 (-290 *3) (-290 *3))) (-4 *3 (-13 (-970) (-784))) + (-12 (-5 *2 (-1 (-290 *3) (-290 *3))) (-4 *3 (-13 (-970) (-783))) (-5 *1 (-200 *3 *4)) (-14 *4 (-587 (-1084))))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-217 *5 *6)) (-14 *5 (-707)) @@ -16094,8 +16062,8 @@ (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-627 *5)) (-4 *5 (-970)) (-4 *6 (-970)) (-5 *2 (-627 *6)) (-5 *1 (-279 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-290 *5)) (-4 *5 (-784)) - (-4 *6 (-784)) (-5 *2 (-290 *6)) (-5 *1 (-288 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-290 *5)) (-4 *5 (-783)) + (-4 *6 (-783)) (-5 *2 (-290 *6)) (-5 *1 (-288 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *9 *5)) (-5 *4 (-310 *5 *6 *7 *8)) (-4 *5 (-337)) (-4 *6 (-1141 *5)) (-4 *7 (-1141 (-381 *6))) (-4 *8 (-316 *5 *6 *7)) @@ -16136,8 +16104,8 @@ ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-513)) (-5 *1 (-392 *3)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-13 (-970) (-784))) - (-4 *6 (-13 (-970) (-784))) (-4 *2 (-404 *6)) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-13 (-970) (-783))) + (-4 *6 (-13 (-970) (-783))) (-4 *2 (-404 *6)) (-5 *1 (-395 *5 *4 *6 *2)) (-4 *4 (-404 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-1013)) (-4 *6 (-1013)) @@ -16146,15 +16114,15 @@ (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-460 *3)) (-4 *3 (-1119)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *1 (-477 *3 *4)) (-4 *3 (-1013)) - (-4 *4 (-784)))) + (-4 *4 (-783)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-538 *5)) (-4 *5 (-337)) (-4 *6 (-337)) (-5 *2 (-538 *6)) (-5 *1 (-537 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *6 *5)) - (-5 *4 (-3 (-2 (|:| -3100 *5) (|:| |coeff| *5)) "failed")) + (-5 *4 (-3 (-2 (|:| -1347 *5) (|:| |coeff| *5)) "failed")) (-4 *5 (-337)) (-4 *6 (-337)) - (-5 *2 (-2 (|:| -3100 *6) (|:| |coeff| *6))) + (-5 *2 (-2 (|:| -1347 *6) (|:| |coeff| *6))) (-5 *1 (-537 *5 *6)))) ((*1 *2 *3 *4) (|partial| -12 (-5 *3 (-1 *2 *5)) (-5 *4 (-3 *5 "failed")) @@ -16215,15 +16183,15 @@ (-5 *1 (-647 *5 *6 *4 *7 *8 *2)) (-4 *4 (-1141 (-381 *6))) (-4 *8 (-1141 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-970)) (-4 *9 (-970)) (-4 *5 (-784)) - (-4 *6 (-729)) (-4 *2 (-878 *9 *7 *5)) + (-12 (-5 *3 (-1 *9 *8)) (-4 *8 (-970)) (-4 *9 (-970)) (-4 *5 (-783)) + (-4 *6 (-729)) (-4 *2 (-877 *9 *7 *5)) (-5 *1 (-665 *5 *6 *7 *8 *9 *4 *2)) (-4 *7 (-729)) - (-4 *4 (-878 *8 *6 *5)))) + (-4 *4 (-877 *8 *6 *5)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-784)) (-4 *6 (-784)) (-4 *7 (-729)) - (-4 *9 (-970)) (-4 *2 (-878 *9 *8 *6)) + (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-783)) (-4 *6 (-783)) (-4 *7 (-729)) + (-4 *9 (-970)) (-4 *2 (-877 *9 *8 *6)) (-5 *1 (-666 *5 *6 *7 *8 *9 *4 *2)) (-4 *8 (-729)) - (-4 *4 (-878 *9 *7 *5)))) + (-4 *4 (-877 *9 *7 *5)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-672 *5 *7)) (-4 *5 (-970)) (-4 *6 (-970)) (-4 *7 (-663)) (-5 *2 (-672 *6 *7)) @@ -16236,58 +16204,58 @@ (-4 *6 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*6 (-729)) (-4 *2 (-13 (-1013) - (-10 -8 (-15 -1602 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-707)))))) - (-5 *1 (-880 *6 *7 *8 *5 *2)) (-4 *5 (-878 *8 *6 *7)))) + (-10 -8 (-15 -1628 ($ $ $)) (-15 * ($ $ $)) (-15 ** ($ $ (-707)))))) + (-5 *1 (-879 *6 *7 *8 *5 *2)) (-4 *5 (-877 *8 *6 *7)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-886 *5)) (-4 *5 (-1119)) - (-4 *6 (-1119)) (-5 *2 (-886 *6)) (-5 *1 (-885 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-885 *5)) (-4 *5 (-1119)) + (-4 *6 (-1119)) (-5 *2 (-885 *6)) (-5 *1 (-884 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-872 *5)) (-4 *5 (-970)) - (-4 *6 (-970)) (-5 *2 (-872 *6)) (-5 *1 (-907 *5 *6)))) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-871 *5)) (-4 *5 (-970)) + (-4 *6 (-970)) (-5 *2 (-871 *6)) (-5 *1 (-907 *5 *6)))) ((*1 *2 *3 *2) - (-12 (-5 *3 (-1 *2 (-881 *4))) (-4 *4 (-970)) - (-4 *2 (-878 (-881 *4) *5 *6)) (-4 *5 (-729)) + (-12 (-5 *3 (-1 *2 (-880 *4))) (-4 *4 (-970)) + (-4 *2 (-877 (-880 *4) *5 *6)) (-4 *5 (-729)) (-4 *6 - (-13 (-784) - (-10 -8 (-15 -1430 ((-1084) $)) - (-15 -1611 ((-3 $ "failed") (-1084)))))) + (-13 (-783) + (-10 -8 (-15 -1438 ((-1084) $)) + (-15 -1638 ((-3 $ "failed") (-1084)))))) (-5 *1 (-910 *4 *5 *6 *2)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-4 *5 (-513)) (-4 *6 (-513)) @@ -16312,14 +16280,14 @@ (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1008 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *2 (-1008 *6)) (-5 *1 (-1004 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1008 *5)) (-4 *5 (-782)) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1008 *5)) (-4 *5 (-781)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *2 (-587 *6)) (-5 *1 (-1004 *5 *6)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1006 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *2 (-1006 *6)) (-5 *1 (-1005 *5 *6)))) ((*1 *2 *3 *1) - (-12 (-5 *3 (-1 *4 *4)) (-4 *1 (-1009 *4 *2)) (-4 *4 (-782)) + (-12 (-5 *3 (-1 *4 *4)) (-4 *1 (-1009 *4 *2)) (-4 *4 (-781)) (-4 *2 (-1058 *4)))) ((*1 *2 *3 *4) (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1065 *5)) (-4 *5 (-1119)) @@ -16343,7 +16311,7 @@ (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1132 *5)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *2 (-1132 *6)) (-5 *1 (-1131 *5 *6)))) ((*1 *2 *3 *4) - (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1132 *5)) (-4 *5 (-782)) + (-12 (-5 *3 (-1 *6 *5)) (-5 *4 (-1132 *5)) (-4 *5 (-781)) (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *2 (-1065 *6)) (-5 *1 (-1131 *5 *6)))) ((*1 *2 *3 *4) @@ -16369,41 +16337,43 @@ (-4 *5 (-1119)) (-4 *6 (-1119)) (-5 *2 (-1165 *6)) (-5 *1 (-1164 *5 *6)))) ((*1 *1 *2 *1) - (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-1180 *3 *4)) (-4 *3 (-784)) + (-12 (-5 *2 (-1 *4 *4)) (-4 *1 (-1180 *3 *4)) (-4 *3 (-783)) (-4 *4 (-970)))) ((*1 *1 *2 *1) (-12 (-5 *2 (-1 *3 *3)) (-4 *3 (-970)) (-5 *1 (-1186 *3 *4)) - (-4 *4 (-780))))) -(((*1 *2 *1 *1) (-12 (-4 *1 (-282)) (-5 *2 (-108))))) -(((*1 *2 *2) - (-12 (-4 *3 (-13 (-513) (-784) (-961 (-521)))) (-5 *1 (-167 *3 *2)) - (-4 *2 (-13 (-27) (-1105) (-404 (-154 *3)))))) - ((*1 *2 *2 *3) - (-12 (-5 *3 (-1084)) (-4 *4 (-13 (-513) (-784) (-961 (-521)))) 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\ No newline at end of file |