diff options
| -rw-r--r-- | src/ChangeLog | 10 | ||||
| -rw-r--r-- | src/algebra/aggcat.spad.pamphlet | 9 | ||||
| -rw-r--r-- | src/algebra/attreg.spad.pamphlet | 5 | ||||
| -rw-r--r-- | src/algebra/mset.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/algebra/tree.spad.pamphlet | 3 | ||||
| -rw-r--r-- | src/share/algebra/browse.daase | 2726 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 5843 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 6 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 7923 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 19776 |
10 files changed, 18161 insertions, 18143 deletions
diff --git a/src/ChangeLog b/src/ChangeLog index 0eb674e2..b9fc989d 100644 --- a/src/ChangeLog +++ b/src/ChangeLog @@ -1,5 +1,15 @@ 2013-05-17 Gabriel Dos Reis <gdr@integrable-solutions.net> + * algebra/attreg.spad.pamphlet (AttributeRegistry): Remove + shallowlyMutble. + * algebra/aggcat.spad.pamphlet (BagAggregate): Extend + ShallowlyMutableAggregate. + (ExtensibleLinearAggregate): Likewise. + * algebra/mset.spad.pamphlet (Multiset): Likewise. + * algebra/tree.spad.pamphlet (Tree): Likewise. + +2013-05-17 Gabriel Dos Reis <gdr@integrable-solutions.net> + * algebra/tree.spad.pamphlet(BinaryTreeCategory): Extend ShallowlyMutableAggregate S. (BinarySearchTree): Remove redundant shallowlyMutable attribute. diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet index baa4a420..77a0b829 100644 --- a/src/algebra/aggcat.spad.pamphlet +++ b/src/algebra/aggcat.spad.pamphlet @@ -338,9 +338,7 @@ import List ++ and where the order in which objects are inserted determines the order ++ of extraction. ++ Examples of bags are stacks, queues, and dequeues. -BagAggregate(S:Type): Category == HomogeneousAggregate S with - shallowlyMutable - ++ shallowlyMutable means that elements of bags may be destructively changed. +BagAggregate(S:Type): Category == ShallowlyMutableAggregate S with bag: List S -> % ++ bag([x,y,...,z]) creates a bag with elements x,y,...,z. extract!: % -> S @@ -2052,7 +2050,7 @@ import FiniteLinearAggregate ++ Insertion and deletion however is generally slow since an entirely new ++ data structure must be created for the result. OneDimensionalArrayAggregate(S:Type): Category == - FiniteLinearAggregate S with shallowlyMutable + Join(FiniteLinearAggregate S,ShallowlyMutableAggregate S) add parts x == [qelt(x, i) for i in minIndex x .. maxIndex x] sort!(f, a) == quickSort(f, a)$FiniteLinearAggregateSort(S, %) @@ -2318,8 +2316,7 @@ import Integer ++ concatenation efficient. However, access to elements of these ++ extensible aggregates is generally slow since access is made from the end. ++ See \spadtype{FlexibleArray} for an exception. -ExtensibleLinearAggregate(S:Type):Category == LinearAggregate S with - shallowlyMutable +ExtensibleLinearAggregate(S:Type):Category == Join(LinearAggregate S,ShallowlyMutableAggregate S) with concat!: (%,S) -> % ++ concat!(u,x) destructively adds element x to the end of u. concat!: (%,%) -> % diff --git a/src/algebra/attreg.spad.pamphlet b/src/algebra/attreg.spad.pamphlet index 97ecc7a2..8fd926b0 100644 --- a/src/algebra/attreg.spad.pamphlet +++ b/src/algebra/attreg.spad.pamphlet @@ -21,11 +21,6 @@ AttributeRegistry(): Category == with commutative("*") ++ \spad{commutative("*")} is true if it has an operation ++ \spad{"*": (D,D) -> D} which is commutative. - shallowlyMutable - ++ \spad{shallowlyMutable} is true if its values - ++ have immediate components that are updateable (mutable). - ++ Note: the properties of any component domain are irrevelant to the - ++ \spad{shallowlyMutable} proper. unitsKnown ++ \spad{unitsKnown} is true if a monoid (a multiplicative semigroup ++ with a 1) has \spad{unitsKnown} means that diff --git a/src/algebra/mset.spad.pamphlet b/src/algebra/mset.spad.pamphlet index 9d564ee9..e4dd72e7 100644 --- a/src/algebra/mset.spad.pamphlet +++ b/src/algebra/mset.spad.pamphlet @@ -23,8 +23,7 @@ ++ Examples: ++ References: ++ Description: A multiset is a set with multiplicities. -Multiset(S: SetCategory): Join(MultisetAggregate S,FiniteAggregate S) with - shallowlyMutable +Multiset(S: SetCategory): Join(MultisetAggregate S,FiniteAggregate S,ShallowlyMutableAggregate S) with multiset: () -> % ++ multiset()$D creates an empty multiset of domain D. multiset: S -> % diff --git a/src/algebra/tree.spad.pamphlet b/src/algebra/tree.spad.pamphlet index 985f6dc5..d3c10e91 100644 --- a/src/algebra/tree.spad.pamphlet +++ b/src/algebra/tree.spad.pamphlet @@ -30,8 +30,7 @@ import List ++ Each tree is either empty or else is a {\it node} consisting of a value and ++ a list of (sub)trees. Tree(S: SetCategory): T==C where - T== Join(RecursiveAggregate S,FiniteAggregate S) with - shallowlyMutable + T== Join(RecursiveAggregate S,FiniteAggregate S,ShallowlyMutableAggregate S) with tree: (S,List %) -> % ++ tree(nd,ls) creates a tree with value nd, and children ++ ls. diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 585394a3..ed2de6cb 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(1963102 . 3577824390) +(1961975 . 3577831632) (-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."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}"))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,7 +46,7 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}. The \\spad{yi}'s are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p, y)} returns \\spad{[y1,...,yn]} such that \\spad{p(yi) = 0}; Note: the returned symbols \\spad{y1},{}...,{}yn are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-3993 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T)) +((-3992 . T) (-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3988 . T) (-3993 . T) (-3987 . T)) NIL (-30) ((|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,x,y,a..b,c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b, c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,x,y,xMin..xMax,yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) @@ -56,14 +56,14 @@ NIL ((|constructor| (NIL "This domain represents the syntax for an add-expression.")) (|body| (((|SpadAst|) $) "base(\\spad{d}) returns the actual body of the add-domain expression `d'.")) (|base| (((|SpadAst|) $) "\\spad{base(d)} returns the base domain(\\spad{s}) of the add-domain expression."))) NIL NIL -(-32 R -3093) +(-32 R -3092) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p, n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p, x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p, y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL -((|HasCategory| |#1| (QUOTE (-951 (-485))))) +((|HasCategory| |#1| (QUOTE (-950 (-484))))) (-33 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -3996))) +((|HasAttribute| |#1| (QUOTE -3995))) (-34) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|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} := empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL @@ -74,7 +74,7 @@ NIL NIL (-36 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Maybe| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|))) |#1| $) "\\spad{assoc(k,u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \\spad{nothing} if \\spad{u} has no key \\spad{k}."))) -((-3996 . T) (-3997 . T)) +((-3995 . T) (-3996 . T)) NIL (-37 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) @@ -82,20 +82,20 @@ NIL NIL (-38 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL (-39 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p, [a1,...,an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and \\spad{a1},{}...,{}an."))) NIL NIL -(-40 -3093 UP UPUP -2615) +(-40 -3092 UP UPUP -2614) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) -(-41 R -3093) +((-3988 |has| (-350 |#2|) (-312)) (-3993 |has| (-350 |#2|) (-312)) (-3987 |has| (-350 |#2|) (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090)))))) (|HasCategory| (-350 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) +(-41 R -3092) ((|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}'s which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f, [a1,...,an])} removes the \\spad{ai}'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| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) +((-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -364) (|devaluate| |#1|))))) (-42 OV E P) ((|constructor| (NIL "This package factors multivariate polynomials over the domain of \\spadtype{AlgebraicNumber} by allowing the user to specify a list of algebraic numbers generating the particular extension to factor over.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|) (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}. \\spad{p} is presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#3|) |#3| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,lan)} factors the polynomial \\spad{p} over the extension generated by the algebraic numbers given by the list \\spad{lan}."))) NIL @@ -106,31 +106,31 @@ NIL ((|HasCategory| |#1| (QUOTE (-258)))) (-44 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,..,an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{ai * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) +((-3992 |has| |#1| (-495)) (-3990 . T) (-3989 . T)) +((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-45 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-3996 . T) (-3997 . T)) -((OR (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))))) +((-3995 . T) (-3996 . T)) +((OR (-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-756)))) (-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))))) (-46 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL -((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) +((|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312)))) (-47 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#1|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(p,e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(r,e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#2| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-48) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) (-49) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function `f'.")) (|parameters| (((|List| (|Identifier|)) $) "\\spad{parameters(f)} returns the list of parameters bound by `f'."))) NIL NIL (-50 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,p)} changes each coefficient of \\spad{p} by the application of \\spad{f}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the homogeneous degree of \\spad{p}.")) (|retractable?| (((|Boolean|) $) "\\spad{retractable?(p)} tests if \\spad{p} is a 0-form,{} \\spadignore{i.e.} if degree(\\spad{p}) = 0.")) (|homogeneous?| (((|Boolean|) $) "\\spad{homogeneous?(p)} tests if all of the terms of \\spad{p} have the same degree.")) (|exp| (($ (|List| (|Integer|))) "\\spad{exp([i1,...in])} returns \\spad{u_1\\^{i_1} ... u_n\\^{i_n}}")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(n)} returns the \\spad{n}th multiplicative generator,{} a basis term.")) (|coefficient| ((|#1| $ $) "\\spad{coefficient(p,u)} returns the coefficient of the term in \\spad{p} containing the basis term \\spad{u} if such a term exists,{} and 0 otherwise. Error: if the second argument \\spad{u} is not a basis element.")) (|reductum| (($ $) "\\spad{reductum(p)},{} where \\spad{p} is an antisymmetric polynomial,{} returns \\spad{p} minus the leading term of \\spad{p} if \\spad{p} has at least two terms,{} and 0 otherwise.")) (|leadingBasisTerm| (($ $) "\\spad{leadingBasisTerm(p)} returns the leading basis term of antisymmetric polynomial \\spad{p}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(p)} returns the leading coefficient of antisymmetric polynomial \\spad{p}."))) -((-3993 . T)) +((-3992 . T)) NIL (-51) ((|constructor| (NIL "\\spadtype{Any} implements a type that packages up objects and their types in objects of \\spadtype{Any}. Roughly speaking that means that if \\spad{s : S} then when converted to \\spadtype{Any},{} the new object will include both the original object and its type. This is a way of converting arbitrary objects into a single type without losing any of the original information. Any object can be converted to one of \\spadtype{Any}. The original object can be recovered by `is-case' pattern matching as exemplified here and \\spad{AnyFunctions1}.")) (|obj| (((|None|) $) "\\spad{obj(a)} essentially returns the original object that was converted to \\spadtype{Any} except that the type is forced to be \\spadtype{None}.")) (|dom| (((|SExpression|) $) "\\spad{dom(a)} returns a \\spadgloss{LISP} form of the type of the original object that was converted to \\spadtype{Any}.")) (|any| (($ (|SExpression|) (|None|)) "\\spad{any(type,object)} is a technical function for creating an \\spad{object} of \\spadtype{Any}. Arugment \\spad{type} is a \\spadgloss{LISP} form for the \\spad{type} of \\spad{object}."))) @@ -144,7 +144,7 @@ NIL ((|constructor| (NIL "\\spad{ApplyUnivariateSkewPolynomial} (internal) allows univariate skew polynomials to be applied to appropriate modules.")) (|apply| ((|#2| |#3| (|Mapping| |#2| |#2|) |#2|) "\\spad{apply(p, f, m)} returns \\spad{p(m)} where the action is given by \\spad{x m = f(m)}. \\spad{f} must be an \\spad{R}-pseudo linear map on \\spad{M}."))) NIL NIL -(-54 |Base| R -3093) +(-54 |Base| R -3092) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,...,rn], expr, n)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,...,rn], expr)} applies the rules \\spad{r1},{}...,{}rn to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}rn is applicable to the expression."))) NIL NIL @@ -158,28 +158,28 @@ NIL NIL (-57 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,a)} assign \\spad{a(i,j)} to \\spad{f(a(i,j))} for all \\spad{i, j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,a,b,r)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} when both \\spad{a(i,j)} and \\spad{b(i,j)} exist; else \\spad{c(i,j) = f(r, b(i,j))} when \\spad{a(i,j)} does not exist; else \\spad{c(i,j) = f(a(i,j),r)} when \\spad{b(i,j)} does not exist; otherwise \\spad{c(i,j) = f(r,r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i, j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = f(a(i,j))} for all \\spad{i, j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,j,v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,i,v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,i,j,r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|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}'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}")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL (-58 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-59 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),...]}."))) NIL NIL (-60 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-61 R L) ((|constructor| (NIL "\\spadtype{AssociatedEquations} provides functions to compute the associated equations needed for factoring operators")) (|associatedEquations| (((|Record| (|:| |minor| (|List| (|PositiveInteger|))) (|:| |eq| |#2|) (|:| |minors| (|List| (|List| (|PositiveInteger|)))) (|:| |ops| (|List| |#2|))) |#2| (|PositiveInteger|)) "\\spad{associatedEquations(op, m)} returns \\spad{[w, eq, lw, lop]} such that \\spad{eq(w) = 0} where \\spad{w} is the given minor,{} and \\spad{lw_i = lop_i(w)} for all the other minors.")) (|uncouplingMatrices| (((|Vector| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{uncouplingMatrices(M)} returns \\spad{[A_1,...,A_n]} such that if \\spad{y = [y_1,...,y_n]} is a solution of \\spad{y' = M y},{} then \\spad{[\\$y_j',y_j'',...,y_j^{(n)}\\$] = \\$A_j y\\$} for all \\spad{j}'s.")) (|associatedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| (|List| (|PositiveInteger|))))) |#2| (|PositiveInteger|)) "\\spad{associatedSystem(op, m)} returns \\spad{[M,w]} such that the \\spad{m}-th associated equation system to \\spad{L} is \\spad{w' = M w}."))) NIL ((|HasCategory| |#1| (QUOTE (-312)))) (-62 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}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-63 S) ((|constructor| (NIL "This is the category of Spad abstract syntax trees."))) NIL @@ -201,12 +201,12 @@ NIL NIL NIL (-68) -((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|shallowlyMutable| ((|attribute|) "\\spad{shallowlyMutable} is \\spad{true} if its values have immediate components that are updateable (mutable). Note: the properties of any component domain are irrevelant to the \\spad{shallowlyMutable} proper.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) -((-3996 . T) ((-3998 "*") . T) (-3997 . T) (-3993 . T) (-3991 . T) (-3990 . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3992 . T) (-3995 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3983 . T)) +((|constructor| (NIL "This category exports the attributes in the AXIOM Library")) (|canonical| ((|attribute|) "\\spad{canonical} is \\spad{true} if and only if distinct elements have distinct data structures. For example,{} a domain of mathematical objects which has the \\spad{canonical} attribute means that two objects are mathematically equal if and only if their data structures are equal.")) (|multiplicativeValuation| ((|attribute|) "\\spad{multiplicativeValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.")) (|additiveValuation| ((|attribute|) "\\spad{additiveValuation} implies \\spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} is \\spad{true} if all of its ideals are finitely generated.")) (|central| ((|attribute|) "\\spad{central} is \\spad{true} if,{} given an algebra over a ring \\spad{R},{} the image of \\spad{R} is the center of the algebra,{} \\spadignore{i.e.} the set of members of the algebra which commute with all others is precisely the image of \\spad{R} in the algebra.")) (|partiallyOrderedSet| ((|attribute|) "\\spad{partiallyOrderedSet} is \\spad{true} if a set with \\spadop{<} which is transitive,{} but \\spad{not(a < b or a = b)} does not necessarily imply \\spad{b<a}.")) (|arbitraryPrecision| ((|attribute|) "\\spad{arbitraryPrecision} means the user can set the precision for subsequent calculations.")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalsClosed} is \\spad{true} if \\spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.")) (|canonicalUnitNormal| ((|attribute|) "\\spad{canonicalUnitNormal} is \\spad{true} if we can choose a canonical representative for each class of associate elements,{} that is \\spad{associates?(a,b)} returns \\spad{true} if and only if \\spad{unitCanonical(a) = unitCanonical(b)}.")) (|noZeroDivisors| ((|attribute|) "\\spad{noZeroDivisors} is \\spad{true} if \\spad{x * y \\~~= 0} implies both \\spad{x} and \\spad{y} are non-zero.")) (|rightUnitary| ((|attribute|) "\\spad{rightUnitary} is \\spad{true} if \\spad{x * 1 = x} for all \\spad{x}.")) (|leftUnitary| ((|attribute|) "\\spad{leftUnitary} is \\spad{true} if \\spad{1 * x = x} for all \\spad{x}.")) (|unitsKnown| ((|attribute|) "\\spad{unitsKnown} is \\spad{true} if a monoid (a multiplicative semigroup with a 1) has \\spad{unitsKnown} means that the operation \\spadfun{recip} can only return \"failed\" if its argument is not a unit.")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} is \\spad{true} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative.")) (|finiteAggregate| ((|attribute|) "\\spad{finiteAggregate} is \\spad{true} if it is an aggregate with a finite number of elements."))) +((-3995 . T) ((-3997 "*") . T) (-3992 . T) (-3990 . T) (-3989 . T) (-3988 . T) (-3993 . T) (-3987 . T) (-3986 . T) (-3985 . T) (-3984 . T) (-3983 . T) (-3991 . T) (-3994 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-3982 . T)) NIL (-69 R) ((|constructor| (NIL "Automorphism \\spad{R} is the multiplicative group of automorphisms of \\spad{R}.")) (|morphism| (($ (|Mapping| |#1| |#1| (|Integer|))) "\\spad{morphism(f)} returns the morphism given by \\spad{f^n(x) = f(x,n)}.") (($ (|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|)) "\\spad{morphism(f, g)} returns the invertible morphism given by \\spad{f},{} where \\spad{g} is the inverse of \\spad{f}..") (($ (|Mapping| |#1| |#1|)) "\\spad{morphism(f)} returns the non-invertible morphism given by \\spad{f}."))) -((-3993 . T)) +((-3992 . T)) NIL (-70 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a, [b1,...,bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,...,bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a, b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{b}."))) @@ -222,24 +222,24 @@ NIL NIL (-73 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 pl and 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{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 ls.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n, s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-74 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-3998 "*")))) +((|HasAttribute| |#1| (QUOTE (-3997 "*")))) (-75 A S) -((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) +((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#2| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#2| $) "\\spad{insert!(x,u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#2| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#2|)) "\\spad{bag([x,y,...,z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}."))) NIL NIL (-76 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."))) -((-3997 . T)) +((|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}."))) +((-3996 . T)) NIL (-77) ((|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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) (-78) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Identifier|) (|List| (|Property|))) "\\spad{binding(n,props)} constructs a binding with name `n' and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Identifier|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -254,11 +254,11 @@ NIL NIL (-81) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1013)))) (|HasCategory| (-85) (QUOTE (-553 (-473)))) (|HasCategory| (-85) (QUOTE (-756))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-85) (QUOTE (-1013))) (|HasCategory| (-85) (QUOTE (-552 (-772)))) (|HasCategory| (-85) (QUOTE (-72)))) (-82 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}"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL (-83 S) ((|constructor| (NIL "This is the category of Boolean logic structures.")) (|or| (($ $ $) "\\spad{x or y} returns the disjunction of \\spad{x} and \\spad{y}.")) (|and| (($ $ $) "\\spad{x and y} returns the conjunction of \\spad{x} and \\spad{y}.")) (|not| (($ $) "\\spad{not x} returns the complement or negation of \\spad{x}."))) @@ -280,22 +280,22 @@ NIL ((|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 [\\spad{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 NIL -(-88 -3093 UP) +(-88 -3092 UP) ((|constructor| (NIL "\\spadtype{BoundIntegerRoots} provides functions to find lower bounds on the integer roots of a polynomial.")) (|integerBound| (((|Integer|) |#2|) "\\spad{integerBound(p)} returns a lower bound on the negative integer roots of \\spad{p},{} and 0 if \\spad{p} has no negative integer roots."))) NIL NIL (-89 |p|) ((|constructor| (NIL "Stream-based implementation of Zp: \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-90 |p|) ((|constructor| (NIL "Stream-based implementation of 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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-89 |#1|) (QUOTE (-822))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-89 |#1|) (QUOTE (-934))) (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-741))) (|HasCategory| (-89 |#1|) (QUOTE (-757)))) (|HasCategory| (-89 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-1067))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-89 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-822)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-89 |#1|) (QUOTE (-821))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-120))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-473)))) (|HasCategory| (-89 |#1|) (QUOTE (-933))) (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-89 |#1|) (QUOTE (-740))) (|HasCategory| (-89 |#1|) (QUOTE (-756)))) (|HasCategory| (-89 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-1066))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-330)))) (|HasCategory| (-89 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-89 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-89 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-89 |#1|) (QUOTE (-189))) (|HasCategory| (-89 |#1|) (QUOTE (-811 (-1090)))) (|HasCategory| (-89 |#1|) (QUOTE (-190))) (|HasCategory| (-89 |#1|) (QUOTE (-809 (-1090)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -89) (|devaluate| |#1|)) (|%list| (QUOTE -89) (|devaluate| |#1|)))) (|HasCategory| (-89 |#1|) (QUOTE (-258))) (|HasCategory| (-89 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-89 |#1|) (QUOTE (-821)))) (|HasCategory| (-89 |#1|) (QUOTE (-118))))) (-91 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" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) +((|HasAttribute| |#1| (QUOTE -3996))) (-92 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,\"right\",b)} (also written \\axiom{\\spad{b} . right := \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,\"left\",b)} (also written \\axiom{a . left := \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "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 @@ -306,40 +306,40 @@ NIL NIL (-94 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"))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-95 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) NIL NIL (-96) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL (-97 A S) -((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) +((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) NIL NIL (-98 S) -((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-3997 . T) (-3996 . T)) +((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,v,right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}."))) +((-3996 . T) (-3995 . T)) NIL (-99 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#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."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-100 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."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-101) ((|constructor| (NIL "Byte is the datatype of 8-bit sized unsigned integer values.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "bitor(\\spad{x},{}\\spad{y}) returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'.")) (|byte| (($ (|NonNegativeInteger|)) "\\spad{byte(x)} injects the unsigned integer value `v' into the Byte algebra. `v' must be non-negative and less than 256."))) NIL NIL (-102) ((|constructor| (NIL "ByteBuffer provides datatype for buffers of bytes. This domain differs from PrimitiveArray Byte in that it is not as rigid as PrimitiveArray Byte. That is,{} the typical use of ByteBuffer is to pre-allocate a vector of Byte of some capacity `n'. The array can then store up to `n' bytes. The actual interesting bytes count (the length of the buffer) is therefore different from the capacity. The length is no more than the capacity,{} but it can be set dynamically as needed. This functionality is used for example when reading bytes from input/output devices where we use buffers to transfer data in and out of the system. Note: a value of type ByteBuffer is 0-based indexed,{} as opposed \\indented{6}{Vector,{} but not unlike PrimitiveArray Byte.}")) (|setLength!| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{setLength!(buf,n)} sets the number of active bytes in the `buf'. Error if `n' is more than the capacity.")) (|capacity| (((|NonNegativeInteger|) $) "\\spad{capacity(buf)} returns the pre-allocated maximum size of `buf'.")) (|byteBuffer| (($ (|NonNegativeInteger|)) "\\spad{byteBuffer(n)} creates a buffer of capacity \\spad{n},{} and length 0."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-757)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) (|HasCategory| (-101) (QUOTE (-553 (-773)))) (|HasCategory| (-101) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-101) (QUOTE (-757))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-101) (QUOTE (-1014))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1014))))) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-756)))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) (|HasCategory| (-101) (QUOTE (-552 (-772)))) (|HasCategory| (-101) (QUOTE (-553 (-473)))) (OR (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-101) (QUOTE (-756))) (OR (|HasCategory| (-101) (QUOTE (-72))) (|HasCategory| (-101) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-101) (QUOTE (-1013))) (|HasCategory| (-101) (QUOTE (-72))) (-12 (|HasCategory| (-101) (QUOTE (-260 (-101)))) (|HasCategory| (-101) (QUOTE (-1013))))) (-103) ((|constructor| (NIL "This datatype describes byte order of machine values stored memory.")) (|unknownEndian| (($) "\\spad{unknownEndian} for none of the above.")) (|bigEndian| (($) "\\spad{bigEndian} describes big endian host")) (|littleEndian| (($) "\\spad{littleEndian} describes little endian host"))) NIL @@ -358,13 +358,13 @@ NIL NIL (-107) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,D) -> D} which is commutative."))) -(((-3998 "*") . T)) +(((-3997 "*") . T)) NIL -(-108 |minix| -2622 R) +(-108 |minix| -2621 R) ((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,...idim) = +1/0/-1} if \\spad{i1,...,idim} is an even/is nota /is an odd permutation of \\spad{minix,...,minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,[i1,...,idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t, [4,1,2,3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,i,j,k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,i,j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,2,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(i,k,j,l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = t(l,j,k,i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,i,j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,1,3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,j) = sum(h=1..dim,t(h,i,h,j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,i,s,j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,2,t,1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,j,k,l) = sum(h=1..dim,s(i,h,j)*t(h,k,l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,rank t, s, 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N, t[i1,..,iN,k]*s[k,j1,..,jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,j,k,l) = s(i,j)*t(k,l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,[i1,...,iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k,l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,i,j,k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,i,j)} gives a component of a rank 2 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree."))) NIL NIL -(-109 |minix| -2622 S T$) +(-109 |minix| -2621 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL @@ -386,8 +386,8 @@ NIL NIL (-114) ((|constructor| (NIL "This domain allows classes of characters to be defined and manipulated efficiently.")) (|alphanumeric| (($) "\\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}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) +((-3995 . T) (-3985 . T) (-3996 . T)) +((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-320)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (|HasCategory| (-117) (QUOTE (-320))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (-115 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL @@ -402,7 +402,7 @@ NIL NIL (-118) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Maybe| $) $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-3993 . T)) +((-3992 . T)) NIL (-119 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial 'x,{} then it returns the characteristic polynomial expressed as a polynomial in 'x."))) @@ -410,9 +410,9 @@ NIL NIL (-120) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-3993 . T)) +((-3992 . T)) NIL -(-121 -3093 UP UPUP) +(-121 -3092 UP UPUP) ((|constructor| (NIL "Tools to send a point to infinity on an algebraic curve.")) (|chvar| (((|Record| (|:| |func| |#3|) (|:| |poly| |#3|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) |#3| |#3|) "\\spad{chvar(f(x,y), p(x,y))} returns \\spad{[g(z,t), q(z,t), c1(z), c2(z), n]} such that under the change of variable \\spad{x = c1(z)},{} \\spad{y = t * c2(z)},{} one gets \\spad{f(x,y) = g(z,t)}. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{z} and \\spad{t} is \\spad{q(z, t) = 0}.")) (|eval| ((|#3| |#3| (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{eval(p(x,y), f(x), g(x))} returns \\spad{p(f(x), y * g(x))}.")) (|goodPoint| ((|#1| |#3| |#3|) "\\spad{goodPoint(p, q)} returns an integer a such that a is neither a pole of \\spad{p(x,y)} nor a branch point of \\spad{q(x,y) = 0}.")) (|rootPoly| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| (|Fraction| |#2|)) (|:| |radicand| |#2|)) (|Fraction| |#2|) (|NonNegativeInteger|)) "\\spad{rootPoly(g, n)} returns \\spad{[m, c, P]} such that \\spad{c * g ** (1/n) = P ** (1/m)} thus if \\spad{y**n = g},{} then \\spad{z**m = P} where \\spad{z = c * y}.")) (|radPoly| (((|Union| (|Record| (|:| |radicand| (|Fraction| |#2|)) (|:| |deg| (|NonNegativeInteger|))) "failed") |#3|) "\\spad{radPoly(p(x, y))} returns \\spad{[c(x), n]} if \\spad{p} is of the form \\spad{y**n - c(x)},{} \"failed\" otherwise.")) (|mkIntegral| (((|Record| (|:| |coef| (|Fraction| |#2|)) (|:| |poly| |#3|)) |#3|) "\\spad{mkIntegral(p(x,y))} returns \\spad{[c(x), q(x,z)]} such that \\spad{z = c * y} is integral. The algebraic relation between \\spad{x} and \\spad{y} is \\spad{p(x, y) = 0}. The algebraic relation between \\spad{x} and \\spad{z} is \\spad{q(x, z) = 0}."))) NIL NIL @@ -423,14 +423,14 @@ NIL (-123 A S) ((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasAttribute| |#1| (QUOTE -3996))) +((|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasAttribute| |#1| (QUOTE -3995))) (-124 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|) $) "\\spad{select(p,u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) == [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) == [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} ~= \\spad{y}]}.") (($ (|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{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,u,x,z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,u,x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL NIL (-125 |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."))) -((-3991 . T) (-3990 . T) (-3993 . T)) +((-3990 . T) (-3989 . T) (-3992 . T)) NIL (-126) ((|constructor| (NIL "\\indented{1}{The purpose of this package is to provide reasonable plots of} functions with singularities.")) (|clipWithRanges| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|)))) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{clipWithRanges(pointLists,xMin,xMax,yMin,yMax)} performs clipping on a list of lists of points,{} \\spad{pointLists}. Clipping is done within the specified ranges of \\spad{xMin},{} \\spad{xMax} and \\spad{yMin},{} \\spad{yMax}. This function is used internally by the \\fakeAxiomFun{iClipParametric} subroutine in this package.")) (|clipParametric| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clipParametric(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clipParametric(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.")) (|clip| (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{clip(ll)} performs two-dimensional clipping on a list of lists of points,{} \\spad{ll}; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|List| (|Point| (|DoubleFloat|)))) "\\spad{clip(l)} performs two-dimensional clipping on a curve \\spad{l},{} which is a list of points; the default parameters \\spad{1/2} for the fraction and \\spad{5/1} for the scale are used in the \\fakeAxiomFun{iClipParametric} subroutine,{} which is called by this function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|) (|Fraction| (|Integer|)) (|Fraction| (|Integer|))) "\\spad{clip(p,frac,sc)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable \\spad{y = f(x)}; the fraction parameter is specified by \\spad{frac} and the scale parameter is specified by \\spad{sc} for use in the \\spadfun{clip} function.") (((|Record| (|:| |brans| (|List| (|List| (|Point| (|DoubleFloat|))))) (|:| |xValues| (|Segment| (|DoubleFloat|))) (|:| |yValues| (|Segment| (|DoubleFloat|)))) (|Plot|)) "\\spad{clip(p)} performs two-dimensional clipping on a plot,{} \\spad{p},{} from the domain \\spadtype{Plot} for the graph of one variable,{} \\spad{y = f(x)}; the default parameters \\spad{1/4} for the fraction and \\spad{5/1} for the scale are used in the \\spadfun{clip} function."))) @@ -452,7 +452,7 @@ NIL ((|constructor| (NIL "Color() specifies a domain of 27 colors provided in the \\Language{} system (the colors mix additively).")) (|color| (($ (|Integer|)) "\\spad{color(i)} returns a color of the indicated hue \\spad{i}.")) (|numberOfHues| (((|PositiveInteger|)) "\\spad{numberOfHues()} returns the number of total hues,{} set in totalHues.")) (|hue| (((|Integer|) $) "\\spad{hue(c)} returns the hue index of the indicated color \\spad{c}.")) (|blue| (($) "\\spad{blue()} returns the position of the blue hue from total hues.")) (|green| (($) "\\spad{green()} returns the position of the green hue from total hues.")) (|yellow| (($) "\\spad{yellow()} returns the position of the yellow hue from total hues.")) (|red| (($) "\\spad{red()} returns the position of the red hue from total hues.")) (+ (($ $ $) "\\spad{c1 + c2} additively mixes the two colors \\spad{c1} and \\spad{c2}.")) (* (($ (|DoubleFloat|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}.") (($ (|PositiveInteger|) $) "\\spad{s * c},{} returns the color \\spad{c},{} whose weighted shade has been scaled by \\spad{s}."))) NIL NIL -(-131 R -3093) +(-131 R -3092) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n), n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n), n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})/P(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n), n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n), n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f, x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} n!.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n, r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} n!/(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n, r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} n!/(r! * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -483,10 +483,10 @@ NIL (-138 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 (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3992)) (|HasAttribute| |#2| (QUOTE -3995)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496)))) +((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3991)) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495)))) (-139 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})"))) -((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 OR (|has| |#1| (-495)) (-12 (|has| |#1| (-258)) (|has| |#1| (-821)))) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3991 |has| |#1| (-6 -3991)) (-3994 |has| |#1| (-6 -3994)) (-1376 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-140 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."))) @@ -498,8 +498,8 @@ NIL NIL (-142 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}."))) -((-3989 OR (|has| |#1| (-496)) (-12 (|has| |#1| (-258)) (|has| |#1| (-822)))) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3992 |has| |#1| (-6 -3992)) (-3995 |has| |#1| (-6 -3995)) (-1377 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . 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T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . 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(|map| (((|Complex| |#2|) (|Mapping| |#2| |#1|) (|Complex| |#1|)) "\\spad{map(f,u)} maps \\spad{f} onto real and imaginary parts of \\spad{u}."))) NIL @@ -514,7 +514,7 @@ NIL NIL (-146) ((|constructor| (NIL "The category of commutative rings with unity,{} \\spadignore{i.e.} rings where \\spadop{*} is commutative,{} and which have a multiplicative identity. element.")) (|commutative| ((|attribute| "*") "multiplication is commutative."))) -(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-147) ((|constructor| (NIL "This category is the root of the I/O conduits.")) (|close!| (($ $) "\\spad{close!(c)} closes the conduit \\spad{c},{} changing its state to one that is invalid for future read or write operations."))) @@ -522,7 +522,7 @@ NIL NIL (-148 R) ((|constructor| (NIL "\\spadtype{ContinuedFraction} implements general \\indented{1}{continued fractions.\\space{2}This version is not restricted to simple,{}} \\indented{1}{finite fractions and uses the \\spadtype{Stream} as a} \\indented{1}{representation.\\space{2}The arithmetic functions assume that the} \\indented{1}{approximants alternate below/above the convergence point.} \\indented{1}{This is enforced by ensuring the partial numerators and partial} \\indented{1}{denominators are greater than 0 in the Euclidean domain view of \\spad{R}} \\indented{1}{(\\spadignore{i.e.} \\spad{sizeLess?(0, x)}).}")) (|complete| (($ $) "\\spad{complete(x)} causes all entries in \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed. If \\spadvar{\\spad{x}} is an infinite continued fraction,{} a user-initiated interrupt is necessary to stop the computation.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(x,n)} causes the first \\spadvar{\\spad{n}} entries in the continued fraction \\spadvar{\\spad{x}} to be computed. Normally entries are only computed as needed.")) (|denominators| (((|Stream| |#1|) $) "\\spad{denominators(x)} returns the stream of denominators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|numerators| (((|Stream| |#1|) $) "\\spad{numerators(x)} returns the stream of numerators of the approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|convergents| (((|Stream| (|Fraction| |#1|)) $) "\\spad{convergents(x)} returns the stream of the convergents of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be finite.")) (|approximants| (((|Stream| (|Fraction| |#1|)) $) "\\spad{approximants(x)} returns the stream of approximants of the continued fraction \\spadvar{\\spad{x}}. If the continued fraction is finite,{} then the stream will be infinite and periodic with period 1.")) (|reducedForm| (($ $) "\\spad{reducedForm(x)} puts the continued fraction \\spadvar{\\spad{x}} in reduced form,{} \\spadignore{i.e.} the function returns an equivalent continued fraction of the form \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(x)} extracts the whole part of \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{wholePart(x) = b0}.")) (|partialQuotients| (((|Stream| |#1|) $) "\\spad{partialQuotients(x)} extracts the partial quotients in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialQuotients(x) = [b0,b1,b2,b3,...]}.")) (|partialDenominators| (((|Stream| |#1|) $) "\\spad{partialDenominators(x)} extracts the denominators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialDenominators(x) = [b1,b2,b3,...]}.")) (|partialNumerators| (((|Stream| |#1|) $) "\\spad{partialNumerators(x)} extracts the numerators in \\spadvar{\\spad{x}}. That is,{} if \\spad{x = continuedFraction(b0, [a1,a2,a3,...], [b1,b2,b3,...])},{} then \\spad{partialNumerators(x) = [a1,a2,a3,...]}.")) (|reducedContinuedFraction| (($ |#1| (|Stream| |#1|)) "\\spad{reducedContinuedFraction(b0,b)} constructs a continued fraction in the following way: if \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + 1/(b1 + 1/(b2 + ...))}. That is,{} the result is the same as \\spad{continuedFraction(b0,[1,1,1,...],[b1,b2,b3,...])}.")) (|continuedFraction| (($ |#1| (|Stream| |#1|) (|Stream| |#1|)) "\\spad{continuedFraction(b0,a,b)} constructs a continued fraction in the following way: if \\spad{a = [a1,a2,...]} and \\spad{b = [b1,b2,...]} then the result is the continued fraction \\spad{b0 + a1/(b1 + a2/(b2 + ...))}.") (($ (|Fraction| |#1|)) "\\spad{continuedFraction(r)} converts the fraction \\spadvar{\\spad{r}} with components of type \\spad{R} to a continued fraction over \\spad{R}."))) -(((-3998 "*") . T) (-3989 . T) (-3994 . T) (-3988 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") . T) (-3988 . T) (-3993 . T) (-3987 . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-149) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(c,n)} returns the first binding associated with `n'. Otherwise `nothing.")) (|push| (($ (|Binding|) $) "\\spad{push(c,b)} augments the contour with binding `b'.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -539,7 +539,7 @@ NIL (-152 R S CS) ((|constructor| (NIL "This package supports matching patterns involving complex expressions")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(cexpr, pat, res)} matches the pattern \\spad{pat} to the complex expression \\spad{cexpr}. res contains the variables of \\spad{pat} which are already matched and their matches."))) NIL -((|HasCategory| (-858 |#2|) (|%list| (QUOTE -797) (|devaluate| |#1|)))) +((|HasCategory| (-857 |#2|) (|%list| (QUOTE -796) (|devaluate| |#1|)))) (-153 R) ((|constructor| (NIL "This package \\undocumented{}")) (|multiEuclideanTree| (((|List| |#1|) (|List| |#1|) |#1|) "\\spad{multiEuclideanTree(l,r)} \\undocumented{}")) (|chineseRemainder| (((|List| |#1|) (|List| (|List| |#1|)) (|List| |#1|)) "\\spad{chineseRemainder(llv,lm)} returns a list of values,{} each of which corresponds to the Chinese remainder of the associated element of \\axiom{\\spad{llv}} and axiom{\\spad{lm}}. This is more efficient than applying chineseRemainder several times.") ((|#1| (|List| |#1|) (|List| |#1|)) "\\spad{chineseRemainder(lv,lm)} returns a value \\axiom{\\spad{v}} such that,{} if \\spad{x} is \\axiom{\\spad{lv}.\\spad{i}} modulo \\axiom{\\spad{lm}.\\spad{i}} for all \\axiom{\\spad{i}},{} then \\spad{x} is \\axiom{\\spad{v}} modulo \\axiom{\\spad{lm}(1)*lm(2)*...*lm(\\spad{n})}.")) (|modTree| (((|List| |#1|) |#1| (|List| |#1|)) "\\spad{modTree(r,l)} \\undocumented{}"))) NIL @@ -576,7 +576,7 @@ NIL ((|constructor| (NIL "This domain enumerates the three kinds of constructors available in OpenAxiom: category constructors,{} domain constructors,{} and package constructors.")) (|package| (($) "`package' is the kind of package constructors.")) (|domain| (($) "`domain' is the kind of domain constructors")) (|category| (($) "`category' is the kind of category constructors"))) NIL NIL -(-162 R -3093) +(-162 R -3092) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -604,23 +604,23 @@ NIL ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a dual vector space basis,{} given by symbols.}")) (|dual| (($ (|LinearBasis| |#1|)) "\\spad{dual x} constructs the dual vector of a linear element which is part of a basis."))) NIL NIL -(-169 -3093 UP UPUP R) +(-169 -3092 UP UPUP R) ((|constructor| (NIL "This package provides functions for computing the residues of a function on an algebraic curve.")) (|doubleResultant| ((|#2| |#4| (|Mapping| |#2| |#2|)) "\\spad{doubleResultant(f, ')} returns \\spad{p}(\\spad{x}) whose roots are rational multiples of the residues of \\spad{f} at all its finite poles. Argument ' is the derivation to use."))) NIL NIL -(-170 -3093 FP) +(-170 -3092 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,k,v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and q= size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,k,v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,k,v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-171) ((|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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) (-172) ((|constructor| (NIL "This domain represents the syntax of a definition.")) (|body| (((|SpadAst|) $) "\\spad{body(d)} returns the right hand side of the definition `d'.")) (|signature| (((|Signature|) $) "\\spad{signature(d)} returns the signature of the operation being defined. Note that this list may be partial in that it contains only the types actually specified in the definition.")) (|head| (((|HeadAst|) $) "\\spad{head(d)} returns the head of the definition `d'. This is a list of identifiers starting with the name of the operation followed by the name of the parameters,{} if any."))) NIL NIL -(-173 R -3093) +(-173 R -3092) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1="failed") (|:| |pole| #2="potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f, x, a, b, ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f, x = a..b, \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| #1#) (|:| |pole| #2#)) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f, x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -634,19 +634,19 @@ NIL NIL (-176 S) ((|constructor| (NIL "Linked list implementation of a Dequeue")) (|dequeue| (($ (|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}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-177 |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}."))) -((-3993 . T)) +((-3992 . T)) NIL -(-178 R -3093) +(-178 R -3092) ((|constructor| (NIL "\\spadtype{DefiniteIntegrationTools} provides common tools used by the definite integration of both rational and elementary functions.")) (|checkForZero| (((|Union| (|Boolean|) "failed") (|SparseUnivariatePolynomial| |#2|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.") (((|Union| (|Boolean|) "failed") (|Polynomial| |#1|) (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{checkForZero(p, x, a, b, incl?)} is \\spad{true} if \\spad{p} has a zero for \\spad{x} between a and \\spad{b},{} \\spad{false} otherwise,{} \"failed\" if this cannot be determined. Check for a and \\spad{b} inclusive if incl? is \\spad{true},{} exclusive otherwise.")) (|computeInt| (((|Union| (|OrderedCompletion| |#2|) "failed") (|Kernel| |#2|) |#2| (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{computeInt(x, g, a, b, eval?)} returns the integral of \\spad{f} for \\spad{x} between a and \\spad{b},{} assuming that \\spad{g} is an indefinite integral of \\spad{f} and \\spad{f} has no pole between a and \\spad{b}. If \\spad{eval?} is \\spad{true},{} then \\spad{g} can be evaluated safely at \\spad{a} and \\spad{b},{} provided that they are finite values. Otherwise,{} limits must be computed.")) (|ignore?| (((|Boolean|) (|String|)) "\\spad{ignore?(s)} is \\spad{true} if \\spad{s} is the string that tells the integrator to assume that the function has no pole in the integration interval."))) NIL NIL (-179) ((|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.")) (|nan?| (((|Boolean|) $) "\\spad{nan? x} holds if \\spad{x} is a Not a Number floating point data in the IEEE 754 sense.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3770 . T) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-180) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Bi''(x) - x * Bi(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{Ai''(x) - x * Ai(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,x)} is the modified Bessel function of the first kind,{} \\spad{K(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,x) = \\%pi/2*(I(-v,x) - I(v,x))/sin(v*\\%pi)}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,x)} is the modified Bessel function of the first kind,{} \\spad{I(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,x)} is the Bessel function of the second kind,{} \\spad{Y(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,x) = (J(v,x) cos(v*\\%pi) - J(-v,x))/sin(v*\\%pi)}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,x)} is the Bessel function of the first kind,{} \\spad{J(v,x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n, x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x, y)} is the Euler beta function,{} \\spad{B(x,y)},{} defined by \\indented{2}{\\spad{Beta(x,y) = integrate(t^(x-1)*(1-t)^(y-1), t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t), t=0..\\%infinity)}.}"))) @@ -654,19 +654,19 @@ NIL NIL (-181 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}"))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3997 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72)))) (-182 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 (-183 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."))) -((-3997 . T)) +((-3996 . T)) NIL (-184 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%."))) -((-3993 . T)) +((-3992 . T)) NIL (-185 S T$) ((|constructor| (NIL "This category captures the interface of domains with a distinguished operation named \\spad{differentiate}. Usually,{} additional properties are wanted. For example,{} that it obeys the usual Leibniz identity of differentiation of product,{} in case of differential rings. One could also want \\spad{differentiate} to obey the chain rule when considering differential manifolds. The lack of specific requirement in this category is an implicit admission that currently \\Language{} is not expressive enough to express the most general notion of differentiation in an adequate manner,{} suitable for computational purposes.")) (D ((|#2| $) "\\spad{D x} is a shorthand for \\spad{differentiate x}")) (|differentiate| ((|#2| $) "\\spad{differentiate x} compute the derivative of \\spad{x}."))) @@ -678,7 +678,7 @@ NIL NIL (-187 R) ((|constructor| (NIL "An \\spad{R}-module equipped with a distinguised differential operator. If \\spad{R} is a differential ring,{} then differentiation on the module should extend differentiation on the differential ring \\spad{R}. The latter can be the null operator. In that case,{} the differentiation operator on the module is just an \\spad{R}-linear operator. For that reason,{} we do not require that the ring \\spad{R} be a DifferentialRing; \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL (-188 S) ((|constructor| (NIL "This category is like \\spadtype{DifferentialDomain} where the target of the differentiation operator is the same as its source.")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x, n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,n)} returns the \\spad{n}\\spad{-}th derivative of \\spad{x}."))) @@ -690,7 +690,7 @@ NIL NIL (-190) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline"))) -((-3993 . T)) +((-3992 . T)) NIL (-191) ((|constructor| (NIL "Dioid is the class of semirings where the addition operation induces a canonical order relation."))) @@ -699,28 +699,28 @@ NIL (-192 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select!(p,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is not \\spad{true}.")) (|remove!| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove!(p,d)} destructively changes dictionary \\spad{d} by removeing all entries \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}.") (($ |#2| $) "\\spad{remove!(x,d)} destructively changes dictionary \\spad{d} by removing all entries \\spad{y} such that \\axiom{\\spad{y} = \\spad{x}}.")) (|dictionary| (($ (|List| |#2|)) "\\spad{dictionary([x,y,...,z])} creates a dictionary consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{dictionary()}\\$\\spad{D} creates an empty dictionary of type \\spad{D}."))) NIL -((|HasAttribute| |#1| (QUOTE -3996))) +((|HasAttribute| |#1| (QUOTE -3995))) (-193 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}."))) -((-3997 . T)) +((-3996 . T)) NIL (-194) ((|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 -(-195 S -2622 R) +(-195 S -2621 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#3| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-718))) (|HasCategory| |#3| (QUOTE (-757))) (|HasAttribute| |#3| (QUOTE -3993)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-664))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-962))) (|HasCategory| |#3| (QUOTE (-1014)))) -(-196 -2622 R) +((|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-717))) (|HasCategory| |#3| (QUOTE (-756))) (|HasAttribute| |#3| (QUOTE -3992)) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#3| (QUOTE (-663))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-961))) (|HasCategory| |#3| (QUOTE (-1013)))) +(-196 -2621 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim."))) -((-3990 |has| |#2| (-962)) (-3991 |has| |#2| (-962)) (-3993 |has| |#2| (-6 -3993)) (-3996 . T)) +((-3989 |has| |#2| (-961)) (-3990 |has| |#2| (-961)) (-3992 |has| |#2| (-6 -3992)) (-3995 . T)) NIL -(-197 -2622 R) +(-197 -2621 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."))) -((-3990 |has| |#2| (-962)) (-3991 |has| |#2| (-962)) (-3993 |has| |#2| (-6 -3993)) (-3996 . 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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 @@ -734,7 +734,7 @@ NIL NIL (-201) ((|constructor| (NIL "A division ring (sometimes called a skew field),{} \\spadignore{i.e.} a not necessarily commutative ring where all non-zero elements have multiplicative inverses.")) (|inv| (($ $) "\\spad{inv x} returns the multiplicative inverse of \\spad{x}. Error: if \\spad{x} is 0.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-202 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."))) @@ -742,20 +742,20 @@ NIL NIL (-203 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}"))) -((-3997 . T) (-3996 . 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(QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-950 (-484)))) (|HasCategory| |#3| (QUOTE (-1013)))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#3| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#3| (QUOTE (-809 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasAttribute| |#3| (QUOTE -3992)) (-12 (|HasCategory| |#3| (QUOTE (-190))) (|HasCategory| |#3| (QUOTE (-961))))) (-12 (|HasCategory| |#3| (QUOTE (-189))) (|HasCategory| |#3| (QUOTE (-961)))) (-12 (|HasCategory| |#3| (QUOTE (-811 (-1090)))) (|HasCategory| |#3| (QUOTE (-961)))) (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-21))) (|HasCategory| |#3| (QUOTE (-23))) (|HasCategory| |#3| (QUOTE (-104))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-552 (-772)))) (|HasCategory| |#3| (QUOTE (-72))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (-212 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-190)))) (-213 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p, s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p, s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p, s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} := makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL (-214 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}."))) -((-3996 . T) (-3997 . T)) +((-3995 . T) (-3996 . T)) NIL (-215 |Ex|) ((|constructor| (NIL "TopLevelDrawFunctions provides top level functions for drawing graphics of expressions.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d)} 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)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = 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)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{makeObject(f(x,y),x = a..b,y = 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)}; \\spad{f(x,y)} appears as the default title.") (((|ThreeSpace| (|DoubleFloat|)) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f(x,y),x = a..b,y = 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)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f(t),g(t),h(t)),t = a..b,l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = 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)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSurface| |#1|) (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l)} 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)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|))) "\\spad{draw(f(x,y),x = a..b,y = 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)}; \\spad{f(x,y)} appears in the title bar.") (((|ThreeDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x,y),x = a..b,y = 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)}; \\spad{f(x,y)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t),h(t)),t = a..b,l)} draws the graph of the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)},{} \\spad{z = h(t)} as \\spad{t} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{h(t)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|))) "\\spad{draw(curve(f(t),g(t)),t = 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)}; \\spad{(f(t),g(t))} appears in the title bar.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| |#1|) (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f(t),g(t)),t = 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)}; \\spad{(f(t),g(t))} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|))) "\\spad{draw(f(x),x = a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,b)} to \\spad{max(a,b)}; \\spad{f(x)} appears in the title bar.") (((|TwoDimensionalViewport|) |#1| (|SegmentBinding| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f(x),x = 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)}; \\spad{f(x)} is the default title,{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -827,15 +827,15 @@ NIL (-224 S R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL -((|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-189)))) +((|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-189)))) (-225 R) ((|constructor| (NIL "Extension of a base differential space with a derivation. \\blankline")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,d,n)} is a shorthand for \\spad{differentiate(x,d,n)}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,d)} is a shorthand for \\spad{differentiate(x,d)}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,d,n)} computes the \\spad{n}\\spad{-}th derivative of \\spad{x} using a derivation extending \\spad{d} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,d)} computes the derivative of \\spad{x},{} extending differentiation \\spad{d} on \\spad{R}."))) NIL NIL (-226 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"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#3| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#3| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#3| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#3| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#3| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#3| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#3| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#3| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-227 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.")) (|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 @@ -848,11 +848,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1's in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0's and 1's into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-230 R -3093) +(-230 R -3092) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{pi()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-231 R -3093) +(-231 R -3092) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f, k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,...,kn],f,x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log, exp, tan, atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f, x)} returns \\spad{[g, [k1,...,kn], [h1,...,hn]]} such that \\spad{g = normalize(f, x)} and each \\spad{ki} was rewritten as \\spad{hi} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f, x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -875,10 +875,10 @@ NIL (-236 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 (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013)))) (-237 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}."))) -((-3997 . T)) +((-3996 . T)) NIL (-238 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}."))) @@ -899,14 +899,14 @@ NIL (-242 S |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#3| $ |#2| |#3|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#3| $ |#2|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#3| $ |#2| |#3|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) +((|HasAttribute| |#1| (QUOTE -3996))) (-243 |Dom| |Im|) ((|constructor| (NIL "An eltable aggregate is one which can be viewed as a function. For example,{} the list \\axiom{[1,{}7,{}4]} can applied to 0,{}1,{} and 2 respectively will return the integers 1,{}7,{} and 4; thus this list may be viewed as mapping 0 to 1,{} 1 to 7 and 2 to 4. In general,{} an aggregate can map members of a domain {\\em Dom} to an image domain {\\em Im}.")) (|qsetelt!| ((|#2| $ |#1| |#2|) "\\spad{qsetelt!(u,x,y)} sets the image of \\axiom{\\spad{x}} to be \\axiom{\\spad{y}} under \\axiom{\\spad{u}},{} without checking that \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If such a check is required use the function \\axiom{setelt}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(u,x,y)} sets the image of \\spad{x} to be \\spad{y} under \\spad{u},{} assuming \\spad{x} is in the domain of \\spad{u}. Error: if \\spad{x} is not in the domain of \\spad{u}.")) (|qelt| ((|#2| $ |#1|) "\\spad{qelt(u, x)} applies \\axiom{\\spad{u}} to \\axiom{\\spad{x}} without checking whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}}. If \\axiom{\\spad{x}} is not in the domain of \\axiom{\\spad{u}} a memory-access violation may occur. If a check on whether \\axiom{\\spad{x}} is in the domain of \\axiom{\\spad{u}} is required,{} use the function \\axiom{elt}.")) (|elt| ((|#2| $ |#1| |#2|) "\\spad{elt(u, x, y)} applies \\spad{u} to \\spad{x} if \\spad{x} is in the domain of \\spad{u},{} and returns \\spad{y} otherwise. For example,{} if \\spad{u} is a polynomial in \\axiom{\\spad{x}} over the rationals,{} \\axiom{elt(\\spad{u},{}\\spad{n},{}0)} may define the coefficient of \\axiom{\\spad{x}} to the power \\spad{n},{} returning 0 when \\spad{n} is out of range."))) NIL NIL -(-244 S R |Mod| -2038 -3519 |exactQuo|) +(-244 S R |Mod| -2037 -3518 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-245 S) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) @@ -914,7 +914,7 @@ NIL NIL (-246) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-3989 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-247) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: March 18,{} 2010. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|interactiveEnv| (($) "the current interactive environment in effect.")) (|currentEnv| (($) "the current normal environment in effect.")) (|putProperties| (($ (|Identifier|) (|List| (|Property|)) $) "\\spad{putProperties(n,props,e)} set the list of properties of \\spad{n} to \\spad{props} in \\spad{e}.")) (|getProperties| (((|List| (|Property|)) (|Identifier|) $) "\\spad{getBinding(n,e)} returns the list of properties of \\spad{n} in \\spad{e}.")) (|putProperty| (($ (|Identifier|) (|Identifier|) (|SExpression|) $) "\\spad{putProperty(n,p,v,e)} binds the property \\spad{(p,v)} to \\spad{n} in the topmost scope of \\spad{e}.")) (|getProperty| (((|Maybe| (|SExpression|)) (|Identifier|) (|Identifier|) $) "\\spad{getProperty(n,p,e)} returns the value of property with name \\spad{p} for the symbol \\spad{n} in environment \\spad{e}. Otherwise,{} \\spad{nothing}.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -926,16 +926,16 @@ NIL NIL (-249 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| (($ $ $) "\\spad{subst(eq1,eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the lhs of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations \\spad{e1} and \\spad{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."))) -((-3993 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3990 |has| |#1| (-962)) (-3991 |has| |#1| (-962))) -((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-664)))) +((-3992 OR (|has| |#1| (-961)) (|has| |#1| (-413))) (-3989 |has| |#1| (-961)) (-3990 |has| |#1| (-961))) +((|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663)))) (|HasCategory| |#1| (QUOTE (-413))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-254))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-413)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-663)))) (-250 S R) ((|constructor| (NIL "This package provides operations for mapping the sides of equations.")) (|map| (((|Equation| |#2|) (|Mapping| |#2| |#1|) (|Equation| |#1|)) "\\spad{map(f,eq)} returns an equation where \\spad{f} is applied to the sides of \\spad{eq}"))) NIL NIL (-251 |Key| |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are compared using \\spadfun{eq?}. Thus keys are considered equal only if they are the same instance of a structure."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772))))) (-252) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL @@ -943,16 +943,16 @@ NIL (-253 S) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) +((|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (-254) ((|constructor| (NIL "An expression space is a set which is closed under certain operators.")) (|odd?| (((|Boolean|) $) "\\spad{odd? x} is \\spad{true} if \\spad{x} is an odd integer.")) (|even?| (((|Boolean|) $) "\\spad{even? x} is \\spad{true} if \\spad{x} is an even integer.")) (|definingPolynomial| (($ $) "\\spad{definingPolynomial(x)} returns an expression \\spad{p} such that \\spad{p(x) = 0}.")) (|minPoly| (((|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{minPoly(k)} returns \\spad{p} such that \\spad{p(k) = 0}.")) (|eval| (($ $ (|BasicOperator|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|BasicOperator|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|BasicOperator|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ $)) "\\spad{eval(x, s, f)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, f)} replaces every \\spad{s(a1,..,am)} in \\spad{x} by \\spad{f(a1,..,am)} for any \\spad{a1},{}...,{}\\spad{am}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}\\spad{an}.") (($ $ (|List| (|Symbol|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [f1,...,fm])} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.")) (|freeOf?| (((|Boolean|) $ (|Symbol|)) "\\spad{freeOf?(x, s)} tests if \\spad{x} does not contain any operator whose name is \\spad{s}.") (((|Boolean|) $ $) "\\spad{freeOf?(x, y)} tests if \\spad{x} does not contain any occurrence of \\spad{y},{} where \\spad{y} is a single kernel.")) (|map| (($ (|Mapping| $ $) (|Kernel| $)) "\\spad{map(f, k)} returns \\spad{op(f(x1),...,f(xn))} where \\spad{k = op(x1,...,xn)}.")) (|kernel| (($ (|BasicOperator|) (|List| $)) "\\spad{kernel(op, [f1,...,fn])} constructs \\spad{op(f1,...,fn)} without evaluating it.") (($ (|BasicOperator|) $) "\\spad{kernel(op, x)} constructs \\spad{op}(\\spad{x}) without evaluating it.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(x, s)} tests if \\spad{x} is a kernel and is the name of its operator is \\spad{s}.") (((|Boolean|) $ (|BasicOperator|)) "\\spad{is?(x, op)} tests if \\spad{x} is a kernel and is its operator is op.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} tests if \\% accepts \\spad{op} as applicable to its elements.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\%.")) (|operators| (((|List| (|BasicOperator|)) $) "\\spad{operators(f)} returns all the basic operators appearing in \\spad{f},{} no matter what their levels are.")) (|tower| (((|List| (|Kernel| $)) $) "\\spad{tower(f)} returns all the kernels appearing in \\spad{f},{} no matter what their levels are.")) (|kernels| (((|List| (|Kernel| $)) $) "\\spad{kernels(f)} returns the list of all the top-level kernels appearing in \\spad{f},{} but not the ones appearing in the arguments of the top-level kernels.")) (|mainKernel| (((|Union| (|Kernel| $) "failed") $) "\\spad{mainKernel(f)} returns a kernel of \\spad{f} with maximum nesting level,{} or if \\spad{f} has no kernels (\\spadignore{i.e.} \\spad{f} is a constant).")) (|height| (((|NonNegativeInteger|) $) "\\spad{height(f)} returns the highest nesting level appearing in \\spad{f}. Constants have height 0. Symbols have height 1. For any operator op and expressions \\spad{f1},{}...,{}fn,{} \\spad{op(f1,...,fn)} has height equal to \\spad{1 + max(height(f1),...,height(fn))}.")) (|distribute| (($ $ $) "\\spad{distribute(f, g)} expands all the kernels in \\spad{f} that contain \\spad{g} in their arguments and that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or a \\spadfunFrom{paren}{ExpressionSpace} expression.") (($ $) "\\spad{distribute(f)} expands all the kernels in \\spad{f} that are formally enclosed by a \\spadfunFrom{box}{ExpressionSpace} or \\spadfunFrom{paren}{ExpressionSpace} expression.")) (|paren| (($ (|List| $)) "\\spad{paren([f1,...,fn])} returns \\spad{(f1,...,fn)}. This prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(paren [x, 2])} returns the formal kernel \\spad{atan((x, 2))}.") (($ $) "\\spad{paren(f)} returns (\\spad{f}). This prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(paren 1)} returns the formal kernel log((1)).")) (|box| (($ (|List| $)) "\\spad{box([f1,...,fn])} returns \\spad{(f1,...,fn)} with a 'box' around them that prevents the \\spad{fi} from being evaluated when operators are applied to them,{} and makes them applicable to a unary operator. For example,{} \\spad{atan(box [x, 2])} returns the formal kernel \\spad{atan(x, 2)}.") (($ $) "\\spad{box(f)} returns \\spad{f} with a 'box' around it that prevents \\spad{f} from being evaluated when operators are applied to it. For example,{} \\spad{log(1)} returns 0,{} but \\spad{log(box 1)} returns the formal kernel log(1).")) (|subst| (($ $ (|List| (|Kernel| $)) (|List| $)) "\\spad{subst(f, [k1...,kn], [g1,...,gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|List| (|Equation| $))) "\\spad{subst(f, [k1 = g1,...,kn = gn])} replaces the kernels \\spad{k1},{}...,{}kn by \\spad{g1},{}...,{}gn formally in \\spad{f}.") (($ $ (|Equation| $)) "\\spad{subst(f, k = g)} replaces the kernel \\spad{k} by \\spad{g} formally in \\spad{f}.")) (|elt| (($ (|BasicOperator|) (|List| $)) "\\spad{elt(op,[x1,...,xn])} or \\spad{op}([\\spad{x1},{}...,{}xn]) applies the \\spad{n}-ary operator \\spad{op} to \\spad{x1},{}...,{}xn.") (($ (|BasicOperator|) $ $ $ $) "\\spad{elt(op,x,y,z,t)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z},{} \\spad{t}) applies the 4-ary operator \\spad{op} to \\spad{x},{} \\spad{y},{} \\spad{z} and \\spad{t}.") (($ (|BasicOperator|) $ $ $) "\\spad{elt(op,x,y,z)} or \\spad{op}(\\spad{x},{} \\spad{y},{} \\spad{z}) applies the ternary operator \\spad{op} to \\spad{x},{} \\spad{y} and \\spad{z}.") (($ (|BasicOperator|) $ $) "\\spad{elt(op,x,y)} or \\spad{op}(\\spad{x},{} \\spad{y}) applies the binary operator \\spad{op} to \\spad{x} and \\spad{y}.") (($ (|BasicOperator|) $) "\\spad{elt(op,x)} or \\spad{op}(\\spad{x}) applies the unary operator \\spad{op} to \\spad{x}."))) NIL NIL -(-255 -3093 S) +(-255 -3092 S) ((|constructor| (NIL "This package allows a map from any expression space into any object to be lifted to a kernel over the expression set,{} using a given property of the operator of the kernel.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|String|) (|Kernel| |#1|)) "\\spad{map(f, p, k)} uses the property \\spad{p} of the operator of \\spad{k},{} in order to lift \\spad{f} and apply it to \\spad{k}."))) NIL NIL -(-256 E -3093) +(-256 E -3092) ((|constructor| (NIL "This package allows a mapping \\spad{E} -> \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f, k)} returns \\spad{g = op(f(a1),...,f(an))} where \\spad{k = op(a1,...,an)}."))) NIL NIL @@ -962,7 +962,7 @@ NIL NIL (-258) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,...,fn],z)} returns a list of coefficients \\spad{[a1, ..., an]} such that \\spad{ z / prod fi = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,y,z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a gcd of \\spad{x} and \\spad{y}. The gcd is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-259 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -972,7 +972,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f, [x1 = v1,...,xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-261 -3093) +(-261 -3092) ((|constructor| (NIL "This package is to be used in conjuction with \\indented{12}{the CycleIndicators package. It provides an evaluation} \\indented{12}{function for SymmetricPolynomials.}")) (|eval| ((|#1| (|Mapping| |#1| (|Integer|)) (|SymmetricPolynomial| (|Fraction| (|Integer|)))) "\\spad{eval(f,s)} evaluates the cycle index \\spad{s} by applying \\indented{1}{the function \\spad{f} to each integer in a monomial partition,{}} \\indented{1}{forms their product and sums the results over all monomials.}"))) NIL NIL @@ -986,12 +986,12 @@ NIL NIL (-264 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))}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-474)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-934))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757))) (OR (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-741))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-757)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-1067))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-330)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-797 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-581 (-485)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-812 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-810 (-1091)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1167) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-822)))) (|HasCategory| (-1167 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-473)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-933))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-756))) (OR (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-740))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-756)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-1066))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-330)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-796 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-580 (-484)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-189))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-811 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-190))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-809 (-1090)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -260) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (|%list| (QUOTE -241) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)) (|%list| (QUOTE -1166) (|devaluate| |#1|) (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#4|)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-258))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-821)))) (|HasCategory| (-1166 |#1| |#2| |#3| |#4|) (QUOTE (-118))))) (-265 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."))) -((-3993 OR (-12 (|has| |#1| (-496)) (OR (|has| |#1| (-962)) (|has| |#1| (-413)))) (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496))) -((OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-581 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1026)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-962)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-951 (-485)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) +((-3992 OR (-12 (|has| |#1| (-495)) (OR (|has| |#1| (-961)) (|has| |#1| (-413)))) (|has| |#1| (-961)) (|has| |#1| (-413))) (-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) ((-3997 "*") |has| |#1| (-495)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-495)) (-3987 |has| |#1| (-495))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-580 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961))))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-1025)))) (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961)))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-25)))) (OR (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#1| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-950 (-484)))))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) (-266 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 @@ -1000,7 +1000,7 @@ NIL ((|constructor| (NIL "This package provides functions to convert functional expressions to power series.")) (|series| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{series(f,x = a,n)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a); terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{series(f,x = a)} expands the expression \\spad{f} as a series in powers of (\\spad{x} - a).") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{series(f,n)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{series(f)} returns a series expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{series(x)} returns \\spad{x} viewed as a series.")) (|puiseux| (((|Any|) |#2| (|Equation| |#2|) (|Fraction| (|Integer|))) "\\spad{puiseux(f,x = a,n)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{puiseux(f,x = a)} expands the expression \\spad{f} as a Puiseux series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Fraction| (|Integer|))) "\\spad{puiseux(f,n)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{puiseux(f)} returns a Puiseux expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{puiseux(x)} returns \\spad{x} viewed as a Puiseux series.")) (|laurent| (((|Any|) |#2| (|Equation| |#2|) (|Integer|)) "\\spad{laurent(f,x = a,n)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{laurent(f,x = a)} expands the expression \\spad{f} as a Laurent series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|Integer|)) "\\spad{laurent(f,n)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{laurent(f)} returns a Laurent expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{laurent(x)} returns \\spad{x} viewed as a Laurent series.")) (|taylor| (((|Any|) |#2| (|Equation| |#2|) (|NonNegativeInteger|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}; terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2| (|Equation| |#2|)) "\\spad{taylor(f,x = a)} expands the expression \\spad{f} as a Taylor series in powers of \\spad{(x - a)}.") (((|Any|) |#2| (|NonNegativeInteger|)) "\\spad{taylor(f,n)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least \\spad{n}.") (((|Any|) |#2|) "\\spad{taylor(f)} returns a Taylor expansion of the expression \\spad{f}. Note: \\spad{f} should have only one variable; the series will be expanded in powers of that variable.") (((|Any|) (|Symbol|)) "\\spad{taylor(x)} returns \\spad{x} viewed as a Taylor series."))) NIL NIL -(-268 R -3093) +(-268 R -3092) ((|constructor| (NIL "Taylor series solutions of explicit ODE's.")) (|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq, y, x = a, [b0,...,bn])} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, [b0,...,b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq, y, x = a, y a = b)} is equivalent to \\spad{seriesSolve(eq=0, y, x=a, y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq, y, x = a, b)} is equivalent to \\spad{seriesSolve(eq = 0, y, x = a, y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,y, x=a, b)} is equivalent to \\spad{seriesSolve(eq, y, x=a, y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a,[y1 a = b1,..., yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1=0,...,eqn=0], [y1,...,yn], x=a, [b1,...,bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x=a, [b1,...,bn])} is equivalent to \\spad{seriesSolve([eq1,...,eqn], [y1,...,yn], x = a, [y1 a = b1,..., yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,...,eqn],[y1,...,yn],x = a,[y1 a = b1,...,yn a = bn])} returns a taylor series solution of \\spad{[eq1,...,eqn]} around \\spad{x = a} with initial conditions \\spad{yi(a) = bi}. Note: eqi must be of the form \\spad{fi(x, y1 x, y2 x,..., yn x) y1'(x) + gi(x, y1 x, y2 x,..., yn x) = h(x, y1 x, y2 x,..., yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,y,x=a,[b0,...,b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x, y x, y'(x),..., y(n-1)(x)) y(n)(x) + g(x,y x,y'(x),...,y(n-1)(x)) = h(x,y x, y'(x),..., y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,y,x=a, y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x, y x) y'(x) + g(x, y x) = h(x, y x)}."))) NIL NIL @@ -1010,8 +1010,8 @@ NIL NIL (-270 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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-271 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},{}...,{}rm are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1022,8 +1022,8 @@ NIL NIL (-273 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The operation is commutative."))) -((-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-717)))) +((-3990 . T) (-3989 . T)) +((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| (-484) (QUOTE (-716)))) (-274 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an, f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,[max(ei, fi) ci])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,...,an}} and \\spad{{b1,...,bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f, e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s, e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}'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|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} \\spad{a1}\\^\\spad{e1} ... an\\^en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) NIL @@ -1031,26 +1031,26 @@ NIL (-275 S) ((|constructor| (NIL "The free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,[ni * si])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are non-negative integers. The operation is commutative."))) NIL -((|HasCategory| (-695) (QUOTE (-717)))) +((|HasCategory| (-694) (QUOTE (-716)))) (-276 S R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#2| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#2| |#3| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#3| |#3|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#3| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#2| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) NIL -((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) +((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) (-277 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the gcd of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,q,n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,r,e,p2)} returns \\spad{p1 + monomial(e,r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-278 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."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-279 S -3093) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-279 S -3092) ((|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})\\$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})\\$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**(q**(d*i)) for \\spad{i} in 0..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},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'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| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-320)))) -(-280 -3093) +(-280 -3092) ((|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})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,d} form {\\em F} and {\\em f,g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\$SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i), 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,d) = reduce(+,[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(q**(d*i)) for \\spad{i} in 0..n/d])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\$ as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\$ as \\spad{F}-vectorspace."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-281 E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: 12 June 1992 Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|argument| ((|#1| $) "\\spad{argument(x)} returns the argument of a given sin/cos expressions")) (|sin?| (((|Boolean|) $) "\\spad{sin?(x)} returns \\spad{true} if term is a sin,{} otherwise \\spad{false}")) (|cos| (($ |#1|) "\\spad{cos(x)} makes a cos kernel for use in Fourier series")) (|sin| (($ |#1|) "\\spad{sin(x)} makes a sin kernel for use in Fourier series"))) @@ -1060,7 +1060,7 @@ NIL ((|constructor| (NIL "Represntation of data needed to instantiate a domain constructor.")) (|lookupFunction| (((|Identifier|) $) "\\spad{lookupFunction x} returns the name of the lookup function associated with the functor data \\spad{x}.")) (|categories| (((|PrimitiveArray| (|ConstructorCall| (|CategoryConstructor|))) $) "\\spad{categories x} returns the list of categories forms each domain object obtained from the domain data \\spad{x} belongs to.")) (|encodingDirectory| (((|PrimitiveArray| (|NonNegativeInteger|)) $) "\\spad{encodintDirectory x} returns the directory of domain-wide entity description.")) (|attributeData| (((|List| (|Pair| (|Syntax|) (|NonNegativeInteger|))) $) "\\spad{attributeData x} returns the list of attribute-predicate bit vector index pair associated with the functor data \\spad{x}.")) (|domainTemplate| (((|DomainTemplate|) $) "\\spad{domainTemplate x} returns the domain template vector associated with the functor data \\spad{x}."))) NIL NIL -(-283 -3093 UP UPUP R) +(-283 -3092 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1068,33 +1068,33 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,d)} \\undocumented{}"))) NIL NIL -(-285 S -3093 UP UPUP R) +(-285 S -3092 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-286 -3093 UP UPUP R) +(-286 -3092 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id, f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h, d, d', g, r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a, b, n)} makes the divisor \\spad{nP} where P: \\spad{(x = a, y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a, b)} makes the divisor P: \\spad{(x = a, y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL (-287 S R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL -((|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) +((|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|)))) (-288 R) ((|constructor| (NIL "This category provides a selection of evaluation operations depending on what the argument type \\spad{R} provides.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f, ex)} evaluates ex,{} applying \\spad{f} to values of type \\spad{R} in ex."))) NIL NIL (-289 |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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) -(-290 S -3093 UP UPUP) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) +(-290 S -3092 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#3|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#3|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#2|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#3|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#2|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#3|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#2|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#3|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#2|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#2| |#2|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) NIL ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-312)))) -(-291 -3093 UP UPUP) +(-291 -3092 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in \\spad{u1},{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f, D)} returns \\spad{[h,d,d',g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d, discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,a,b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a, y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x, d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(wi)} with respect to \\spad{(w1,...,wn)} where \\spad{(w1,...,wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,...,An], D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,...,wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,...,wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,...,A(n-1)],D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.")) (|yCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{yCoordinates(f)} returns \\spad{[[A1,...,An], D]} such that \\spad{f = (A1 + A2 y +...+ An y**(n-1)) / D}.")) (|inverseIntegralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrixAtInfinity()} returns \\spad{M} such that \\spad{M (v1,...,vn) = (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|integralMatrixAtInfinity| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrixAtInfinity()} returns \\spad{M} such that \\spad{(v1,...,vn) = M (1, y, ..., y**(n-1))} where \\spad{(v1,...,vn)} is the local integral basis at infinity returned by \\spad{infIntBasis()}.")) (|inverseIntegralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{inverseIntegralMatrix()} returns \\spad{M} such that \\spad{M (w1,...,wn) = (1, y, ..., y**(n-1))} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|integralMatrix| (((|Matrix| (|Fraction| |#2|))) "\\spad{integralMatrix()} returns \\spad{M} such that \\spad{(w1,...,wn) = M (1, y, ..., y**(n-1))},{} where \\spad{(w1,...,wn)} is the integral basis of \\spadfunFrom{integralBasis}{FunctionFieldCategory}.")) (|reduceBasisAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{reduceBasisAtInfinity(b1,...,bn)} returns \\spad{(x**i * bj)} for all \\spad{i},{}\\spad{j} such that \\spad{x**i*bj} is locally integral at infinity.")) (|normalizeAtInfinity| (((|Vector| $) (|Vector| $)) "\\spad{normalizeAtInfinity(v)} makes \\spad{v} normal at infinity.")) (|complementaryBasis| (((|Vector| $) (|Vector| $)) "\\spad{complementaryBasis(b1,...,bn)} returns the complementary basis \\spad{(b1',...,bn')} of \\spad{(b1,...,bn)}.")) (|integral?| (((|Boolean|) $ |#2|) "\\spad{integral?(f, p)} tests whether \\spad{f} is locally integral at \\spad{p(x) = 0}.") (((|Boolean|) $ |#1|) "\\spad{integral?(f, a)} tests whether \\spad{f} is locally integral at \\spad{x = a}.") (((|Boolean|) $) "\\spad{integral?()} tests if \\spad{f} is integral over \\spad{k[x]}.")) (|integralAtInfinity?| (((|Boolean|) $) "\\spad{integralAtInfinity?()} tests if \\spad{f} is locally integral at infinity.")) (|integralBasisAtInfinity| (((|Vector| $)) "\\spad{integralBasisAtInfinity()} returns the local integral basis at infinity.")) (|integralBasis| (((|Vector| $)) "\\spad{integralBasis()} returns the integral basis for the curve.")) (|ramified?| (((|Boolean|) |#2|) "\\spad{ramified?(p)} tests whether \\spad{p(x) = 0} is ramified.") (((|Boolean|) |#1|) "\\spad{ramified?(a)} tests whether \\spad{x = a} is ramified.")) (|ramifiedAtInfinity?| (((|Boolean|)) "\\spad{ramifiedAtInfinity?()} tests if infinity is ramified.")) (|singular?| (((|Boolean|) |#2|) "\\spad{singular?(p)} tests whether \\spad{p(x) = 0} is singular.") (((|Boolean|) |#1|) "\\spad{singular?(a)} tests whether \\spad{x = a} is singular.")) (|singularAtInfinity?| (((|Boolean|)) "\\spad{singularAtInfinity?()} tests if there is a singularity at infinity.")) (|branchPoint?| (((|Boolean|) |#2|) "\\spad{branchPoint?(p)} tests whether \\spad{p(x) = 0} is a branch point.") (((|Boolean|) |#1|) "\\spad{branchPoint?(a)} tests whether \\spad{x = a} is a branch point.")) (|branchPointAtInfinity?| (((|Boolean|)) "\\spad{branchPointAtInfinity?()} tests if there is a branch point at infinity.")) (|rationalPoint?| (((|Boolean|) |#1| |#1|) "\\spad{rationalPoint?(a, b)} tests if \\spad{(x=a,y=b)} is on the curve.")) (|absolutelyIrreducible?| (((|Boolean|)) "\\spad{absolutelyIrreducible?()} tests if the curve absolutely irreducible?")) (|genus| (((|NonNegativeInteger|)) "\\spad{genus()} returns the genus of one absolutely irreducible component")) (|numberOfComponents| (((|NonNegativeInteger|)) "\\spad{numberOfComponents()} returns the number of absolutely irreducible components."))) -((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 |has| (-350 |#2|) (-312)) (-3993 |has| (-350 |#2|) (-312)) (-3987 |has| (-350 |#2|) (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-292 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f, p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) @@ -1102,15 +1102,15 @@ NIL NIL (-293 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) (-294 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-295 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(GF,{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-296 GF) ((|constructor| (NIL "FiniteFieldFunctions(GF) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) @@ -1126,43 +1126,43 @@ NIL NIL (-299) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see ch.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-300 R UP -3093) +(-300 R UP -3092) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-301 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((OR (|HasCategory| (-818 |#1|) (QUOTE (-118))) (|HasCategory| (-818 |#1|) (QUOTE (-320)))) (|HasCategory| (-818 |#1|) (QUOTE (-120))) (|HasCategory| (-818 |#1|) (QUOTE (-320))) (|HasCategory| (-818 |#1|) (QUOTE (-118)))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((OR (|HasCategory| (-817 |#1|) (QUOTE (-118))) (|HasCategory| (-817 |#1|) (QUOTE (-320)))) (|HasCategory| (-817 |#1|) (QUOTE (-120))) (|HasCategory| (-817 |#1|) (QUOTE (-320))) (|HasCategory| (-817 |#1|) (QUOTE (-118)))) (-302 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-303 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(GF,{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-304 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-305 GF) ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,x**q,x**(q**2),...,x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(GF) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(GF) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(GF) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(GF) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(GF) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(GF) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(GF) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(GF) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-306 -3093 GF) +(-306 -3092 GF) ((|constructor| (NIL "\\spad{FiniteFieldPolynomialPackage2}(\\spad{F},{}GF) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-307 -3093 FP FPP) +(-307 -3092 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL (-308 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(GF,{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((OR (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-118)))) (-309 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{ls}."))) @@ -1170,7 +1170,7 @@ NIL NIL (-310 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,...,an\\^en)} returns \\spad{[[a1, e1],...,[an, en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x, n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x, n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-3993 . T)) +((-3992 . T)) NIL (-311 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1178,7 +1178,7 @@ NIL NIL (-312) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-313 S) ((|constructor| (NIL "This domain provides a basic model of files to save arbitrary values. The operations provide sequential access to the contents.")) (|readIfCan!| (((|Union| |#1| "failed") $) "\\spad{readIfCan!(f)} returns a value from the file \\spad{f},{} if possible. If \\spad{f} is not open for reading,{} or if \\spad{f} is at the end of file then \\spad{\"failed\"} is the result."))) @@ -1191,10 +1191,10 @@ NIL (-315 S R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#2|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#2|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#2| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#2| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#2|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#2|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#2| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#2| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#2| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#2| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#2|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#2|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#2|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) NIL -((|HasCategory| |#2| (QUOTE (-496)))) +((|HasCategory| |#2| (QUOTE (-495)))) (-316 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,b,c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Lie algebra \\spad{(A,+,*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,+,@)} we can construct a Jordan algebra \\spad{(A,+,*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\"*\")} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,a,b) = 0 = 2*associator(a,b,b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,b,a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,b,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,a,b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don't know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,...,vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,...,vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,...,vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,...,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,...,am],[v1,...,vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,...,am],[v1,...,vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,[v1,...,vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,...,vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,v2,...,vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,...,vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,...,vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) +((-3992 |has| |#1| (-495)) (-3990 . T) (-3989 . T)) NIL (-317 A S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|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})}.")) (|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} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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}) holds 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 \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) @@ -1202,7 +1202,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-72)))) (-318 S) ((|constructor| (NIL "A finite aggregate is a homogeneous aggregate with a finite number of elements.")) (|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})}.")) (|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} \\indented{1}{in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} holds. 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}) holds 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 \\spad{p(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})}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#u} returns the number of items in \\spad{u}."))) -((-3996 . T)) +((-3995 . T)) NIL (-319 S) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\spad{random()} returns a random element from the set.")) (|lookup| (((|PositiveInteger|) $) "\\spad{lookup(x)} returns a positive integer such that \\spad{x = index lookup x}.")) (|index| (($ (|PositiveInteger|)) "\\spad{index(i)} takes a positive integer \\spad{i} less than or equal to \\spad{size()} and returns the \\spad{i}\\spad{-}th element of the set. This operation establishs a bijection between the elements of the finite set and \\spad{1..size()}.")) (|size| (((|NonNegativeInteger|)) "\\spad{size()} returns the number of elements in the set."))) @@ -1218,15 +1218,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-312)))) (-322 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,..,vn])} is the \\spad{n}-by-\\spad{n} matrix ( Tr(\\spad{vi} * vj) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,..,vn])} returns \\spad{determinant(traceMatrix([v1,..,vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,..,an],[v1,..,vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,...,vm], basis)} returns the coordinates of the \\spad{vi}'s with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL (-323 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014)))) +((|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013)))) (-324 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|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{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|) $) "\\spad{sorted?(p,a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(<=,{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(<=,{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,a,b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-3996 . T)) +((-3995 . T)) NIL (-325 S A R B) ((|constructor| (NIL "\\spad{FiniteLinearAggregateFunctions2} provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad{[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1234,7 +1234,7 @@ NIL NIL (-326 |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.fr)")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}xn],{} [\\spad{v1},{}...,{}vn])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3990 . T) (-3989 . T)) NIL (-327 S V) ((|constructor| (NIL "This package exports 3 sorting algorithms which work over FiniteLinearAggregates.")) (|shellSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{shellSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the shellSort algorithm.")) (|heapSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{heapSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the heapsort algorithm.")) (|quickSort| ((|#2| (|Mapping| (|Boolean|) |#1| |#1|) |#2|) "\\spad{quickSort(f, agg)} sorts the aggregate agg with the ordering function \\spad{f} using the quicksort algorithm."))) @@ -1243,14 +1243,14 @@ NIL (-328 S R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL -((|HasCategory| |#2| (QUOTE (-581 (-485))))) +((|HasCategory| |#2| (QUOTE (-580 (-484))))) (-329 R) ((|constructor| (NIL "\\spad{S} is \\spadtype{FullyLinearlyExplicitRingOver R} means that \\spad{S} is a \\spadtype{LinearlyExplicitRingOver R} and,{} in addition,{} if \\spad{R} is a \\spadtype{LinearlyExplicitRingOver Integer},{} then so is \\spad{S}"))) NIL NIL (-330) ((|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|atan| (($ $ $) "\\spad{atan(x,y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n, b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f, n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-3979 . T) (-3987 . T) (-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3978 . T) (-3986 . T) (-3770 . T) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-331 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf, lv, eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf, eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in lp.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) @@ -1262,15 +1262,15 @@ NIL NIL (-333 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."))) -((-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) +((-3990 . T) (-3989 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-334 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.fr)")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) ((|HasCategory| |#1| (QUOTE (-146)))) (-335 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.fr)")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis, c: R)} such that \\spad{x} equals \\spad{reduce(+, map(x +-> monom(x.k, x.c), lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL (-336 S) ((|constructor| (NIL "A free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'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| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1279,7 +1279,7 @@ NIL (-337 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'s are nonnegative integers. The multiplication is not commutative."))) NIL -((|HasCategory| |#1| (QUOTE (-757)))) +((|HasCategory| |#1| (QUOTE (-756)))) (-338) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) NIL @@ -1290,13 +1290,13 @@ NIL NIL (-340 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|NonNegativeInteger|)) "\\spad{generator(i)} is the \\spad{i}th Hall Basis element")) (|shallowExpand| (((|OutputForm|) $) "\\spad{shallowExpand(x)} \\undocumented{}")) (|deepExpand| (((|OutputForm|) $) "\\spad{deepExpand(x)} \\undocumented{}")) (|dimension| (((|NonNegativeInteger|)) "\\spad{dimension()} is the rank of this Lie algebra"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL -(-341 -3093 UP UPUP R) +(-341 -3092 UP UPUP R) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 11 Jul 1990")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{order(x)} \\undocumented"))) NIL NIL -(-342 -3093 UP) +(-342 -3092 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: June 18,{} 2010 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of \\spad{ISSAC'93},{} Kiev,{} ACM Press.}")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p, [[j, Dj, Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,Dj,Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL @@ -1310,28 +1310,28 @@ NIL NIL (-345) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-346 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\"+\") does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\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'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's precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,e,b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -3979)) (|HasAttribute| |#1| (QUOTE -3987))) +((|HasAttribute| |#1| (QUOTE -3978)) (|HasAttribute| |#1| (QUOTE -3986))) (-347) ((|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(\"+\") 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'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'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\"."))) -((-3771 . T) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3770 . T) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-348 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 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| #1="nil" #2="sqfr" #3="irred" #4="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| #1# #2# #3# #4#) $ (|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| #1# #2# #3# #4#)) (|:| |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| #1# #2# #3# #4#)) (|:| |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."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-456 (-1091) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1135))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1135)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-392)))) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-455 (-1090) $))) (|HasCategory| |#1| (QUOTE (-260 $))) (|HasCategory| |#1| (QUOTE (-241 $ $))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-1134))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-1134)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-392)))) (-349 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."))) NIL NIL (-350 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 gcd's between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-3983 -12 (|has| |#1| (-6 -3994)) (|has| |#1| (-392)) (|has| |#1| (-6 -3983))) (-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-951 (-1091)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-934))) (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-741))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-484))) (-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +((-3982 -12 (|has| |#1| (-6 -3993)) (|has| |#1| (-392)) (|has| |#1| (-6 -3982))) (-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-950 (-1090)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-933))) (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-740))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-483))) (-12 (|HasAttribute| |#1| (QUOTE -3982)) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392)))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) (-351 A B) ((|constructor| (NIL "This package extends a map between integral domains to a map between Fractions over those domains by applying the map to the numerators and denominators.")) (|map| (((|Fraction| |#2|) (|Mapping| |#2| |#1|) (|Fraction| |#1|)) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of the fraction \\spad{frac}."))) NIL @@ -1342,28 +1342,28 @@ NIL NIL (-353 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(vi * vj)} ),{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,..,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} vn are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,...,vm])} returns the coordinates of the \\spad{vi}'s with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL (-354 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL -((|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485))))) +((|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-355 S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don't retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) NIL NIL -(-356 R -3093 UP A) +(-356 R -3092 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,x)} should be local but conditional.")) (|minimize| (($ $) "\\spad{minimize(I)} returns a reduced set of generators for \\spad{I}.")) (|denom| ((|#1| $) "\\spad{denom(1/d * (f1,...,fn))} returns \\spad{d}.")) (|numer| (((|Vector| |#4|) $) "\\spad{numer(1/d * (f1,...,fn))} = the vector \\spad{[f1,...,fn]}.")) (|norm| ((|#2| $) "\\spad{norm(I)} returns the norm of the ideal \\spad{I}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} returns the vector \\spad{[f1,...,fn]}.")) (|ideal| (($ (|Vector| |#4|)) "\\spad{ideal([f1,...,fn])} returns the ideal \\spad{(f1,...,fn)}."))) -((-3993 . T)) +((-3992 . T)) NIL (-357 R1 F1 U1 A1 R2 F2 U2 A2) ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,i)} \\undocumented{}"))) NIL NIL -(-358 R -3093 UP A |ibasis|) +(-358 R -3092 UP A |ibasis|) ((|constructor| (NIL "Module representation of fractional ideals.")) (|module| (($ (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{module(I)} returns \\spad{I} viewed has a module over \\spad{R}.") (($ (|Vector| |#4|)) "\\spad{module([f1,...,fn])} = the module generated by \\spad{(f1,...,fn)} over \\spad{R}.")) (|norm| ((|#2| $) "\\spad{norm(f)} returns the norm of the module \\spad{f}.")) (|basis| (((|Vector| |#4|) $) "\\spad{basis((f1,...,fn))} = the vector \\spad{[f1,...,fn]}."))) NIL -((|HasCategory| |#4| (|%list| (QUOTE -951) (|devaluate| |#2|)))) +((|HasCategory| |#4| (|%list| (QUOTE -950) (|devaluate| |#2|)))) (-359 AR R AS S) ((|constructor| (NIL "\\spad{FramedNonAssociativeAlgebraFunctions2} implements functions between two framed non associative algebra domains defined over different rings. The function map is used to coerce between algebras over different domains having the same structural constants.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the coordinates of \\spad{u} to get an element in \\spad{AS} via identification of the basis of \\spad{AR} as beginning part of the basis of \\spad{AS}."))) NIL @@ -1374,7 +1374,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-312)))) (-361 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn't fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,...,an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{vi * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,...,am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{ai} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-3993 |has| |#1| (-496)) (-3991 . T) (-3990 . T)) +((-3992 |has| |#1| (-495)) (-3990 . T) (-3989 . T)) NIL (-362 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)}."))) @@ -1383,10 +1383,10 @@ NIL (-363 S R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f, k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $)) (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#2| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#2|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#2|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#2|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#2| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n, x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,...,mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,f)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,op)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x, n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,...,an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo's in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo, [x1,...,xn])} returns \\spad{'foo(x1,...,xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo, x, y, z, t)} returns \\spad{'foo(x,y,z,t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo, x, y, z)} returns \\spad{'foo(x,y,z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo, x, y)} returns \\spad{'foo(x,y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo, x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#2| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) NIL -((|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-1026))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) +((|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-1025))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) (-364 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| $))) "\\spad{eval(x, s, n, f)} replaces every \\spad{s(a1,...,am)**n} in \\spad{x} by \\spad{f(a1,...,am)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a1,...,an)**ni} in \\spad{x} by \\spad{fi(a1,...,an)} for any \\spad{a1},{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x, [s1,...,sm], [n1,...,nm], [f1,...,fm])} replaces every \\spad{si(a)**ni} in \\spad{x} by \\spad{fi(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x, [s1,...,sm], [f1,...,fm], y)} replaces every \\spad{si(a)} in \\spad{x} by \\spad{fi(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x, s, f, y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f, [foo1,...,foon])} unquotes all the \\spad{fooi}'s in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f, foo)} unquotes all the foo'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}."))) -((-3993 OR (|has| |#1| (-962)) (|has| |#1| (-413))) (-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) ((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-496)) (-3988 |has| |#1| (-496))) +((-3992 OR (|has| |#1| (-961)) (|has| |#1| (-413))) (-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) ((-3997 "*") |has| |#1| (-495)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-495)) (-3987 |has| |#1| (-495))) NIL (-365 R A S B) ((|constructor| (NIL "This package allows a mapping \\spad{R} -> \\spad{S} to be lifted to a mapping from a function space over \\spad{R} to a function space over \\spad{S}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, a)} applies \\spad{f} to all the constants in \\spad{R} appearing in \\spad{a}."))) @@ -1403,36 +1403,36 @@ NIL (-368 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 (-757))) (|HasCategory| |#2| (QUOTE (-320)))) +((|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320)))) (-369 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((-3995 . T) (-3985 . T) (-3996 . T)) NIL (-370 S A R B) ((|constructor| (NIL "\\spad{FiniteSetAggregateFunctions2} provides functions involving two finite set aggregates where the underlying domains might be different. An example of this is to create a set of rational numbers by mapping a function across a set of integers,{} where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,a,r)} successively applies \\spad{reduce(f,x,r)} to more and more leading sub-aggregates \\spad{x} of aggregate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,a2,...]},{} then \\spad{scan(f,a,r)} returns \\spad {[reduce(f,[a1],r),reduce(f,[a1,a2],r),...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,a,r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialised to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,[1,2,3],0)} does a \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as an identity element for the function.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,a)} applies function \\spad{f} to each member of aggregate \\spad{a},{} creating a new aggregate with a possibly different underlying domain."))) NIL NIL -(-371 R -3093) +(-371 R -3092) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-372 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#2| |#1|) "\\spad{makeCos(e,r)} makes a sin expression with given argument and coefficient")) (|makeSin| (($ |#2| |#1|) "\\spad{makeSin(e,r)} makes a sin expression with given argument and coefficient")) (|coerce| (($ (|FourierComponent| |#2|)) "\\spad{coerce(c)} converts sin/cos terms into Fourier Series") (($ |#1|) "\\spad{coerce(r)} converts coefficients into Fourier Series"))) -((-3983 -12 (|has| |#1| (-6 -3983)) (|has| |#2| (-6 -3983))) (-3990 . T) (-3991 . T) (-3993 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -3983)) (|HasAttribute| |#2| (QUOTE -3983)))) -(-373 R -3093) +((-3982 -12 (|has| |#1| (-6 -3982)) (|has| |#2| (-6 -3982))) (-3989 . T) (-3990 . T) (-3992 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -3982)) (|HasAttribute| |#2| (QUOTE -3982)))) +(-373 R -3092) ((|constructor| (NIL "\\spadtype{FunctionSpaceIntegration} provides functions for the indefinite integration of real-valued functions.")) (|integrate| (((|Union| |#2| (|List| |#2|)) |#2| (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable."))) NIL NIL -(-374 R -3093) +(-374 R -3092) ((|constructor| (NIL "Provides some special functions over an integral domain.")) (|iiabs| ((|#2| |#2|) "\\spad{iiabs(x)} should be local but conditional.")) (|iiGamma| ((|#2| |#2|) "\\spad{iiGamma(x)} should be local but conditional.")) (|airyBi| ((|#2| |#2|) "\\spad{airyBi(x)} returns the airybi function applied to \\spad{x}")) (|airyAi| ((|#2| |#2|) "\\spad{airyAi(x)} returns the airyai function applied to \\spad{x}")) (|besselK| ((|#2| |#2| |#2|) "\\spad{besselK(x,y)} returns the besselk function applied to \\spad{x} and \\spad{y}")) (|besselI| ((|#2| |#2| |#2|) "\\spad{besselI(x,y)} returns the besseli function applied to \\spad{x} and \\spad{y}")) (|besselY| ((|#2| |#2| |#2|) "\\spad{besselY(x,y)} returns the bessely function applied to \\spad{x} and \\spad{y}")) (|besselJ| ((|#2| |#2| |#2|) "\\spad{besselJ(x,y)} returns the besselj function applied to \\spad{x} and \\spad{y}")) (|polygamma| ((|#2| |#2| |#2|) "\\spad{polygamma(x,y)} returns the polygamma function applied to \\spad{x} and \\spad{y}")) (|digamma| ((|#2| |#2|) "\\spad{digamma(x)} returns the digamma function applied to \\spad{x}")) (|Beta| ((|#2| |#2| |#2|) "\\spad{Beta(x,y)} returns the beta function applied to \\spad{x} and \\spad{y}")) (|Gamma| ((|#2| |#2| |#2|) "\\spad{Gamma(a,x)} returns the incomplete Gamma function applied to a and \\spad{x}") ((|#2| |#2|) "\\spad{Gamma(f)} returns the formal Gamma function applied to \\spad{f}")) (|abs| ((|#2| |#2|) "\\spad{abs(f)} returns the absolute value operator applied to \\spad{f}")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a special function operator")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a special function operator."))) NIL NIL -(-375 R -3093) +(-375 R -3092) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1, a2)} returns \\spad{[a, q1, q2, q]} such that \\spad{k(a1, a2) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for \\spad{a2} may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve \\spad{a2}; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,...,an])} returns \\spad{[a, [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-376 R -3093) +(-376 R -3092) ((|constructor| (NIL "This package provides function which replaces transcendental kernels in a function space by random integers. The correspondence between the kernels and the integers is fixed between calls to new().")) (|newReduc| (((|Void|)) "\\spad{newReduc()} \\undocumented")) (|bringDown| (((|SparseUnivariatePolynomial| (|Fraction| (|Integer|))) |#2| (|Kernel| |#2|)) "\\spad{bringDown(f,k)} \\undocumented") (((|Fraction| (|Integer|)) |#2|) "\\spad{bringDown(f)} \\undocumented"))) NIL NIL @@ -1440,10 +1440,10 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-378 R -3093 UP) +(-378 R -3092 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL -((|HasCategory| |#2| (QUOTE (-951 (-48))))) +((|HasCategory| |#2| (QUOTE (-950 (-48))))) (-379) ((|constructor| (NIL "Creates and manipulates objects which correspond to FORTRAN data types,{} including array dimensions.")) (|fortranCharacter| (($) "\\spad{fortranCharacter()} returns CHARACTER,{} an element of FortranType")) (|fortranDoubleComplex| (($) "\\spad{fortranDoubleComplex()} returns DOUBLE COMPLEX,{} an element of FortranType")) (|fortranComplex| (($) "\\spad{fortranComplex()} returns COMPLEX,{} an element of FortranType")) (|fortranLogical| (($) "\\spad{fortranLogical()} returns LOGICAL,{} an element of FortranType")) (|fortranInteger| (($) "\\spad{fortranInteger()} returns INTEGER,{} an element of FortranType")) (|fortranDouble| (($) "\\spad{fortranDouble()} returns DOUBLE PRECISION,{} an element of FortranType")) (|fortranReal| (($) "\\spad{fortranReal()} returns REAL,{} an element of FortranType")) (|construct| (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|List| (|Polynomial| (|Integer|))) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType") (($ (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) (|List| (|Symbol|)) (|Boolean|)) "\\spad{construct(type,dims)} creates an element of FortranType")) (|external?| (((|Boolean|) $) "\\spad{external?(u)} returns \\spad{true} if \\spad{u} is declared to be EXTERNAL")) (|dimensionsOf| (((|List| (|Polynomial| (|Integer|))) $) "\\spad{dimensionsOf(t)} returns the dimensions of \\spad{t}")) (|scalarTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{scalarTypeOf(t)} returns the FORTRAN data type of \\spad{t}")) (|coerce| (($ (|FortranScalarType|)) "\\spad{coerce(t)} creates an element from a scalar type"))) NIL @@ -1460,7 +1460,7 @@ NIL ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,sqf,pd,r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r,sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,listOfDegrees,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,p,listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,p,r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,d,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,listOfDegrees,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein's criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein'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's criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-383 R UP -3093) +(-383 R UP -3092) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,p)} returns the lp norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri's norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,n)} returns the \\spad{n}th Bombieri's norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri's norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1498,16 +1498,16 @@ NIL NIL (-392) ((|constructor| (NIL "This category describes domains where \\spadfun{gcd} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common gcd of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-393 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"))) -((-3993 |has| (-350 (-858 |#1|)) (-496)) (-3991 . T) (-3990 . T)) -((|HasCategory| (-350 (-858 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-350 (-858 |#1|)) (QUOTE (-496)))) +((-3992 |has| (-350 (-857 |#1|)) (-495)) (-3990 . T) (-3989 . T)) +((|HasCategory| (-350 (-857 |#1|)) (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-350 (-857 |#1|)) (QUOTE (-495)))) (-394 |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"))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(((-3997 "*") |has| |#2| (-146)) (-3988 |has| |#2| (-495)) (-3993 |has| |#2| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) (-395 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,prime,lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it's conditional."))) NIL @@ -1534,7 +1534,7 @@ NIL NIL (-401 |vl| R IS E |ff| P) ((|constructor| (NIL "This package \\undocumented")) (* (($ |#6| $) "\\spad{p*x} \\undocumented")) (|multMonom| (($ |#2| |#4| $) "\\spad{multMonom(r,e,x)} \\undocumented")) (|build| (($ |#2| |#3| |#4|) "\\spad{build(r,i,e)} \\undocumented")) (|unitVector| (($ |#3|) "\\spad{unitVector(x)} \\undocumented")) (|monomial| (($ |#2| (|ModuleMonomial| |#3| |#4| |#5|)) "\\spad{monomial(r,x)} \\undocumented")) (|reductum| (($ $) "\\spad{reductum(x)} \\undocumented")) (|leadingIndex| ((|#3| $) "\\spad{leadingIndex(x)} \\undocumented")) (|leadingExponent| ((|#4| $) "\\spad{leadingExponent(x)} \\undocumented")) (|leadingMonomial| (((|ModuleMonomial| |#3| |#4| |#5|) $) "\\spad{leadingMonomial(x)} \\undocumented")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL (-402 E V R P Q) ((|constructor| (NIL "Gosper's summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b, n, new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1542,8 +1542,8 @@ NIL NIL (-403 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(lp)} returns the polynomial set whose members are the polynomials of \\axiom{lp}."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) (-404 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra''. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product'' 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 @@ -1572,7 +1572,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module'',{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) (|Zero| (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-411 |lv| -3093 R) +(-411 |lv| -3092 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1582,23 +1582,23 @@ NIL NIL (-413) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-3993 . T)) +((-3992 . T)) NIL (-414 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|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.")) (|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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) (-415 |Key| |Entry| |Tbl| |dent|) ((|constructor| (NIL "A sparse table has a default entry,{} which is returned if no other value has been explicitly stored for a key."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772))))) (-416 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)}"))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) (-417) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{pi()} returns the symbolic \\%\\spad{pi}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL (-418) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the case expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the has expression `e'."))) @@ -1606,29 +1606,29 @@ NIL NIL (-419 |Key| |Entry| |hashfn|) ((|constructor| (NIL "This domain provides access to the underlying Lisp hash tables. By varying the hashfn parameter,{} tables suited for different purposes can be obtained."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772))))) (-420) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre's book Lie Groups -- 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{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-421 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p, perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . 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|#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-950 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-961))))) (|HasCategory| (-484) (QUOTE (-756))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1013)))) (-12 (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-1013)))) (|HasAttribute| |#2| (QUOTE -3992)) (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-961)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-961)))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-72))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (-423) ((|constructor| (NIL "This domain represents the header of a definition.")) (|parameters| (((|List| (|ParameterAst|)) $) "\\spad{parameters(h)} gives the parameters specified in the definition header `h'.")) (|name| (((|Identifier|) $) "\\spad{name(h)} returns the name of the operation defined defined.")) (|headAst| (($ (|Identifier|) (|List| (|ParameterAst|))) "\\spad{headAst(f,[x1,..,xn])} constructs a function definition header."))) NIL NIL (-424 S) ((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-425 -3093 UP UPUP R) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-425 -3092 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}'s are integers and the \\spad{P}'s are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1638,12 +1638,12 @@ NIL NIL (-427) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating hexadecimal expansions.")) (|hex| (($ (|Fraction| (|Integer|))) "\\spad{hex(r)} converts a rational number to a hexadecimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(h)} returns the fractional part of a hexadecimal expansion."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) (-428 A S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#2| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#2|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#2|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#2| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#2| |#2|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL -((|HasAttribute| |#1| (QUOTE -3996)) (|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) +((|HasAttribute| |#1| (QUOTE -3995)) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (-429 S) ((|constructor| (NIL "A homogeneous aggregate is an aggregate of elements all of the same type. In the current system,{} all aggregates are homogeneous. Two attributes characterize classes of aggregates. Aggregates from domains with attribute \\spadatt{finiteAggregate} have a finite number of members. Those with attribute \\spadatt{shallowlyMutable} allow an element to be modified or updated without changing its overall value.")) (|member?| (((|Boolean|) |#1| $) "\\spad{member?(x,u)} tests if \\spad{x} is a member of \\spad{u}. For collections,{} \\axiom{member?(\\spad{x},{}\\spad{u}) = reduce(or,{}[x=y for \\spad{y} in \\spad{u}],{}\\spad{false})}.")) (|members| (((|List| |#1|) $) "\\spad{members(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|parts| (((|List| |#1|) $) "\\spad{parts(u)} returns a list of the consecutive elements of \\spad{u}. For collections,{} \\axiom{parts([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = (\\spad{x},{}\\spad{y},{}...,{}\\spad{z})}.")) (|count| (((|NonNegativeInteger|) |#1| $) "\\spad{count(x,u)} returns the number of occurrences of \\spad{x} in \\spad{u}. For collections,{} \\axiom{count(\\spad{x},{}\\spad{u}) = reduce(+,{}[x=y for \\spad{y} in \\spad{u}],{}0)}.") (((|NonNegativeInteger|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{count(p,u)} returns the number of elements \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. For collections,{} \\axiom{count(\\spad{p},{}\\spad{u}) = reduce(+,{}[1 for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})],{}0)}.")) (|every?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{every?(f,u)} tests if \\spad{p}(\\spad{x}) is \\spad{true} for all elements \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{every?(\\spad{p},{}\\spad{u}) = reduce(and,{}map(\\spad{f},{}\\spad{u}),{}\\spad{true},{}\\spad{false})}.")) (|any?| (((|Boolean|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{any?(p,u)} tests if \\axiom{\\spad{p}(\\spad{x})} is \\spad{true} for any element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{any?(\\spad{p},{}\\spad{u}) = reduce(or,{}map(\\spad{f},{}\\spad{u}),{}\\spad{false},{}\\spad{true})}.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\axiom{\\spad{f}(\\spad{x})}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) NIL @@ -1664,3113 +1664,3109 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-434 -3093 UP |AlExt| |AlPol|) +(-434 -3092 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP's.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p, f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-435) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| $ (QUOTE (-962))) (|HasCategory| $ (QUOTE (-951 (-485))))) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| $ (QUOTE (-961))) (|HasCategory| $ (QUOTE (-950 (-484))))) (-436 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan \\spad{Aug/87}} This is the basic one dimensional array data type."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (-437 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray's of PrimitiveArray's."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) (-438 K R UP) ((|constructor| (NIL "\\indented{1}{Author: Clifton Williamson} Date Created: 9 August 1993 Date Last Updated: 3 December 1993 Basic Operations: chineseRemainder,{} factorList Related Domains: PAdicWildFunctionFieldIntegralBasis(\\spad{K},{}\\spad{R},{}UP,{}\\spad{F}) Also See: WildFunctionFieldIntegralBasis,{} FunctionFieldIntegralBasis AMS Classifications: Keywords: function field,{} finite field,{} integral basis Examples: References: Description:")) (|chineseRemainder| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|List| |#3|) (|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|NonNegativeInteger|)) "\\spad{chineseRemainder(lu,lr,n)} \\undocumented")) (|listConjugateBases| (((|List| (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) (|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{listConjugateBases(bas,q,n)} returns the list \\spad{[bas,bas^Frob,bas^(Frob^2),...bas^(Frob^(n-1))]},{} where \\spad{Frob} raises the coefficients of all polynomials appearing in the basis \\spad{bas} to the \\spad{q}th power.")) (|factorList| (((|List| (|SparseUnivariatePolynomial| |#1|)) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorList(k,n,m,j)} \\undocumented"))) NIL NIL -(-439 R UP -3093) +(-439 R UP -3092) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{mi} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn} and \\spad{mi} is a record \\spad{[basis,basisDen,basisInv]}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then a basis \\spad{v1,...,vn} for \\spad{mi} is given by \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1, m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,m2,d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,matrixOut,prime,n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,sing,n)} is \\spad{gcd(sing,g)} where \\spad{g} is the gcd of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL -(-440 |mn|) -((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| (-85) (QUOTE (-260 (-85)))) (|HasCategory| (-85) (QUOTE (-1014)))) (|HasCategory| (-85) (QUOTE (-554 (-474)))) (|HasCategory| (-85) (QUOTE (-757))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-85) (QUOTE (-1014))) (|HasCategory| (-85) (QUOTE (-553 (-773)))) (|HasCategory| (-85) (QUOTE (-72)))) -(-441 K R UP L) +(-440 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 NIL -(-442) +(-441) ((|constructor| (NIL "\\indented{1}{This domain implements a container of information} about the AXIOM library")) (|fullDisplay| (((|Void|) $) "\\spad{fullDisplay(ic)} prints all of the information contained in \\axiom{\\spad{ic}}.")) (|display| (((|Void|) $) "\\spad{display(ic)} prints a summary of the information contained in \\axiom{\\spad{ic}}.")) (|elt| (((|String|) $ (|Symbol|)) "\\spad{elt(ic,s)} selects a particular field from \\axiom{\\spad{ic}}. Valid fields are \\axiom{name,{} nargs,{} exposed,{} type,{} abbreviation,{} kind,{} origin,{} params,{} condition,{} doc}."))) NIL NIL -(-443 R Q A B) +(-442 R Q A B) ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,...,qn])} returns \\spad{[[p1,...,pn], d]} such that \\spad{qi = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,...,qn])} returns \\spad{[p1,...,pn]} such that \\spad{qi = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}'s.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,...,qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}qn."))) NIL NIL -(-444 -3093 |Expon| |VarSet| |DPoly|) +(-443 -3092 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,f,lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL -((|HasCategory| |#3| (QUOTE (-554 (-1091))))) -(-445 |vl| |nv|) +((|HasCategory| |#3| (QUOTE (-553 (-1090))))) +(-444 |vl| |nv|) ((|constructor| (NIL "\\indented{2}{This package provides functions for the primary decomposition of} polynomial ideals over the rational numbers. The ideals are members of the \\spadtype{PolynomialIdeals} domain,{} and the polynomial generators are required to be from the \\spadtype{DistributedMultivariatePolynomial} domain.")) (|contract| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|List| (|OrderedVariableList| |#1|))) "\\spad{contract(I,lvar)} contracts the ideal \\spad{I} to the polynomial ring \\spad{F[lvar]}.")) (|primaryDecomp| (((|List| (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{primaryDecomp(I)} returns a list of primary ideals such that their intersection is the ideal \\spad{I}.")) (|radical| (((|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radical(I)} returns the radical of the ideal \\spad{I}.")) (|prime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{prime?(I)} tests if the ideal \\spad{I} is prime.")) (|zeroDimPrimary?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrimary?(I)} tests if the ideal \\spad{I} is 0-dimensional primary.")) (|zeroDimPrime?| (((|Boolean|) (|PolynomialIdeals| (|Fraction| (|Integer|)) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|OrderedVariableList| |#1|) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{zeroDimPrime?(I)} tests if the ideal \\spad{I} is a 0-dimensional prime."))) NIL NIL -(-446 T$) +(-445 T$) ((|constructor| (NIL "This is the category of all domains that implement idempotent operations."))) -(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3057 (|f| |x| |x|) |x|))) . T)) +(((|%Rule| |idempotence| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (-3056 (|f| |x| |x|) |x|))) . T)) NIL -(-447) +(-446) ((|constructor| (NIL "This domain provides representation for plain identifiers. It differs from Symbol in that it does not support any form of scripting. It is a plain basic data structure. \\blankline")) (|gensym| (($) "\\spad{gensym()} returns a new identifier,{} different from any other identifier in the running system"))) NIL NIL -(-448 A S) +(-447 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian groups over an abelian group \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) -(-449 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +(-448 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of abelian monoids over an abelian monoid \\spad{A} of} generators indexed by the ordered set \\spad{S}. All items have finite support. Only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) -(-450 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +(-449 A S) ((|constructor| (NIL "This category represents the direct product of some set with respect to an ordered indexing set.")) (|terms| (((|List| (|IndexedProductTerm| |#1| |#2|)) $) "\\spad{terms x} returns the list of terms in \\spad{x}. Each term is a pair of a support (the first component) and the corresponding value (the second component).")) (|reductum| (($ $) "\\spad{reductum(z)} returns a new element created by removing the leading coefficient/support pair from the element \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingSupport| ((|#2| $) "\\spad{leadingSupport(z)} returns the index of leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(z)} returns the coefficient of the leading (with respect to the ordering on the indexing set) monomial of \\spad{z}. Error: if \\spad{z} has no support.")) (|monomial| (($ |#1| |#2|) "\\spad{monomial(a,s)} constructs a direct product element with the \\spad{s} component set to \\spad{a}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,z)} returns the new element created by applying the function \\spad{f} to each component of the direct product element \\spad{z}."))) NIL NIL -(-451 A S) +(-450 A S) ((|constructor| (NIL "Indexed direct products of objects over a set \\spad{A} of generators indexed by an ordered set \\spad{S}. All items have finite support.")) (|combineWithIf| (($ $ $ (|Mapping| |#1| |#1| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{combineWithIf(u,v,f,p)} returns the result of combining index-wise,{} coefficients of \\spad{u} and \\spad{u} if when satisfy the predicate \\spad{p}. Those pairs of coefficients which fail\\spad{p} are implicitly ignored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) -(-452 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +(-451 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoids \\spad{A} of} generators indexed by the ordered set \\spad{S}. The inherited order is lexicographical. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) -(-453 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +(-452 A S) ((|constructor| (NIL "\\indented{1}{Indexed direct products of ordered abelian monoid sups \\spad{A},{}} generators indexed by the ordered set \\spad{S}. All items have finite support: only non-zero terms are stored."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) -(-454 A S) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) +(-453 A S) ((|constructor| (NIL "An indexed product term is a utility domain used in the representation of indexed direct product objects.")) (|coefficient| ((|#1| $) "\\spad{coefficient t} returns the coefficient of the tern \\spad{t}.")) (|index| ((|#2| $) "\\spad{index t} returns the index of the term \\spad{t}.")) (|term| (($ |#2| |#1|) "\\spad{term(s,a)} constructs a term with index \\spad{s} and coefficient \\spad{a}."))) NIL NIL -(-455 S A B) +(-454 S A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#2|) (|List| |#3|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#2| |#3|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-456 A B) +(-455 A B) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation'' substitutions. The difference between this and \\spadtype{Evalable} is that the operations in this category specify the substitution as a pair of arguments rather than as an equation.")) (|eval| (($ $ (|List| |#1|) (|List| |#2|)) "\\spad{eval(f, [x1,...,xn], [v1,...,vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ |#1| |#2|) "\\spad{eval(f, x, v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-457 S E |un|) +(-456 S E |un|) ((|constructor| (NIL "Internal implementation of a free abelian monoid."))) NIL -((|HasCategory| |#2| (QUOTE (-717)))) -(-458 S |mn|) +((|HasCategory| |#2| (QUOTE (-716)))) +(-457 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan \\spad{July/87},{} modified SMW \\spad{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}"))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-459) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-458) ((|constructor| (NIL "This domain represents AST for conditional expressions.")) (|elseBranch| (((|SpadAst|) $) "thenBranch(\\spad{e}) returns the `else-branch' of `e'.")) (|thenBranch| (((|SpadAst|) $) "\\spad{thenBranch(e)} returns the `then-branch' of `e'.")) (|condition| (((|SpadAst|) $) "\\spad{condition(e)} returns the condition of the if-expression `e'."))) NIL NIL -(-460 |p| |n|) +(-459 |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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((OR (|HasCategory| (-518 |#1|) (QUOTE (-118))) (|HasCategory| (-518 |#1|) (QUOTE (-320)))) (|HasCategory| (-518 |#1|) (QUOTE (-120))) (|HasCategory| (-518 |#1|) (QUOTE (-320))) (|HasCategory| (-518 |#1|) (QUOTE (-118)))) -(-461 R |Row| |Col| M) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((OR (|HasCategory| (-517 |#1|) (QUOTE (-118))) (|HasCategory| (-517 |#1|) (QUOTE (-320)))) (|HasCategory| (-517 |#1|) (QUOTE (-120))) (|HasCategory| (-517 |#1|) (QUOTE (-320))) (|HasCategory| (-517 |#1|) (QUOTE (-118)))) +(-460 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,{} m*h and h*m are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -3997))) -(-462 R |Row| |Col| M QF |Row2| |Col2| M2) +((|HasAttribute| |#3| (QUOTE -3996))) +(-461 R |Row| |Col| M QF |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{InnerMatrixQuotientFieldFunctions} provides functions on matrices over an integral domain which involve the quotient field of that integral domain. The functions rowEchelon and inverse return matrices with entries in the quotient field.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|inverse| (((|Union| |#8| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square. Note: the result will have entries in the quotient field.")) (|rowEchelon| ((|#8| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}. the result will have entries in the quotient field."))) NIL -((|HasAttribute| |#7| (QUOTE -3997))) -(-463) +((|HasAttribute| |#7| (QUOTE -3996))) +(-462) ((|constructor| (NIL "This domain represents an `import' of types.")) (|imports| (((|List| (|TypeAst|)) $) "\\spad{imports(x)} returns the list of imported types.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::ImportAst constructs an ImportAst for the list if types `ts'."))) NIL NIL -(-464) +(-463) ((|constructor| (NIL "This domain represents the `in' iterator syntax.")) (|sequence| (((|SpadAst|) $) "\\spad{sequence(i)} returns the sequence expression being iterated over by `i'.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the `in' iterator 'i'"))) NIL NIL -(-465 S) +(-464 S) ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL -(-466) +(-465) ((|constructor| (NIL "This category describes input byte stream conduits.")) (|readBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{readBytes!(c,b)} reads byte sequences from conduit `c' into the byte buffer `b'. The actual number of bytes written is returned,{} and the length of `b' is set to that amount.")) (|readUInt32!| (((|Maybe| (|UInt32|)) $) "\\spad{readUInt32!(cond)} attempts to read a \\spad{UInt32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt32!| (((|Maybe| (|Int32|)) $) "\\spad{readInt32!(cond)} attempts to read an \\spad{Int32} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt16!| (((|Maybe| (|UInt16|)) $) "\\spad{readUInt16!(cond)} attempts to read a \\spad{UInt16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt16!| (((|Maybe| (|Int16|)) $) "\\spad{readInt16!(cond)} attempts to read an \\spad{Int16} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readUInt8!| (((|Maybe| (|UInt8|)) $) "\\spad{readUInt8!(cond)} attempts to read a \\spad{UInt8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readInt8!| (((|Maybe| (|Int8|)) $) "\\spad{readInt8!(cond)} attempts to read an \\spad{Int8} value from the input conduit `cond'. Returns the value if successful,{} otherwise \\spad{nothing}.")) (|readByte!| (((|Maybe| (|Byte|)) $) "\\spad{readByte!(cond)} attempts to read a byte from the input conduit `cond'. Returns the read byte if successful,{} otherwise \\spad{nothing}."))) NIL NIL -(-467 GF) +(-466 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(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{**}{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 GF(2^m) using normal bases\",{} Information and Computation 78,{} 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 GF(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} 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 GF."))) NIL NIL -(-468) +(-467) ((|constructor| (NIL "This domain provides representation for binary files open for input operations. `Binary' here means that the conduits do not interpret their contents.")) (|position!| (((|SingleInteger|) $ (|SingleInteger|)) "position(\\spad{f},{}\\spad{p}) sets the current byte-position to `i'.")) (|position| (((|SingleInteger|) $) "\\spad{position(f)} returns the current byte-position in the file `f'.")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(ifile)} holds if `ifile' is in open state.")) (|eof?| (((|Boolean|) $) "\\spad{eof?(ifile)} holds when the last read reached end of file.")) (|inputBinaryFile| (($ (|String|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputBinaryFile(f)} returns an input conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-469 R) +(-468 R) ((|constructor| (NIL "This package provides operations to create incrementing functions.")) (|incrementBy| (((|Mapping| |#1| |#1|) |#1|) "\\spad{incrementBy(n)} produces a function which adds \\spad{n} to whatever argument it is given. For example,{} if {\\spad{f} := increment(\\spad{n})} then \\spad{f x} is \\spad{x+n}.")) (|increment| (((|Mapping| |#1| |#1|)) "\\spad{increment()} produces a function which adds \\spad{1} to whatever argument it is given. For example,{} if {\\spad{f} := increment()} then \\spad{f x} is \\spad{x+1}."))) NIL NIL -(-470 |Varset|) +(-469 |Varset|) ((|constructor| (NIL "\\indented{2}{IndexedExponents of an ordered set of variables gives a representation} for the degree of polynomials in commuting variables. It gives an ordered pairing of non negative integer exponents with variables"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-695) (QUOTE (-1014))))) -(-471 K -3093 |Par|) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-694) (QUOTE (-1013))))) +(-470 K -3092 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,eps,factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to br used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol, eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL -(-472) +(-471) NIL NIL NIL -(-473) +(-472) ((|constructor| (NIL "Default infinity signatures for the interpreter; Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|minusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{minusInfinity()} returns minusInfinity.")) (|plusInfinity| (((|OrderedCompletion| (|Integer|))) "\\spad{plusInfinity()} returns plusIinfinity.")) (|infinity| (((|OnePointCompletion| (|Integer|))) "\\spad{infinity()} returns infinity."))) NIL NIL -(-474) +(-473) ((|constructor| (NIL "Domain of parsed forms which can be passed to the interpreter. This is also the interface between algebra code and facilities in the interpreter.")) (|compile| (((|Symbol|) (|Symbol|) (|List| $)) "\\spad{compile(f, [t1,...,tn])} forces the interpreter to compile the function \\spad{f} with signature \\spad{(t1,...,tn) -> ?}. returns the symbol \\spad{f} if successful. Error: if \\spad{f} was not defined beforehand in the interpreter,{} or if the \\spad{ti}'s are not valid types,{} or if the compiler fails.")) (|declare| (((|Symbol|) (|List| $)) "\\spad{declare(t)} returns a name \\spad{f} such that \\spad{f} has been declared to the interpreter to be of type \\spad{t},{} but has not been assigned a value yet. Note: \\spad{t} should be created as \\spad{devaluate(T)\\$Lisp} where \\spad{T} is the actual type of \\spad{f} (this hack is required for the case where \\spad{T} is a mapping type).")) (|parseString| (($ (|String|)) "parseString is the inverse of unparse. It parses a string to InputForm.")) (|unparse| (((|String|) $) "\\spad{unparse(f)} returns a string \\spad{s} such that the parser would transform \\spad{s} to \\spad{f}. Error: if \\spad{f} is not the parsed form of a string.")) (|flatten| (($ $) "\\spad{flatten(s)} returns an input form corresponding to \\spad{s} with all the nested operations flattened to triples using new local variables. If \\spad{s} is a piece of code,{} this speeds up the compilation tremendously later on.")) (|One| (($) "\\spad{1} returns the input form corresponding to 1.")) (|Zero| (($) "\\spad{0} returns the input form corresponding to 0.")) (** (($ $ (|Integer|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.") (($ $ (|NonNegativeInteger|)) "\\spad{a ** b} returns the input form corresponding to \\spad{a ** b}.")) (/ (($ $ $) "\\spad{a / b} returns the input form corresponding to \\spad{a / b}.")) (* (($ $ $) "\\spad{a * b} returns the input form corresponding to \\spad{a * b}.")) (+ (($ $ $) "\\spad{a + b} returns the input form corresponding to \\spad{a + b}.")) (|lambda| (($ $ (|List| (|Symbol|))) "\\spad{lambda(code, [x1,...,xn])} returns the input form corresponding to \\spad{(x1,...,xn) +-> code} if \\spad{n > 1},{} or to \\spad{x1 +-> code} if \\spad{n = 1}.")) (|function| (($ $ (|List| (|Symbol|)) (|Symbol|)) "\\spad{function(code, [x1,...,xn], f)} returns the input form corresponding to \\spad{f(x1,...,xn) == code}.")) (|binary| (($ $ (|List| $)) "\\spad{binary(op, [a1,...,an])} returns the input form corresponding to \\spad{a1 op a2 op ... op an}.")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} makes \\spad{s} into an input form.")) (|interpret| (((|Any|) $) "\\spad{interpret(f)} passes \\spad{f} to the interpreter."))) NIL NIL -(-475 R) +(-474 R) ((|constructor| (NIL "Tools for manipulating input forms.")) (|interpret| ((|#1| (|InputForm|)) "\\spad{interpret(f)} passes \\spad{f} to the interpreter,{} and transforms the result into an object of type \\spad{R}.")) (|packageCall| (((|InputForm|) (|Symbol|)) "\\spad{packageCall(f)} returns the input form corresponding to \\spad{f}\\$\\spad{R}."))) NIL NIL -(-476 |Coef| UTS) +(-475 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-477 K -3093 |Par|) +(-476 K -3092 |Par|) ((|constructor| (NIL "This is an internal package for computing approximate solutions to systems of polynomial equations. The parameter \\spad{K} specifies the coefficient field of the input polynomials and must be either \\spad{Fraction(Integer)} or \\spad{Complex(Fraction Integer)}. The parameter \\spad{F} specifies where the solutions must lie and can be one of the following: \\spad{Float},{} \\spad{Fraction(Integer)},{} \\spad{Complex(Float)},{} \\spad{Complex(Fraction Integer)}. The last parameter specifies the type of the precision operand and must be either \\spad{Fraction(Integer)} or \\spad{Float}.")) (|makeEq| (((|List| (|Equation| (|Polynomial| |#2|))) (|List| |#2|) (|List| (|Symbol|))) "\\spad{makeEq(lsol,lvar)} returns a list of equations formed by corresponding members of \\spad{lvar} and \\spad{lsol}.")) (|innerSolve| (((|List| (|List| |#2|)) (|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) |#3|) "\\spad{innerSolve(lnum,lden,lvar,eps)} returns a list of solutions of the system of polynomials \\spad{lnum},{} with the side condition that none of the members of \\spad{lden} vanish identically on any solution. Each solution is expressed as a list corresponding to the list of variables in \\spad{lvar} and with precision specified by \\spad{eps}.")) (|innerSolve1| (((|List| |#2|) (|Polynomial| |#1|) |#3|) "\\spad{innerSolve1(p,eps)} returns the list of the zeros of the polynomial \\spad{p} with precision \\spad{eps}.") (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{innerSolve1(up,eps)} returns the list of the zeros of the univariate polynomial \\spad{up} with precision \\spad{eps}."))) NIL NIL -(-478 R BP |pMod| |nextMod|) +(-477 R BP |pMod| |nextMod|) ((|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(f,p)} reduces the coefficients of the polynomial \\spad{f} modulo the prime \\spad{p}.")) (|modularGcd| ((|#2| (|List| |#2|)) "\\spad{modularGcd(listf)} computes the gcd of the list of polynomials \\spad{listf} by modular methods.")) (|modularGcdPrimitive| ((|#2| (|List| |#2|)) "\\spad{modularGcdPrimitive(f1,f2)} computes the gcd of the two polynomials \\spad{f1} and \\spad{f2} by modular methods."))) NIL NIL -(-479 OV E R P) +(-478 OV E R P) ((|constructor| (NIL "\\indented{2}{This is an inner package for factoring multivariate polynomials} over various coefficient domains in characteristic 0. The univariate factor operation is passed as a parameter. Multivariate hensel lifting is used to lift the univariate factorization")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}. \\spad{p} is represented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#3|)) (|SparseUnivariatePolynomial| |#3|))) "\\spad{factor(p,ufact)} factors the multivariate polynomial \\spad{p} by specializing variables and calling the univariate factorizer \\spad{ufact}."))) NIL NIL -(-480 K UP |Coef| UTS) +(-479 K UP |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an arbitrary finite field.")) (|generalInfiniteProduct| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#4| |#4|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#4| |#4|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#4| |#4|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-481 |Coef| UTS) +(-480 |Coef| UTS) ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over a field of prime order.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-482 R UP) +(-481 R UP) ((|constructor| (NIL "Find the sign of a polynomial around a point or infinity.")) (|signAround| (((|Union| (|Integer|) #1="failed") |#2| |#1| (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| |#1| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,r,i,f)} \\undocumented") (((|Union| (|Integer|) #1#) |#2| (|Integer|) (|Mapping| (|Union| (|Integer|) #1#) |#1|)) "\\spad{signAround(u,i,f)} \\undocumented"))) NIL NIL -(-483 S) +(-482 S) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) NIL NIL -(-484) +(-483) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,b)},{} \\spad{0<=a<b>1},{} \\spad{(a,b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,b,p)},{} \\spad{0<=a,b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{a-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-485) +(-484) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3983 . T) (-3987 . T) (-3982 . T) (-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-486) +(-485) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 16 bits."))) NIL NIL -(-487) +(-486) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 32 bits."))) NIL NIL -(-488) +(-487) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 64 bits."))) NIL NIL -(-489) +(-488) ((|constructor| (NIL "This domain is a datatype for (signed) integer values of precision 8 bits."))) NIL NIL -(-490 |Key| |Entry| |addDom|) +(-489 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) -(-491 R -3093) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772))))) +(-490 R -3092) ((|constructor| (NIL "This package provides functions for the integration of algebraic integrands over transcendental functions.")) (|algint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|SparseUnivariatePolynomial| |#2|) (|SparseUnivariatePolynomial| |#2|))) "\\spad{algint(f, x, y, d)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}; \\spad{d} is the derivation to use on \\spad{k[x]}."))) NIL NIL -(-492 R0 -3093 UP UPUP R) +(-491 R0 -3092 UP UPUP R) ((|constructor| (NIL "This package provides functions for integrating a function on an algebraic curve.")) (|palginfieldint| (((|Union| |#5| "failed") |#5| (|Mapping| |#3| |#3|)) "\\spad{palginfieldint(f, d)} returns an algebraic function \\spad{g} such that \\spad{dg = f} if such a \\spad{g} exists,{} \"failed\" otherwise. Argument \\spad{f} must be a pure algebraic function.")) (|palgintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{palgintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}. Argument \\spad{f} must be a pure algebraic function.")) (|algintegrate| (((|IntegrationResult| |#5|) |#5| (|Mapping| |#3| |#3|)) "\\spad{algintegrate(f, d)} integrates \\spad{f} with respect to the derivation \\spad{d}."))) NIL NIL -(-493) +(-492) ((|constructor| (NIL "This package provides functions to lookup bits in integers")) (|bitTruth| (((|Boolean|) (|Integer|) (|Integer|)) "\\spad{bitTruth(n,m)} returns \\spad{true} if coefficient of 2**m in abs(\\spad{n}) is 1")) (|bitCoef| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{bitCoef(n,m)} returns the coefficient of 2**m in abs(\\spad{n})")) (|bitLength| (((|Integer|) (|Integer|)) "\\spad{bitLength(n)} returns the number of bits to represent abs(\\spad{n})"))) NIL NIL -(-494 R) +(-493 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{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3770 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-495 S) +(-494 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."))) NIL NIL -(-496) +(-495) ((|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."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-497 R -3093) +(-496 R -3092) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1="failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,x,k,[k1,...,kn])} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}kn (the \\spad{ki}'s must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f, x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f, x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,x,[g1,...,gn])} returns functions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} and \\spad{d(h+sum(ci log(gi)))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #1#) |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f, x, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL -(-498 I) +(-497 I) ((|constructor| (NIL "\\indented{1}{This Package contains basic methods for integer factorization.} The factor operation employs trial division up to 10,{}000. It then tests to see if \\spad{n} is a perfect power before using Pollards rho method. Because Pollards method may fail,{} the result of factor may contain composite factors. We should also employ Lenstra's eliptic curve method.")) (|PollardSmallFactor| (((|Union| |#1| "failed") |#1|) "\\spad{PollardSmallFactor(n)} returns a factor of \\spad{n} or \"failed\" if no one is found")) (|BasicMethod| (((|Factored| |#1|) |#1|) "\\spad{BasicMethod(n)} returns the factorization of integer \\spad{n} by trial division")) (|squareFree| (((|Factored| |#1|) |#1|) "\\spad{squareFree(n)} returns the square free factorization of integer \\spad{n}")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(n)} returns the full factorization of integer \\spad{n}"))) NIL NIL -(-499 R -3093 L) +(-498 R -3092 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x, y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,g,x,y,z,t,c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| #1#)) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op, g, x, y, d, p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,k,f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,k,k,p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| #2="failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f, g, x, y, foo, t, c)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| #2#) |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #2#) |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f, g, x, y, foo, d, p)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a, b, x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f, x, y, [u1,...,un], z, t, c)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) #3#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f, x, y, [u1,...,un], d, p)} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4="failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f, x, y, g, z, t, c)} returns functions \\spad{[h, d]} such that \\spad{dh/dx = f(x,y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) #4#) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f, x, y, g, d, p)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f, x, y, z, t, c)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,y)dx = c f(t,y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f, x, y, d, p)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) -(-500) +((|HasCategory| |#3| (|%list| (QUOTE -600) (|devaluate| |#2|)))) +(-499) ((|constructor| (NIL "This package provides various number theoretic functions on the integers.")) (|sumOfKthPowerDivisors| (((|Integer|) (|Integer|) (|NonNegativeInteger|)) "\\spad{sumOfKthPowerDivisors(n,k)} returns the sum of the \\spad{k}th powers of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. the sum of the \\spad{k}th powers of the divisors of \\spad{n} is often denoted by \\spad{sigma_k(n)}.")) (|sumOfDivisors| (((|Integer|) (|Integer|)) "\\spad{sumOfDivisors(n)} returns the sum of the integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The sum of the divisors of \\spad{n} is often denoted by \\spad{sigma(n)}.")) (|numberOfDivisors| (((|Integer|) (|Integer|)) "\\spad{numberOfDivisors(n)} returns the number of integers between 1 and \\spad{n} (inclusive) which divide \\spad{n}. The number of divisors of \\spad{n} is often denoted by \\spad{tau(n)}.")) (|moebiusMu| (((|Integer|) (|Integer|)) "\\spad{moebiusMu(n)} returns the Moebius function \\spad{mu(n)}. \\spad{mu(n)} is either \\spad{-1},{}0 or 1 as follows: \\spad{mu(n) = 0} if \\spad{n} is divisible by a square > 1,{} \\spad{mu(n) = (-1)^k} if \\spad{n} is square-free and has \\spad{k} distinct prime divisors.")) (|legendre| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{legendre(a,p)} returns the Legendre symbol \\spad{L(a/p)}. \\spad{L(a/p) = (-1)**((p-1)/2) mod p} (\\spad{p} prime),{} which is 0 if \\spad{a} is 0,{} 1 if \\spad{a} is a quadratic residue \\spad{mod p} and \\spad{-1} otherwise. Note: because the primality test is expensive,{} if it is known that \\spad{p} is prime then use \\spad{jacobi(a,p)}.")) (|jacobi| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{jacobi(a,b)} returns the Jacobi symbol \\spad{J(a/b)}. When \\spad{b} is odd,{} \\spad{J(a/b) = product(L(a/p) for p in factor b )}. Note: by convention,{} 0 is returned if \\spad{gcd(a,b) ~= 1}. Iterative \\spad{O(log(b)^2)} version coded by Michael Monagan June 1987.")) (|harmonic| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{harmonic(n)} returns the \\spad{n}th harmonic number. This is \\spad{H[n] = sum(1/k,k=1..n)}.")) (|fibonacci| (((|Integer|) (|Integer|)) "\\spad{fibonacci(n)} returns the \\spad{n}th Fibonacci number. the Fibonacci numbers \\spad{F[n]} are defined by \\spad{F[0] = F[1] = 1} and \\spad{F[n] = F[n-1] + F[n-2]}. The algorithm has running time \\spad{O(log(n)^3)}. Reference: Knuth,{} The Art of Computer Programming Vol 2,{} Semi-Numerical Algorithms.")) (|eulerPhi| (((|Integer|) (|Integer|)) "\\spad{eulerPhi(n)} returns the number of integers between 1 and \\spad{n} (including 1) which are relatively prime to \\spad{n}. This is the Euler phi function \\spad{\\phi(n)} is also called the totient function.")) (|euler| (((|Integer|) (|Integer|)) "\\spad{euler(n)} returns the \\spad{n}th Euler number. This is \\spad{2^n E(n,1/2)},{} where \\spad{E(n,x)} is the \\spad{n}th Euler polynomial.")) (|divisors| (((|List| (|Integer|)) (|Integer|)) "\\spad{divisors(n)} returns a list of the divisors of \\spad{n}.")) (|chineseRemainder| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{chineseRemainder(x1,m1,x2,m2)} returns \\spad{w},{} where \\spad{w} is such that \\spad{w = x1 mod m1} and \\spad{w = x2 mod m2}. Note: \\spad{m1} and \\spad{m2} must be relatively prime.")) (|bernoulli| (((|Fraction| (|Integer|)) (|Integer|)) "\\spad{bernoulli(n)} returns the \\spad{n}th Bernoulli number. this is \\spad{B(n,0)},{} where \\spad{B(n,x)} is the \\spad{n}th Bernoulli polynomial."))) NIL NIL -(-501 -3093 UP UPUP R) +(-500 -3092 UP UPUP R) ((|constructor| (NIL "algebraic Hermite redution.")) (|HermiteIntegrate| (((|Record| (|:| |answer| |#4|) (|:| |logpart| |#4|)) |#4| (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, ')} returns \\spad{[g,h]} such that \\spad{f = g' + h} and \\spad{h} has a only simple finite normal poles."))) NIL NIL -(-502 -3093 UP) +(-501 -3092 UP) ((|constructor| (NIL "Hermite integration,{} transcendental case.")) (|HermiteIntegrate| (((|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |logpart| (|Fraction| |#2|)) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{HermiteIntegrate(f, D)} returns \\spad{[g, h, s, p]} such that \\spad{f = Dg + h + s + p},{} \\spad{h} has a squarefree denominator normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. Furthermore,{} \\spad{h} and \\spad{s} have no polynomial parts. \\spad{D} is the derivation to use on \\spadtype{UP}."))) NIL NIL -(-503 R -3093 L) +(-502 R -3092 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| #1="failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op, g, kx, y, x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| #1#) |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| #1#) |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp, f, g, x, y, foo)} returns a function \\spad{z(x,y)} such that \\spad{dz/dx + n * df/dx z(x,y) = g(x,y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a, b, x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f, x, y, [u1,...,un])} returns functions \\spad{[h,[[ci, ui]]]} such that the \\spad{ui}'s are among \\spad{[u1,...,un]} and \\spad{d(h + sum(ci log(ui)))/dx = f(x,y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f, x, y, g)} returns functions \\spad{[h, c]} such that \\spad{dh/dx = f(x,y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f, x, y)} returns the integral of \\spad{f(x,y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL -((|HasCategory| |#3| (|%list| (QUOTE -601) (|devaluate| |#2|)))) -(-504 R -3093) +((|HasCategory| |#3| (|%list| (QUOTE -600) (|devaluate| |#2|)))) +(-503 R -3092) ((|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| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-1054)))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-570))))) -(-505 -3093 UP) +((-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-1053)))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-569))))) +(-504 -3092 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f, [g1,...,gn])} returns fractions \\spad{[h,[[ci, gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(ci log(gi)))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f, g)} returns fractions \\spad{[h, c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL -(-506 S) +(-505 S) ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-507 -3093) +(-506 -3092) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f, x, g)} returns fractions \\spad{[h, c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h, c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f, x, [g1,...,gn])} returns fractions \\spad{[h, [[ci,gi]]]} such that the \\spad{gi}'s are among \\spad{[g1,...,gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(ci log(gi)))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f, x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f, x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL -(-508 R) +(-507 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."))) -((-3771 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3770 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-509) +(-508) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists."))) NIL NIL -(-510 R -3093) +(-509 R -3092) ((|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| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-570))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-496)))) -(-511 -3093 UP) +((-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-239))) (|HasCategory| |#2| (QUOTE (-569))) (|HasCategory| |#2| (QUOTE (-950 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-239)))) (|HasCategory| |#1| (QUOTE (-495)))) +(-510 -3092 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|)) #1="failed") |#1|) |#1|) "\\spad{primintfldpoly(p, ', t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f, ', [u1,...,un])} returns \\spad{[v, [c1,...,cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[ci * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f, ', g)} returns \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f, ', foo, [u1,...,un])} returns \\spad{[v, [c1,...,cn], a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,[ci * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f, ', foo, g)} returns either \\spad{[v, c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) #1#) |#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|)) #1#) |#1|)) "\\spad{primintegrate(f, ', foo)} returns \\spad{[g, a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-512 R -3093) +(-511 R -3092) ((|constructor| (NIL "This package computes the inverse Laplace Transform.")) (|inverseLaplace| (((|Union| |#2| "failed") |#2| (|Symbol|) (|Symbol|)) "\\spad{inverseLaplace(f, s, t)} returns the Inverse Laplace transform of \\spad{f(s)} using \\spad{t} as the new variable or \"failed\" if unable to find a closed form."))) NIL NIL -(-513) +(-512) ((|constructor| (NIL "This category describes byte stream conduits supporting both input and output operations."))) NIL NIL -(-514) +(-513) ((|constructor| (NIL "\\indented{2}{This domain provides representation for binary files open} \\indented{2}{for input and output operations.} See Also: InputBinaryFile,{} OutputBinaryFile")) (|isOpen?| (((|Boolean|) $) "\\spad{isOpen?(f)} holds if `f' is in open state.")) (|inputOutputBinaryFile| (($ (|String|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{inputOutputBinaryFile(f)} returns an input/output conduit obtained by opening the file designated by `f' as a binary file."))) NIL NIL -(-515) +(-514) ((|constructor| (NIL "This domain provides constants to describe directions of IO conduits (file,{} etc) mode of operations.")) (|closed| (($) "\\spad{closed} indicates that the IO conduit has been closed.")) (|bothWays| (($) "\\spad{bothWays} indicates that an IO conduit is for both input and output.")) (|output| (($) "\\spad{output} indicates that an IO conduit is for output")) (|input| (($) "\\spad{input} indicates that an IO conduit is for input."))) NIL NIL -(-516) +(-515) ((|constructor| (NIL "This domain provides representation for ARPA Internet \\spad{IP4} addresses.")) (|resolve| (((|Maybe| $) (|Hostname|)) "\\spad{resolve(h)} returns the \\spad{IP4} address of host `h'.")) (|bytes| (((|DataArray| 4 (|Byte|)) $) "\\spad{bytes(x)} returns the bytes of the numeric address `x'.")) (|ip4Address| (($ (|String|)) "\\spad{ip4Address(a)} builds a numeric address out of the ASCII form `a'."))) NIL NIL -(-517 |p| |unBalanced?|) +(-516 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements Zp,{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-518 |p|) +(-517 |p|) ((|constructor| (NIL "InnerPrimeField(\\spad{p}) implements the field with \\spad{p} elements. Note: argument \\spad{p} MUST be a prime (this domain does not check). See \\spadtype{PrimeField} for a domain that does check."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) -(-519) +(-518) ((|constructor| (NIL "A package to print strings without line-feed nor carriage-return.")) (|iprint| (((|Void|) (|String|)) "\\axiom{iprint(\\spad{s})} prints \\axiom{\\spad{s}} at the current position of the cursor."))) NIL NIL -(-520 -3093) +(-519 -3092) ((|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 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}."))) -((-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-951 (-1091))))) -(-521 E -3093) +((-3990 . T) (-3989 . T)) +((|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-950 (-1090))))) +(-520 E -3092) ((|constructor| (NIL "\\indented{1}{Internally used by the integration packages} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 12 August 1992 Keywords: integration.")) (|map| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |mainpart| |#1|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#1|) (|:| |logand| |#1|))))) "failed")) "\\spad{map(f,ufe)} \\undocumented") (((|Union| |#2| "failed") (|Mapping| |#2| |#1|) (|Union| |#1| "failed")) "\\spad{map(f,ue)} \\undocumented") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") (|Mapping| |#2| |#1|) (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed")) "\\spad{map(f,ure)} \\undocumented") (((|IntegrationResult| |#2|) (|Mapping| |#2| |#1|) (|IntegrationResult| |#1|)) "\\spad{map(f,ire)} \\undocumented"))) NIL NIL -(-522 R -3093) +(-521 R -3092) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL NIL -(-523) +(-522) ((|constructor| (NIL "This domain provides representations for the intermediate form data structure used by the Spad elaborator.")) (|irDef| (($ (|Identifier|) (|InternalTypeForm|) $) "\\spad{irDef(f,ts,e)} returns an IR representation for a definition of a function named \\spad{f},{} with signature \\spad{ts} and body \\spad{e}.")) (|irCtor| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irCtor(n,t)} returns an IR for a constructor reference of type designated by the type form \\spad{t}")) (|irVar| (($ (|Identifier|) (|InternalTypeForm|)) "\\spad{irVar(x,t)} returns an IR for a variable reference of type designated by the type form \\spad{t}"))) NIL NIL -(-524 I) +(-523 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 NIL -(-525 GF) +(-524 GF) ((|constructor| (NIL "This package exports the function generateIrredPoly that computes a monic irreducible polynomial of degree \\spad{n} over a finite field.")) (|generateIrredPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{generateIrredPoly(n)} generates an irreducible univariate polynomial of the given degree \\spad{n} over the finite field."))) NIL NIL -(-526 R) +(-525 R) ((|constructor| (NIL "\\indented{2}{This package allows a sum of logs over the roots of a polynomial} \\indented{2}{to be expressed as explicit logarithms and arc tangents,{} provided} \\indented{2}{that the indexing polynomial can be factored into quadratics.} Date Created: 21 August 1988 Date Last Updated: 4 October 1993")) (|complexIntegrate| (((|Expression| |#1|) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{complexIntegrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|integrate| (((|Union| (|Expression| |#1|) (|List| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{integrate(f, x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a real variable..")) (|complexExpand| (((|Expression| |#1|) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| (|Expression| |#1|)) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|IntegrationResult| (|Fraction| (|Polynomial| |#1|)))) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,x) + ... + sum_{Pn(a)=0} Q(a,x)} where \\spad{P1},{}...,{}Pn are the factors of \\spad{P}."))) NIL ((|HasCategory| |#1| (QUOTE (-120)))) -(-527) +(-526) ((|constructor| (NIL "IrrRepSymNatPackage contains functions for computing the ordinary irreducible representations of symmetric groups on \\spad{n} letters {\\em {1,2,...,n}} in Young's natural form and their dimensions. These representations can be labelled by number partitions of \\spad{n},{} \\spadignore{i.e.} a weakly decreasing sequence of integers summing up to \\spad{n},{} \\spadignore{e.g.} {\\em [3,3,3,1]} labels an irreducible representation for \\spad{n} equals 10. Note: whenever a \\spadtype{List Integer} appears in a signature,{} a partition required.")) (|irreducibleRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|)) (|List| (|Permutation| (|Integer|)))) "\\spad{irreducibleRepresentation(lambda,listOfPerm)} is the list of the irreducible representations corresponding to {\\em lambda} in Young's natural form for the list of permutations given by {\\em listOfPerm}.") (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{irreducibleRepresentation(lambda)} is the list of the two irreducible representations corresponding to the partition {\\em lambda} in Young's natural form for the following two generators of the symmetric group,{} whose elements permute {\\em {1,2,...,n}},{} namely {\\em (1 2)} (2-cycle) and {\\em (1 2 ... n)} (\\spad{n}-cycle).") (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|Permutation| (|Integer|))) "\\spad{irreducibleRepresentation(lambda,pi)} is the irreducible representation corresponding to partition {\\em lambda} in Young's natural form of the permutation {\\em pi} in the symmetric group,{} whose elements permute {\\em {1,2,...,n}}.")) (|dimensionOfIrreducibleRepresentation| (((|NonNegativeInteger|) (|List| (|PositiveInteger|))) "\\spad{dimensionOfIrreducibleRepresentation(lambda)} is the dimension of the ordinary irreducible representation of the symmetric group corresponding to {\\em lambda}. Note: the Robinson-Thrall hook formula is implemented."))) NIL NIL -(-528 R E V P TS) +(-527 R E V P TS) ((|constructor| (NIL "\\indented{1}{An internal package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a square-free} \\indented{1}{triangular set.} \\indented{1}{The main operation is \\axiomOpFrom{rur}{InternalRationalUnivariateRepresentationPackage}.} \\indented{1}{It is based on the {\\em generic} algorithm description in [1]. \\newline References:} [1] \\spad{D}. LAZARD \"Solving Zero-dimensional Algebraic Systems\" \\indented{4}{Journal of Symbolic Computation,{} 1992,{} 13,{} 117-131}")) (|checkRur| (((|Boolean|) |#5| (|List| |#5|)) "\\spad{checkRur(ts,lus)} returns \\spad{true} if \\spad{lus} is a rational univariate representation of \\spad{ts}.")) (|rur| (((|List| |#5|) |#5| (|Boolean|)) "\\spad{rur(ts,univ?)} returns a rational univariate representation of \\spad{ts}. This assumes that the lowest polynomial in \\spad{ts} is a variable \\spad{v} which does not occur in the other polynomials of \\spad{ts}. This variable will be used to define the simple algebraic extension over which these other polynomials will be rewritten as univariate polynomials with degree one. If \\spad{univ?} is \\spad{true} then these polynomials will have a constant initial."))) NIL NIL -(-529) +(-528) ((|constructor| (NIL "This domain represents a `has' expression.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the is expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the is expression `e'."))) NIL NIL -(-530 E V R P) +(-529 E V R P) ((|constructor| (NIL "tools for the summation packages.")) (|sum| (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2|) "\\spad{sum(p(n), n)} returns \\spad{P(n)},{} the indefinite sum of \\spad{p(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{P(n+1) - P(n) = a(n)}.") (((|Record| (|:| |num| |#4|) (|:| |den| (|Integer|))) |#4| |#2| (|Segment| |#4|)) "\\spad{sum(p(n), n = a..b)} returns \\spad{p(a) + p(a+1) + ... + p(b)}."))) NIL NIL -(-531 |Coef|) +(-530 |Coef|) ((|constructor| (NIL "InnerSparseUnivariatePowerSeries is an internal domain \\indented{2}{used for creating sparse Taylor and Laurent series.}")) (|cAcsch| (($ $) "\\spad{cAcsch(f)} computes the inverse hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsech| (($ $) "\\spad{cAsech(f)} computes the inverse hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcoth| (($ $) "\\spad{cAcoth(f)} computes the inverse hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtanh| (($ $) "\\spad{cAtanh(f)} computes the inverse hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcosh| (($ $) "\\spad{cAcosh(f)} computes the inverse hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsinh| (($ $) "\\spad{cAsinh(f)} computes the inverse hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsch| (($ $) "\\spad{cCsch(f)} computes the hyperbolic cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSech| (($ $) "\\spad{cSech(f)} computes the hyperbolic secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCoth| (($ $) "\\spad{cCoth(f)} computes the hyperbolic cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTanh| (($ $) "\\spad{cTanh(f)} computes the hyperbolic tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCosh| (($ $) "\\spad{cCosh(f)} computes the hyperbolic cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSinh| (($ $) "\\spad{cSinh(f)} computes the hyperbolic sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcsc| (($ $) "\\spad{cAcsc(f)} computes the arccosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsec| (($ $) "\\spad{cAsec(f)} computes the arcsecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcot| (($ $) "\\spad{cAcot(f)} computes the arccotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAtan| (($ $) "\\spad{cAtan(f)} computes the arctangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAcos| (($ $) "\\spad{cAcos(f)} computes the arccosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cAsin| (($ $) "\\spad{cAsin(f)} computes the arcsine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCsc| (($ $) "\\spad{cCsc(f)} computes the cosecant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSec| (($ $) "\\spad{cSec(f)} computes the secant of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCot| (($ $) "\\spad{cCot(f)} computes the cotangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cTan| (($ $) "\\spad{cTan(f)} computes the tangent of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cCos| (($ $) "\\spad{cCos(f)} computes the cosine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cSin| (($ $) "\\spad{cSin(f)} computes the sine of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cLog| (($ $) "\\spad{cLog(f)} computes the logarithm of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cExp| (($ $) "\\spad{cExp(f)} computes the exponential of the power series \\spad{f}. For use when the coefficient ring is commutative.")) (|cRationalPower| (($ $ (|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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-485)) (|devaluate| |#1|)))) (|HasCategory| (-485) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-485)))))) -(-532 |Coef|) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-484)) (|devaluate| |#1|)))) (|HasCategory| (-484) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-484)))))) +(-531 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -(((-3998 "*") |has| |#1| (-496)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-496)))) -(-533) +(((-3997 "*") |has| |#1| (-495)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-495)))) +(-532) ((|constructor| (NIL "This domain provides representations for internal type form.")) (|mappingMode| (($ $ (|List| $)) "\\spad{mappingMode(r,ts)} returns a mapping mode with return mode \\spad{r},{} and parameter modes \\spad{ts}.")) (|categoryMode| (($) "\\spad{categoryMode} is a constant mode denoting Category.")) (|voidMode| (($) "\\spad{voidMode} is a constant mode denoting Void.")) (|noValueMode| (($) "\\spad{noValueMode} is a constant mode that indicates that the value of an expression is to be ignored.")) (|jokerMode| (($) "\\spad{jokerMode} is a constant that stands for any mode in a type inference context"))) NIL NIL -(-534 A B) +(-533 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|InfiniteTuple| |#2|) (|Mapping| |#2| |#1|) (|InfiniteTuple| |#1|)) "\\spad{map(f,[x0,x1,x2,...])} returns \\spad{[f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-535 A B C) +(-534 A B C) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,a,b)} \\undocumented"))) NIL NIL -(-536 R -3093 FG) +(-535 R -3092 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and FG should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f, [k1,...,kn], [x1,...,xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{xi's} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{ki's},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL -(-537 S) +(-536 S) ((|constructor| (NIL "This package implements 'infinite tuples' for the interpreter. The representation is a stream.")) (|construct| (((|Stream| |#1|) $) "\\spad{construct(t)} converts an infinite tuple to a stream.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,s)} returns \\spad{[s,f(s),f(f(s)),...]}.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,t)} returns \\spad{[x for x in t | p(x)]}.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,t)} returns \\spad{[x for x in t while not p(x)]}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,t)} returns \\spad{[x for x in t while p(x)]}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,t)} replaces the tuple \\spad{t} by \\spad{[f(x) for x in t]}."))) NIL NIL -(-538 S |Index| |Entry|) +(-537 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 -3997)) (|HasCategory| |#2| (QUOTE (-757))) (|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#3| (QUOTE (-1014)))) -(-539 |Index| |Entry|) +((|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-756))) (|HasAttribute| |#1| (QUOTE -3995)) (|HasCategory| |#3| (QUOTE (-1013)))) +(-538 |Index| |Entry|) ((|constructor| (NIL "An indexed aggregate is a many-to-one mapping of indices to entries. For example,{} a one-dimensional-array is an indexed aggregate where the index is an integer. Also,{} a table is an indexed aggregate where the indices and entries may have any type.")) (|swap!| (((|Void|) $ |#1| |#1|) "\\spad{swap!(u,i,j)} interchanges elements \\spad{i} and \\spad{j} of aggregate \\spad{u}. No meaningful value is returned.")) (|fill!| (($ $ |#2|) "\\spad{fill!(u,x)} replaces each entry in aggregate \\spad{u} by \\spad{x}. The modified \\spad{u} is returned as value.")) (|first| ((|#2| $) "\\spad{first(u)} returns the first element \\spad{x} of \\spad{u}. Note: for collections,{} \\axiom{first([\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]) = \\spad{x}}. Error: if \\spad{u} is empty.")) (|minIndex| ((|#1| $) "\\spad{minIndex(u)} returns the minimum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{minIndex(a) = reduce(min,{}[\\spad{i} for \\spad{i} in indices a])}; for lists,{} \\axiom{minIndex(a) = 1}.")) (|maxIndex| ((|#1| $) "\\spad{maxIndex(u)} returns the maximum index \\spad{i} of aggregate \\spad{u}. Note: in general,{} \\axiom{maxIndex(\\spad{u}) = reduce(max,{}[\\spad{i} for \\spad{i} in indices \\spad{u}])}; if \\spad{u} is a list,{} \\axiom{maxIndex(\\spad{u}) = \\#u}.")) (|entry?| (((|Boolean|) |#2| $) "\\spad{entry?(x,u)} tests if \\spad{x} equals \\axiom{\\spad{u} . \\spad{i}} for some index \\spad{i}.")) (|indices| (((|List| |#1|) $) "\\spad{indices(u)} returns a list of indices of aggregate \\spad{u} in no particular order.")) (|index?| (((|Boolean|) |#1| $) "\\spad{index?(i,u)} tests if \\spad{i} is an index of aggregate \\spad{u}.")) (|entries| (((|List| |#2|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) NIL NIL -(-540) +(-539) ((|constructor| (NIL "This domain represents the join of categories ASTs.")) (|categories| (((|List| (|TypeAst|)) $) "catehories(\\spad{x}) returns the types in the join `x'.")) (|coerce| (($ (|List| (|TypeAst|))) "ts::JoinAst construct the AST for a join of the types `ts'."))) NIL NIL -(-541 R A) +(-540 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)."))) -((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T)) -((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) -(-542) +((-3992 OR (-2562 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-495)))) (-3990 . T) (-3989 . T)) +((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) +(-541) ((|constructor| (NIL "This is the datatype for the JVM bytecodes."))) NIL NIL -(-543) +(-542) ((|constructor| (NIL "JVM class file access bitmask and values.")) (|jvmAbstract| (($) "The class was declared abstract; therefore object of this class may not be created.")) (|jvmInterface| (($) "The class file represents an interface,{} not a class.")) (|jvmSuper| (($) "Instruct the JVM to treat base clss method invokation specially.")) (|jvmFinal| (($) "The class was declared final; therefore no derived class allowed.")) (|jvmPublic| (($) "The class was declared public,{} therefore may be accessed from outside its package"))) NIL NIL -(-544) +(-543) ((|constructor| (NIL "JVM class file constant pool tags.")) (|jvmNameAndTypeConstantTag| (($) "The correspondong constant pool entry represents the name and type of a field or method info.")) (|jvmInterfaceMethodConstantTag| (($) "The correspondong constant pool entry represents an interface method info.")) (|jvmMethodrefConstantTag| (($) "The correspondong constant pool entry represents a class method info.")) (|jvmFieldrefConstantTag| (($) "The corresponding constant pool entry represents a class field info.")) (|jvmStringConstantTag| (($) "The corresponding constant pool entry is a string constant info.")) (|jvmClassConstantTag| (($) "The corresponding constant pool entry represents a class or and interface.")) (|jvmDoubleConstantTag| (($) "The corresponding constant pool entry is a double constant info.")) (|jvmLongConstantTag| (($) "The corresponding constant pool entry is a long constant info.")) (|jvmFloatConstantTag| (($) "The corresponding constant pool entry is a float constant info.")) (|jvmIntegerConstantTag| (($) "The corresponding constant pool entry is an integer constant info.")) (|jvmUTF8ConstantTag| (($) "The corresponding constant pool entry is sequence of bytes representing Java \\spad{UTF8} string constant."))) NIL NIL -(-545) +(-544) ((|constructor| (NIL "JVM class field access bitmask and values.")) (|jvmTransient| (($) "The field was declared transient.")) (|jvmVolatile| (($) "The field was declared volatile.")) (|jvmFinal| (($) "The field was declared final; therefore may not be modified after initialization.")) (|jvmStatic| (($) "The field was declared static.")) (|jvmProtected| (($) "The field was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The field was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The field was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-546) +(-545) ((|constructor| (NIL "JVM class method access bitmask and values.")) (|jvmStrict| (($) "The method was declared fpstrict; therefore floating-point mode is FP-strict.")) (|jvmAbstract| (($) "The method was declared abstract; therefore no implementation is provided.")) (|jvmNative| (($) "The method was declared native; therefore implemented in a language other than Java.")) (|jvmSynchronized| (($) "The method was declared synchronized.")) (|jvmFinal| (($) "The method was declared final; therefore may not be overriden. in derived classes.")) (|jvmStatic| (($) "The method was declared static.")) (|jvmProtected| (($) "The method was declared protected; therefore may be accessed withing derived classes.")) (|jvmPrivate| (($) "The method was declared private; threfore can be accessed only within the defining class.")) (|jvmPublic| (($) "The method was declared public; therefore mey accessed from outside its package."))) NIL NIL -(-547) +(-546) ((|constructor| (NIL "This is the datatype for the JVM opcodes."))) NIL NIL -(-548 |Entry|) +(-547 |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."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) -(-549 S |Key| |Entry|) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3860 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) +(-548 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 -(-550 |Key| |Entry|) +(-549 |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}."))) -((-3997 . T)) +((-3996 . T)) NIL -(-551 S) +(-550 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."))) NIL -((|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#1| (QUOTE (-554 (-801 (-485)))))) -(-552 R S) +((|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#1| (QUOTE (-553 (-800 (-484)))))) +(-551 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"))) NIL NIL -(-553 S) +(-552 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 NIL -(-554 S) +(-553 S) ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-555 -3093 UP) +(-554 -3092 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic's algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,a_1,a_2,ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,a_1,a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL -(-556 S) +(-555 S) ((|constructor| (NIL "A is coercible from \\spad{B} iff any element of domain \\spad{B} can be automically converted into an element of domain A.")) (|coerce| (($ |#1|) "\\spad{coerce(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-557) +(-556) ((|constructor| (NIL "This domain implements Kleene's 3-valued propositional logic.")) (|case| (((|Boolean|) $ (|[\|\|]| |true|)) "\\spad{s case true} holds if the value of `x' is `true'.") (((|Boolean|) $ (|[\|\|]| |unknown|)) "\\spad{x case unknown} holds if the value of `x' is `unknown'") (((|Boolean|) $ (|[\|\|]| |false|)) "\\spad{x case false} holds if the value of `x' is `false'")) (|unknown| (($) "the indefinite `unknown'"))) NIL NIL -(-558 S) +(-557 S) ((|constructor| (NIL "A is convertible from \\spad{B} iff any element of domain \\spad{B} can be explicitly converted into an element of domain A.")) (|convert| (($ |#1|) "\\spad{convert(s)} transforms `s' into an element of `\\%'."))) NIL NIL -(-559 A R S) +(-558 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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-756)))) -(-560 S R) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-755)))) +(-559 S R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#2|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) NIL NIL -(-561 R) +(-560 R) ((|constructor| (NIL "The category of all left algebras over an arbitrary ring.")) (|coerce| (($ |#1|) "\\spad{coerce(r)} returns \\spad{r} * 1 where 1 is the identity of the left algebra."))) -((-3993 . T)) +((-3992 . T)) NIL -(-562 R -3093) +(-561 R -3092) ((|constructor| (NIL "This package computes the forward Laplace Transform.")) (|laplace| ((|#2| |#2| (|Symbol|) (|Symbol|)) "\\spad{laplace(f, t, s)} returns the Laplace transform of \\spad{f(t)} using \\spad{s} as the new variable. This is \\spad{integral(exp(-s*t)*f(t), t = 0..\\%plusInfinity)}. Returns the formal object \\spad{laplace(f, t, s)} if it cannot compute the transform."))) NIL NIL -(-563 R UP) +(-562 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"))) -((-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3989 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) -(-564 R E V P TS ST) +((-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3988 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) +(-563 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(lp,{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(lp,{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(ts)} returns \\axiom{ts} in an normalized shape if \\axiom{ts} is zero-dimensional."))) NIL NIL -(-565 OV E Z P) +(-564 OV E Z P) ((|constructor| (NIL "Package for leading coefficient determination in the lifting step. Package working for every \\spad{R} euclidean with property \"F\".")) (|distFact| (((|Union| (|Record| (|:| |polfac| (|List| |#4|)) (|:| |correct| |#3|) (|:| |corrfact| (|List| (|SparseUnivariatePolynomial| |#3|)))) "failed") |#3| (|List| (|SparseUnivariatePolynomial| |#3|)) (|Record| (|:| |contp| |#3|) (|:| |factors| (|List| (|Record| (|:| |irr| |#4|) (|:| |pow| (|Integer|)))))) (|List| |#3|) (|List| |#1|) (|List| |#3|)) "\\spad{distFact(contm,unilist,plead,vl,lvar,lval)},{} where \\spad{contm} is the content of the evaluated polynomial,{} \\spad{unilist} is the list of factors of the evaluated polynomial,{} \\spad{plead} is the complete factorization of the leading coefficient,{} \\spad{vl} is the list of factors of the leading coefficient evaluated,{} \\spad{lvar} is the list of variables,{} \\spad{lval} is the list of values,{} returns a record giving the list of leading coefficients to impose on the univariate factors,{}")) (|polCase| (((|Boolean|) |#3| (|NonNegativeInteger|) (|List| |#3|)) "\\spad{polCase(contprod, numFacts, evallcs)},{} where \\spad{contprod} is the product of the content of the leading coefficient of the polynomial to be factored with the content of the evaluated polynomial,{} \\spad{numFacts} is the number of factors of the leadingCoefficient,{} and evallcs is the list of the evaluated factors of the leadingCoefficient,{} returns \\spad{true} if the factors of the leading Coefficient can be distributed with this valuation."))) NIL NIL -(-566) +(-565) ((|constructor| (NIL "This domain represents assignment expressions.")) (|rhs| (((|SpadAst|) $) "\\spad{rhs(e)} returns the right hand side of the assignment expression `e'.")) (|lhs| (((|SpadAst|) $) "\\spad{lhs(e)} returns the left hand side of the assignment expression `e'."))) NIL NIL -(-567 |VarSet| R |Order|) +(-566 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(lv)} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-3993 . T)) +((-3992 . T)) NIL -(-568 R |ls|) +(-567 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(lp,{} norm?)} decomposes the variety associated with \\axiom{lp} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{lp} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(lp)} returns the lexicographical Groebner basis of \\axiom{lp}. If \\axiom{lp} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(lp)} returns the lexicographical Groebner basis of \\axiom{lp} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(lp)} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(lp)} returns \\spad{true} iff \\axiom{lp} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{lp}."))) NIL NIL -(-569 R -3093) +(-568 R -3092) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{li(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{Ci(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{Si(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{Ei(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-570) +(-569) ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%pi)} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{li(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{Ci(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{Si(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{Ei(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-571 |lv| -3093) +(-570 |lv| -3092) ((|constructor| (NIL "\\indented{1}{Given a Groebner basis \\spad{B} with respect to the total degree ordering for} a zero-dimensional ideal \\spad{I},{} compute a Groebner basis with respect to the lexicographical ordering by using linear algebra.")) (|transform| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|)) "\\spad{transform }\\undocumented")) (|choosemon| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{choosemon }\\undocumented")) (|intcompBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{intcompBasis }\\undocumented")) (|anticoord| (((|DistributedMultivariatePolynomial| |#1| |#2|) (|List| |#2|) (|DistributedMultivariatePolynomial| |#1| |#2|) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{anticoord }\\undocumented")) (|coord| (((|Vector| |#2|) (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{coord }\\undocumented")) (|computeBasis| (((|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{computeBasis }\\undocumented")) (|minPol| (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented") (((|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|OrderedVariableList| |#1|)) "\\spad{minPol }\\undocumented")) (|totolex| (((|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{totolex }\\undocumented")) (|groebgen| (((|Record| (|:| |glbase| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |glval| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{groebgen }\\undocumented")) (|linGenPos| (((|Record| (|:| |gblist| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |gvlist| (|List| (|Integer|)))) (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|))) "\\spad{linGenPos }\\undocumented"))) NIL NIL -(-572) +(-571) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3861 (-1074)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773)))) (|HasCategory| (-51) (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-554 (-474)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1014)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| (-51) (QUOTE (-1014))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| (-51))) (QUOTE (-553 (-773))))) -(-573 R A) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-260 (-2 (|:| -3860 (-1073)) (|:| |entry| (-51)))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-552 (-772)))) (|HasCategory| (-51) (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-553 (-473)))) (-12 (|HasCategory| (-51) (QUOTE (-260 (-51)))) (|HasCategory| (-51) (QUOTE (-1013)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-1013))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| (-51) (QUOTE (-1013))) (|HasCategory| (-51) (QUOTE (-72))) (OR (|HasCategory| (-51) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-72)))) (|HasCategory| (-51) (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| (-51))) (QUOTE (-552 (-772))))) +(-572 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$A} to define the Lie bracket \\spad{a*b := (a *\\$A b - b *\\$A a)} (commutator). Note that the notation \\spad{[a,b]} cannot be used due to restrictions of the current compiler. This domain only gives a Lie algebra if the Jacobi-identity \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} holds for all \\spad{a},{}\\spad{b},{}\\spad{c} in \\spad{A}. This relation can be checked by \\spad{lieAdmissible?()\\$A}. \\blankline If the underlying algebra is of type \\spadtype{FramedNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank,{} together with a fixed \\spad{R}-module basis),{} then the same is \\spad{true} for the associated Lie algebra. Also,{} if the underlying algebra is of type \\spadtype{FiniteRankNonAssociativeAlgebra(R)} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank),{} then the same is \\spad{true} for the associated Lie algebra.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} coerces the element \\spad{a} of the algebra \\spad{A} to an element of the Lie algebra \\spadtype{AssociatedLieAlgebra}(\\spad{R},{}A)."))) -((-3993 OR (-2563 (|has| |#2| (-316 |#1|)) (|has| |#1| (-496))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-496)))) (-3991 . T) (-3990 . T)) -((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) -(-574 S R) +((-3992 OR (-2562 (|has| |#2| (-316 |#1|)) (|has| |#1| (-495))) (-12 (|has| |#2| (-361 |#1|)) (|has| |#1| (-495)))) (-3990 . T) (-3989 . T)) +((OR (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (|%list| (QUOTE -361) (|devaluate| |#1|))))) (|HasCategory| |#2| (|%list| (QUOTE -316) (|devaluate| |#1|)))) +(-573 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{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-312)))) -(-575 R) +(-574 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{x/r} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3990 . T) (-3989 . T)) NIL -(-576 R FE) +(-575 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit \\spad{lim(x -> a,f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) #1="failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),x=a,\"left\")} computes the left hand real limit \\spad{lim(x -> a-,f(x))}; \\spad{limit(f(x),x=a,\"right\")} computes the right hand real limit \\spad{lim(x -> a+,f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) #1#))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),x = a)} computes the real limit \\spad{lim(x -> a,f(x))}."))) NIL NIL -(-577 R) +(-576 R) ((|constructor| (NIL "Computation of limits for rational functions.")) (|complexLimit| (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|OnePointCompletion| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OnePointCompletion| (|Polynomial| |#1|)))) "\\spad{complexLimit(f(x),x = a)} computes the complex limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.")) (|limit| (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|String|)) "\\spad{limit(f(x),x,a,\"left\")} computes the real limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a} from the left; limit(\\spad{f}(\\spad{x}),{}\\spad{x},{}a,{}\"right\") computes the corresponding limit as \\spad{x} approaches \\spad{a} from the right.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2="failed") (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}.") (((|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#)) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|))) #1#))) #2#) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|OrderedCompletion| (|Polynomial| |#1|)))) "\\spad{limit(f(x),x = a)} computes the real two-sided limit of \\spad{f} as its argument \\spad{x} approaches \\spad{a}."))) NIL NIL -(-578 |vars|) +(-577 |vars|) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: July 2,{} 2010 Date Last Modified: July 2,{} 2010 Descrption: \\indented{2}{Representation of a vector space basis,{} given by symbols.}")) (|dual| (($ (|DualBasis| |#1|)) "\\spad{dual f} constructs the dual vector of a linear form which is part of a basis."))) NIL NIL -(-579 S R) +(-578 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}'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}'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}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-2561 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) -(-580 K B) +((-2560 (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-312)))) +(-579 K B) ((|constructor| (NIL "A simple data structure for elements that form a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear element with respect to the basis \\spad{B}.")) (|linearElement| (($ (|List| |#1|)) "\\spad{linearElement [x1,..,xn]} returns a linear element \\indented{1}{with coordinates \\spad{[x1,..,xn]} with respect to} the basis elements \\spad{B}."))) -((-3991 . T) (-3990 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-578 |#2|) (QUOTE (-1014))))) -(-581 R) +((-3990 . T) (-3989 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-577 |#2|) (QUOTE (-1013))))) +(-580 R) ((|constructor| (NIL "An extension of left-module with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A, v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}.")) (|leftReducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Vector| $) $) "\\spad{reducedSystem([v1,...,vn],u)} returns a matrix \\spad{M} with coefficients in \\spad{R} and a vector \\spad{w} such that the system of equations \\spad{c1*v1 + ... + cn*vn = u} has the same solution as \\spad{c * M = w} where \\spad{c} is the row vector \\spad{[c1,...cn]}.") (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftReducedSystem [v1,...,vn]} returns a matrix \\spad{M} with coefficients in \\spad{R} such that the system of equations \\spad{c1*v1 + ... + cn*vn = 0\\$\\%} has the same solution as \\spad{c * M = 0} where \\spad{c} is the row vector \\spad{[c1,...cn]}."))) NIL NIL -(-582 K B) +(-581 K B) ((|constructor| (NIL "A simple data structure for linear forms on a vector space of finite dimension over a given field,{} with a given symbolic basis.")) (|coordinates| (((|Vector| |#1|) $) "\\spad{coordinates x} returns the coordinates of the linear form with respect to the basis \\spad{DualBasis B}.")) (|linearForm| (($ (|List| |#1|)) "\\spad{linearForm [x1,..,xn]} constructs a linear form with coordinates \\spad{[x1,..,xn]} with respect to the basis elements \\spad{DualBasis B}."))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL -(-583 S) +(-582 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-linear set if it is stable by dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet,{} RightLinearSet."))) NIL NIL -(-584 S) +(-583 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil} is the empty list."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-585 A B) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-584 A B) ((|constructor| (NIL "\\spadtype{ListFunctions2} implements utility functions that operate on two kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#2|) (|Mapping| |#2| |#1|) (|List| |#1|)) "\\spad{map(fn,u)} applies \\spad{fn} to each element of list \\spad{u} and returns a new list with the results. For example \\spad{map(square,[1,2,3]) = [1,4,9]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{reduce(fn,u,ident)} successively uses the binary function \\spad{fn} on the elements of list \\spad{u} and the result of previous applications. \\spad{ident} is returned if the \\spad{u} is empty. Note the order of application in the following examples: \\spad{reduce(fn,[1,2,3],0) = fn(3,fn(2,fn(1,0)))} and \\spad{reduce(*,[2,3],1) = 3 * (2 * 1)}.")) (|scan| (((|List| |#2|) (|Mapping| |#2| |#1| |#2|) (|List| |#1|) |#2|) "\\spad{scan(fn,u,ident)} successively uses the binary function \\spad{fn} to reduce more and more of list \\spad{u}. \\spad{ident} is returned if the \\spad{u} is empty. The result is a list of the reductions at each step. See \\spadfun{reduce} for more information. Examples: \\spad{scan(fn,[1,2],0) = [fn(2,fn(1,0)),fn(1,0)]} and \\spad{scan(*,[2,3],1) = [2 * 1, 3 * (2 * 1)]}."))) NIL NIL -(-586 A B) +(-585 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, a, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la, lb, f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la, lb, a, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la, lb, b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la, lb, a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la, lb)} creates a map with no default source or target values defined by lists \\spad{la} and lb of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index lb. Error: if \\spad{la} and lb are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) NIL NIL -(-587 A B C) +(-586 A B C) ((|constructor| (NIL "\\spadtype{ListFunctions3} implements utility functions that operate on three kinds of lists,{} each with a possibly different type of element.")) (|map| (((|List| |#3|) (|Mapping| |#3| |#1| |#2|) (|List| |#1|) (|List| |#2|)) "\\spad{map(fn,list1, u2)} applies the binary function \\spad{fn} to corresponding elements of lists \\spad{u1} and \\spad{u2} and returns a list of the results (in the same order). Thus \\spad{map(/,[1,2,3],[4,5,6]) = [1/4,2/4,1/2]}. The computation terminates when the end of either list is reached. That is,{} the length of the result list is equal to the minimum of the lengths of \\spad{u1} and \\spad{u2}."))) NIL NIL -(-588 T$) +(-587 T$) ((|constructor| (NIL "This domain represents AST for Spad literals."))) NIL NIL -(-589 S) +(-588 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-left linear set if it is stable by left-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: RightLinearSet.")) (* (($ |#1| $) "\\spad{s*x} is the left-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-590 S) +(-589 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,y,d)} replace \\spad{x}'s with \\spad{y}'s in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-591 R) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-590 R) ((|constructor| (NIL "The category of left modules over an rng (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the rng. \\blankline"))) NIL NIL -(-592 S E |un|) +(-591 S E |un|) ((|constructor| (NIL "This internal package represents monoid (abelian or not,{} with or without inverses) as lists and provides some common operations to the various flavors of monoids.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f, a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExpon(f, a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|commutativeEquality| (((|Boolean|) $ $) "\\spad{commutativeEquality(x,y)} returns \\spad{true} if \\spad{x} and \\spad{y} are equal assuming commutativity")) (|plus| (($ $ $) "\\spad{plus(x, y)} returns \\spad{x + y} where \\spad{+} is the monoid operation,{} which is assumed commutative.") (($ |#1| |#2| $) "\\spad{plus(s, e, x)} returns \\spad{e * s + x} where \\spad{+} is the monoid operation,{} which is assumed commutative.")) (|leftMult| (($ |#1| $) "\\spad{leftMult(s, a)} returns \\spad{s * a} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|rightMult| (($ $ |#1|) "\\spad{rightMult(a, s)} returns \\spad{a * s} where \\spad{*} is the monoid operation,{} which is assumed non-commutative.")) (|makeUnit| (($) "\\spad{makeUnit()} returns the unit element of the monomial.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(l)} returns the number of monomials forming \\spad{l}.")) (|reverse!| (($ $) "\\spad{reverse!(l)} reverses the list of monomials forming \\spad{l},{} destroying the element \\spad{l}.")) (|reverse| (($ $) "\\spad{reverse(l)} reverses the list of monomials forming \\spad{l}. This has some effect if the monoid is non-abelian,{} \\spadignore{i.e.} \\spad{reverse(a1\\^e1 ... an\\^en) = an\\^en ... a1\\^e1} which is different.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(l, n)} returns the factor of the n^th monomial of \\spad{l}.")) (|nthExpon| ((|#2| $ (|Integer|)) "\\spad{nthExpon(l, n)} returns the exponent of the n^th monomial of \\spad{l}.")) (|makeMulti| (($ (|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|)))) "\\spad{makeMulti(l)} returns the element whose list of monomials is \\spad{l}.")) (|makeTerm| (($ |#1| |#2|) "\\spad{makeTerm(s, e)} returns the monomial \\spad{s} exponentiated by \\spad{e} (\\spadignore{e.g.} s^e or \\spad{e} * \\spad{s}).")) (|listOfMonoms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{listOfMonoms(l)} returns the list of the monomials forming \\spad{l}.")) (|outputForm| (((|OutputForm|) $ (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Mapping| (|OutputForm|) (|OutputForm|) (|OutputForm|)) (|Integer|)) "\\spad{outputForm(l, fop, fexp, unit)} converts the monoid element represented by \\spad{l} to an \\spadtype{OutputForm}. Argument unit is the output form for the \\spadignore{unit} of the monoid (\\spadignore{e.g.} 0 or 1),{} \\spad{fop(a, b)} is the output form for the monoid operation applied to \\spad{a} and \\spad{b} (\\spadignore{e.g.} \\spad{a + b},{} \\spad{a * b},{} \\spad{ab}),{} and \\spad{fexp(a, n)} is the output form for the exponentiation operation applied to \\spad{a} and \\spad{n} (\\spadignore{e.g.} \\spad{n a},{} \\spad{n * a},{} \\spad{a ** n},{} \\spad{a\\^n})."))) NIL NIL -(-593 A S) +(-592 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,i..j,x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) := \\spad{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{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,u,k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,u,i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) -(-594 S) +((|HasAttribute| |#1| (QUOTE -3996))) +(-593 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{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{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}) == concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,u,v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) == concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#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}) == concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL NIL -(-595 M R S) +(-594 M R S) ((|constructor| (NIL "Localize(\\spad{M},{}\\spad{R},{}\\spad{S}) produces fractions with numerators from an \\spad{R} module \\spad{M} and denominators from some multiplicative subset \\spad{D} of \\spad{R}.")) (|denom| ((|#3| $) "\\spad{denom x} returns the denominator of \\spad{x}.")) (|numer| ((|#1| $) "\\spad{numer x} returns the numerator of \\spad{x}.")) (/ (($ |#1| |#3|) "\\spad{m / d} divides the element \\spad{m} by \\spad{d}.") (($ $ |#3|) "\\spad{x / d} divides the element \\spad{x} by \\spad{d}."))) -((-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-715)))) -(-596 R -3093 L) +((-3990 . T) (-3989 . T)) +((|HasCategory| |#1| (QUOTE (-714)))) +(-595 R -3092 L) ((|constructor| (NIL "\\spad{ElementaryFunctionLODESolver} provides the top-level functions for finding closed form solutions of linear ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#3| |#2| (|Symbol|) |#2| (|List| |#2|)) "\\spad{solve(op, g, x, a, [y0,...,ym])} returns either the solution of the initial value problem \\spad{op y = g, y(a) = y0, y'(a) = y1,...} or \"failed\" if the solution cannot be found; \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) "failed") |#3| |#2| (|Symbol|)) "\\spad{solve(op, g, x)} returns either a solution of the ordinary differential equation \\spad{op y = g} or \"failed\" if no non-trivial solution can be found; When found,{} the solution is returned in the form \\spad{[h, [b1,...,bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{op y = 0}. A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; \\spad{x} is the dependent variable."))) NIL NIL -(-597 A -2493) +(-596 A -2492) ((|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}}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) -(-598 A) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) +(-597 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator1} defines a ring of differential operators with coefficients in a differential ring A. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) -(-599 A M) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) +(-598 A M) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperator2} defines a ring of differential operators with coefficients in a differential ring A and acting on an A-module \\spad{M}. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|differentiate| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) -(-600 S A) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) +(-599 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) NIL ((|HasCategory| |#2| (QUOTE (-312)))) -(-601 A) +(-600 A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,a)} using a more efficient method.")) (|symmetricPower| (($ $ (|NonNegativeInteger|)) "\\spad{symmetricPower(a,n)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}.")) (|symmetricProduct| (($ $ $) "\\spad{symmetricProduct(a,b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}.")) (|adjoint| (($ $) "\\spad{adjoint(a)} returns the adjoint operator of a.")) (D (($) "\\spad{D()} provides the operator corresponding to a derivation in the ring \\spad{A}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-602 -3093 UP) +(-601 -3092 UP) ((|constructor| (NIL "\\spadtype{LinearOrdinaryDifferentialOperatorFactorizer} provides a factorizer for linear ordinary differential operators whose coefficients are rational functions.")) (|factor1| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor1(a)} returns the factorisation of a,{} assuming that a has no first-order right factor.")) (|factor| (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{factor(a)} returns the factorisation of a.") (((|List| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{factor(a, zeros)} returns the factorisation of a. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-603 A L) +(-602 A L) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorsOps} provides symmetric products and sums for linear ordinary differential operators.")) (|directSum| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{directSum(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use.")) (|symmetricPower| ((|#2| |#2| (|NonNegativeInteger|) (|Mapping| |#1| |#1|)) "\\spad{symmetricPower(a,n,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of \\spad{n} solutions of \\spad{a}. \\spad{D} is the derivation to use.")) (|symmetricProduct| ((|#2| |#2| |#2| (|Mapping| |#1| |#1|)) "\\spad{symmetricProduct(a,b,D)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the products of a solution of \\spad{a} by a solution of \\spad{b}. \\spad{D} is the derivation to use."))) NIL NIL -(-604 S) +(-603 S) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-605) +(-604) ((|constructor| (NIL "`Logic' provides the basic operations for lattices,{} \\spadignore{e.g.} boolean algebra.")) (|\\/| (($ $ $) "\\spadignore{ \\/ } returns the logical `join',{} \\spadignore{e.g.} `or'.")) (|/\\| (($ $ $) "\\spadignore { /\\ }returns the logical `meet',{} \\spadignore{e.g.} `and'.")) (~ (($ $) "\\spad{~(x)} returns the logical complement of \\spad{x}."))) NIL NIL -(-606 R) +(-605 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such exists."))) NIL NIL -(-607 |VarSet| R) +(-606 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-3991 . T) (-3990 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-3990 . T) (-3989 . T)) ((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-146)))) -(-608 A S) +(-607 A S) ((|constructor| (NIL "A list aggregate is a model for a linked list data structure. A linked list is a versatile data structure. Insertion and deletion are efficient and searching is a linear operation.")) (|list| (($ |#2|) "\\spad{list(x)} returns the list of one element \\spad{x}."))) NIL NIL -(-609 S) +(-608 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}."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-610 -3093 |Row| |Col| M) +(-609 -3092 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| #1="failed") |#4| |#3|) "\\spad{particularSolution(A,B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| #1#)) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-611 -3093) +(-610 -3092) ((|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'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|) #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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |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|) #1#)) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-612 R E OV P) +(-611 R E OV P) ((|constructor| (NIL "this package finds the solutions of linear systems presented as a list of polynomials.")) (|linSolve| (((|Record| (|:| |particular| (|Union| (|Vector| (|Fraction| |#4|)) "failed")) (|:| |basis| (|List| (|Vector| (|Fraction| |#4|))))) (|List| |#4|) (|List| |#3|)) "\\spad{linSolve(lp,lvar)} finds the solutions of the linear system of polynomials \\spad{lp} = 0 with respect to the list of symbols \\spad{lvar}."))) NIL NIL -(-613 |n| R) +(-612 |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."))) -((-3993 . T) (-3996 . T) (-3990 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-614) +((-3992 . T) (-3995 . T) (-3989 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3997 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495))) (OR (|HasAttribute| |#2| (QUOTE (-3997 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) +(-613) ((|constructor| (NIL "This domain represents `literal sequence' syntax.")) (|elements| (((|List| (|SpadAst|)) $) "\\spad{elements(e)} returns the list of expressions in the `literal' list `e'."))) NIL NIL -(-615 |VarSet|) +(-614 |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{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.fr).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(vl,{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{vl},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{\\spad{LyndonWordsList1}(vl,{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{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|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL NIL -(-616 A S) +(-615 A S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\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| ((|#2| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\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|) |#2|) $) "\\spad{select(f,st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(f,st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,st) = [x for x in st | not f(x)]}."))) NIL NIL -(-617 S) +(-616 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least 'n' explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length <= \\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)]}."))) NIL NIL -(-618) +(-617) ((|constructor| (NIL "This domain represents the syntax of a macro definition.")) (|body| (((|SpadAst|) $) "\\spad{body(m)} returns the right hand side of the definition `m'.")) (|head| (((|HeadAst|) $) "\\spad{head(m)} returns the head of the macro definition `m'. This is a list of identifiers starting with the name of the macro followed by the name of the parameters,{} if any."))) NIL NIL -(-619 |VarSet|) +(-618 |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.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{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 NIL -(-620 A) +(-619 A) ((|constructor| (NIL "various Currying operations.")) (|recur| ((|#1| (|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|NonNegativeInteger|) |#1|) "\\spad{recur(n,g,x)} is \\spad{g(n,g(n-1,..g(1,x)..))}.")) (|iter| ((|#1| (|Mapping| |#1| |#1|) (|NonNegativeInteger|) |#1|) "\\spad{iter(f,n,x)} applies \\spad{f n} times to \\spad{x}."))) NIL NIL -(-621 A C) +(-620 A C) ((|constructor| (NIL "various Currying operations.")) (|arg2| ((|#2| |#1| |#2|) "\\spad{arg2(a,c)} selects its second argument.")) (|arg1| ((|#1| |#1| |#2|) "\\spad{arg1(a,c)} selects its first argument."))) NIL NIL -(-622 A B C) +(-621 A B C) ((|constructor| (NIL "various Currying operations.")) (|comp| ((|#3| (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{comp(f,g,x)} is \\spad{f(g x)}."))) NIL NIL -(-623) +(-622) ((|constructor| (NIL "This domain represents a mapping type AST. A mapping AST \\indented{2}{is a syntactic description of a function type,{} \\spadignore{e.g.} its result} \\indented{2}{type and the list of its argument types.}")) (|target| (((|TypeAst|) $) "\\spad{target(s)} returns the result type AST for `s'.")) (|source| (((|List| (|TypeAst|)) $) "\\spad{source(s)} returns the parameter type AST list of `s'.")) (|mappingAst| (($ (|List| (|TypeAst|)) (|TypeAst|)) "\\spad{mappingAst(s,t)} builds the mapping AST \\spad{s} -> \\spad{t}")) (|coerce| (($ (|Signature|)) "sig::MappingAst builds a MappingAst from the Signature `sig'."))) NIL NIL -(-624 A) +(-623 A) ((|constructor| (NIL "various Currying operations.")) (|recur| (((|Mapping| |#1| (|NonNegativeInteger|) |#1|) (|Mapping| |#1| (|NonNegativeInteger|) |#1|)) "\\spad{recur(g)} is the function \\spad{h} such that \\indented{1}{\\spad{h(n,x)= g(n,g(n-1,..g(1,x)..))}.}")) (** (((|Mapping| |#1| |#1|) (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{f**n} is the function which is the \\spad{n}-fold application \\indented{1}{of \\spad{f}.}")) (|id| ((|#1| |#1|) "\\spad{id x} is \\spad{x}.")) (|fixedPoint| (((|List| |#1|) (|Mapping| (|List| |#1|) (|List| |#1|)) (|Integer|)) "\\spad{fixedPoint(f,n)} is the fixed point of function \\indented{1}{\\spad{f} which is assumed to transform a list of length} \\indented{1}{\\spad{n}.}") ((|#1| (|Mapping| |#1| |#1|)) "\\spad{fixedPoint f} is the fixed point of function \\spad{f}. \\indented{1}{\\spadignore{i.e.} such that \\spad{fixedPoint f = f(fixedPoint f)}.}")) (|coerce| (((|Mapping| |#1|) |#1|) "\\spad{coerce A} changes its argument into a \\indented{1}{nullary function.}")) (|nullary| (((|Mapping| |#1|) |#1|) "\\spad{nullary A} changes its argument into a \\indented{1}{nullary function.}"))) NIL NIL -(-625 A C) +(-624 A C) ((|constructor| (NIL "various Currying operations.")) (|diag| (((|Mapping| |#2| |#1|) (|Mapping| |#2| |#1| |#1|)) "\\spad{diag(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a = f(a,a)}.}")) (|constant| (((|Mapping| |#2| |#1|) (|Mapping| |#2|)) "\\spad{vu(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g a= f ()}.}")) (|curry| (((|Mapping| |#2|) (|Mapping| |#2| |#1|) |#1|) "\\spad{cu(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g ()= f a}.}")) (|const| (((|Mapping| |#2| |#1|) |#2|) "\\spad{const c} is a function which produces \\spad{c} when \\indented{1}{applied to its argument.}"))) NIL NIL -(-626 A B C) +(-625 A B C) ((|constructor| (NIL "various Currying operations.")) (* (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#2|) (|Mapping| |#2| |#1|)) "\\spad{f*g} is the function \\spad{h} \\indented{1}{such that \\spad{h x= f(g x)}.}")) (|twist| (((|Mapping| |#3| |#2| |#1|) (|Mapping| |#3| |#1| |#2|)) "\\spad{twist(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f(b,a)}.}")) (|constantLeft| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#2|)) "\\spad{constantLeft(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f b}.}")) (|constantRight| (((|Mapping| |#3| |#1| |#2|) (|Mapping| |#3| |#1|)) "\\spad{constantRight(f)} is the function \\spad{g} \\indented{1}{such that \\spad{g (a,b)= f a}.}")) (|curryLeft| (((|Mapping| |#3| |#2|) (|Mapping| |#3| |#1| |#2|) |#1|) "\\spad{curryLeft(f,a)} is the function \\spad{g} \\indented{1}{such that \\spad{g b = f(a,b)}.}")) (|curryRight| (((|Mapping| |#3| |#1|) (|Mapping| |#3| |#1| |#2|) |#2|) "\\spad{curryRight(f,b)} is the function \\spad{g} such that \\indented{1}{\\spad{g a = f(a,b)}.}"))) NIL NIL -(-627 S R |Row| |Col|) +(-626 S R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#2| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#2| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#4|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#2|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#3| |#3| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#4| $ |#4|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#2|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#2| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#2|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#3|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#4|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#2| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise."))) NIL -((|HasAttribute| |#2| (QUOTE (-3998 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-496)))) -(-628 R |Row| |Col|) +((|HasAttribute| |#2| (QUOTE (-3997 "*"))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-495)))) +(-627 R |Row| |Col|) ((|constructor| (NIL "\\spadtype{MatrixCategory} is a general matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col. A domain belonging to this category will be shallowly mutable. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a Row is the same as the index of the first column in a matrix and vice versa.")) (|inverse| (((|Union| $ "failed") $) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|minordet| ((|#1| $) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| $) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. Error: if the matrix is not square.")) (|nullSpace| (((|List| |#3|) $) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#1|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (** (($ $ (|Integer|)) "\\spad{m**n} computes an integral power of the matrix \\spad{m}. Error: if matrix is not square or if the matrix is square but not invertible.") (($ $ (|NonNegativeInteger|)) "\\spad{x ** n} computes a non-negative integral power of the matrix \\spad{x}. Error: if the matrix is not square.")) (* ((|#2| |#2| $) "\\spad{r * x} is the product of the row vector \\spad{r} and the matrix \\spad{x}. Error: if the dimensions are incompatible.") ((|#3| $ |#3|) "\\spad{x * c} is the product of the matrix \\spad{x} and the column vector \\spad{c}. Error: if the dimensions are incompatible.") (($ (|Integer|) $) "\\spad{n * x} is an integer multiple.") (($ $ |#1|) "\\spad{x * r} is the right scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ |#1| $) "\\spad{r*x} is the left scalar multiple of the scalar \\spad{r} and the matrix \\spad{x}.") (($ $ $) "\\spad{x * y} is the product of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (- (($ $) "\\spad{-x} returns the negative of the matrix \\spad{x}.") (($ $ $) "\\spad{x - y} is the difference of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (+ (($ $ $) "\\spad{x + y} is the sum of the matrices \\spad{x} and \\spad{y}. Error: if the dimensions are incompatible.")) (|setsubMatrix!| (($ $ (|Integer|) (|Integer|) $) "\\spad{setsubMatrix(x,i1,j1,y)} destructively alters the matrix \\spad{x}. Here \\spad{x(i,j)} is set to \\spad{y(i-i1+1,j-j1+1)} for \\spad{i = i1,...,i1-1+nrows y} and \\spad{j = j1,...,j1-1+ncols y}.")) (|subMatrix| (($ $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subMatrix(x,i1,i2,j1,j2)} extracts the submatrix \\spad{[x(i,j)]} where the index \\spad{i} ranges from \\spad{i1} to \\spad{i2} and the index \\spad{j} ranges from \\spad{j1} to \\spad{j2}.")) (|swapColumns!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapColumns!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th columns of \\spad{m}. This destructively alters the matrix.")) (|swapRows!| (($ $ (|Integer|) (|Integer|)) "\\spad{swapRows!(m,i,j)} interchanges the \\spad{i}th and \\spad{j}th rows of \\spad{m}. This destructively alters the matrix.")) (|setelt| (($ $ (|List| (|Integer|)) (|List| (|Integer|)) $) "\\spad{setelt(x,rowList,colList,y)} destructively alters the matrix \\spad{x}. If \\spad{y} is \\spad{m}-by-\\spad{n},{} \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then \\spad{x(i<k>,j<l>)} is set to \\spad{y(k,l)} for \\spad{k = 1,...,m} and \\spad{l = 1,...,n}.")) (|elt| (($ $ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{elt(x,rowList,colList)} returns an \\spad{m}-by-\\spad{n} matrix consisting of elements of \\spad{x},{} where \\spad{m = \\# rowList} and \\spad{n = \\# colList}. If \\spad{rowList = [i<1>,i<2>,...,i<m>]} and \\spad{colList = [j<1>,j<2>,...,j<n>]},{} then the \\spad{(k,l)}th entry of \\spad{elt(x,rowList,colList)} is \\spad{x(i<k>,j<l>)}.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|vertConcat| (($ $ $) "\\spad{vertConcat(x,y)} vertically concatenates two matrices with an equal number of columns. The entries of \\spad{y} appear below of the entries of \\spad{x}. Error: if the matrices do not have the same number of columns.")) (|horizConcat| (($ $ $) "\\spad{horizConcat(x,y)} horizontally concatenates two matrices with an equal number of rows. The entries of \\spad{y} appear to the right of the entries of \\spad{x}. Error: if the matrices do not have the same number of rows.")) (|squareTop| (($ $) "\\spad{squareTop(m)} returns an \\spad{n}-by-\\spad{n} matrix consisting of the first \\spad{n} rows of the \\spad{m}-by-\\spad{n} matrix \\spad{m}. Error: if \\spad{m < n}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.") (($ |#2|) "\\spad{transpose(r)} converts the row \\spad{r} to a row matrix.")) (|coerce| (($ |#3|) "\\spad{coerce(col)} converts the column \\spad{col} to a column matrix.")) (|diagonalMatrix| (($ (|List| $)) "\\spad{diagonalMatrix([m1,...,mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{ri := nrows mi},{} \\spad{ci := ncols mi},{} then \\spad{m} is an (r1+..+rk) by (c1+..+ck) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|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}'s on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|Mapping| |#1| (|Integer|) (|Integer|))) "\\spad{matrix(n,m,f)} construcys and \\spad{n * m} matrix with the \\spad{(i,j)} entry equal to \\spad{f(i,j)}.") (($ (|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."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-629 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +(-628 R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{MatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#5| (|Mapping| |#5| |#1| |#5|) |#4| |#5|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices \\spad{i} and \\spad{j}.")) (|map| (((|Union| |#8| "failed") (|Mapping| (|Union| |#5| "failed") |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}.") ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-630 R |Row| |Col| M) +(-629 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 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} ~=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} ~=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."))) NIL -((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496)))) -(-631 R) +((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495)))) +(-630 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."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-496))) (|HasAttribute| |#1| (QUOTE (-3998 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-632 R) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-258))) (|HasCategory| |#1| (QUOTE (-495))) (|HasAttribute| |#1| (QUOTE (-3997 "*"))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-631 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{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 NIL -(-633 T$) +(-632 T$) ((|constructor| (NIL "This domain implements the notion of optional value,{} where a computation may fail to produce expected value.")) (|nothing| (($) "\\spad{nothing} represents failure or absence of value.")) (|autoCoerce| ((|#1| $) "\\spad{autoCoerce} is a courtesy coercion function used by the compiler in case it knows that `x' really is a \\spadtype{T}.")) (|case| (((|Boolean|) $ (|[\|\|]| |nothing|)) "\\spad{x case nothing} holds if the value for \\spad{x} is missing.") (((|Boolean|) $ (|[\|\|]| |#1|)) "\\spad{x case T} returns \\spad{true} if \\spad{x} is actually a data of type \\spad{T}.")) (|just| (($ |#1|) "\\spad{just x} injects the value `x' into \\%."))) NIL NIL -(-634 R Q) +(-633 R Q) ((|constructor| (NIL "MatrixCommonDenominator provides functions to compute the common denominator of a matrix of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| (|Matrix| |#1|)) (|:| |den| |#1|)) (|Matrix| |#2|)) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|clearDenominator| (((|Matrix| |#1|) (|Matrix| |#2|)) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the elements of \\spad{q}.")) (|commonDenominator| ((|#1| (|Matrix| |#2|)) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the elements of \\spad{q}."))) NIL NIL -(-635 S) +(-634 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}."))) -((-3997 . T)) +((-3996 . T)) NIL -(-636 U) +(-635 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 gcd of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) NIL NIL -(-637) +(-636) ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: ?? Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,b,c,d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,t,u,f,s1,l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1="undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,g,s1,s2,l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,s1,s2,l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) #1#) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,g,h,j,s1,s2,l)} \\undocumented"))) NIL NIL -(-638 OV E -3093 PG) +(-637 OV E -3092 PG) ((|constructor| (NIL "Package for factorization of multivariate polynomials over finite fields.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field. \\spad{p} is represented as a univariate polynomial with multivariate coefficients over a finite field.") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} produces the complete factorization of the multivariate polynomial \\spad{p} over a finite field."))) NIL NIL -(-639 R) +(-638 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."))) NIL NIL -(-640 S D1 D2 I) +(-639 S D1 D2 I) ((|constructor| (NIL "transforms top-level objects into compiled functions.")) (|compiledFunction| (((|Mapping| |#4| |#2| |#3|) |#1| (|Symbol|) (|Symbol|)) "\\spad{compiledFunction(expr,x,y)} returns a function \\spad{f: (D1, D2) -> I} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(D1, D2)}")) (|binaryFunction| (((|Mapping| |#4| |#2| |#3|) (|Symbol|)) "\\spad{binaryFunction(s)} is a local function"))) NIL NIL -(-641 S) +(-640 S) ((|constructor| (NIL "MakeFloatCompiledFunction transforms top-level objects into compiled Lisp functions whose arguments are Lisp floats. This by-passes the \\Language{} compiler and interpreter,{} thereby gaining several orders of magnitude.")) (|makeFloatFunction| (((|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|) (|Symbol|)) "\\spad{makeFloatFunction(expr, x, y)} returns a Lisp function \\spad{f: (\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat}) -> \\axiomType{DoubleFloat}} defined by \\spad{f(x, y) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\spad{(\\axiomType{DoubleFloat}, \\axiomType{DoubleFloat})}.") (((|Mapping| (|DoubleFloat|) (|DoubleFloat|)) |#1| (|Symbol|)) "\\spad{makeFloatFunction(expr, x)} returns a Lisp function \\spad{f: \\axiomType{DoubleFloat} -> \\axiomType{DoubleFloat}} defined by \\spad{f(x) == expr}. Function \\spad{f} is compiled and directly applicable to objects of type \\axiomType{DoubleFloat}."))) NIL NIL -(-642 S) +(-641 S) ((|constructor| (NIL "transforms top-level objects into interpreter functions.")) (|function| (((|Symbol|) |#1| (|Symbol|) (|List| (|Symbol|))) "\\spad{function(e, foo, [x1,...,xn])} creates a function \\spad{foo(x1,...,xn) == e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x, y)} creates a function \\spad{foo(x, y) = e}.") (((|Symbol|) |#1| (|Symbol|) (|Symbol|)) "\\spad{function(e, foo, x)} creates a function \\spad{foo(x) == e}.") (((|Symbol|) |#1| (|Symbol|)) "\\spad{function(e, foo)} creates a function \\spad{foo() == e}."))) NIL NIL -(-643 S T$) +(-642 S T$) ((|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 \\spad{part1} is \\spad{a} and \\spad{part2} is \\spad{b}."))) NIL NIL -(-644 S -2670 I) +(-643 S -2669 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 -(-645 E OV R P) +(-644 E OV R P) ((|constructor| (NIL "This package provides the functions for the multivariate \"lifting\",{} using an algorithm of Paul Wang. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|lifting1| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|List| |#4|) (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#4|)))) (|List| (|NonNegativeInteger|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{lifting1(u,lv,lu,lr,lp,lt,ln,t,r)} \\undocumented")) (|lifting| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|SparseUnivariatePolynomial| |#3|)) (|List| |#3|) (|List| |#4|) (|List| (|NonNegativeInteger|)) |#3|) "\\spad{lifting(u,lv,lu,lr,lp,ln,r)} \\undocumented")) (|corrPoly| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| |#3|) (|List| (|NonNegativeInteger|)) (|List| (|SparseUnivariatePolynomial| |#4|)) (|Vector| (|List| (|SparseUnivariatePolynomial| |#3|))) |#3|) "\\spad{corrPoly(u,lv,lr,ln,lu,t,r)} \\undocumented"))) NIL NIL -(-646 R) +(-645 R) ((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i, i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) \\~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-647 R1 UP1 UPUP1 R2 UP2 UPUP2) +(-646 R1 UP1 UPUP1 R2 UP2 UPUP2) ((|constructor| (NIL "Lifting of a map through 2 levels of polynomials.")) (|map| ((|#6| (|Mapping| |#4| |#1|) |#3|) "\\spad{map(f, p)} lifts \\spad{f} to the domain of \\spad{p} then applies it to \\spad{p}."))) NIL NIL -(-648) +(-647) ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-649 R |Mod| -2038 -3519 |exactQuo|) +(-648 R |Mod| -2037 -3518 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-650 R P) +(-649 R P) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-651 IS E |ff|) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3991 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-650 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,e)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL -(-652 R M) +(-651 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f, u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1, op2)} sets the adjoint of \\spad{op1} to be \\spad{op2}. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-653 R |Mod| -2038 -3519 |exactQuo|) +(-652 R |Mod| -2037 -3518 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-3993 . T)) +((-3992 . T)) NIL -(-654 S R) +(-653 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) NIL NIL -(-655 R) +(-654 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL -(-656 -3093) +(-655 -3092) ((|constructor| (NIL "\\indented{1}{MoebiusTransform(\\spad{F}) is the domain of fractional linear (Moebius)} transformations over \\spad{F}.")) (|eval| (((|OnePointCompletion| |#1|) $ (|OnePointCompletion| |#1|)) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).") ((|#1| $ |#1|) "\\spad{eval(m,x)} returns \\spad{(a*x + b)/(c*x + d)} where \\spad{m = moebius(a,b,c,d)} (see \\spadfunFrom{moebius}{MoebiusTransform}).")) (|recip| (($ $) "\\spad{recip(m)} = recip() * \\spad{m}") (($) "\\spad{recip()} returns \\spad{matrix [[0,1],[1,0]]} representing the map \\spad{x -> 1 / x}.")) (|scale| (($ $ |#1|) "\\spad{scale(m,h)} returns \\spad{scale(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{scale(k)} returns \\spad{matrix [[k,0],[0,1]]} representing the map \\spad{x -> k * x}.")) (|shift| (($ $ |#1|) "\\spad{shift(m,h)} returns \\spad{shift(h) * m} (see \\spadfunFrom{shift}{MoebiusTransform}).") (($ |#1|) "\\spad{shift(k)} returns \\spad{matrix [[1,k],[0,1]]} representing the map \\spad{x -> x + k}.")) (|moebius| (($ |#1| |#1| |#1| |#1|) "\\spad{moebius(a,b,c,d)} returns \\spad{matrix [[a,b],[c,d]]}."))) -((-3993 . T)) +((-3992 . T)) NIL -(-657 S) +(-656 S) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-658) +(-657) ((|constructor| (NIL "Monad is the class of all multiplicative monads,{} \\spadignore{i.e.} sets with a binary operation.")) (** (($ $ (|PositiveInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|PositiveInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,1) := a}.")) (|rightPower| (($ $ (|PositiveInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,1) := a}.")) (* (($ $ $) "\\spad{a*b} is the product of \\spad{a} and \\spad{b} in a set with a binary operation."))) NIL NIL -(-659 S) +(-658 S) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-660) +(-659) ((|constructor| (NIL "\\indented{1}{MonadWithUnit is the class of multiplicative monads with unit,{}} \\indented{1}{\\spadignore{i.e.} sets with a binary operation and a unit element.} Axioms \\indented{3}{leftIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{3}\\tab{30} 1*x=x} \\indented{3}{rightIdentity(\"*\":(\\%,{}\\%)->\\%,{}1)\\space{2}\\tab{30} x*1=x} Common Additional Axioms \\indented{3}{unitsKnown---if \"recip\" says \"failed\",{} that PROVES input wasn't a unit}")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if such an element doesn't exist or cannot be determined (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{a**n} returns the \\spad{n}\\spad{-}th power of \\spad{a},{} defined by repeated squaring.")) (|leftPower| (($ $ (|NonNegativeInteger|)) "\\spad{leftPower(a,n)} returns the \\spad{n}\\spad{-}th left power of \\spad{a},{} \\spadignore{i.e.} \\spad{leftPower(a,n) := a * leftPower(a,n-1)} and \\spad{leftPower(a,0) := 1}.")) (|rightPower| (($ $ (|NonNegativeInteger|)) "\\spad{rightPower(a,n)} returns the \\spad{n}\\spad{-}th right power of \\spad{a},{} \\spadignore{i.e.} \\spad{rightPower(a,n) := rightPower(a,n-1) * a} and \\spad{rightPower(a,0) := 1}.")) (|one?| (((|Boolean|) $) "\\spad{one?(a)} tests whether \\spad{a} is the unit 1.")) (|One| (($) "1 returns the unit element,{} denoted by 1."))) NIL NIL -(-661 S R UP) +(-660 S R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#2|) (|Vector| $) (|Mapping| |#2| |#2|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#3| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#3|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#3|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#3|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#3|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) NIL ((|HasCategory| |#2| (QUOTE (-299))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-320)))) -(-662 R UP) +(-661 R UP) ((|constructor| (NIL "A \\spadtype{MonogenicAlgebra} is an algebra of finite rank which can be generated by a single element.")) (|derivationCoordinates| (((|Matrix| |#1|) (|Vector| $) (|Mapping| |#1| |#1|)) "\\spad{derivationCoordinates(b, ')} returns \\spad{M} such that \\spad{b' = M b}.")) (|lift| ((|#2| $) "\\spad{lift(z)} returns a minimal degree univariate polynomial up such that \\spad{z=reduce up}.")) (|convert| (($ |#2|) "\\spad{convert(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|reduce| (((|Union| $ "failed") (|Fraction| |#2|)) "\\spad{reduce(frac)} converts the fraction \\spad{frac} to an algebra element.") (($ |#2|) "\\spad{reduce(up)} converts the univariate polynomial \\spad{up} to an algebra element,{} reducing by the \\spad{definingPolynomial()} if necessary.")) (|definingPolynomial| ((|#2|) "\\spad{definingPolynomial()} returns the minimal polynomial which \\spad{generator()} satisfies.")) (|generator| (($) "\\spad{generator()} returns the generator for this domain."))) -((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 |has| |#1| (-312)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-663 S) +(-662 S) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) NIL NIL -(-664) +(-663) ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (|one?| (((|Boolean|) $) "\\spad{one?(x)} tests if \\spad{x} is equal to 1.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|One| (($) "1 is the multiplicative identity."))) NIL NIL -(-665 T$) +(-664 T$) ((|constructor| (NIL "This domain implements monoid operations.")) (|monoidOperation| (($ (|Mapping| |#1| |#1| |#1|) |#1|) "\\spad{monoidOperation(f,e)} constructs a operation from the binary mapping \\spad{f} with neutral value \\spad{e}."))) -(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3056 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3056 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-666 T$) +(-665 T$) ((|constructor| (NIL "This is the category of all domains that implement monoid operations")) (|neutralValue| ((|#1| $) "\\spad{neutralValue f} returns the neutral value of the monoid operation \\spad{f}."))) -(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3057 (|f| |x| (-2413 |f|)) |x|) (|exit| 1 (-3057 (|f| (-2413 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |neutrality| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|)) (SEQ (-3056 (|f| |x| (-2412 |f|)) |x|) (|exit| 1 (-3056 (|f| (-2412 |f|) |x|) |x|))))) . T) ((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-667 -3093 UP) +(-666 -3092 UP) ((|constructor| (NIL "Tools for handling monomial extensions.")) (|decompose| (((|Record| (|:| |poly| |#2|) (|:| |normal| (|Fraction| |#2|)) (|:| |special| (|Fraction| |#2|))) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{decompose(f, D)} returns \\spad{[p,n,s]} such that \\spad{f = p+n+s},{} all the squarefree factors of \\spad{denom(n)} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{denom(s)} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{n} and \\spad{s} are proper fractions (no pole at infinity). \\spad{D} is the derivation to use.")) (|normalDenom| ((|#2| (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{normalDenom(f, D)} returns the product of all the normal factors of \\spad{denom(f)}. \\spad{D} is the derivation to use.")) (|splitSquarefree| (((|Record| (|:| |normal| (|Factored| |#2|)) (|:| |special| (|Factored| |#2|))) |#2| (|Mapping| |#2| |#2|)) "\\spad{splitSquarefree(p, D)} returns \\spad{[n_1 n_2\\^2 ... n_m\\^m, s_1 s_2\\^2 ... s_q\\^q]} such that \\spad{p = n_1 n_2\\^2 ... n_m\\^m s_1 s_2\\^2 ... s_q\\^q},{} each \\spad{n_i} is normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D} and each \\spad{s_i} is special \\spad{w}.\\spad{r}.\\spad{t} \\spad{D}. \\spad{D} is the derivation to use.")) (|split| (((|Record| (|:| |normal| |#2|) (|:| |special| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{split(p, D)} returns \\spad{[n,s]} such that \\spad{p = n s},{} all the squarefree factors of \\spad{n} are normal \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} and \\spad{s} is special \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D}. \\spad{D} is the derivation to use."))) NIL NIL -(-668 |VarSet| E1 E2 R S PR PS) +(-667 |VarSet| E1 E2 R S PR PS) ((|constructor| (NIL "\\indented{1}{Utilities for MPolyCat} Author: Manuel Bronstein Date Created: 1987 Date Last Updated: 28 March 1990 (PG)")) (|reshape| ((|#7| (|List| |#5|) |#6|) "\\spad{reshape(l,p)} \\undocumented")) (|map| ((|#7| (|Mapping| |#5| |#4|) |#6|) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-669 |Vars1| |Vars2| E1 E2 R PR1 PR2) +(-668 |Vars1| |Vars2| E1 E2 R PR1 PR2) ((|constructor| (NIL "This package \\undocumented")) (|map| ((|#7| (|Mapping| |#2| |#1|) |#6|) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-670 E OV R PPR) +(-669 E OV R PPR) ((|constructor| (NIL "\\indented{3}{This package exports a factor operation for multivariate polynomials} with coefficients which are polynomials over some ring \\spad{R} over which we can factor. It is used internally by packages such as the solve package which need to work with polynomials in a specific set of variables with coefficients which are polynomials in all the other variables.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors a polynomial with polynomial coefficients.")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails.")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-671 |vl| R) +(-670 |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."))) -(((-3998 "*") |has| |#2| (-146)) (-3989 |has| |#2| (-496)) (-3994 |has| |#2| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-822))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-822)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-822)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-496)))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| (-774 |#1|) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| (-774 |#1|) (QUOTE (-554 (-474))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-672 E OV R PRF) +(((-3997 "*") |has| |#2| (-146)) (-3988 |has| |#2| (-495)) (-3993 |has| |#2| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-821))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-773 |#1|) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-773 |#1|) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-671 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 NIL -(-673 E OV R P) +(-672 E OV R P) ((|constructor| (NIL "\\indented{1}{MRationalFactorize contains the factor function for multivariate} polynomials over the quotient field of a ring \\spad{R} such that the package MultivariateFactorize can factor multivariate polynomials over \\spad{R}.")) (|factor| (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} with coefficients which are fractions of elements of \\spad{R}."))) NIL NIL -(-674 R S M) +(-673 R S M) ((|constructor| (NIL "\\spad{MonoidRingFunctions2} implements functions between two monoid rings defined with the same monoid over different rings.")) (|map| (((|MonoidRing| |#2| |#3|) (|Mapping| |#2| |#1|) (|MonoidRing| |#1| |#3|)) "\\spad{map(f,u)} maps \\spad{f} onto the coefficients \\spad{f} the element \\spad{u} of the monoid ring to create an element of a monoid ring with the same monoid \\spad{b}."))) NIL NIL -(-675 R M) +(-674 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}."))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-757)))) -(-676 S) +((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-756)))) +(-675 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}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-677 S) +((-3995 . T) (-3985 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-676 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-3986 . T) (-3997 . T)) +((-3985 . T) (-3996 . T)) NIL -(-678) +(-677) ((|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 NIL -(-679 S) +(-678 S) ((|constructor| (NIL "This package exports tools for merging lists")) (|mergeDifference| (((|List| |#1|) (|List| |#1|) (|List| |#1|)) "\\spad{mergeDifference(l1,l2)} returns a list of elements in \\spad{l1} not present in \\spad{l2}. Assumes lists are ordered and all \\spad{x} in \\spad{l2} are also in \\spad{l1}."))) NIL NIL -(-680 |Coef| |Var|) +(-679 |Coef| |Var|) ((|constructor| (NIL "\\spadtype{MultivariateTaylorSeriesCategory} is the most general multivariate Taylor series category.")) (|integrate| (($ $ |#2|) "\\spad{integrate(f,x)} returns the anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{x} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|polynomial| (((|Polynomial| |#1|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,k1,k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#1|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| (((|NonNegativeInteger|) $ |#2| (|NonNegativeInteger|)) "\\spad{order(f,x,n)} returns \\spad{min(n,order(f,x))}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(f,x)} returns the order of \\spad{f} viewed as a series in \\spad{x} may result in an infinite loop if \\spad{f} has no non-zero terms.")) (|monomial| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,[x1,x2,...,xk],[n1,n2,...,nk])} returns \\spad{a * x1^n1 * ... * xk^nk}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{monomial(a,x,n)} returns \\spad{a*x^n}.")) (|extend| (($ $ (|NonNegativeInteger|)) "\\spad{extend(f,n)} causes all terms of \\spad{f} of degree \\spad{<= n} to be computed.")) (|coefficient| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(f,[x1,x2,...,xk],[n1,n2,...,nk])} returns the coefficient of \\spad{x1^n1 * ... * xk^nk} in \\spad{f}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{coefficient(f,x,n)} returns the coefficient of \\spad{x^n} in \\spad{f}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL -(-681 OV E R P) +(-680 OV E R P) ((|constructor| (NIL "\\indented{2}{This is the top level package for doing multivariate factorization} over basic domains like \\spadtype{Integer} or \\spadtype{Fraction Integer}.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain where \\spad{p} is represented as a univariate polynomial with multivariate coefficients") (((|Factored| |#4|) |#4|) "\\spad{factor(p)} factors the multivariate polynomial \\spad{p} over its coefficient domain"))) NIL NIL -(-682 E OV R P) +(-681 E OV R P) ((|constructor| (NIL "Author : \\spad{P}.Gianni This package provides the functions for the computation of the square free decomposition of a multivariate polynomial. It uses the package GenExEuclid for the resolution of the equation \\spad{Af + Bg = h} and its generalization to \\spad{n} polynomials over an integral domain and the package \\spad{MultivariateLifting} for the \"multivariate\" lifting.")) (|normDeriv2| (((|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{normDeriv2 should} be local")) (|myDegree| (((|List| (|NonNegativeInteger|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|NonNegativeInteger|)) "\\spad{myDegree should} be local")) (|lift| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|SparseUnivariatePolynomial| |#3|) |#4| (|List| |#2|) (|List| (|NonNegativeInteger|)) (|List| |#3|)) "\\spad{lift should} be local")) (|check| (((|Boolean|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|)))) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{check should} be local")) (|coefChoose| ((|#4| (|Integer|) (|Factored| |#4|)) "\\spad{coefChoose should} be local")) (|intChoose| (((|Record| (|:| |upol| (|SparseUnivariatePolynomial| |#3|)) (|:| |Lval| (|List| |#3|)) (|:| |Lfact| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) (|:| |ctpol| |#3|)) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{intChoose should} be local")) (|nsqfree| (((|Record| (|:| |unitPart| |#4|) (|:| |suPart| (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#4|)) (|:| |exponent| (|Integer|)))))) (|SparseUnivariatePolynomial| |#4|) (|List| |#2|) (|List| (|List| |#3|))) "\\spad{nsqfree should} be local")) (|consnewpol| (((|Record| (|:| |pol| (|SparseUnivariatePolynomial| |#4|)) (|:| |polval| (|SparseUnivariatePolynomial| |#3|))) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#3|) (|Integer|)) "\\spad{consnewpol should} be local")) (|univcase| (((|Factored| |#4|) |#4| |#2|) "\\spad{univcase should} be local")) (|compdegd| (((|Integer|) (|List| (|Record| (|:| |factor| (|SparseUnivariatePolynomial| |#3|)) (|:| |exponent| (|Integer|))))) "\\spad{compdegd should} be local")) (|squareFreePrim| (((|Factored| |#4|) |#4|) "\\spad{squareFreePrim(p)} compute the square free decomposition of a primitive multivariate polynomial \\spad{p}.")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p} presented as a univariate polynomial with multivariate coefficients.") (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} computes the square free decomposition of a multivariate polynomial \\spad{p}."))) NIL NIL -(-683 S R) +(-682 S R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) NIL NIL -(-684 R) +(-683 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{r*(a*b) = (r*a)*b = a*(r*b)}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,n)} is recursively defined to be \\spad{plenaryPower(a,n-1)*plenaryPower(a,n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL -(-685 S) +(-684 S) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-686) +(-685) ((|constructor| (NIL "NonAssociativeRng is a basic ring-type structure,{} not necessarily commutative or associative,{} and not necessarily with unit. Axioms \\indented{2}{x*(y+z) = x*y + x*z} \\indented{2}{(x+y)*z = x*z + y*z} Common Additional Axioms \\indented{2}{noZeroDivisors\\space{2}ab = 0 => \\spad{a=0} or \\spad{b=0}}")) (|antiCommutator| (($ $ $) "\\spad{antiCommutator(a,b)} returns \\spad{a*b+b*a}.")) (|commutator| (($ $ $) "\\spad{commutator(a,b)} returns \\spad{a*b-b*a}.")) (|associator| (($ $ $ $) "\\spad{associator(a,b,c)} returns \\spad{(a*b)*c-a*(b*c)}."))) NIL NIL -(-687 S) +(-686 S) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-688) +(-687) ((|constructor| (NIL "A NonAssociativeRing is a non associative rng which has a unit,{} the multiplication is not necessarily commutative or associative.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(n)} coerces the integer \\spad{n} to an element of the ring.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring."))) NIL NIL -(-689 |Par|) +(-688 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-690 -3093) +(-689 -3092) ((|constructor| (NIL "\\spadtype{NumericContinuedFraction} provides functions \\indented{2}{for converting floating point numbers to continued fractions.}")) (|continuedFraction| (((|ContinuedFraction| (|Integer|)) |#1|) "\\spad{continuedFraction(f)} converts the floating point number \\spad{f} to a reduced continued fraction."))) NIL NIL -(-691 P -3093) +(-690 P -3092) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,b)} computes the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''."))) NIL NIL -(-692 T$) +(-691 T$) NIL NIL NIL -(-693 UP -3093) +(-692 UP -3092) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL -(-694 R) +(-693 R) ((|constructor| (NIL "NonLinearSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving. The solutions are given in the algebraic closure of \\spad{R} whenever possible.")) (|solve| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solve(lp)} finds the solution in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions in the algebraic closure of \\spad{R} of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}.")) (|solveInField| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{solveInField(lp)} finds the solution of the list \\spad{lp} of rational functions with respect to all the symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{solveInField(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-695) +(-694) ((|constructor| (NIL "\\spadtype{NonNegativeInteger} provides functions for non \\indented{2}{negative integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : \\spad{x*y = y*x}.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(a,i)} shift \\spad{a} by \\spad{i} bits.")) (|exquo| (((|Union| $ "failed") $ $) "\\spad{exquo(a,b)} returns the quotient of \\spad{a} and \\spad{b},{} or \"failed\" if \\spad{b} is zero or \\spad{a} rem \\spad{b} is zero.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(a,b)} returns a record containing both remainder and quotient.")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two non negative integers \\spad{a} and \\spad{b}.")) (|rem| (($ $ $) "\\spad{a rem b} returns the remainder of \\spad{a} and \\spad{b}.")) (|quo| (($ $ $) "\\spad{a quo b} returns the quotient of \\spad{a} and \\spad{b},{} forgetting the remainder."))) -(((-3998 "*") . T)) +(((-3997 "*") . T)) NIL -(-696 R -3093) +(-695 R -3092) ((|constructor| (NIL "NonLinearFirstOrderODESolver provides a function for finding closed form first integrals of nonlinear ordinary differential equations of order 1.")) (|solve| (((|Union| |#2| "failed") |#2| |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(M(x,y), N(x,y), y, x)} returns \\spad{F(x,y)} such that \\spad{F(x,y) = c} for a constant \\spad{c} is a first integral of the equation \\spad{M(x,y) dx + N(x,y) dy = 0},{} or \"failed\" if no first-integral can be found."))) NIL NIL -(-697) +(-696) ((|constructor| (NIL "\\spadtype{None} implements a type with no objects. It is mainly used in technical situations where such a thing is needed (\\spadignore{e.g.} the interpreter and some of the internal \\spadtype{Expression} code)."))) NIL NIL -(-698 S) +(-697 S) ((|constructor| (NIL "\\spadtype{NoneFunctions1} implements functions on \\spadtype{None}. It particular it includes a particulary dangerous coercion from any other type to \\spadtype{None}.")) (|coerce| (((|None|) |#1|) "\\spad{coerce(x)} changes \\spad{x} into an object of type \\spadtype{None}."))) NIL NIL -(-699 R |PolR| E |PolE|) +(-698 R |PolR| E |PolE|) ((|constructor| (NIL "This package implements the norm of a polynomial with coefficients in a monogenic algebra (using resultants)")) (|norm| ((|#2| |#4|) "\\spad{norm q} returns the norm of \\spad{q},{} \\spadignore{i.e.} the product of all the conjugates of \\spad{q}."))) NIL NIL -(-700 R E V P TS) +(-699 R E V P TS) ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}ts)} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}ts)} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}ts)} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}ts)} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-701 -3093 |ExtF| |SUEx| |ExtP| |n|) +(-700 -3092 |ExtF| |SUEx| |ExtP| |n|) ((|constructor| (NIL "This package \\undocumented")) (|Frobenius| ((|#4| |#4|) "\\spad{Frobenius(x)} \\undocumented")) (|retractIfCan| (((|Union| (|SparseUnivariatePolynomial| (|SparseUnivariatePolynomial| |#1|)) "failed") |#4|) "\\spad{retractIfCan(x)} \\undocumented")) (|normFactors| (((|List| |#4|) |#4|) "\\spad{normFactors(x)} \\undocumented"))) NIL NIL -(-702 BP E OV R P) +(-701 BP E OV R P) ((|constructor| (NIL "Package for the determination of the coefficients in the lifting process. Used by \\spadtype{MultivariateLifting}. This package will work for every euclidean domain \\spad{R} which has property \\spad{F},{} \\spadignore{i.e.} there exists a factor operation in \\spad{R[x]}.")) (|listexp| (((|List| (|NonNegativeInteger|)) |#1|) "\\spad{listexp }\\undocumented")) (|npcoef| (((|Record| (|:| |deter| (|List| (|SparseUnivariatePolynomial| |#5|))) (|:| |dterm| (|List| (|List| (|Record| (|:| |expt| (|NonNegativeInteger|)) (|:| |pcoef| |#5|))))) (|:| |nfacts| (|List| |#1|)) (|:| |nlead| (|List| |#5|))) (|SparseUnivariatePolynomial| |#5|) (|List| |#1|) (|List| |#5|)) "\\spad{npcoef }\\undocumented"))) NIL NIL -(-703 |Par|) +(-702 |Par|) ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the Rational Numbers. The results are expressed as floating numbers or as rational numbers depending on the type of the parameter Par.")) (|realEigenvectors| (((|List| (|Record| (|:| |outval| |#1|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#1|))))) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvectors(m,eps)} returns a list of records each one containing a real eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} as floats or rational numbers depending on the type of \\spad{eps} .")) (|realEigenvalues| (((|List| |#1|) (|Matrix| (|Fraction| (|Integer|))) |#1|) "\\spad{realEigenvalues(m,eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as floats or rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|))) (|Symbol|)) "\\spad{characteristicPolynomial(m,x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with variable \\spad{x}. Fraction \\spad{P} RN.") (((|Polynomial| (|Fraction| (|Integer|))) (|Matrix| (|Fraction| (|Integer|)))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over RN with a new symbol as variable."))) NIL NIL -(-704 R |VarSet|) +(-703 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{SMP} in order to speed up operations related to pseudo-division and gcd. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . 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T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-1090))))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-1090))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2560 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))))) (OR (-12 (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2560 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) (-2560 (|HasCategory| |#1| (QUOTE (-38 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2560 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) (-2560 (|HasCategory| |#1| (QUOTE (-483))))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-1090)))) (-2560 (|HasCategory| |#1| (QUOTE (-904 (-484))))))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-704 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and gcd for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedResultant2}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedResultant1}(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} cb]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}cb]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + cb * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} cb]} such that \\axiom{\\spad{g}} is a gcd of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + cb * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial gcd in \\axiom{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| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{c^n * a = q*b +r} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\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|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{c^n * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a -r} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|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)}"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-706 R S) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3991 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-705 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-707 R) +(-706 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| (QUOTE (-38 (-350 (-485)))))) -(-708 R E V P) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) +(-707 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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.}"))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-709 S) +(-708 S) ((|constructor| (NIL "Numeric provides real and complex numerical evaluation functions for various symbolic types.")) (|numericIfCan| (((|Union| (|Float|) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Expression| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numericIfCan(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Float|) "failed") (|Polynomial| |#1|)) "\\spad{numericIfCan(x)} returns a real approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.")) (|complexNumericIfCan| (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Expression| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| |#1|)) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumericIfCan(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places,{} or \"failed\" if \\axiom{\\spad{x}} is not a constant.") (((|Union| (|Complex| (|Float|)) "failed") (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumericIfCan(x)} returns a complex approximation of \\spad{x},{} or \"failed\" if \\axiom{\\spad{x}} is not constant.")) (|complexNumeric| (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Expression| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|))) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| (|Complex| |#1|)))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x}") (((|Complex| (|Float|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|)) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Polynomial| (|Complex| |#1|))) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) (|Complex| |#1|) (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) (|Complex| |#1|)) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.") (((|Complex| (|Float|)) |#1| (|PositiveInteger|)) "\\spad{complexNumeric(x, n)} returns a complex approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Complex| (|Float|)) |#1|) "\\spad{complexNumeric(x)} returns a complex approximation of \\spad{x}.")) (|numeric| (((|Float|) (|Expression| |#1|) (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Expression| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Fraction| (|Polynomial| |#1|)) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Fraction| (|Polynomial| |#1|))) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) (|Polynomial| |#1|) (|PositiveInteger|)) "\\spad{numeric(x,n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) (|Polynomial| |#1|)) "\\spad{numeric(x)} returns a real approximation of \\spad{x}.") (((|Float|) |#1| (|PositiveInteger|)) "\\spad{numeric(x, n)} returns a real approximation of \\spad{x} up to \\spad{n} decimal places.") (((|Float|) |#1|) "\\spad{numeric(x)} returns a real approximation of \\spad{x}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-962))) (|HasCategory| |#1| (QUOTE (-146)))) -(-710) +((-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-961))) (|HasCategory| |#1| (QUOTE (-146)))) +(-709) ((|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 NIL -(-711) +(-710) ((|constructor| (NIL "This package is a suite of functions for the numerical integration of an ordinary differential equation of \\spad{n} variables: \\blankline \\indented{8}{\\center{dy/dx = \\spad{f}(\\spad{y},{}\\spad{x})\\space{5}\\spad{y} is an \\spad{n}-vector}} \\blankline \\par All the routines are based on a 4-th order Runge-Kutta kernel. These routines generally have as arguments: \\spad{n},{} the number of dependent variables; \\spad{x1},{} the initial point; \\spad{h},{} the step size; \\spad{y},{} a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h}; \\spad{derivs},{} a function which computes the right hand side of the ordinary differential equation: \\spad{derivs(dydx,y,x)} computes \\spad{dydx},{} a vector which contains the derivative information. \\blankline \\par In order of increasing complexity:\\begin{items} \\blankline \\item \\spad{rk4(y,n,x1,h,derivs)} advances the solution vector to \\spad{x1 + h} and return the values in \\spad{y}. \\blankline \\item \\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. \\blankline \\item Starting with \\spad{y} at \\spad{x1},{} \\spad{rk4f(y,n,x1,x2,ns,derivs)} uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. Argument \\spad{x2},{} is the final point,{} and \\spad{ns},{} the number of steps to take. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} takes a 5-th order Runge-Kutta step with monitoring of local truncation to ensure accuracy and adjust stepsize. The function takes two half steps and one full step and scales the difference in solutions at the final point. If the error is within \\spad{eps},{} the step is taken and the result is returned. If the error is not within \\spad{eps},{} the stepsize if decreased and the procedure is tried again until the desired accuracy is reached. Upon input,{} an trial step size must be given and upon return,{} an estimate of the next step size to use is returned as well as the step size which produced the desired accuracy. The scaled error is computed as \\center{\\spad{error = MAX(ABS((y2steps(i) - y1step(i))/yscal(i)))}} and this is compared against \\spad{eps}. If this is greater than \\spad{eps},{} the step size is reduced accordingly to \\center{\\spad{hnew = 0.9 * hdid * (error/eps)**(-1/4)}} If the error criterion is satisfied,{} then we check if the step size was too fine and return a more efficient one. If \\spad{error > \\spad{eps} * (6.0E-04)} then the next step size should be \\center{\\spad{hnext = 0.9 * hdid * (error/\\spad{eps})**(\\spad{-1/5})}} Otherwise \\spad{hnext = 4.0 * hdid} is returned. A more detailed discussion of this and related topics can be found in the book \"Numerical Recipies\" by \\spad{W}.Press,{} \\spad{B}.\\spad{P}. Flannery,{} \\spad{S}.A. Teukolsky,{} \\spad{W}.\\spad{T}. Vetterling published by Cambridge University Press. Argument \\spad{step} is a record of 3 floating point numbers \\spad{(try , did , next)},{} \\spad{eps} is the required accuracy,{} \\spad{yscal} is the scaling vector for the difference in solutions. On input,{} \\spad{step.try} should be the guess at a step size to achieve the accuracy. On output,{} \\spad{step.did} contains the step size which achieved the accuracy and \\spad{step.next} is the next step size to use. \\blankline \\item \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is the same as \\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} except that the user must provide the 7 scratch arrays \\spad{t1-t7} of size \\spad{n}. \\blankline \\item \\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver program which uses \\spad{rk4qc} to integrate \\spad{n} ordinary differential equations starting at \\spad{x1} to \\spad{x2},{} keeping the local truncation error to within \\spad{eps} by changing the local step size. The scaling vector is defined as \\center{\\spad{yscal(i) = abs(y(i)) + abs(h*dydx(i)) + tiny}} where \\spad{y(i)} is the solution at location \\spad{x},{} \\spad{dydx} is the ordinary differential equation's right hand side,{} \\spad{h} is the current step size and \\spad{tiny} is 10 times the smallest positive number representable. The user must supply an estimate for a trial step size and the maximum number of calls to \\spad{rk4qc} to use. Argument \\spad{x2} is the final point,{} \\spad{eps} is local truncation,{} \\spad{ns} is the maximum number of call to \\spad{rk4qc} to use. \\end{items}")) (|rk4f| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4f(y,n,x1,x2,ns,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Starting with \\spad{y} at \\spad{x1},{} this function uses \\spad{ns} fixed steps of a 4-th order Runge-Kutta integrator to advance the solution vector to \\spad{x2} and return the values in \\spad{y}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4qc| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs,t1,t2,t3,t4,t5,t6,t7)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Record| (|:| |tryValue| (|Float|)) (|:| |did| (|Float|)) (|:| |next| (|Float|))) (|Float|) (|Vector| (|Float|)) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4qc(y,n,x1,step,eps,yscal,derivs)} is a subfunction for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. This function takes a 5-th order Runge-Kutta \\spad{step} with monitoring of local truncation to ensure accuracy and adjust stepsize. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4a| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4a(y,n,x1,x2,eps,h,ns,derivs)} is a driver function for the numerical integration of an ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector using a 4-th order Runge-Kutta method. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.")) (|rk4| (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Vector| (|Float|))) "\\spad{rk4(y,n,x1,h,derivs,t1,t2,t3,t4)} is the same as \\spad{rk4(y,n,x1,h,derivs)} except that you must provide 4 scratch arrays \\spad{t1}-\\spad{t4} of size \\spad{n}. For details,{} see \\con{NumericalOrdinaryDifferentialEquations}.") (((|Void|) (|Vector| (|Float|)) (|Integer|) (|Float|) (|Float|) (|Mapping| (|Void|) (|Vector| (|Float|)) (|Vector| (|Float|)) (|Float|))) "\\spad{rk4(y,n,x1,h,derivs)} uses a 4-th order Runge-Kutta method to numerically integrate the ordinary differential equation {\\em dy/dx = f(y,x)} of \\spad{n} variables,{} where \\spad{y} is an \\spad{n}-vector. Argument \\spad{y} is a vector of initial conditions of length \\spad{n} which upon exit contains the solution at \\spad{x1 + h},{} \\spad{n} is the number of dependent variables,{} \\spad{x1} is the initial point,{} \\spad{h} is the step size,{} and \\spad{derivs} is a function which computes the right hand side of the ordinary differential equation. For details,{} see \\spadtype{NumericalOrdinaryDifferentialEquations}."))) NIL NIL -(-712) +(-711) ((|constructor| (NIL "This suite of routines performs numerical quadrature using algorithms derived from the basic trapezoidal rule. Because the error term of this rule contains only even powers of the step size (for open and closed versions),{} fast convergence can be obtained if the integrand is sufficiently smooth. \\blankline Each routine returns a Record of type TrapAns,{} which contains\\indent{3} \\newline value (\\spadtype{Float}):\\tab{20} estimate of the integral \\newline error (\\spadtype{Float}):\\tab{20} estimate of the error in the computation \\newline totalpts (\\spadtype{Integer}):\\tab{20} total number of function evaluations \\newline success (\\spadtype{Boolean}):\\tab{20} if the integral was computed within the user specified error criterion \\indent{0}\\indent{0} To produce this estimate,{} each routine generates an internal sequence of sub-estimates,{} denoted by {\\em S(i)},{} depending on the routine,{} to which the various convergence criteria are applied. The user must supply a relative accuracy,{} \\spad{eps_r},{} and an absolute accuracy,{} \\spad{eps_a}. Convergence is obtained when either \\center{\\spad{ABS(S(i) - S(i-1)) < eps_r * ABS(S(i-1))}} \\center{or \\spad{ABS(S(i) - S(i-1)) < eps_a}} are \\spad{true} statements. \\blankline The routines come in three families and three flavors: \\newline\\tab{3} closed:\\tab{20}romberg,{}\\tab{30}simpson,{}\\tab{42}trapezoidal \\newline\\tab{3} open: \\tab{20}rombergo,{}\\tab{30}simpsono,{}\\tab{42}trapezoidalo \\newline\\tab{3} adaptive closed:\\tab{20}aromberg,{}\\tab{30}asimpson,{}\\tab{42}atrapezoidal \\par The {\\em S(i)} for the trapezoidal family is the value of the integral using an equally spaced absicca trapezoidal rule for that level of refinement. \\par The {\\em S(i)} for the simpson family is the value of the integral using an equally spaced absicca simpson rule for that level of refinement. \\par The {\\em S(i)} for the romberg family is the estimate of the integral using an equally spaced absicca romberg method. For the \\spad{i}\\spad{-}th level,{} this is an appropriate combination of all the previous trapezodial estimates so that the error term starts with the \\spad{2*(i+1)} power only. \\par The three families come in a closed version,{} where the formulas include the endpoints,{} an open version where the formulas do not include the endpoints and an adaptive version,{} where the user is required to input the number of subintervals over which the appropriate closed family integrator will apply with the usual convergence parmeters for each subinterval. This is useful where a large number of points are needed only in a small fraction of the entire domain. \\par Each routine takes as arguments: \\newline \\spad{f}\\tab{10} integrand \\newline a\\tab{10} starting point \\newline \\spad{b}\\tab{10} ending point \\newline \\spad{eps_r}\\tab{10} relative error \\newline \\spad{eps_a}\\tab{10} absolute error \\newline \\spad{nmin} \\tab{10} refinement level when to start checking for convergence (> 1) \\newline \\spad{nmax} \\tab{10} maximum level of refinement \\par The adaptive routines take as an additional parameter \\newline \\spad{nint}\\tab{10} the number of independent intervals to apply a closed \\indented{1}{family integrator of the same name.} \\par Notes: \\newline Closed family level \\spad{i} uses \\spad{1 + 2**i} points. \\newline Open family level \\spad{i} uses \\spad{1 + 3**i} points.")) (|trapezoidalo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidalo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpsono| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpsono(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|rombergo| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{rombergo(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spad{fn} over the open interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|trapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{trapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the trapezoidal method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|simpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{simpson(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the simpson method to numerically integrate function \\spad{fn} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|romberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|)) "\\spad{romberg(fn,a,b,epsrel,epsabs,nmin,nmax)} uses the romberg method to numerically integrate function \\spadvar{\\spad{fn}} over the closed interval \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax}. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|atrapezoidal| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{atrapezoidal(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive trapezoidal method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|asimpson| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{asimpson(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive simpson method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details.")) (|aromberg| (((|Record| (|:| |value| (|Float|)) (|:| |error| (|Float|)) (|:| |totalpts| (|Integer|)) (|:| |success| (|Boolean|))) (|Mapping| (|Float|) (|Float|)) (|Float|) (|Float|) (|Float|) (|Float|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{aromberg(fn,a,b,epsrel,epsabs,nmin,nmax,nint)} uses the adaptive romberg method to numerically integrate function \\spad{fn} over the closed interval from \\spad{a} to \\spad{b},{} with relative accuracy \\spad{epsrel} and absolute accuracy \\spad{epsabs},{} with the refinement levels for convergence checking vary from \\spad{nmin} to \\spad{nmax},{} and where \\spad{nint} is the number of independent intervals to apply the integrator. The value returned is a record containing the value of the integral,{} the estimate of the error in the computation,{} the total number of function evaluations,{} and either a boolean value which is \\spad{true} if the integral was computed within the user specified error criterion. See \\spadtype{NumericalQuadrature} for details."))) NIL NIL -(-713 |Curve|) +(-712 |Curve|) ((|constructor| (NIL "\\indented{1}{Author: Clifton \\spad{J}. Williamson} Date Created: Bastille Day 1989 Date Last Updated: 5 June 1990 Keywords: Examples: Package for constructing tubes around 3-dimensional parametric curves.")) (|tube| (((|TubePlot| |#1|) |#1| (|DoubleFloat|) (|Integer|)) "\\spad{tube(c,r,n)} creates a tube of radius \\spad{r} around the curve \\spad{c}."))) NIL NIL -(-714 S) +(-713 S) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-715) +(-714) ((|constructor| (NIL "Ordered sets which are also abelian groups,{} such that the addition preserves the ordering.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is \\spad{1} if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} and \\spad{0} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} holds when \\spad{x} is less than \\spad{0}."))) NIL NIL -(-716 S) +(-715 S) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-717) +(-716) ((|constructor| (NIL "Ordered sets which are also abelian monoids,{} such that the addition preserves the ordering.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} holds when \\spad{x} is greater than \\spad{0}."))) NIL NIL -(-718) +(-717) ((|constructor| (NIL "This domain is an OrderedAbelianMonoid with a \\spadfun{sup} operation added. The purpose of the \\spadfun{sup} operator in this domain is to act as a supremum with respect to the partial order imposed by \\spadop{-},{} rather than with respect to the total \\spad{>} order (since that is \"max\"). \\blankline")) (|sup| (($ $ $) "\\spad{sup(x,y)} returns the least element from which both \\spad{x} and \\spad{y} can be subtracted."))) NIL NIL -(-719) +(-718) ((|constructor| (NIL "Ordered sets which are also abelian semigroups,{} such that the addition preserves the ordering. \\indented{2}{\\spad{ x < y => x+z < y+z}}"))) NIL NIL -(-720 S R) +(-719 S R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#2| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#2| |#2| |#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#2| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#2| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#2| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#2| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#2| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#2| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#2| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#2| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#2| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) NIL -((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-320)))) -(-721 R) +((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-320)))) +(-720 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,ri,rj,rk,rE,rI,rJ,rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-722) +(-721) ((|constructor| (NIL "Ordered sets which are also abelian cancellation monoids,{} such that the addition preserves the ordering."))) NIL NIL -(-723 R) +(-722 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485)))))) (OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-910 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) -(-724 OR R OS S) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (OR (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-350 (-484)))))) (OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-909 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) +(-723 OR R OS S) ((|constructor| (NIL "\\spad{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 -(-725 R -3093 L) +(-724 R -3092 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op, g, x)} returns \\spad{[f, [y1,...,ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{yi}'s form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-726 R -3093) +(-725 R -3092) ((|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| #1="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| #1#) (|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| #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| #2#) (|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 -(-727 R -3093) +(-726 R -3092) ((|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 -(-728 -3093 UP UPUP R) +(-727 -3092 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 -(-729 -3093 UP L LQ) +(-728 -3092 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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}'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}'s are the affine singularities of \\spad{op},{} and the \\spad{e_i}'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 -(-730 -3093 UP L LQ) +(-729 -3092 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[ai D^i], a)} returns the operator \\spad{+/[ai (D+a)^i]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, zeros, ezfactor)} returns \\spad{[[f1, L1], [f2, L2], ... , [fk, Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z=0}. \\spad{zeros(C(x),H(x,y))} returns all the \\spad{P_i(x)}'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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{Li z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op, ric)} returns \\spad{[[a1, L1], [a2, L2], ... , [ak, Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}'s in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1, p1], [m2, p2], ... , [mk, pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree mj for some \\spad{j},{} and its leading coefficient is then a zero of 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 {gcd(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-731 -3093 UP) +(-730 -3092 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|) #1="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}'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|) #1#)) (|:| |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}'s form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-732 -3093 L UP A LO) +(-731 -3092 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 -(-733 -3093 UP) +(-732 -3092 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}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{Li z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op, ezfactor)} returns \\spad{[[f1,L1], [f2,L2],..., [fk,Lk]]} such that the singular ++ part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}'s (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int ai}} is \\spad{Li z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op, zeros, ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op, zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") 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The value \"failed\" is returned if no particular solution is found. Note: the method of variations of parameters is used.")) (|variationOfParameters| (((|Union| (|Vector| |#1|) "failed") |#2| |#1| (|List| |#1|)) "\\spad{variationOfParameters(op, g, [f1,...,fm])} returns \\spad{[u1,...,um]} such that a particular solution of the equation \\spad{op y = g} is \\spad{f1 int(u1) + ... + fm int(um)} where \\spad{[f1,...,fm]} are linearly independent and \\spad{op(fi)=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,...,fn], q, D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,...,fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),...,fn^(i-1)]}."))) 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T) (-3989 . T) (-3992 . 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T) (-3991 . T) (-3990 . T)) +(((-3997 "*") |has| |#2| (-312)) (-3988 |has| |#2| (-312)) (-3993 |has| |#2| (-312)) (-3987 |has| |#2| (-312)) (-3992 . T) (-3990 . T) (-3989 . T)) ((|HasCategory| |#2| (QUOTE (-312)))) -(-739 S) +(-738 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 -(-740 S) +(-739 S) ((|constructor| (NIL "\\indented{3}{The free monoid on a set \\spad{S} is the monoid of finite products of} the form \\spad{reduce(*,[si ** ni])} where the \\spad{si}'s are in \\spad{S},{} and the \\spad{ni}'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}.")) (|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}. monomial of \\spad{x}.")) (|rquo| (((|Union| $ "failed") $ |#1|) "\\spad{rquo(x, s)} returns the exact right quotient of \\spad{x} by \\spad{s}.")) (|lquo| (((|Union| $ "failed") $ |#1|) "\\spad{lquo(x, s)} returns the exact left quotient of \\spad{x} by \\spad{s}.")) (|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| $) "\\spad{first(x)} returns the first letter of \\spad{x}."))) NIL -((|HasCategory| |#1| (QUOTE (-757)))) -(-741) +((|HasCategory| |#1| (QUOTE (-756)))) +(-740) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-742 P R) +(-741 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite'' in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} 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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) ((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-190)))) -(-743 S) +(-742 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-3996 . T) (-3986 . T) (-3997 . T)) +((-3995 . T) (-3985 . T) (-3996 . T)) NIL -(-744 R) +(-743 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."))) -((-3993 |has| |#1| (-756))) -((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) -(-745 R S) +((-3992 |has| |#1| (-755))) +((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) +(-744 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 -(-746 R) +(-745 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120)))) -(-747 A S) +(-746 A S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#2|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#2| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-748 S) +(-747 S) ((|constructor| (NIL "This category specifies the interface for operators used to build terms,{} in the sense of Universal Algebra. The domain parameter \\spad{S} provides representation for the `external name' of an operator.")) (|is?| (((|Boolean|) $ |#1|) "\\spad{is?(op,n)} holds if the name of the operator \\spad{op} is \\spad{n}.")) (|arity| (((|Arity|) $) "\\spad{arity(op)} returns the arity of the operator \\spad{op}.")) (|name| ((|#1| $) "\\spad{name(op)} returns the externam name of \\spad{op}."))) NIL NIL -(-749) +(-748) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \"k\" (constructors),{} \"d\" (domains),{} \"c\" (categories) or \"p\" (packages)."))) NIL NIL -(-750) +(-749) ((|constructor| (NIL "This the datatype for an operator-signature pair.")) (|construct| (($ (|Identifier|) (|Signature|)) "\\spad{construct(op,sig)} construct a signature-operator with operator name `op',{} and signature `sig'.")) (|signature| (((|Signature|) $) "\\spad{signature(x)} returns the signature of `x'."))) NIL NIL -(-751 R) +(-750 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| (($) "\\spad{plusInfinity()} returns +infinity."))) -((-3993 |has| |#1| (-756))) -((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-484)))) -(-752 R S) +((-3992 |has| |#1| (-755))) +((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-21))) (OR (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-755)))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-483)))) +(-751 R S) ((|constructor| (NIL "Lifting of maps to ordered completions. Date Created: 4 Oct 1989 Date Last Updated: 4 Oct 1989")) (|map| (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{map(f, r, p, m)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = \\spad{p} and that \\spad{f}(minusInfinity) = \\spad{m}.") (((|OrderedCompletion| |#2|) (|Mapping| |#2| |#1|) (|OrderedCompletion| |#1|)) "\\spad{map(f, r)} lifts \\spad{f} and applies it to \\spad{r},{} assuming that \\spad{f}(plusInfinity) = plusInfinity and that \\spad{f}(minusInfinity) = minusInfinity."))) NIL NIL -(-753) +(-752) ((|constructor| (NIL "Ordered finite sets.")) (|max| (($) "\\spad{max} is the maximum value of \\%.")) (|min| (($) "\\spad{min} is the minimum value of \\%."))) NIL NIL -(-754 -2622 S) +(-753 -2621 S) ((|constructor| (NIL "\\indented{3}{This package provides ordering functions on vectors which} are suitable parameters for OrderedDirectProduct.")) (|reverseLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{reverseLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by the reverse lexicographic ordering.")) (|totalLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{totalLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the ordering which is total degree refined by lexicographic ordering.")) (|pureLex| (((|Boolean|) (|Vector| |#2|) (|Vector| |#2|)) "\\spad{pureLex(v1,v2)} return \\spad{true} if the vector \\spad{v1} is less than the vector \\spad{v2} in the lexicographic ordering."))) NIL NIL -(-755) +(-754) ((|constructor| (NIL "Ordered sets which are also monoids,{} such that multiplication preserves the ordering. \\blankline"))) NIL NIL -(-756) +(-755) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline"))) -((-3993 . T)) +((-3992 . T)) NIL -(-757) +(-756) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}."))) NIL NIL -(-758 T$ |f|) +(-757 T$ |f|) ((|constructor| (NIL "This domain turns any total ordering \\spad{f} on a type \\spad{T} into a model of the category \\spadtype{OrderedType}."))) NIL -((|HasCategory| |#1| (QUOTE (-553 (-773))))) -(-759 S) +((|HasCategory| |#1| (QUOTE (-552 (-772))))) +(-758 S) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-760) +(-759) ((|constructor| (NIL "Category of types equipped with a total ordering.")) (|min| (($ $ $) "\\spad{min(x,y)} returns the minimum of \\spad{x} and \\spad{y} relative to the ordering.")) (|max| (($ $ $) "\\spad{max(x,y)} returns the maximum of \\spad{x} and \\spad{y} relative to the ordering.")) (>= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is greater or equal than \\spad{y} in the current domain.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} holds if \\spad{x} is less or equal than \\spad{y} in the current domain.")) (> (((|Boolean|) $ $) "\\spad{x > y} holds if \\spad{x} is greater than \\spad{y} in the current domain.")) (< (((|Boolean|) $ $) "\\spad{x < y} holds if \\spad{x} is less than \\spad{y} in the current domain."))) NIL NIL -(-761 S R) +(-760 S R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\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 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''.")) (|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''.")) (|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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),i), i = 0..n)}.}"))) NIL -((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146)))) -(-762 R) +((|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146)))) +(-761 R) ((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\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| $)) $ $) "\\spad{rightDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division''.")) (|rightLcm| (($ $ $) "\\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| $)) $ $) "\\spad{leftDivide(a,b)} returns the pair \\spad{[q,r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division''.")) (|primitivePart| (($ $) "\\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 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''.")) (|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''.")) (|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)}.}"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-763 R C) +(-762 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{\\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{\\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{\\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{\\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 (-312))) (|HasCategory| |#1| (QUOTE (-496)))) -(-764 R |sigma| -3245) +((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) +(-763 R |sigma| -3244) ((|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."))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) -(-765 |x| R |sigma| -3245) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-312)))) +(-764 |x| R |sigma| -3244) ((|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}."))) -((-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) -(-766 R) +((-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-312)))) +(-765 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| (QUOTE (-38 (-350 (-485)))))) -(-767) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) +(-766) ((|constructor| (NIL "Semigroups with compatible ordering."))) NIL NIL -(-768) +(-767) ((|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 -(-769) +(-768) ((|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'' 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'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|OutputForm|)) "\\spad{output(x)} displays the output form \\spad{x} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}.") (((|Void|) (|String|)) "\\spad{output(s)} displays the string \\spad{s} on the ``algebra output'' stream,{} as defined by \\spadsyscom{set output algebra}."))) NIL NIL -(-770 S) +(-769 S) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-771) +(-770) ((|constructor| (NIL "This category describes output byte stream conduits.")) (|writeBytes!| (((|NonNegativeInteger|) $ (|ByteBuffer|)) "\\spad{writeBytes!(c,b)} write bytes from buffer `b' onto the conduit `c'. The actual number of written bytes is returned.")) (|writeUInt8!| (((|Maybe| (|UInt8|)) $ (|UInt8|)) "\\spad{writeUInt8!(c,b)} attempts to write the unsigned 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeInt8!| (((|Maybe| (|Int8|)) $ (|Int8|)) "\\spad{writeInt8!(c,b)} attempts to write the 8-bit value `v' on the conduit `c'. Returns the written value if successful,{} otherwise,{} returns \\spad{nothing}.")) (|writeByte!| (((|Maybe| (|Byte|)) $ (|Byte|)) "\\spad{writeByte!(c,b)} attempts to write the byte `b' on the conduit `c'. Returns the written byte if successful,{} otherwise,{} returns \\spad{nothing}."))) NIL NIL -(-772) +(-771) ((|constructor| (NIL "This domain provides representation for binary files open for output operations. `Binary' here means that the conduits do not interpret their contents.")) (|isOpen?| (((|Boolean|) $) "open?(ifile) holds if `ifile' is in open state.")) (|outputBinaryFile| (($ (|String|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file.") (($ (|FileName|)) "\\spad{outputBinaryFile(f)} returns an output conduit obtained by opening the file named by `f' as a binary file."))) NIL NIL -(-773) +(-772) ((|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| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,lowerlimit,upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,f)} creates the form \\spad{f} with \"x overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|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'''},{} \"f super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op, a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op, a, b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL -(-774 |VariableList|) +(-773 |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 -(-775) +(-774) ((|constructor| (NIL "This domain represents set of overloaded operators (in fact operator descriptors).")) (|members| (((|List| (|FunctionDescriptor|)) $) "\\spad{members(x)} returns the list of operator descriptors,{} \\spadignore{e.g.} signature and implementation slots,{} of the overload set \\spad{x}.")) (|name| (((|Identifier|) $) "\\spad{name(x)} returns the name of the overload set \\spad{x}."))) NIL NIL -(-776 R |vl| |wl| |wtlevel|) +(-775 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: 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)"))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) -(-777 R PS UP) +(-776 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 -(-778 R |x| |pt|) +(-777 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 -(-779 |p|) +(-778 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-780 |p|) +(-779 |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}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-781 |p|) +(-780 |p|) ((|constructor| (NIL "Stream-based implementation of 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)."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-779 |#1|) (QUOTE (-822))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-120))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-474)))) (|HasCategory| (-779 |#1|) (QUOTE (-934))) (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757))) (OR (|HasCategory| (-779 |#1|) (QUOTE (-741))) (|HasCategory| (-779 |#1|) (QUOTE (-757)))) (|HasCategory| (-779 |#1|) (QUOTE (-951 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-1067))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-330)))) (|HasCategory| (-779 |#1|) (QUOTE (-797 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-779 |#1|) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-779 |#1|) (QUOTE (-581 (-485)))) (|HasCategory| (-779 |#1|) (QUOTE (-189))) (|HasCategory| (-779 |#1|) (QUOTE (-812 (-1091)))) (|HasCategory| (-779 |#1|) (QUOTE (-190))) (|HasCategory| (-779 |#1|) (QUOTE (-810 (-1091)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -456) (QUOTE (-1091)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -779) (|devaluate| |#1|)) (|%list| (QUOTE -779) (|devaluate| |#1|)))) (|HasCategory| (-779 |#1|) (QUOTE (-258))) (|HasCategory| (-779 |#1|) (QUOTE (-484))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-779 |#1|) (QUOTE (-822)))) (|HasCategory| (-779 |#1|) (QUOTE (-118))))) -(-782 |p| PADIC) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-778 |#1|) (QUOTE (-821))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-1090)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-120))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-473)))) (|HasCategory| (-778 |#1|) (QUOTE (-933))) (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756))) (OR (|HasCategory| (-778 |#1|) (QUOTE (-740))) (|HasCategory| (-778 |#1|) (QUOTE (-756)))) (|HasCategory| (-778 |#1|) (QUOTE (-950 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-1066))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-330)))) (|HasCategory| (-778 |#1|) (QUOTE (-796 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-778 |#1|) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-778 |#1|) (QUOTE (-580 (-484)))) (|HasCategory| (-778 |#1|) (QUOTE (-189))) (|HasCategory| (-778 |#1|) (QUOTE (-811 (-1090)))) (|HasCategory| (-778 |#1|) (QUOTE (-190))) (|HasCategory| (-778 |#1|) (QUOTE (-809 (-1090)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -455) (QUOTE (-1090)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -260) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (|%list| (QUOTE -241) (|%list| (QUOTE -778) (|devaluate| |#1|)) (|%list| (QUOTE -778) (|devaluate| |#1|)))) (|HasCategory| (-778 |#1|) (QUOTE (-258))) (|HasCategory| (-778 |#1|) (QUOTE (-483))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-778 |#1|) (QUOTE (-821)))) (|HasCategory| (-778 |#1|) (QUOTE (-118))))) +(-781 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of 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)}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (OR (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757)))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-484))) (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) -(-783 S T$) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-950 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (OR (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756)))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))) (|HasCategory| |#2| (|%list| (QUOTE -241) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-483))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-782 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 `p'.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of `p'.")) (|construct| (($ |#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 `s' and `t'."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-1014))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))))) -(-784) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-1013))))) (-12 (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))))) +(-783) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|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'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's lowest value."))) NIL NIL -(-785) +(-784) ((|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 -(-786) +(-785) ((|constructor| (NIL "Representation of parameters to functions or constructors. For the most part,{} they are Identifiers. However,{} in very cases,{} they are \"flags\",{} \\spadignore{e.g.} string literals.")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(x)@String} implicitly coerce the object \\spad{x} to \\spadtype{String}. This function is left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(x)@Identifier} implicitly coerce the object \\spad{x} to \\spadtype{Identifier}. This function is left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} if the parameter AST object \\spad{x} designates a flag.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} if the parameter AST object \\spad{x} designates an \\spadtype{Identifier}."))) NIL NIL -(-787 CF1 CF2) +(-786 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricPlaneCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricPlaneCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-788 |ComponentFunction|) +(-787 |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 -(-789 CF1 CF2) +(-788 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSpaceCurve| |#2|) (|Mapping| |#2| |#1|) (|ParametricSpaceCurve| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-790 |ComponentFunction|) +(-789 |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 -(-791) +(-790) ((|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 -(-792 CF1 CF2) +(-791 CF1 CF2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|ParametricSurface| |#2|) (|Mapping| |#2| |#1|) (|ParametricSurface| |#1|)) "\\spad{map(f,x)} \\undocumented"))) NIL NIL -(-793 |ComponentFunction|) +(-792 |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 -(-794) +(-793) ((|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's,{}\\spad{l1} 1's,{}\\spad{l2} 2's,{}...,{}\\spad{ln} \\spad{n}'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}'s,{} and 4 \\spad{5}'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| (|PositiveInteger|))) (|Stream| (|List| (|PositiveInteger|)))) "\\spad{conjugates(lp)} is the stream of conjugates of a stream \\indented{1}{of partitions \\spad{lp}.}")) (|conjugate| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{conjugate(pt)} is the conjugate of the partition \\spad{pt}."))) NIL NIL -(-795 R) +(-794 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 -(-796 R S L) +(-795 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 -(-797 S) +(-796 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 -(-798 |Base| |Subject| |Pat|) +(-797 |Base| |Subject| |Pat|) ((|constructor| (NIL "This package provides the top-level pattern macthing functions.")) (|Is| (((|PatternMatchResult| |#1| |#2|) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a match of the form \\spad{[v1 = e1,...,vn = en]}; returns an empty match if \\spad{expr} is exactly equal to pat. returns a \\spadfun{failed} match if pat does not match \\spad{expr}.") (((|List| (|Equation| (|Polynomial| |#2|))) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|List| (|Equation| |#2|)) |#2| |#3|) "\\spad{Is(expr, pat)} matches the pattern pat on the expression \\spad{expr} and returns a list of matches \\spad{[v1 = e1,...,vn = en]}; returns an empty list if either \\spad{expr} is exactly equal to pat or if pat does not match \\spad{expr}.") (((|PatternMatchListResult| |#1| |#2| (|List| |#2|)) (|List| |#2|) |#3|) "\\spad{Is([e1,...,en], pat)} matches the pattern pat on the list of expressions \\spad{[e1,...,en]} and returns the result.")) (|is?| (((|Boolean|) (|List| |#2|) |#3|) "\\spad{is?([e1,...,en], pat)} tests if the list of expressions \\spad{[e1,...,en]} matches the pattern pat.") (((|Boolean|) |#2| |#3|) "\\spad{is?(expr, pat)} tests if the expression \\spad{expr} matches the pattern pat."))) NIL -((-12 (-2561 (|HasCategory| |#2| (QUOTE (-951 (-1091))))) (-2561 (|HasCategory| |#2| (QUOTE (-962))))) (-12 (|HasCategory| |#2| (QUOTE (-962))) (-2561 (|HasCategory| |#2| (QUOTE (-951 (-1091)))))) (|HasCategory| |#2| (QUOTE (-951 (-1091))))) -(-799 R S) +((-12 (-2560 (|HasCategory| |#2| (QUOTE (-950 (-1090))))) (-2560 (|HasCategory| |#2| (QUOTE (-961))))) (-12 (|HasCategory| |#2| (QUOTE (-961))) (-2560 (|HasCategory| |#2| (QUOTE (-950 (-1090)))))) (|HasCategory| |#2| (QUOTE (-950 (-1090))))) +(-798 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'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},{}\\spad{e1}),{}...,{}(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 -(-800 R A B) +(-799 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}(\\spad{a1})),{}...,{}(vn,{}\\spad{f}(an))]."))) NIL NIL -(-801 R) +(-800 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 pn to the copy,{} which is returned.")) (|setPredicates| (($ $ (|List| (|Any|))) "\\spad{setPredicates(p, [p1,...,pn])} attaches the predicate \\spad{p1} and ... and 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 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 '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 -(-802 R -2670) +(-801 R -2669) ((|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 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 -(-803 R S) +(-802 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 -(-804 |VarSet|) +(-803 |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.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 -(-805 UP R) +(-804 UP R) ((|constructor| (NIL "This package \\undocumented")) (|compose| ((|#1| |#1| |#1|) "\\spad{compose(p,q)} \\undocumented"))) NIL NIL -(-806 A T$ S) +(-805 A T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#2| $ |#3|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#2| $ |#3|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-807 T$ S) +(-806 T$ S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains with a distinguished} \\indented{2}{operation named \\spad{differentiate} for partial differentiation with} \\indented{2}{respect to some domain of variables.} See Also: \\indented{2}{DifferentialDomain,{} PartialDifferentialSpace}")) (D ((|#1| $ |#2|) "\\spad{D(x,v)} is a shorthand for \\spad{differentiate(x,v)}")) (|differentiate| ((|#1| $ |#2|) "\\spad{differentiate(x,v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) NIL NIL -(-808 UP -3093) +(-807 UP -3092) ((|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 -(-809 R S) +(-808 R S) ((|constructor| (NIL "A partial differential \\spad{R}-module with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL -(-810 S) +(-809 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline"))) -((-3993 . T)) +((-3992 . T)) NIL -(-811 A S) +(-810 A S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#2|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#2|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#2| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#2|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-812 S) +(-811 S) ((|constructor| (NIL "\\indented{2}{This category captures the interface of domains stable by partial} \\indented{2}{differentiation with respect to variables from some domain.} See Also: \\indented{2}{PartialDifferentialDomain}")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,[s1,...,sn],[n1,...,nn])} is a shorthand for \\spad{differentiate(x,[s1,...,sn],[n1,...,nn])}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,s,n)} is a shorthand for \\spad{differentiate(x,s,n)}.") (($ $ (|List| |#1|)) "\\spad{D(x,[s1,...sn])} is a shorthand for \\spad{differentiate(x,[s1,...sn])}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,[s1,...,sn],[n1,...,nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,s,n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}\\spad{-}th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,[s1,...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x, s1)..., sn)}."))) NIL NIL -(-813 S) +(-812 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})'s")) (|ptree| (($ $ $) "\\spad{ptree(x,y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-814 S) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-813 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,...,n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-3993 . T)) -((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-757)))) -(-815 |n| R) +((-3992 . T)) +((OR (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-756)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-756)))) +(-814 |n| R) ((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} Ch. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of x:\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} ch.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$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 -(-816 S) +(-815 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p, el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|support| (((|Set| |#1|) $) "\\spad{support p} returns the set of points not fixed by the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-3993 . T)) +((-3992 . T)) NIL -(-817 S) +(-816 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,m,n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,0,1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|support| (((|Set| |#1|) $) "\\spad{support(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) NIL NIL -(-818 |p|) +(-817 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) ((|HasCategory| $ (QUOTE (-120))) (|HasCategory| $ (QUOTE (-118))) (|HasCategory| $ (QUOTE (-320)))) -(-819 R E |VarSet| S) +(-818 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,p,v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-820 R S) +(-819 R S) ((|constructor| (NIL "\\indented{1}{PolynomialFactorizationByRecursionUnivariate} \\spad{R} is a \\spadfun{PolynomialFactorizationExplicit} domain,{} \\spad{S} is univariate polynomials over \\spad{R} We are interested in handling SparseUnivariatePolynomials over \\spad{S},{} is a variable we shall call \\spad{z}")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|randomR| ((|#1|) "\\spad{randomR()} produces a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#2|)) "failed") (|List| (|SparseUnivariatePolynomial| |#2|)) (|SparseUnivariatePolynomial| |#2|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,...,pn],p)} returns the list of polynomials \\spad{[q1,...,qn]} such that \\spad{sum qi/pi = p / prod pi},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL NIL -(-821 S) +(-820 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| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} 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 (-118)))) -(-822) +(-821) ((|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| (((|Maybe| $) $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \\spad{nothing} if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1, ..., fn], g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod fi = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}'s exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,q)} returns the gcd of the univariate polynomials \\spad{p} 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}."))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-823 R0 -3093 UP UPUP R) +(-822 R0 -3092 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 -(-824 UP UPUP R) +(-823 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 -(-825 UP UPUP) +(-824 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 -(-826 R) +(-825 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'' form has only one fractional term per prime in the denominator,{} while the ``p-adic'' 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} ``p-adically'' 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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-827 R) +(-826 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 -(-828 E OV R P) +(-827 E OV R P) ((|gcdPrimitive| ((|#4| (|List| |#4|)) "\\spad{gcdPrimitive lp} computes the gcd of the list of primitive polynomials lp.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.") ((|#4| |#4| |#4|) "\\spad{gcdPrimitive(p,q)} computes the gcd of the primitive polynomials \\spad{p} and \\spad{q}.")) (|gcd| (((|SparseUnivariatePolynomial| |#4|) (|List| (|SparseUnivariatePolynomial| |#4|))) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") (((|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}.") ((|#4| (|List| |#4|)) "\\spad{gcd(lp)} computes the gcd of the list of polynomials \\spad{lp}.") ((|#4| |#4| |#4|) "\\spad{gcd(p,q)} computes the gcd of the two polynomials \\spad{p} and \\spad{q}."))) NIL NIL -(-829) +(-828) ((|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'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's Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik'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's Cube acting on integers 10*i+j for 1 <= \\spad{i} <= 6,{} 1 <= \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(li)} constructs the janko group acting on the 100 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(li)} constructs the mathieu group acting on the 24 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(li)} constructs the mathieu group acting on the 23 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(li)} constructs the mathieu group acting on the 22 integers given in the list {\\em li}. Note: duplicates in the list will be removed. Error: if {\\em li} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(li)} constructs the mathieu group acting on the 12 integers given in the list {\\em li}. Note: duplicates in the list will be removed Error: if {\\em li} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(li)} constructs the mathieu group acting on the 11 integers given in the list {\\em li}. Note: duplicates in the list will be removed. error,{} if {\\em li} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,...,ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,...,ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,...,nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em ni}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(li)} constructs the alternating group acting on the integers in the list {\\em li},{} generators are in general the {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (li.1,li.2)} with {\\em n-2}-cycle {\\em (li.3,...,li.n)} and the 3-cycle {\\em (li.1,li.2,li.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,2)} with {\\em n-2}-cycle {\\em (3,...,n)} and the 3-cycle {\\em (1,2,3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(li)} constructs the symmetric group acting on the integers in the list {\\em li},{} generators are the cycle given by {\\em li} and the 2-cycle {\\em (li.1,li.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,...,n)} and the 2-cycle {\\em (1,2)}."))) NIL NIL -(-830 -3093) +(-829 -3092) ((|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 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 -(-831) +(-830) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = y*x")) (|gcd| (($ $ $) "\\spad{gcd(a,b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-3998 "*") . T)) +(((-3997 "*") . T)) NIL -(-832 R) +(-831 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 -(-833) +(-832) ((|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| (((|Maybe| (|List| $)) (|List| $) $) "\\spad{expressIdealMember([f1,...,fn],h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \\spad{nothing} 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)}"))) -((-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-834 |xx| -3093) +(-833 |xx| -3092) ((|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 -(-835 -3093 P) +(-834 -3092 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,l2)} \\undocumented"))) NIL NIL -(-836 R |Var| |Expon| GR) +(-835 R |Var| |Expon| GR) ((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that pl is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(pl) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in pl is inconsistent. It is assumed that 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{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} ~= 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{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{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{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{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{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{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 -(-837) +(-836) ((|constructor| (NIL "The Plot domain supports plotting of functions defined over a real number system. A real number system is a model for the real numbers and as such may be an approximation. For example floating point numbers and infinite continued fractions. The facilities at this point are limited to 2-dimensional plots or either a single function or a parametric function.")) (|debug| (((|Boolean|) (|Boolean|)) "\\spad{debug(true)} turns debug mode on \\spad{debug(false)} turns debug mode off")) (|numFunEvals| (((|Integer|)) "\\spad{numFunEvals()} returns the number of points computed")) (|setAdaptive| (((|Boolean|) (|Boolean|)) "\\spad{setAdaptive(true)} turns adaptive plotting on \\spad{setAdaptive(false)} turns adaptive plotting off")) (|adaptive?| (((|Boolean|)) "\\spad{adaptive?()} determines whether plotting be done adaptively")) (|setScreenResolution| (((|Integer|) (|Integer|)) "\\spad{setScreenResolution(i)} sets the screen resolution to \\spad{i}")) (|screenResolution| (((|Integer|)) "\\spad{screenResolution()} returns the screen resolution")) (|setMaxPoints| (((|Integer|) (|Integer|)) "\\spad{setMaxPoints(i)} sets the maximum number of points in a plot to \\spad{i}")) (|maxPoints| (((|Integer|)) "\\spad{maxPoints()} returns the maximum number of points in a plot")) (|setMinPoints| (((|Integer|) (|Integer|)) "\\spad{setMinPoints(i)} sets the minimum number of points in a plot to \\spad{i}")) (|minPoints| (((|Integer|)) "\\spad{minPoints()} returns the minimum number of points in a plot")) (|tRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{tRange(p)} returns the range of the parameter in a parametric plot \\spad{p}")) (|refine| (($ $) "\\spad{refine(p)} performs a refinement on the plot \\spad{p}") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{refine(x,r)} \\undocumented")) (|zoom| (($ $ (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r,s)} \\undocumented") (($ $ (|Segment| (|DoubleFloat|))) "\\spad{zoom(x,r)} \\undocumented")) (|parametric?| (((|Boolean|) $) "\\spad{parametric? determines} whether it is a parametric plot?")) (|plotPolar| (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) "\\spad{plotPolar(f)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[0,2*\\%pi]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plotPolar(f,a..b)} plots the polar curve \\spad{r = f(theta)} as theta ranges over the interval \\spad{[a,b]}; this is the same as the parametric curve \\spad{x = f(t) * cos(t)},{} \\spad{y = f(t) * sin(t)}.")) (|pointPlot| (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{pointPlot(t +-> (f(t),g(t)),a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.")) (|plot| (($ $ (|Segment| (|DoubleFloat|))) "\\spad{plot(x,r)} \\undocumented") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b,c..d,e..f)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}; \\spad{x}-range of \\spad{[c,d]} and \\spad{y}-range of \\spad{[e,f]} are noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,g,a..b)} plots the parametric curve \\spad{x = f(t)},{} \\spad{y = g(t)} as \\spad{t} ranges over the interval \\spad{[a,b]}.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b,c..d)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|List| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|DoubleFloat|))) "\\spad{plot([f1,...,fm],a..b)} plots the functions \\spad{y = f1(x)},{}...,{} \\spad{y = fm(x)} on the interval \\spad{a..b}.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b,c..d)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}; \\spad{y}-range of \\spad{[c,d]} is noted in Plot object.") (($ (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|))) "\\spad{plot(f,a..b)} plots the function \\spad{f(x)} on the interval \\spad{[a,b]}."))) NIL NIL -(-838 S) +(-837 S) ((|constructor| (NIL "\\spad{PlotFunctions1} provides facilities for plotting curves where functions SF -> 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 -(-839) +(-838) ((|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 -(-840) +(-839) ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-841) +(-840) ((|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 'x and no other quantity.")) (|assert| (((|Expression| (|Integer|)) (|Symbol|) (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}."))) NIL NIL -(-842 R -3093) +(-841 R -3092) ((|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 'x and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|Identifier|)) "\\spad{assert(x, s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL -(-843 S A B) +(-842 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 -(-844 S R -3093) +(-843 S R -3092) ((|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 -(-845 I) +(-844 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 -(-846 S E) +(-845 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 -(-847 S R L) +(-846 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 -(-848 S E V R P) +(-847 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 -797) (|devaluate| |#1|)))) -(-849 -2670) +((|HasCategory| |#3| (|%list| (QUOTE -796) (|devaluate| |#1|)))) +(-848 -2669) ((|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 fn to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x, foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL -(-850 R -3093 -2670) +(-849 R -3092 -2669) ((|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 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 -(-851 S R Q) +(-850 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 -(-852 S) +(-851 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 -(-853 S R P) +(-852 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 -(-854) +(-853) ((|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 -(-855 R) +(-854 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-856 |lv| R) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-855 |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 -(-857 |TheField| |ThePols|) +(-856 |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},{}sn)} is the number of sign variations in the list of non null numbers [s1::l]@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},{}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 (-756)))) -(-858 R) +((|HasCategory| |#1| (QUOTE (-755)))) +(-857 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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1091) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1091) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1091) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1091) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-859 R S) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-1090) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1090) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1090) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1090) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1090) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-858 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 -(-860 |x| R) +(-859 |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 -(-861 S R E |VarSet|) +(-860 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 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 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 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 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 (-822))) (|HasAttribute| |#2| (QUOTE -3994)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330)))) (|HasCategory| |#4| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485)))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#4| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) -(-862 R E |VarSet|) +((|HasCategory| |#2| (QUOTE (-821))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#4| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| |#4| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#4| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) +(-861 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 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 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 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 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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL -(-863 E V R P -3093) +(-862 E V R P -3092) ((|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},{}...,{}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 -(-864 E |Vars| R P S) +(-863 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 -(-865 E V R P -3093) +(-864 E V R P -3092) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f, n)} returns \\spad{[m,c,r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-392)))) -(-866) +(-865) ((|constructor| (NIL "This domain represents network port numbers (notable TCP and UDP).")) (|port| (($ (|SingleInteger|)) "\\spad{port(n)} constructs a PortNumber from the integer `n'."))) NIL NIL -(-867) +(-866) ((|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|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-868 R E) +(-867 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and terms indexed by their exponents (from an arbitrary ordered abelian monoid). This type is used,{} for example,{} by the \\spadtype{DistributedMultivariatePolynomial} domain where the exponent domain is a direct product of non negative integers.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (|fmecg| (($ $ |#2| |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) -(-869 R L) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3993))) +(-868 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 -(-870 S) +(-869 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt's.} Minimum index is 0 in this type,{} cannot be changed"))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-871 A B) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-870 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 -(-872) +(-871) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f, x = a..b)} returns the formal definite integral of \\spad{f} dx for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f, x)} returns the formal integral of \\spad{f} dx."))) NIL NIL -(-873 -3093) +(-872 -3092) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,...,pn], [a1,...,an], a)} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'s. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,...,pn], [a1,...,an])} returns \\spad{[[c1,...,cn], [q1,...,qn], q]} such that then \\spad{k(a1,...,an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{ai = qi(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}'s are the defining polynomials for the \\spad{ai}'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}'s are the defining polynomials for the \\spad{ai}'s. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve \\spad{a2}. This operation uses \\spadfun{resultant}."))) NIL NIL -(-874 I) +(-873 I) ((|constructor| (NIL "The \\spadtype{IntegerPrimesPackage} implements a modification of Rabin'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'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 \\spad{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 -(-875) +(-874) ((|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 -(-876 A B) +(-875 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"))) -((-3993 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) -((OR (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-718))) (|HasCategory| |#2| (QUOTE (-718)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664))))) (-12 (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-664)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-757))))) -(-877) +((-3992 -12 (|has| |#2| (-413)) (|has| |#1| (-413)))) +((OR (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23))))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-320)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-717))) (|HasCategory| |#2| (QUOTE (-717)))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-413))) (|HasCategory| |#2| (QUOTE (-413)))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663))))) (-12 (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-663)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-104))) (|HasCategory| |#2| (QUOTE (-104)))) (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-756))))) +(-876) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Identifier|) (|SExpression|)) "\\spad{property(n,val)} constructs a property with name `n' and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Identifier|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL NIL -(-878 T$) +(-877 T$) ((|constructor| (NIL "This domain implements propositional formula build over a term domain,{} that itself belongs to PropositionalLogic")) (|disjunction| (($ $ $) "\\spad{disjunction(p,q)} returns a formula denoting the disjunction of \\spad{p} and \\spad{q}.")) (|conjunction| (($ $ $) "\\spad{conjunction(p,q)} returns a formula denoting the conjunction of \\spad{p} and \\spad{q}.")) (|isEquiv| (((|Maybe| (|Pair| $ $)) $) "\\spad{isEquiv f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an equivalence formula.")) (|isImplies| (((|Maybe| (|Pair| $ $)) $) "\\spad{isImplies f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is an implication formula.")) (|isOr| (((|Maybe| (|Pair| $ $)) $) "\\spad{isOr f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a disjunction formula.")) (|isAnd| (((|Maybe| (|Pair| $ $)) $) "\\spad{isAnd f} returns a value \\spad{v} such that \\spad{v case Pair(\\%,\\%)} holds if the formula \\spad{f} is a conjunction formula.")) (|isNot| (((|Maybe| $) $) "\\spad{isNot f} returns a value \\spad{v} such that \\spad{v case \\%} holds if the formula \\spad{f} is a negation.")) (|isAtom| (((|Maybe| |#1|) $) "\\spad{isAtom f} returns a value \\spad{v} such that \\spad{v case T} holds if the formula \\spad{f} is a term."))) NIL NIL -(-879 T$) +(-878 T$) ((|constructor| (NIL "This package collects unary functions operating on propositional formulae.")) (|simplify| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{simplify f} returns a formula logically equivalent to \\spad{f} where obvious tautologies have been removed.")) (|atoms| (((|Set| |#1|) (|PropositionalFormula| |#1|)) "\\spad{atoms f} ++ returns the set of atoms appearing in the formula \\spad{f}.")) (|dual| (((|PropositionalFormula| |#1|) (|PropositionalFormula| |#1|)) "\\spad{dual f} returns the dual of the proposition \\spad{f}."))) NIL NIL -(-880 S T$) +(-879 S T$) ((|constructor| (NIL "This package collects binary functions operating on propositional formulae.")) (|map| (((|PropositionalFormula| |#2|) (|Mapping| |#2| |#1|) (|PropositionalFormula| |#1|)) "\\spad{map(f,x)} returns a propositional formula where all atoms in \\spad{x} have been replaced by the result of applying the function \\spad{f} to them."))) NIL NIL -(-881) +(-880) ((|constructor| (NIL "This category declares the connectives of Propositional Logic.")) (|equiv| (($ $ $) "\\spad{equiv(p,q)} returns the logical equivalence of `p',{} `q'.")) (|implies| (($ $ $) "\\spad{implies(p,q)} returns the logical implication of `q' by `p'.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) NIL NIL -(-882 S) +(-881 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-3996 . T) (-3997 . T)) +((-3995 . T) (-3996 . T)) NIL -(-883 R |polR|) +(-882 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{\\spad{semiSubResultantGcdEuclidean1}}{PseudoRemainderSequence},{} \\axiomOpFrom{\\spad{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.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{\\spad{nextsousResultant2}(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{S_{\\spad{e}-1}} where \\axiom{\\spad{P} ~ S_d,{} \\spad{Q} = S_{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = lc(S_d)}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{\\spad{Lazard2}(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)**(\\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{gcd(\\spad{P},{} \\spad{Q})} returns the 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} + \\spad{coef2} * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{\\spad{coef1} * \\spad{P} + \\spad{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{\\spad{semiSubResultantGcdEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = +/- 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{\\spad{semiSubResultantGcdEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = +/- 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}) >= 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 = +/- 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 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}) >= 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}) >= 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}) >= 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{\\spad{semiResultantEuclidean1}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{\\spad{coef1}.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{\\spad{semiResultantEuclidean2}(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) >= degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) NIL ((|HasCategory| |#1| (QUOTE (-392)))) -(-884) +(-883) ((|constructor| (NIL "This domain represents `pretend' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-885) +(-884) ((|constructor| (NIL "Partition is an OrderedCancellationAbelianMonoid which is used as the basis for symmetric polynomial representation of the sums of powers in SymmetricPolynomial. Thus,{} \\spad{(5 2 2 1)} will represent \\spad{s5 * s2**2 * s1}.")) (|conjugate| (($ $) "\\spad{conjugate(p)} returns the conjugate partition of a partition \\spad{p}")) (|pdct| (((|PositiveInteger|) $) "\\spad{pdct(a1**n1 a2**n2 ...)} returns \\spad{n1! * a1**n1 * n2! * a2**n2 * ...}. This function is used in the package \\spadtype{CycleIndicators}.")) (|powers| (((|List| (|Pair| (|PositiveInteger|) (|PositiveInteger|))) $) "\\spad{powers(x)} returns a list of pairs. The second component of each pair is the multiplicity with which the first component occurs in \\spad{li}.")) (|partitions| (((|Stream| $) (|NonNegativeInteger|)) "\\spad{partitions n} returns the stream of all partitions of size \\spad{n}.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\#x} returns the sum of all parts of the partition \\spad{x}.")) (|parts| (((|List| (|PositiveInteger|)) $) "\\spad{parts x} returns the list of decreasing integer sequence making up the partition \\spad{x}.")) (|partition| (($ (|List| (|PositiveInteger|))) "\\spad{partition(li)} converts a list of integers \\spad{li} to a partition"))) NIL NIL -(-886 S |Coef| |Expon| |Var|) +(-885 S |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#4|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#3| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#4|) (|List| |#3|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#4| |#3|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) NIL NIL -(-887 |Coef| |Expon| |Var|) +(-886 |Coef| |Expon| |Var|) ((|constructor| (NIL "\\spadtype{PowerSeriesCategory} is the most general power series category with exponents in an ordered abelian monoid.")) (|complete| (($ $) "\\spad{complete(f)} causes all terms of \\spad{f} to be computed. Note: this results in an infinite loop if \\spad{f} has infinitely many terms.")) (|pole?| (((|Boolean|) $) "\\spad{pole?(f)} determines if the power series \\spad{f} has a pole.")) (|variables| (((|List| |#3|) $) "\\spad{variables(f)} returns a list of the variables occuring in the power series \\spad{f}.")) (|degree| ((|#2| $) "\\spad{degree(f)} returns the exponent of the lowest order term of \\spad{f}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(f)} returns the coefficient of the lowest order term of \\spad{f}")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(f)} returns the monomial of \\spad{f} of lowest order.")) (|monomial| (($ $ (|List| |#3|) (|List| |#2|)) "\\spad{monomial(a,[x1,..,xk],[n1,..,nk])} computes \\spad{a * x1**n1 * .. * xk**nk}.") (($ $ |#3| |#2|) "\\spad{monomial(a,x,n)} computes \\spad{a*x**n}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-888) +(-887) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the x-,{} y-,{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) NIL NIL -(-889 S R E |VarSet| P) +(-888 S R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#5|) (|List| |#5|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#2|) (|:| |polnum| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{remainder(a,{}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{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#5|) (|:| |den| |#2|)) |#5| $) "\\axiom{headRemainder(a,{}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{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{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?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#4|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#4|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#4|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#4|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#4| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#4|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#4|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#4| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#5|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#5|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) NIL -((|HasCategory| |#2| (QUOTE (-496)))) -(-890 R E |VarSet| P) +((|HasCategory| |#2| (QUOTE (-495)))) +(-889 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?(ps)} returns \\spad{true} iff \\axiom{ps} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{ps}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(lp,{}cs)} returns \\axiom{lr} such that every polynomial in \\axiom{lr} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}cs)} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(lp,{}cs)} returns \\axiom{lr} such that the leading monomial of every polynomial in \\axiom{lr} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{cs} and \\axiom{(lp,{}cs)} and \\axiom{(lr,{}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,{}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{ps},{} \\axiom{r*a - c*b} lies in the ideal generated by \\axiom{ps}. Furthermore,{} if \\axiom{\\spad{R}} is a gcd-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}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{ps} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{ps}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(ps)} returns \\spad{true} iff \\axiom{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?(ps)} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{ps} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(ps)} returns \\spad{true} iff \\axiom{ps} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}ps)} returns \\axiom{us,{}vs,{}ws} such that \\axiom{us} is \\axiom{collectUnder(ps,{}\\spad{v})},{} \\axiom{vs} is \\axiom{collect(ps,{}\\spad{v})} and \\axiom{ws} is \\axiom{collectUpper(ps,{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(ps,{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{ps} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}ps)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ps}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(ps)} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{ps}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(ps)} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{ps}.")) (|mvar| ((|#3| $) "\\axiom{mvar(ps)} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(lp)} returns an element of the domain whose elements are the members of \\axiom{lp} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-3996 . T)) +((-3995 . T)) NIL -(-891 R E V P) +(-890 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(lp,{}lq)} returns the same as \\axiom{irreducibleFactors(concat(lp,{}lq))} assuming that \\axiom{irreducibleFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*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 gcd techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(lp)} returns \\axiom{lf} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lf = [\\spad{f1},{}...,{}fm]} then \\axiom{p1*p2*...\\spad{*pn=0}} means \\axiom{f1*f2*...\\spad{*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(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{lp}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in the content of every polynomial of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{lp}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(lp,{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(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(lp)} returns \\axiom{lg} where \\axiom{lg} is a list of the gcds of every pair in \\axiom{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(lp,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{lq} and \\axiom{lp} generate the same ideal in \\axiom{R^(\\spad{-1}) \\spad{P}} and \\axiom{lq} has rank not higher than the one of \\axiom{lp}. Moreover,{} \\axiom{lq} is computed by reducing \\axiom{lp} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{lp}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(lp,{}pred?,{}redOp?,{}redOp)} returns \\axiom{lq} where \\axiom{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(lp)} returns \\axiom{lq} such that \\axiom{lp} and and \\axiom{lq} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{lq}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(lp)} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{lp}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(lp)} returns \\axiom{lq} such that \\axiom{lp} and \\axiom{lq} generate the same ideal and no polynomial in \\axiom{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},{}lf)} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}lf,{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(lp,{}lf,{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(lp,{}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(lp,{}lf)} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{lp} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{lp} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{lf}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(lp)} returns \\axiom{bps,{}nbps} where \\axiom{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(lp)} returns \\axiom{lps,{}nlps} where \\axiom{lps} is a list of the linear polynomials in 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(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(lp)} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{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?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{bps} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}ps)} returns \\axiom{gps,{}bps} where \\axiom{gps} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{ps} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{bps} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(lp)} returns \\spad{true} iff the number of polynomials in \\axiom{lp} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}llp)} returns \\spad{true} iff for every \\axiom{lp} in \\axiom{llp} certainlySubVariety?(newlp,{}lp) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}lp)} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{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 gcd-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(lp)} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in lp]} if \\axiom{\\spad{R}} is gcd-domain else returns \\axiom{lp}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(lp,{}lq,{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(lp,{}lq)),{}lq)} assuming that \\axiom{remOp(lq)} returns \\axiom{lq} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(lp,{}lq)} returns the same as \\axiom{removeRedundantFactors(concat(lp,{}lq))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some polynomial \\axiom{qj} associated to \\axiom{pj}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(lp,{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}lp))} assuming that \\axiom{removeRedundantFactors(lp)} returns \\axiom{lp} up to replacing some polynomial \\axiom{pj} in \\axiom{lp} by some some polynomial \\axiom{qj} associated to \\axiom{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(lp)} returns \\axiom{lq} such that if \\axiom{lp = [\\spad{p1},{}...,{}pn]} and \\axiom{lq = [\\spad{q1},{}...,{}qm]} then the product \\axiom{p1*p2*...*pn} vanishes iff the product \\axiom{q1*q2*...*qm} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{pj},{} and no polynomial in \\axiom{lq} divides another polynomial in \\axiom{lq}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{lq} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is gcd-domain,{} the polynomials in \\axiom{lq} are pairwise without common non trivial factor."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258)))) (|HasCategory| |#1| (QUOTE (-392)))) -(-892 K) +(-891 K) ((|constructor| (NIL "PseudoLinearNormalForm provides a function for computing a block-companion form for pseudo-linear operators.")) (|companionBlocks| (((|List| (|Record| (|:| C (|Matrix| |#1|)) (|:| |g| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{companionBlocks(m, v)} returns \\spad{[[C_1, g_1],...,[C_k, g_k]]} such that each \\spad{C_i} is a companion block and \\spad{m = diagonal(C_1,...,C_k)}.")) (|changeBase| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{changeBase(M, A, sig, der)}: computes the new matrix of a pseudo-linear transform given by the matrix \\spad{M} under the change of base A")) (|normalForm| (((|Record| (|:| R (|Matrix| |#1|)) (|:| A (|Matrix| |#1|)) (|:| |Ainv| (|Matrix| |#1|))) (|Matrix| |#1|) (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{normalForm(M, sig, der)} returns \\spad{[R, A, A^{-1}]} such that the pseudo-linear operator whose matrix in the basis \\spad{y} is \\spad{M} had matrix \\spad{R} in the basis \\spad{z = A y}. \\spad{der} is a \\spad{sig}-derivation."))) NIL NIL -(-893 |VarSet| E RC P) +(-892 |VarSet| E RC P) ((|constructor| (NIL "This package computes square-free decomposition of multivariate polynomials over a coefficient ring which is an arbitrary gcd domain. The requirement on the coefficient domain guarantees that the \\spadfun{content} can be removed so that factors will be primitive as well as square-free. Over an infinite ring of finite characteristic,{}it may not be possible to guarantee that the factors are square-free.")) (|squareFree| (((|Factored| |#4|) |#4|) "\\spad{squareFree(p)} returns the square-free factorization of the polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime."))) NIL NIL -(-894 R) +(-893 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,l,r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-895 R1 R2) +(-894 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,p)} \\undocumented"))) NIL NIL -(-896 R) +(-895 R) ((|constructor| (NIL "This package \\undocumented")) (|shade| ((|#1| (|Point| |#1|)) "\\spad{shade(pt)} returns the fourth element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} shade to express a fourth dimension.")) (|hue| ((|#1| (|Point| |#1|)) "\\spad{hue(pt)} returns the third element of the two dimensional point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} hue to express a third dimension.")) (|color| ((|#1| (|Point| |#1|)) "\\spad{color(pt)} returns the fourth element of the point,{} \\spad{pt},{} although no assumptions are made with regards as to how the components of higher dimensional points are interpreted. This function is defined for the convenience of the user using specifically,{} color to express a fourth dimension.")) (|phiCoord| ((|#1| (|Point| |#1|)) "\\spad{phiCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical coordinate system.")) (|thetaCoord| ((|#1| (|Point| |#1|)) "\\spad{thetaCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|rCoord| ((|#1| (|Point| |#1|)) "\\spad{rCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a spherical or a cylindrical coordinate system.")) (|zCoord| ((|#1| (|Point| |#1|)) "\\spad{zCoord(pt)} returns the third element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian or a cylindrical coordinate system.")) (|yCoord| ((|#1| (|Point| |#1|)) "\\spad{yCoord(pt)} returns the second element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system.")) (|xCoord| ((|#1| (|Point| |#1|)) "\\spad{xCoord(pt)} returns the first element of the point,{} \\spad{pt},{} although no assumptions are made as to the coordinate system being used. This function is defined for the convenience of the user dealing with a Cartesian coordinate system."))) NIL NIL -(-897 K) +(-896 K) ((|constructor| (NIL "This is the description of any package which provides partial functions on a domain belonging to TranscendentalFunctionCategory.")) (|acschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acschIfCan(z)} returns acsch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asechIfCan(z)} returns asech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acothIfCan(z)} returns acoth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanhIfCan(z)} returns atanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acoshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acoshIfCan(z)} returns acosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinhIfCan(z)} returns asinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cschIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cschIfCan(z)} returns csch(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sechIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sechIfCan(z)} returns sech(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cothIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cothIfCan(z)} returns coth(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanhIfCan(z)} returns tanh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|coshIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{coshIfCan(z)} returns cosh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinhIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinhIfCan(z)} returns sinh(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acscIfCan(z)} returns acsc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asecIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asecIfCan(z)} returns asec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acotIfCan(z)} returns acot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|atanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{atanIfCan(z)} returns atan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|acosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{acosIfCan(z)} returns acos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|asinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{asinIfCan(z)} returns asin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cscIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cscIfCan(z)} returns csc(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|secIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{secIfCan(z)} returns sec(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cotIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cotIfCan(z)} returns cot(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|tanIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{tanIfCan(z)} returns tan(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|cosIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{cosIfCan(z)} returns cos(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|sinIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{sinIfCan(z)} returns sin(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|logIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{logIfCan(z)} returns log(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|expIfCan| (((|Union| |#1| "failed") |#1|) "\\spad{expIfCan(z)} returns exp(\\spad{z}) if possible,{} and \"failed\" otherwise.")) (|nthRootIfCan| (((|Union| |#1| "failed") |#1| (|NonNegativeInteger|)) "\\spad{nthRootIfCan(z,n)} returns the \\spad{n}th root of \\spad{z} if possible,{} and \"failed\" otherwise."))) NIL NIL -(-898 R E OV PPR) +(-897 R E OV PPR) ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-899 K R UP -3093) +(-898 K R UP -3092) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,y]/(f(x,y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If 'basis' is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if 'basisInv' is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-900 R |Var| |Expon| |Dpoly|) +(-899 R |Var| |Expon| |Dpoly|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger's algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) #1="failed")) "\\spad{setStatus(s,t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don't know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) #1#) $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} ~= 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-258))))) -(-901 |vl| |nv|) +(-900 |vl| |nv|) ((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet2} adds a function \\spadfun{radicalSimplify} which uses \\spadtype{IdealDecompositionPackage} to simplify the representation of a quasi-algebraic set. A quasi-algebraic set is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). Quasi-algebraic sets are implemented in the domain \\spadtype{QuasiAlgebraicSet},{} where two simplification routines are provided: \\spadfun{idealSimplify} and \\spadfun{simplify}. The function \\spadfun{radicalSimplify} is added for comparison study only. Because the domain \\spadtype{IdealDecompositionPackage} provides facilities for computing with radical ideals,{} it is necessary to restrict the ground ring to the domain \\spadtype{Fraction Integer},{} and the polynomial ring to be of type \\spadtype{DistributedMultivariatePolynomial}. The routine \\spadfun{radicalSimplify} uses these to compute groebner basis of radical ideals and is inefficient and restricted when compared to the two in \\spadtype{QuasiAlgebraicSet}.")) (|radicalSimplify| (((|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|)))) (|QuasiAlgebraicSet| (|Fraction| (|Integer|)) (|OrderedVariableList| |#1|) (|DirectProduct| |#2| (|NonNegativeInteger|)) (|DistributedMultivariatePolynomial| |#1| (|Fraction| (|Integer|))))) "\\spad{radicalSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using using groebner basis of radical ideals"))) NIL NIL -(-902 R E V P TS) +(-901 R E V P TS) ((|constructor| (NIL "A package for removing redundant quasi-components and redundant branches when decomposing a variety by means of quasi-components of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact that the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu?}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-903) +(-902) ((|constructor| (NIL "This domain implements simple database queries")) (|value| (((|String|) $) "\\spad{value(q)} returns the value (\\spadignore{i.e.} right hand side) of \\axiom{\\spad{q}}.")) (|variable| (((|Symbol|) $) "\\spad{variable(q)} returns the variable (\\spadignore{i.e.} left hand side) of \\axiom{\\spad{q}}.")) (|equation| (($ (|Symbol|) (|String|)) "\\spad{equation(s,\"a\")} creates a new equation."))) NIL NIL -(-904 A S) +(-903 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 (-822))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-951 (-1091)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-934))) (|HasCategory| |#2| (QUOTE (-741))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-1067)))) -(-905 S) +((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-950 (-1090)))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-933))) (|HasCategory| |#2| (QUOTE (-740))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-1066)))) +(-904 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}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-906 A B R S) +(-905 A B R S) ((|constructor| (NIL "This package extends a function between integral domains to a mapping between their quotient fields.")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(func,frac)} applies the function \\spad{func} to the numerator and denominator of \\spad{frac}."))) NIL NIL -(-907 |n| K) +(-906 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) NIL NIL -(-908) +(-907) ((|constructor| (NIL "This domain represents the syntax of a quasiquote \\indented{2}{expression.}")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the syntax for the expression being quoted."))) NIL NIL -(-909 S) +(-908 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|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\#q}.")) (|rotate!| (($ $) "\\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."))) -((-3996 . T) (-3997 . T)) +((-3995 . T) (-3996 . T)) NIL -(-910 R) +(-909 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.}"))) -((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (|%list| (QUOTE -456) (QUOTE (-1091)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-974))) (|HasCategory| |#1| (QUOTE (-484)))) -(-911 S R) +((-3988 |has| |#1| (-246)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-246))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (|%list| (QUOTE -455) (QUOTE (-1090)) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))) (|HasCategory| |#1| (|%list| (QUOTE -241) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (QUOTE (-483)))) +(-910 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 (-484))) (|HasCategory| |#2| (QUOTE (-974))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-246)))) -(-912 R) +((|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-246)))) +(-911 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| $) "\\spad{imagI(q)} extracts the imaginary \\spad{i} part of quaternion \\spad{q}.")) (|conjugate| (($ $) "\\spad{conjugate(q)} negates the imaginary parts of quaternion \\spad{q}."))) -((-3989 |has| |#1| (-246)) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3988 |has| |#1| (-246)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-913 QR R QS S) +(-912 QR R QS S) ((|constructor| (NIL "\\spadtype{QuaternionCategoryFunctions2} implements functions between two quaternion domains. The function \\spadfun{map} is used by the system interpreter to coerce between quaternion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,u)} maps \\spad{f} onto the component parts of the quaternion \\spad{u}."))) NIL NIL -(-914 S) +(-913 S) ((|constructor| (NIL "Linked List implementation of a Queue")) (|queue| (($ (|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}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-915 S) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-914 S) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-916) +(-915) ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-917 -3093 UP UPUP |radicnd| |n|) +(-916 -3092 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-3989 |has| (-350 |#2|) (-312)) (-3994 |has| (-350 |#2|) (-312)) (-3988 |has| (-350 |#2|) (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091)))))) (|HasCategory| (-350 |#2|) (QUOTE (-581 (-485)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 |#2|) (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-812 (-1091))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-810 (-1091)))))) -(-918 |bb|) +((-3988 |has| (-350 |#2|) (-312)) (-3993 |has| (-350 |#2|) (-312)) (-3987 |has| (-350 |#2|) (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-350 |#2|) (QUOTE (-118))) (|HasCategory| (-350 |#2|) (QUOTE (-120))) (|HasCategory| (-350 |#2|) (QUOTE (-299))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-320))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (|HasCategory| (-350 |#2|) (QUOTE (-299)))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-299))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090)))))) (|HasCategory| (-350 |#2|) (QUOTE (-580 (-484)))) (OR (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 |#2|) (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-189))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-811 (-1090))))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-190))) (|HasCategory| (-350 |#2|) (QUOTE (-312)))) (-12 (|HasCategory| (-350 |#2|) (QUOTE (-312))) (|HasCategory| (-350 |#2|) (QUOTE (-809 (-1090)))))) +(-917 |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."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-485) (QUOTE (-822))) (|HasCategory| (-485) (QUOTE (-951 (-1091)))) (|HasCategory| (-485) (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-120))) (|HasCategory| (-485) (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-934))) (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757))) (OR (|HasCategory| (-485) (QUOTE (-741))) (|HasCategory| (-485) (QUOTE (-757)))) (|HasCategory| (-485) (QUOTE (-951 (-485)))) (|HasCategory| (-485) (QUOTE (-1067))) (|HasCategory| (-485) (QUOTE (-797 (-330)))) (|HasCategory| (-485) (QUOTE (-797 (-485)))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-485) (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-485) (QUOTE (-189))) (|HasCategory| (-485) (QUOTE (-812 (-1091)))) (|HasCategory| (-485) (QUOTE (-190))) (|HasCategory| (-485) (QUOTE (-810 (-1091)))) (|HasCategory| (-485) (QUOTE (-456 (-1091) (-485)))) (|HasCategory| (-485) (QUOTE (-260 (-485)))) (|HasCategory| (-485) (QUOTE (-241 (-485) (-485)))) (|HasCategory| (-485) (QUOTE (-258))) (|HasCategory| (-485) (QUOTE (-484))) (|HasCategory| (-485) (QUOTE (-581 (-485)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-485) (QUOTE (-822)))) (|HasCategory| (-485) (QUOTE (-118))))) -(-919) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-484) (QUOTE (-821))) (|HasCategory| (-484) (QUOTE (-950 (-1090)))) (|HasCategory| (-484) (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-120))) (|HasCategory| (-484) (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-933))) (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756))) (OR (|HasCategory| (-484) (QUOTE (-740))) (|HasCategory| (-484) (QUOTE (-756)))) (|HasCategory| (-484) (QUOTE (-950 (-484)))) (|HasCategory| (-484) (QUOTE (-1066))) (|HasCategory| (-484) (QUOTE (-796 (-330)))) (|HasCategory| (-484) (QUOTE (-796 (-484)))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-484) (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-484) (QUOTE (-189))) (|HasCategory| (-484) (QUOTE (-811 (-1090)))) (|HasCategory| (-484) (QUOTE (-190))) (|HasCategory| (-484) (QUOTE (-809 (-1090)))) (|HasCategory| (-484) (QUOTE (-455 (-1090) (-484)))) (|HasCategory| (-484) (QUOTE (-260 (-484)))) (|HasCategory| (-484) (QUOTE (-241 (-484) (-484)))) (|HasCategory| (-484) (QUOTE (-258))) (|HasCategory| (-484) (QUOTE (-483))) (|HasCategory| (-484) (QUOTE (-580 (-484)))) (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (OR (-12 (|HasCategory| $ (QUOTE (-118))) (|HasCategory| (-484) (QUOTE (-821)))) (|HasCategory| (-484) (QUOTE (-118))))) +(-918) ((|constructor| (NIL "This package provides tools for creating radix expansions.")) (|radix| (((|Any|) (|Fraction| (|Integer|)) (|Integer|)) "\\spad{radix(x,b)} converts \\spad{x} to a radix expansion in base \\spad{b}."))) NIL NIL -(-920) +(-919) ((|constructor| (NIL "Random number generators \\indented{2}{All random numbers used in the system should originate from} \\indented{2}{the same generator.\\space{2}This package is intended to be the source.}")) (|seed| (((|Integer|)) "\\spad{seed()} returns the current seed value.")) (|reseed| (((|Void|) (|Integer|)) "\\spad{reseed(n)} restarts the random number generator at \\spad{n}.")) (|size| (((|Integer|)) "\\spad{size()} is the base of the random number generator")) (|randnum| (((|Integer|) (|Integer|)) "\\spad{randnum(n)} is a random number between 0 and \\spad{n}.") (((|Integer|)) "\\spad{randnum()} is a random number between 0 and size()."))) NIL NIL -(-921 RP) +(-920 RP) ((|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} factors an extended squareFree polynomial \\spad{p} over the rational numbers.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} factors an extended polynomial \\spad{p} over the rational numbers."))) NIL NIL -(-922 S) +(-921 S) ((|constructor| (NIL "rational number testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") |#1|) "\\spad{rationalIfCan(x)} returns \\spad{x} as a rational number,{} \"failed\" if \\spad{x} is not a rational number.")) (|rational?| (((|Boolean|) |#1|) "\\spad{rational?(x)} returns \\spad{true} if \\spad{x} is a rational number,{} \\spad{false} otherwise.")) (|rational| (((|Fraction| (|Integer|)) |#1|) "\\spad{rational(x)} returns \\spad{x} as a rational number; error if \\spad{x} is not a rational number."))) NIL NIL -(-923 A S) +(-922 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,\"value\",x)} (also written \\axiom{a . value := \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997)) (|HasCategory| |#2| (QUOTE (-1014)))) -(-924 S) +((|HasAttribute| |#1| (QUOTE -3996)) (|HasCategory| |#2| (QUOTE (-1013)))) +(-923 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{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL NIL -(-925 S) +(-924 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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) NIL NIL -(-926) +(-925) ((|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} ** (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} ** (1/2)}") (($ $ (|PositiveInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} ** (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}}"))) -((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) +((-3988 . T) (-3993 . T) (-3987 . T) (-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3992 . T)) NIL -(-927 R -3093) +(-926 R -3092) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 1 February 1988 Date Last Updated: 2 November 1995 Keywords: elementary,{} function,{} integration.")) (|rischDE| (((|Record| (|:| |ans| |#2|) (|:| |right| |#2|) (|:| |sol?| (|Boolean|))) (|Integer|) |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDE(n, f, g, x, lim, ext)} returns \\spad{[y, h, b]} such that \\spad{dy/dx + n df/dx y = h} and \\spad{b := h = g}. The equation \\spad{dy/dx + n df/dx y = g} has no solution if \\spad{h \\~~= g} (\\spad{y} is a partial solution in that case). Notes: \\spad{lim} is a limited integration function,{} and ext is an extended integration function."))) NIL NIL -(-928 R -3093) +(-927 R -3092) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} elementary case.} Author: Manuel Bronstein Date Created: 12 August 1992 Date Last Updated: 17 August 1992 Keywords: elementary,{} function,{} integration.")) (|rischDEsys| (((|Union| (|List| |#2|) "failed") (|Integer|) |#2| |#2| |#2| (|Symbol|) (|Mapping| (|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|List| |#2|)) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| |#2|)) "\\spad{rischDEsys(n, f, g_1, g_2, x,lim,ext)} returns \\spad{y_1.y_2} such that \\spad{(dy1/dx,dy2/dx) + ((0, - n df/dx),(n df/dx,0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise. \\spad{lim} is a limited integration function,{} \\spad{ext} is an extended integration function."))) NIL NIL -(-929 -3093 UP) +(-928 -3092 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation,{} transcendental case.} Author: Manuel Bronstein Date Created: Jan 1988 Date Last Updated: 2 November 1995")) (|polyRDE| (((|Union| (|:| |ans| (|Record| (|:| |ans| |#2|) (|:| |nosol| (|Boolean|)))) (|:| |eq| (|Record| (|:| |b| |#2|) (|:| |c| |#2|) (|:| |m| (|Integer|)) (|:| |alpha| |#2|) (|:| |beta| |#2|)))) |#2| |#2| |#2| (|Integer|) (|Mapping| |#2| |#2|)) "\\spad{polyRDE(a, B, C, n, D)} returns either: 1. \\spad{[Q, b]} such that \\spad{degree(Q) <= n} and \\indented{3}{\\spad{a Q'+ B Q = C} if \\spad{b = true},{} \\spad{Q} is a partial solution} \\indented{3}{otherwise.} 2. \\spad{[B1, C1, m, \\alpha, \\beta]} such that any polynomial solution \\indented{3}{of degree at most \\spad{n} of \\spad{A Q' + BQ = C} must be of the form} \\indented{3}{\\spad{Q = \\alpha H + \\beta} where \\spad{degree(H) <= m} and} \\indented{3}{\\spad{H} satisfies \\spad{H' + B1 H = C1}.} \\spad{D} is the derivation to use.")) (|baseRDE| (((|Record| (|:| |ans| (|Fraction| |#2|)) (|:| |nosol| (|Boolean|))) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDE(f, g)} returns a \\spad{[y, b]} such that \\spad{y' + fy = g} if \\spad{b = true},{} \\spad{y} is a partial solution otherwise (no solution in that case). \\spad{D} is the derivation to use.")) (|monomRDE| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |c| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDE(f,g,D)} returns \\spad{[A, B, C, T]} such that \\spad{y' + f y = g} has a solution if and only if \\spad{y = Q / T},{} where \\spad{Q} satisfies \\spad{A Q' + B Q = C} and has no normal pole. A and \\spad{T} are polynomials and \\spad{B} and \\spad{C} have no normal poles. \\spad{D} is the derivation to use."))) NIL NIL -(-930 -3093 UP) +(-929 -3092 UP) ((|constructor| (NIL "\\indented{1}{Risch differential equation system,{} transcendental case.} Author: Manuel Bronstein Date Created: 17 August 1992 Date Last Updated: 3 February 1994")) (|baseRDEsys| (((|Union| (|List| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{baseRDEsys(f, g1, g2)} returns fractions \\spad{y_1.y_2} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} if \\spad{y_1,y_2} exist,{} \"failed\" otherwise.")) (|monomRDEsys| (((|Union| (|Record| (|:| |a| |#2|) (|:| |b| (|Fraction| |#2|)) (|:| |h| |#2|) (|:| |c1| (|Fraction| |#2|)) (|:| |c2| (|Fraction| |#2|)) (|:| |t| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomRDEsys(f,g1,g2,D)} returns \\spad{[A, B, H, C1, C2, T]} such that \\spad{(y1', y2') + ((0, -f), (f, 0)) (y1,y2) = (g1,g2)} has a solution if and only if \\spad{y1 = Q1 / T, y2 = Q2 / T},{} where \\spad{B,C1,C2,Q1,Q2} have no normal poles and satisfy A \\spad{(Q1', Q2') + ((H, -B), (B, H)) (Q1,Q2) = (C1,C2)} \\spad{D} is the derivation to use."))) NIL NIL -(-931 S) +(-930 S) ((|constructor| (NIL "This package exports random distributions")) (|rdHack1| (((|Mapping| |#1|) (|Vector| |#1|) (|Vector| (|Integer|)) (|Integer|)) "\\spad{rdHack1(v,u,n)} \\undocumented")) (|weighted| (((|Mapping| |#1|) (|List| (|Record| (|:| |value| |#1|) (|:| |weight| (|Integer|))))) "\\spad{weighted(l)} \\undocumented")) (|uniform| (((|Mapping| |#1|) (|Set| |#1|)) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-932 F1 UP UPUP R F2) +(-931 F1 UP UPUP R F2) ((|constructor| (NIL "\\indented{1}{Finds the order of a divisor over a finite field} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 8 November 1994")) (|order| (((|NonNegativeInteger|) (|FiniteDivisor| |#1| |#2| |#3| |#4|) |#3| (|Mapping| |#5| |#1|)) "\\spad{order(f,u,g)} \\undocumented"))) NIL NIL -(-933) +(-932) ((|constructor| (NIL "This domain represents list reduction syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} return the list of expressions being redcued.")) (|operator| (((|SpadAst|) $) "\\spad{operator(e)} returns the magma operation being applied."))) NIL NIL -(-934) +(-933) ((|constructor| (NIL "The category of real numeric domains,{} \\spadignore{i.e.} convertible to floats."))) NIL NIL -(-935 |Pol|) +(-934 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the integers to arbitrary user-specified precision. The results are returned as a list of isolating intervals which are expressed as records with \"left\" and \"right\" rational number components.")) (|midpoints| (((|List| (|Fraction| (|Integer|))) (|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))))) "\\spad{midpoints(isolist)} returns the list of midpoints for the list of intervals \\spad{isolist}.")) (|midpoint| (((|Fraction| (|Integer|)) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{midpoint(int)} returns the midpoint of the interval \\spad{int}.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} containing exactly one real root of \\spad{pol}; the operation returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-936 |Pol|) +(-935 |Pol|) ((|constructor| (NIL "\\indented{2}{This package provides functions for finding the real zeros} of univariate polynomials over the rational numbers to arbitrary user-specified precision. The results are returned as a list of isolating intervals,{} expressed as records with \"left\" and \"right\" rational number components.")) (|refine| (((|Union| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) "failed") |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{refine(pol, int, range)} takes a univariate polynomial \\spad{pol} and and isolating interval \\spad{int} which must contain exactly one real root of \\spad{pol},{} and returns an isolating interval which is contained within range,{} or \"failed\" if no such isolating interval exists.") (((|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{refine(pol, int, eps)} refines the interval \\spad{int} containing exactly one root of the univariate polynomial \\spad{pol} to size less than the rational number eps.")) (|realZeros| (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|)))) (|Fraction| (|Integer|))) "\\spad{realZeros(pol, int, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol} which lie in the interval expressed by the record \\spad{int}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Fraction| (|Integer|))) "\\spad{realZeros(pol, eps)} returns a list of intervals of length less than the rational number eps for all the real roots of the polynomial \\spad{pol}.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) "\\spad{realZeros(pol, range)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol} which lie in the interval expressed by the record range.") (((|List| (|Record| (|:| |left| (|Fraction| (|Integer|))) (|:| |right| (|Fraction| (|Integer|))))) |#1|) "\\spad{realZeros(pol)} returns a list of isolating intervals for all the real zeros of the univariate polynomial \\spad{pol}."))) NIL NIL -(-937) +(-936) ((|constructor| (NIL "\\indented{1}{This package provides numerical solutions of systems of polynomial} equations for use in ACPLOT.")) (|realSolve| (((|List| (|List| (|Float|))) (|List| (|Polynomial| (|Integer|))) (|List| (|Symbol|)) (|Float|)) "\\spad{realSolve(lp,lv,eps)} = compute the list of the real solutions of the list \\spad{lp} of polynomials with integer coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}.")) (|solve| (((|List| (|Float|)) (|Polynomial| (|Integer|)) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate integer polynomial \\spad{p} with precision \\spad{eps}.") (((|List| (|Float|)) (|Polynomial| (|Fraction| (|Integer|))) (|Float|)) "\\spad{solve(p,eps)} finds the real zeroes of a univariate rational polynomial \\spad{p} with precision \\spad{eps}."))) NIL NIL -(-938 |TheField|) +(-937 |TheField|) ((|constructor| (NIL "This domain implements the real closure of an ordered field.")) (|relativeApprox| (((|Fraction| (|Integer|)) $ $) "\\axiom{relativeApprox(\\spad{n},{}\\spad{p})} gives a relative approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|mainCharacterization| (((|Union| (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) "failed") $) "\\axiom{mainCharacterization(\\spad{x})} is the main algebraic quantity of \\axiom{\\spad{x}} (\\axiom{SEG})")) (|algebraicOf| (($ (|RightOpenIntervalRootCharacterization| $ (|SparseUnivariatePolynomial| $)) (|OutputForm|)) "\\axiom{algebraicOf(char)} is the external number"))) -((-3989 . T) (-3994 . T) (-3988 . T) (-3991 . T) (-3990 . T) ((-3998 "*") . T) (-3993 . T)) -((OR (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-350 (-485)) (QUOTE (-951 (-485))))) -(-939 -3093 L) +((-3988 . T) (-3993 . T) (-3987 . T) (-3990 . T) (-3989 . T) ((-3997 "*") . T) (-3992 . T)) +((OR (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-350 (-484)) (QUOTE (-950 (-484))))) +(-938 -3092 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op, [f1,...,fk])} returns \\spad{[op1,[g1,...,gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{fi} must satisfy \\spad{op fi = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op, s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL -(-940 S) +(-939 S) ((|constructor| (NIL "\\indented{1}{\\spadtype{Reference} is for making a changeable instance} of something.")) (= (((|Boolean|) $ $) "\\spad{a=b} tests if \\spad{a} and \\spad{b} are equal.")) (|setref| ((|#1| $ |#1|) "\\spad{setref(r,s)} reset the reference \\spad{r} to refer to \\spad{s}")) (|deref| ((|#1| $) "\\spad{deref(r)} returns the object referenced by \\spad{r}")) (|ref| (($ |#1|) "\\spad{ref(s)} creates a reference to the object \\spad{s}."))) NIL NIL -(-941 R E V P) +(-940 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(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(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(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) -(-942) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-941) ((|constructor| (NIL "Package for the computation of eigenvalues and eigenvectors. This package works for matrices with coefficients which are rational functions over the integers. (see \\spadtype{Fraction Polynomial Integer}). The eigenvalues and eigenvectors are expressed in terms of radicals.")) (|orthonormalBasis| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{orthonormalBasis(m)} returns the orthogonal matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal. Error: if \\spad{m} is not a symmetric matrix.")) (|gramschmidt| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|List| (|Matrix| (|Expression| (|Integer|))))) "\\spad{gramschmidt(lv)} converts the list of column vectors \\spad{lv} into a set of orthogonal column vectors of euclidean length 1 using the Gram-Schmidt algorithm.")) (|normalise| (((|Matrix| (|Expression| (|Integer|))) (|Matrix| (|Expression| (|Integer|)))) "\\spad{normalise(v)} returns the column vector \\spad{v} divided by its euclidean norm; when possible,{} the vector \\spad{v} is expressed in terms of radicals.")) (|eigenMatrix| (((|Union| (|Matrix| (|Expression| (|Integer|))) "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{eigenMatrix(m)} returns the matrix \\spad{b} such that \\spad{b*m*(inverse b)} is diagonal,{} or \"failed\" if no such \\spad{b} exists.")) (|radicalEigenvalues| (((|List| (|Expression| (|Integer|))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvalues(m)} computes the eigenvalues of the matrix \\spad{m}; when possible,{} the eigenvalues are expressed in terms of radicals.")) (|radicalEigenvector| (((|List| (|Matrix| (|Expression| (|Integer|)))) (|Expression| (|Integer|)) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvector(c,m)} computes the eigenvector(\\spad{s}) of the matrix \\spad{m} corresponding to the eigenvalue \\spad{c}; when possible,{} values are expressed in terms of radicals.")) (|radicalEigenvectors| (((|List| (|Record| (|:| |radval| (|Expression| (|Integer|))) (|:| |radmult| (|Integer|)) (|:| |radvect| (|List| (|Matrix| (|Expression| (|Integer|))))))) (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{radicalEigenvectors(m)} computes the eigenvalues and the corresponding eigenvectors of the matrix \\spad{m}; when possible,{} values are expressed in terms of radicals."))) NIL NIL -(-943 R) +(-942 R) ((|constructor| (NIL "\\spad{RepresentationPackage1} provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,4,3,2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,2,...,n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,...,pik],n)} returns the list of matrices {\\em [(deltai,pi1(i)),...,(deltai,pik(i))]} (Kronecker delta) for the permutations {\\em pi1,...,pik} of {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) if the permutation {\\em pi} is in list notation and permutes {\\em {1,2,...,n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(pi,n)} returns the matrix {\\em (deltai,pi(i))} (Kronecker delta) for a permutation {\\em pi} of {\\em {1,2,...,n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...ak])} calculates the list of Kronecker products of each matrix {\\em ai} with itself for {1 <= \\spad{i} <= \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,...,ak],[b1,...,bk])} calculates the list of Kronecker products of the matrices {\\em ai} and {\\em bi} for {1 <= \\spad{i} <= \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,0,...,0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,1,...,1,0,0,...,0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-3998 "*")))) -(-944 R) +((|HasAttribute| |#1| (QUOTE (-3997 "*")))) +(-943 R) ((|constructor| (NIL "\\spad{RepresentationPackage2} provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,...,0,1,*,...,*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG, numberOfTries)} calls {\\em meatAxe(aG,true,numberOfTries,7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG, randomElements)} calls {\\em meatAxe(aG,false,6,7)},{} only using Parker's fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,true,25,7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,false,25,7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker's fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,randomElements,numberOfTries, maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton's irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker's fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG, vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG, numberOfTries)} uses Norton's irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,numberOfTries)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,aG1)} calls {\\em areEquivalent?(aG0,aG1,true,25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,aG1,randomelements,numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker's \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-258)))) -(-945 S) +(-944 S) ((|constructor| (NIL "Implements multiplication by repeated addition")) (|double| ((|#1| (|PositiveInteger|) |#1|) "\\spad{double(i, r)} multiplies \\spad{r} by \\spad{i} using repeated doubling.")) (+ (($ $ $) "\\spad{x+y} returns the sum of \\spad{x} and \\spad{y}"))) NIL NIL -(-946 S) +(-945 S) ((|constructor| (NIL "Implements exponentiation by repeated squaring")) (|expt| ((|#1| |#1| (|PositiveInteger|)) "\\spad{expt(r, i)} computes r**i by repeated squaring")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}"))) NIL NIL -(-947 S) +(-946 S) ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-948 -3093 |Expon| |VarSet| |FPol| |LFPol|) +(-947 -3092 |Expon| |VarSet| |FPol| |LFPol|) ((|constructor| (NIL "ResidueRing is the quotient of a polynomial ring by an ideal. The ideal is given as a list of generators. The elements of the domain are equivalence classes expressed in terms of reduced elements")) (|lift| ((|#4| $) "\\spad{lift(x)} return the canonical representative of the equivalence class \\spad{x}")) (|coerce| (($ |#4|) "\\spad{coerce(f)} produces the equivalence class of \\spad{f} in the residue ring")) (|reduce| (($ |#4|) "\\spad{reduce(f)} produces the equivalence class of \\spad{f} in the residue ring"))) -(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-949) +(-948) ((|constructor| (NIL "This domain represents `return' expressions.")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression returned by `e'."))) NIL NIL -(-950 A S) +(-949 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-951 S) +(-950 S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#1| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}."))) NIL NIL -(-952 Q R) +(-951 Q R) ((|constructor| (NIL "RetractSolvePackage is an interface to \\spadtype{SystemSolvePackage} that attempts to retract the coefficients of the equations before solving.")) (|solveRetract| (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#2|))))) (|List| (|Polynomial| |#2|)) (|List| (|Symbol|))) "\\spad{solveRetract(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}. The function tries to retract all the coefficients of the equations to \\spad{Q} before solving if possible."))) NIL NIL -(-953 R) +(-952 R) ((|constructor| (NIL "Utilities that provide the same top-level manipulations on fractions than on polynomials.")) (|coerce| (((|Fraction| (|Polynomial| |#1|)) |#1|) "\\spad{coerce(r)} returns \\spad{r} viewed as a rational function over \\spad{R}.")) (|eval| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{eval(f, [v1 = g1,...,vn = gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced. Error: if any \\spad{vi} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, v = g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}. Error: if \\spad{v} is not a symbol.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{eval(f, [v1,...,vn], [g1,...,gn])} returns \\spad{f} with each \\spad{vi} replaced by \\spad{gi} in parallel,{} \\spadignore{i.e.} \\spad{vi}'s appearing inside the \\spad{gi}'s are not replaced.") (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{eval(f, v, g)} returns \\spad{f} with \\spad{v} replaced by \\spad{g}.")) (|multivariate| (((|Fraction| (|Polynomial| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Symbol|)) "\\spad{multivariate(f, v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{univariate(f, v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| (|Symbol|) "failed") (|Fraction| (|Polynomial| |#1|))) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| (|Symbol|)) (|Fraction| (|Polynomial| |#1|))) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL -(-954) +(-953) ((|t| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{t(n)} \\undocumented")) (F (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{F(n,m)} \\undocumented")) (|Beta| (((|Mapping| (|Float|)) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{Beta(n,m)} \\undocumented")) (|chiSquare| (((|Mapping| (|Float|)) (|NonNegativeInteger|)) "\\spad{chiSquare(n)} \\undocumented")) (|exponential| (((|Mapping| (|Float|)) (|Float|)) "\\spad{exponential(f)} \\undocumented")) (|normal| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{normal(f,g)} \\undocumented")) (|uniform| (((|Mapping| (|Float|)) (|Float|) (|Float|)) "\\spad{uniform(f,g)} \\undocumented")) (|chiSquare1| (((|Float|) (|NonNegativeInteger|)) "\\spad{chiSquare1(n)} \\undocumented")) (|exponential1| (((|Float|)) "\\spad{exponential1()} \\undocumented")) (|normal01| (((|Float|)) "\\spad{normal01()} \\undocumented")) (|uniform01| (((|Float|)) "\\spad{uniform01()} \\undocumented"))) NIL NIL -(-955 UP) +(-954 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients which are rational functions with integer coefficients.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-956 R) +(-955 R) ((|constructor| (NIL "\\spadtype{RationalFunctionFactorizer} contains the factor function (called factorFraction) which factors fractions of polynomials by factoring the numerator and denominator. Since any non zero fraction is a unit the usual factor operation will just return the original fraction.")) (|factorFraction| (((|Fraction| (|Factored| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{factorFraction(r)} factors the numerator and the denominator of the polynomial fraction \\spad{r}."))) NIL NIL -(-957 T$) +(-956 T$) ((|constructor| (NIL "This category defines the common interface for RGB color models.")) (|componentUpperBound| ((|#1|) "componentUpperBound is an upper bound for all component values.")) (|blue| ((|#1| $) "\\spad{blue(c)} returns the `blue' component of `c'.")) (|green| ((|#1| $) "\\spad{green(c)} returns the `green' component of `c'.")) (|red| ((|#1| $) "\\spad{red(c)} returns the `red' component of `c'."))) NIL NIL -(-958 T$) +(-957 T$) ((|constructor| (NIL "This category defines the common interface for RGB color spaces.")) (|whitePoint| (($) "whitePoint is the contant indicating the white point of this color space."))) NIL NIL -(-959 R |ls|) +(-958 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a 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}."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| (-704 |#1| (-774 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -704) (|devaluate| |#1|) (|%list| (QUOTE -774) (|devaluate| |#2|)))))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-554 (-474)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-774 |#2|) (QUOTE (-320))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| (-704 |#1| (-774 |#2|)) (QUOTE (-72)))) -(-960) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (|HasCategory| (-703 |#1| (-773 |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -703) (|devaluate| |#1|) (|%list| (QUOTE -773) (|devaluate| |#2|)))))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-553 (-473)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-773 |#2|) (QUOTE (-320))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| (-703 |#1| (-773 |#2|)) (QUOTE (-72)))) +(-959) ((|constructor| (NIL "This package exports integer distributions")) (|ridHack1| (((|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{ridHack1(i,j,k,l)} \\undocumented")) (|geometric| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{geometric(f)} \\undocumented")) (|poisson| (((|Mapping| (|Integer|)) |RationalNumber|) "\\spad{poisson(f)} \\undocumented")) (|binomial| (((|Mapping| (|Integer|)) (|Integer|) |RationalNumber|) "\\spad{binomial(n,f)} \\undocumented")) (|uniform| (((|Mapping| (|Integer|)) (|Segment| (|Integer|))) "\\spad{uniform(s)} \\undocumented"))) NIL NIL -(-961 S) +(-960 S) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) NIL NIL -(-962) +(-961) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-3993 . T)) +((-3992 . T)) NIL -(-963 |xx| -3093) +(-962 |xx| -3092) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL -(-964 S) +(-963 S) ((|constructor| (NIL "\\indented{2}{A set is an \\spad{S}-right linear set if it is stable by right-dilation} \\indented{2}{by elements in the semigroup \\spad{S}.} See Also: LeftLinearSet.")) (* (($ $ |#1|) "\\spad{x*s} is the right-dilation of \\spad{x} by \\spad{s}."))) NIL NIL -(-965 S |m| |n| R |Row| |Col|) +(-964 S |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#6|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#4|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#4|) "\\spad{exquo(m,r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#4| |#4| |#4|) $ $) "\\spad{map(f,a,b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,j) = f(a(i,j),b(i,j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#4| |#4|) $) "\\spad{map(f,a)} returns \\spad{b},{} where \\spad{b(i,j) = a(i,j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#6| $ (|Integer|)) "\\spad{column(m,j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#5| $ (|Integer|)) "\\spad{row(m,i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#4| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#4| $ (|Integer|) (|Integer|) |#4|) "\\spad{elt(m,i,j,r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#4| $ (|Integer|) (|Integer|)) "\\spad{elt(m,i,j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#4|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,j] = -m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,j] = m[j,i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#4|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix."))) NIL -((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-496))) (|HasCategory| |#4| (QUOTE (-146)))) -(-966 |m| |n| R |Row| |Col|) +((|HasCategory| |#4| (QUOTE (-258))) (|HasCategory| |#4| (QUOTE (-312))) (|HasCategory| |#4| (QUOTE (-495))) (|HasCategory| |#4| (QUOTE (-146)))) +(-965 |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."))) -((-3996 . T) (-3991 . T) (-3990 . T)) +((-3995 . T) (-3990 . T) (-3989 . T)) NIL -(-967 |m| |n| R) +(-966 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-3996 . T) (-3991 . T) (-3990 . T)) -((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-496))) (-12 (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1014))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-553 (-773))))) -(-968 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) +((-3995 . T) (-3990 . T) (-3989 . T)) +((|HasCategory| |#3| (QUOTE (-146))) (OR (-12 (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|))))) (|HasCategory| |#3| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#3| (QUOTE (-146))) (|HasCategory| |#3| (QUOTE (-312)))) (|HasCategory| |#3| (QUOTE (-312))) (|HasCategory| |#3| (QUOTE (-258))) (|HasCategory| |#3| (QUOTE (-495))) (-12 (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (|%list| (QUOTE -260) (|devaluate| |#3|)))) (|HasCategory| |#3| (QUOTE (-1013))) (|HasCategory| |#3| (QUOTE (-72))) (|HasCategory| |#3| (QUOTE (-552 (-772))))) +(-967 |m| |n| R1 |Row1| |Col1| M1 R2 |Row2| |Col2| M2) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategoryFunctions2} provides functions between two matrix domains. The functions provided are \\spadfun{map} and \\spadfun{reduce}.")) (|reduce| ((|#7| (|Mapping| |#7| |#3| |#7|) |#6| |#7|) "\\spad{reduce(f,m,r)} returns a matrix \\spad{n} where \\spad{n[i,j] = f(m[i,j],r)} for all indices spad{\\spad{i}} and \\spad{j}.")) (|map| ((|#10| (|Mapping| |#7| |#3|) |#6|) "\\spad{map(f,m)} applies the function \\spad{f} to the elements of the matrix \\spad{m}."))) NIL NIL -(-969 R) +(-968 R) ((|constructor| (NIL "The category of right modules over an rng (ring not necessarily with unit). This is an abelian group which supports right multiplation by elements of the rng. \\blankline"))) NIL NIL -(-970 S) +(-969 S) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) NIL NIL -(-971) +(-970) ((|constructor| (NIL "The category of associative rings,{} not necessarily commutative,{} and not necessarily with a 1. This is a combination of an abelian group and a semigroup,{} with multiplication distributing over addition. \\blankline")) (|annihilate?| (((|Boolean|) $ $) "\\spad{annihilate?(x,y)} holds when the product of \\spad{x} and \\spad{y} is \\spad{0}."))) NIL NIL -(-972 S T$) +(-971 S T$) ((|constructor| (NIL "This domain represents the notion of binding a variable to range over a specific segment (either bounded,{} or half bounded).")) (|segment| ((|#1| $) "\\spad{segment(x)} returns the segment from the right hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{segment(x)} returns \\spad{s}.")) (|variable| (((|Symbol|) $) "\\spad{variable(x)} returns the variable from the left hand side of the \\spadtype{RangeBinding}. For example,{} if \\spad{x} is \\spad{v=s},{} then \\spad{variable(x)} returns \\spad{v}.")) (|equation| (($ (|Symbol|) |#1|) "\\spad{equation(v,s)} creates a segment binding value with variable \\spad{v} and segment \\spad{s}. Note that the interpreter parses \\spad{v=s} to this form."))) NIL -((|HasCategory| |#1| (QUOTE (-1014)))) -(-973 S) +((|HasCategory| |#1| (QUOTE (-1013)))) +(-972 S) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) NIL NIL -(-974) +(-973) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-975 |TheField| |ThePolDom|) +(-974 |TheField| |ThePolDom|) ((|constructor| (NIL "\\axiomType{RightOpenIntervalRootCharacterization} provides work with interval root coding.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{relativeApprox(exp,{}\\spad{c},{}\\spad{p}) = a} is relatively close to exp as a polynomial in \\spad{c} ip to precision \\spad{p}")) (|mightHaveRoots| (((|Boolean|) |#2| $) "\\axiom{mightHaveRoots(\\spad{p},{}\\spad{r})} is \\spad{false} if \\axiom{\\spad{p}.\\spad{r}} is not 0")) (|refine| (($ $) "\\axiom{refine(rootChar)} shrinks isolating interval around \\axiom{rootChar}")) (|middle| ((|#1| $) "\\axiom{middle(rootChar)} is the middle of the isolating interval")) (|size| ((|#1| $) "The size of the isolating interval")) (|right| ((|#1| $) "\\axiom{right(rootChar)} is the right bound of the isolating interval")) (|left| ((|#1| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) NIL NIL -(-976) +(-975) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3983 . T) (-3987 . T) (-3982 . T) (-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-977 S R E V) +(-976 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| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#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!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|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)*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)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#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},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL -((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (|HasCategory| |#2| (QUOTE (-484))) (|HasCategory| |#2| (QUOTE (-38 (-485)))) (|HasCategory| |#2| (QUOTE (-905 (-485)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#4| (QUOTE (-554 (-1091))))) -(-978 R E V) +((|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (|HasCategory| |#2| (QUOTE (-483))) (|HasCategory| |#2| (QUOTE (-38 (-484)))) (|HasCategory| |#2| (QUOTE (-904 (-484)))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#4| (QUOTE (-553 (-1090))))) +(-977 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{gcd(\\spad{r},{}\\spad{p})} returns the gcd of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{\\spad{nextsubResultant2}(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{\\spad{next_sousResultant2}}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{\\spad{LazardQuotient2}(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo 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 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{\\spad{halfExtendedSubResultantGcd2}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}cb]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{\\spad{halfExtendedSubResultantGcd1}(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}cb]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}cb,{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + cb * cb = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a gcd of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a gcd-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)*r = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}lp)} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{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},{}lp)} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{lp}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL -(-979) +(-978) ((|constructor| (NIL "This domain represents the `repeat' iterator syntax.")) (|body| (((|SpadAst|) $) "\\spad{body(e)} returns the body of the loop `e'.")) (|iterators| (((|List| (|SpadAst|)) $) "\\spad{iterators(e)} returns the list of iterators controlling the loop `e'."))) NIL NIL -(-980 S |TheField| |ThePols|) +(-979 S |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#2| |#3| $ |#2|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#3| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#3|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#3| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#3| "failed") |#3| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#3| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#3| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#3| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#3| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-981 |TheField| |ThePols|) +(-980 |TheField| |ThePols|) ((|constructor| (NIL "\\axiomType{RealRootCharacterizationCategory} provides common acces functions for all real root codings.")) (|relativeApprox| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|approximate| ((|#1| |#2| $ |#1|) "\\axiom{approximate(term,{}root,{}prec)} gives an approximation of \\axiom{term} over \\axiom{root} with precision \\axiom{prec}")) (|rootOf| (((|Union| $ "failed") |#2| (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} gives the \\spad{n}th root for the order of the Real Closure")) (|allRootsOf| (((|List| $) |#2|) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} in the Real Closure,{} assumed in order.")) (|definingPolynomial| ((|#2| $) "\\axiom{definingPolynomial(aRoot)} gives a polynomial such that \\axiom{definingPolynomial(aRoot).aRoot = 0}")) (|recip| (((|Union| |#2| "failed") |#2| $) "\\axiom{recip(pol,{}aRoot)} tries to inverse \\axiom{pol} interpreted as \\axiom{aRoot}")) (|positive?| (((|Boolean|) |#2| $) "\\axiom{positive?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is positive")) (|negative?| (((|Boolean|) |#2| $) "\\axiom{negative?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is negative")) (|zero?| (((|Boolean|) |#2| $) "\\axiom{zero?(pol,{}aRoot)} answers if \\axiom{pol} interpreted as \\axiom{aRoot} is \\axiom{0}")) (|sign| (((|Integer|) |#2| $) "\\axiom{sign(pol,{}aRoot)} gives the sign of \\axiom{pol} interpreted as \\axiom{aRoot}"))) NIL NIL -(-982 R E V P TS) +(-981 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are proposed: in the sense of Zariski closure (like in Kalkbrener's algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\axiomType{QCMPACK}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS) and \\axiomType{RSETGCD}(\\spad{R},{}\\spad{E},{}\\spad{V},{}\\spad{P},{}TS). The same way it does not care about the way univariate polynomial gcd (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcd need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiom{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-983 S R E V P) +(-982 S R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{Phd Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#5|) (|Boolean|)) "\\spad{zeroSetSplit(lp,clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{extend(lp,lts)} returns the same as \\spad{concat([extend(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{extend(lp,ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,ts)} if \\spad{lp = [p]} else \\spad{extend(first lp, extend(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{extend(p,lts)} returns the same as \\spad{concat([extend(p,ts) for ts in lts])|}") (((|List| $) |#5| $) "\\spad{extend(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#5|) $) "\\spad{internalAugment(lp,ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp, internalAugment(first lp, ts))}") (($ |#5| $) "\\spad{internalAugment(p,ts)} assumes that \\spad{augment(p,ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#5|) (|List| $)) "\\spad{augment(lp,lts)} returns the same as \\spad{concat([augment(lp,ts) for ts in lts])}") (((|List| $) (|List| |#5|) $) "\\spad{augment(lp,ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp, augment(rest lp, ts))}") (((|List| $) |#5| (|List| $)) "\\spad{augment(p,lts)} returns the same as \\spad{concat([augment(p,ts) for ts in lts])}") (((|List| $) |#5| $) "\\spad{augment(p,ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#5| (|List| $)) "\\spad{intersect(p,lts)} returns the same as \\spad{intersect([p],lts)}") (((|List| $) (|List| |#5|) (|List| $)) "\\spad{intersect(lp,lts)} returns the same as \\spad{concat([intersect(lp,ts) for ts in lts])|}") (((|List| $) (|List| |#5|) $) "\\spad{intersect(lp,ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#5| $) "\\spad{intersect(p,ts)} returns the same as \\spad{intersect([p],ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| $) "\\spad{squareFreePart(p,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#5|) (|:| |tower| $))) |#5| |#5| $) "\\spad{lastSubResultant(p1,p2,ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic 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 gcd \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#5| (|List| $)) |#5| |#5| $) "\\spad{lastSubResultantElseSplit(p1,p2,ts)} returns either \\spad{g} a quasi-monic gcd of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#5| $) "\\spad{invertibleSet(p,ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#5| $) "\\spad{invertible?(p,ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#5| $) "\\spad{invertibleElseSplit?(p,ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#5| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#5| $) "\\spad{algebraicCoefficients?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#5| $) "\\spad{purelyTranscendental?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#5| $) "\\spad{purelyAlgebraic?(p,ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) NIL NIL -(-984 R E V P) +(-983 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,...,xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,...,tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,...,ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,...,Ti]}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(Ti)} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,...,Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,...,Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{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 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 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 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}."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-985 R E V P TS) +(-984 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 gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{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},{}ts)} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}ts)} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}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},{}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},{}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},{}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},{}ts)} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-986) +(-985) ((|constructor| (NIL "This domain represents `restrict' expressions.")) (|target| (((|TypeAst|) $) "\\spad{target(e)} returns the target type of the conversion..")) (|expression| (((|SpadAst|) $) "\\spad{expression(e)} returns the expression being converted."))) NIL NIL -(-987) +(-986) ((|constructor| (NIL "This is the datatype of OpenAxiom runtime values. It exists solely for internal purposes.")) (|eq| (((|Boolean|) $ $) "\\spad{eq(x,y)} holds if both values \\spad{x} and \\spad{y} resides at the same address in memory."))) NIL NIL -(-988 |Base| R -3093) +(-987 |Base| R -3092) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r, [a1,...,an], f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,...,an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f, g, [f1,...,fn])} creates the rewrite rule \\spad{f == eval(eval(g, g is f), [f1,...,fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}fn are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f, g)} creates the rewrite rule: \\spad{f == eval(g, g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-989 |f|) +(-988 |f|) ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-990 |Base| R -3093) +(-989 |Base| R -3092) ((|constructor| (NIL "A ruleset is a set of pattern matching rules grouped together.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,f,n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies all the rules of \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rules| (((|List| (|RewriteRule| |#1| |#2| |#3|)) $) "\\spad{rules(r)} returns the rules contained in \\spad{r}.")) (|ruleset| (($ (|List| (|RewriteRule| |#1| |#2| |#3|))) "\\spad{ruleset([r1,...,rn])} creates the rule set \\spad{{r1,...,rn}}."))) NIL NIL -(-991 R |ls|) +(-990 R |ls|) ((|constructor| (NIL "\\indented{1}{A package for computing the rational univariate representation} \\indented{1}{of a zero-dimensional algebraic variety given by a regular} \\indented{1}{triangular set. This package is essentially an interface for the} \\spadtype{InternalRationalUnivariateRepresentationPackage} constructor. It is used in the \\spadtype{ZeroDimensionalSolvePackage} for solving polynomial systems with finitely many solutions.")) (|rur| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{rur(lp,univ?,check?)} returns the same as \\spad{rur(lp,true)}. Moreover,{} if \\spad{check?} is \\spad{true} then the result is checked.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{rur(lp)} returns the same as \\spad{rur(lp,true)}") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{rur(lp,univ?)} returns a rational univariate representation of \\spad{lp}. This assumes that \\spad{lp} defines a regular triangular \\spad{ts} whose associated variety is zero-dimensional over \\spad{R}. \\spad{rur(lp,univ?)} returns a list of items \\spad{[u,lc]} where \\spad{u} is an irreducible univariate polynomial and each \\spad{c} in \\spad{lc} involves two variables: one from \\spad{ls},{} called the coordinate of \\spad{c},{} and an extra variable which represents any root of \\spad{u}. Every root of \\spad{u} leads to a tuple of values for the coordinates of \\spad{lc}. Moreover,{} a point \\spad{x} belongs to the variety associated with \\spad{lp} iff there exists an item \\spad{[u,lc]} in \\spad{rur(lp,univ?)} and a root \\spad{r} of \\spad{u} such that \\spad{x} is given by the tuple of values for the coordinates of \\spad{lc} evaluated at \\spad{r}. If \\spad{univ?} is \\spad{true} then each polynomial \\spad{c} will have a constant leading coefficient \\spad{w}.\\spad{r}.\\spad{t}. its coordinate. See the example which illustrates the \\spadtype{ZeroDimensionalSolvePackage} package constructor."))) NIL NIL -(-992 R UP M) +(-991 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."))) -((-3989 |has| |#1| (-312)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-812 (-1091))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))))) -(-993 UP SAE UPA) +((-3988 |has| |#1| (-312)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-299))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-299)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-320))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-299))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (|HasCategory| |#1| (QUOTE (-299)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-811 (-1090))))) (-12 (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-312)))) (-12 (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))))) +(-992 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of the rational numbers (\\spadtype{Fraction Integer}).")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-994 UP SAE UPA) +(-993 UP SAE UPA) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of \\spadtype{Fraction Polynomial Integer}.")) (|factor| (((|Factored| |#3|) |#3|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p}."))) NIL NIL -(-995) +(-994) ((|constructor| (NIL "This trivial domain lets us build Univariate Polynomials in an anonymous variable"))) NIL NIL -(-996) +(-995) ((|constructor| (NIL "This is the category of Spad syntax objects."))) NIL NIL -(-997 S) +(-996 S) ((|constructor| (NIL "\\indented{1}{Cache of elements in a set} Author: Manuel Bronstein Date Created: 31 Oct 1988 Date Last Updated: 14 May 1991 \\indented{2}{A sorted cache of a cachable set \\spad{S} is a dynamic structure that} \\indented{2}{keeps the elements of \\spad{S} sorted and assigns an integer to each} \\indented{2}{element of \\spad{S} once it is in the cache. This way,{} equality and ordering} \\indented{2}{on \\spad{S} are tested directly on the integers associated with the elements} \\indented{2}{of \\spad{S},{} once they have been entered in the cache.}")) (|enterInCache| ((|#1| |#1| (|Mapping| (|Integer|) |#1| |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(x, y)} to determine whether \\spad{x < y (f(x,y) < 0), x = y (f(x,y) = 0)},{} or \\spad{x > y (f(x,y) > 0)}. It returns \\spad{x} with an integer associated with it.") ((|#1| |#1| (|Mapping| (|Boolean|) |#1|)) "\\spad{enterInCache(x, f)} enters \\spad{x} in the cache,{} calling \\spad{f(y)} to determine whether \\spad{x} is equal to \\spad{y}. It returns \\spad{x} with an integer associated with it.")) (|cache| (((|List| |#1|)) "\\spad{cache()} returns the current cache as a list.")) (|clearCache| (((|Void|)) "\\spad{clearCache()} empties the cache."))) NIL NIL -(-998) +(-997) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Scope' is a sequence of contours.")) (|currentCategoryFrame| (($) "\\spad{currentCategoryFrame()} returns the category frame currently in effect.")) (|currentScope| (($) "\\spad{currentScope()} returns the scope currently in effect")) (|pushNewContour| (($ (|Binding|) $) "\\spad{pushNewContour(b,s)} pushs a new contour with sole binding `b'.")) (|findBinding| (((|Maybe| (|Binding|)) (|Identifier|) $) "\\spad{findBinding(n,s)} returns the first binding of `n' in `s'; otherwise `nothing'.")) (|contours| (((|List| (|Contour|)) $) "\\spad{contours(s)} returns the list of contours in scope \\spad{s}.")) (|empty| (($) "\\spad{empty()} returns an empty scope."))) NIL NIL -(-999 R) +(-998 R) ((|constructor| (NIL "StructuralConstantsPackage provides functions creating structural constants from a multiplication tables or a basis of a matrix algebra and other useful functions in this context.")) (|coordinates| (((|Vector| |#1|) (|Matrix| |#1|) (|List| (|Matrix| |#1|))) "\\spad{coordinates(a,[v1,...,vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{structuralConstants(basis)} takes the \\spad{basis} of a matrix algebra,{} \\spadignore{e.g.} the result of \\spadfun{basisOfCentroid} and calculates the structural constants. Note,{} that the it is not checked,{} whether \\spad{basis} really is a \\spad{basis} of a matrix algebra.") (((|Vector| (|Matrix| (|Polynomial| |#1|))) (|List| (|Symbol|)) (|Matrix| (|Polynomial| |#1|))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}") (((|Vector| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|)) (|Matrix| (|Fraction| (|Polynomial| |#1|)))) "\\spad{structuralConstants(ls,mt)} determines the structural constants of an algebra with generators \\spad{ls} and multiplication table \\spad{mt},{} the entries of which must be given as linear polynomials in the indeterminates given by \\spad{ls}. The result is in particular useful \\indented{1}{as fourth argument for \\spadtype{AlgebraGivenByStructuralConstants}} \\indented{1}{and \\spadtype{GenericNonAssociativeAlgebra}.}"))) NIL NIL -(-1000 R) +(-999 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"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-1001 (-1091)) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1001 S) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-1000 (-1090)) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-190))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1000 S) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialVariable} adds a commonly used sequential ranking to the set of derivatives of an ordered list of differential indeterminates. A sequential ranking is a ranking \\spadfun{<} of the derivatives with the property that for any derivative \\spad{v},{} there are only a finite number of derivatives \\spad{u} with \\spad{u} \\spadfun{<} \\spad{v}. This domain belongs to \\spadtype{DifferentialVariableCategory}. It defines \\spadfun{weight} to be just \\spadfun{order},{} and it defines a sequential ranking \\spadfun{<} on derivatives \\spad{u} by the lexicographic order on the pair (\\spadfun{variable}(\\spad{u}),{} \\spadfun{order}(\\spad{u}))."))) NIL NIL -(-1002 S) +(-1001 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) NIL -((|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) -(-1003 R S) +((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) +(-1002 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 (-756)))) -(-1004) +((|HasCategory| |#1| (QUOTE (-755)))) +(-1003) ((|constructor| (NIL "This domain represents segement expressions.")) (|bounds| (((|List| (|SpadAst|)) $) "\\spad{bounds(s)} returns the bounds of the segment `s'. If `s' designates an infinite interval,{} then the returns list a singleton list."))) NIL NIL -(-1005 S) +(-1004 S) ((|constructor| (NIL "This domain is used to provide the function argument syntax \\spad{v=a..b}. This is used,{} for example,{} by the top-level \\spadfun{draw} functions."))) NIL -((|HasCategory| (-1002 |#1|) (QUOTE (-1014)))) -(-1006 R S) +((|HasCategory| (-1001 |#1|) (QUOTE (-1013)))) +(-1005 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto \\spadtype{SegmentBinding}\\spad{s}.")) (|map| (((|SegmentBinding| |#2|) (|Mapping| |#2| |#1|) (|SegmentBinding| |#1|)) "\\spad{map(f,v=a..b)} returns the value given by \\spad{v=f(a)..f(b)}."))) NIL NIL -(-1007 S) +(-1006 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{hi(s)} returns the second endpoint of \\spad{s}. Note: \\spad{hi(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) NIL NIL -(-1008 S L) +(-1007 S L) ((|constructor| (NIL "This category provides an interface for expanding segments to a stream of elements.")) (|map| ((|#2| (|Mapping| |#1| |#1|) $) "\\spad{map(f,l..h by k)} produces a value of type \\spad{L} by applying \\spad{f} to each of the succesive elements of the segment,{} that is,{} \\spad{[f(l), f(l+k), ..., f(lN)]},{} where \\spad{lN <= h < lN+k}.")) (|expand| ((|#2| $) "\\spad{expand(l..h by k)} creates value of type \\spad{L} with elements \\spad{l, l+k, ... lN} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand(1..5 by 2) = [1,3,5]}.") ((|#2| (|List| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l, l+k, ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4, 7..9] = [1,2,3,4,7,8,9]}."))) NIL NIL -(-1009) +(-1008) ((|constructor| (NIL "This domain represents a block of expressions.")) (|last| (((|SpadAst|) $) "\\spad{last(e)} returns the last instruction in `e'.")) (|body| (((|List| (|SpadAst|)) $) "\\spad{body(e)} returns the list of expressions in the sequence of instruction `e'."))) NIL NIL -(-1010 S) +(-1009 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)}}"))) -((-3996 . T) (-3986 . T) (-3997 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-1011 A S) +((-3995 . T) (-3985 . T) (-3996 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#1| (QUOTE (-320))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-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.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) NIL NIL -(-1012 S) +(-1011 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#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.")) (|part?| (((|Boolean|) $ $) "\\spad{s} < \\spad{t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-3986 . T)) +((-3985 . T)) NIL -(-1013 S) +(-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}."))) NIL NIL -(-1014) +(-1013) ((|constructor| (NIL "\\spadtype{SetCategory} is the basic category for describing a collection of elements with \\spadop{=} (equality) and \\spadfun{coerce} to output form. \\blankline Conditional Attributes: \\indented{3}{canonical\\tab{15}data structure equality is the same as \\spadop{=}}")) (|latex| (((|String|) $) "\\spad{latex(s)} returns a LaTeX-printable output representation of \\spad{s}.")) (|hash| (((|SingleInteger|) $) "\\spad{hash(s)} calculates a hash code for \\spad{s}."))) NIL NIL -(-1015 |m| |n|) +(-1014 |m| |n|) ((|constructor| (NIL "\\spadtype{SetOfMIntegersInOneToN} implements the subsets of \\spad{M} integers in the interval \\spad{[1..n]}")) (|delta| (((|NonNegativeInteger|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{delta(S,k,p)} returns the number of elements of \\spad{S} which are strictly between \\spad{p} and the k^{th} element of \\spad{S}.")) (|member?| (((|Boolean|) (|PositiveInteger|) $) "\\spad{member?(p, s)} returns \\spad{true} is \\spad{p} is in \\spad{s},{} \\spad{false} otherwise.")) (|enumerate| (((|Vector| $)) "\\spad{enumerate()} returns a vector of all the sets of \\spad{M} integers in \\spad{1..n}.")) (|setOfMinN| (($ (|List| (|PositiveInteger|))) "\\spad{setOfMinN([a_1,...,a_m])} returns the set {\\spad{a_1},{}...,{}a_m}. Error if {\\spad{a_1},{}...,{}a_m} is not a set of \\spad{M} integers in \\spad{1..n}.")) (|elements| (((|List| (|PositiveInteger|)) $) "\\spad{elements(S)} returns the list of the elements of \\spad{S} in increasing order.")) (|replaceKthElement| (((|Union| $ #1="failed") $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{replaceKthElement(S,k,p)} replaces the k^{th} element of \\spad{S} by \\spad{p},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more.")) (|incrementKthElement| (((|Union| $ #1#) $ (|PositiveInteger|)) "\\spad{incrementKthElement(S,k)} increments the k^{th} element of \\spad{S},{} and returns \"failed\" if the result is not a set of \\spad{M} integers in \\spad{1..n} any more."))) NIL NIL -(-1016) +(-1015) ((|constructor| (NIL "This domain allows the manipulation of the usual Lisp values."))) NIL NIL -(-1017 |Str| |Sym| |Int| |Flt| |Expr|) +(-1016 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,...,an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,...,an))} returns \\spad{(a2,...,an)}.")) (|car| (($ $) "\\spad{car((a1,...,an))} returns \\spad{a1}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of Flt; Error: if \\spad{s} is not an atom that also belongs to 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 Sym. Error: if \\spad{s} is not an atom that also belongs to Sym.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of Str. Error: if \\spad{s} is not an atom that also belongs to Str.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,...,an))} returns the list [\\spad{a1},{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to 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 Sym.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to 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 \\%peq(\\spad{s},{}\\spad{t}) is \\spad{true} for pointers."))) NIL NIL -(-1018 |Str| |Sym| |Int| |Flt| |Expr|) +(-1017 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This domain allows the manipulation of Lisp values over arbitrary atomic types."))) NIL NIL -(-1019 R E V P TS) +(-1018 R E V P TS) ((|constructor| (NIL "\\indented{2}{A internal package for removing redundant quasi-components and redundant} \\indented{2}{branches when decomposing a variety by means of quasi-components} \\indented{2}{of regular triangular sets. \\newline} References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{5}{Tech. Report (PoSSo project)} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|branchIfCan| (((|Union| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|))) "failed") (|List| |#4|) |#5| (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{branchIfCan(leq,{}ts,{}lineq,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement.")) (|prepareDecompose| (((|List| (|Record| (|:| |eq| (|List| |#4|)) (|:| |tower| |#5|) (|:| |ineq| (|List| |#4|)))) (|List| |#4|) (|List| |#5|) (|Boolean|) (|Boolean|)) "\\axiom{prepareDecompose(lp,{}lts,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousCases| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)))) "\\axiom{removeSuperfluousCases(llpwt)} is an internal subroutine,{} exported only for developement.")) (|subCase?| (((|Boolean|) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|)) (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) "\\axiom{subCase?(\\spad{lpwt1},{}\\spad{lpwt2})} is an internal subroutine,{} exported only for developement.")) (|removeSuperfluousQuasiComponents| (((|List| |#5|) (|List| |#5|)) "\\axiom{removeSuperfluousQuasiComponents(lts)} removes from \\axiom{lts} any \\spad{ts} such that \\axiom{subQuasiComponent?(ts,{}us)} holds for another \\spad{us} in \\axiom{lts}.")) (|subQuasiComponent?| (((|Boolean|) |#5| (|List| |#5|)) "\\axiom{subQuasiComponent?(ts,{}lus)} returns \\spad{true} iff \\axiom{subQuasiComponent?(ts,{}us)} holds for one \\spad{us} in \\spad{lus}.") (((|Boolean|) |#5| |#5|) "\\axiom{subQuasiComponent?(ts,{}us)} returns \\spad{true} iff \\axiomOpFrom{internalSubQuasiComponent?(ts,{}us)}{QuasiComponentPackage} returs \\spad{true}.")) (|internalSubQuasiComponent?| (((|Union| (|Boolean|) "failed") |#5| |#5|) "\\axiom{internalSubQuasiComponent?(ts,{}us)} returns a boolean \\spad{b} value if the fact the regular zero set of \\axiom{us} contains that of \\axiom{ts} can be decided (and in that case \\axiom{\\spad{b}} gives this inclusion) otherwise returns \\axiom{\"failed\"}.")) (|infRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{infRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalInfRittWu?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalInfRittWu?(\\spad{lp1},{}\\spad{lp2})} is an internal subroutine,{} exported only for developement.")) (|internalSubPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{internalSubPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}} assuming that these lists are sorted increasingly \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{infRittWu?}{RecursivePolynomialCategory}.")) (|subPolSet?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{subPolSet?(\\spad{lp1},{}\\spad{lp2})} returns \\spad{true} iff \\axiom{\\spad{lp1}} is a sub-set of \\axiom{\\spad{lp2}}.")) (|subTriSet?| (((|Boolean|) |#5| |#5|) "\\axiom{subTriSet?(ts,{}us)} returns \\spad{true} iff \\axiom{ts} is a sub-set of \\axiom{us}.")) (|moreAlgebraic?| (((|Boolean|) |#5| |#5|) "\\axiom{moreAlgebraic?(ts,{}us)} returns \\spad{false} iff \\axiom{ts} and \\axiom{us} are both empty,{} or \\axiom{ts} has less elements than \\axiom{us},{} or some variable is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{us} and is not \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|algebraicSort| (((|List| |#5|) (|List| |#5|)) "\\axiom{algebraicSort(lts)} sorts \\axiom{lts} \\spad{w}.\\spad{r}.\\spad{t} \\axiomOpFrom{supDimElseRittWu}{QuasiComponentPackage}.")) (|supDimElseRittWu?| (((|Boolean|) |#5| |#5|) "\\axiom{supDimElseRittWu(ts,{}us)} returns \\spad{true} iff \\axiom{ts} has less elements than \\axiom{us} otherwise if \\axiom{ts} has higher rank than \\axiom{us} \\spad{w}.\\spad{r}.\\spad{t}. Riit and Wu ordering.")) (|stopTable!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTable!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) NIL NIL -(-1020 R E V P TS) +(-1019 R E V P TS) ((|constructor| (NIL "A internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field. There is no need to use directly this package since its main operations are available from \\spad{TS}. \\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of gcd over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of \\spad{AAECC11}} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1021 R E V P) +(-1020 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 gcd of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(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.}"))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-1022) +(-1021) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,0,0] < [0,3,0] < [0,0,3] < [2,1,0] < [2,0,1] < [0,2,1] < [1,2,0] < [1,0,2] < [0,1,2] < [1,1,1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,m,k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,0,3] < [0,1,2] < [0,2,1] < [0,3,0] < [1,0,2] < [1,1,1] < [1,2,0] < [2,0,1] < [2,1,0] < [3,0,0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,m,k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,1,...,(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,...,(m-1)} into {\\em 0,...,(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,3)} is 10,{} since {\\em [0,0,3], [0,1,2], [0,2,1], [0,3,0], [1,0,2], [1,1,1], [1,2,0], [2,0,1], [2,1,0], [3,0,0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,part,number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,lattP,constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,beta,C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,1,0)}. Also,{} {\\em new(1,1,0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|PositiveInteger|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,...,n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|PositiveInteger|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,...,n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,beta,C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em pi} in the corresponding double coset. Note: the resulting permutation {\\em pi} of {\\em {1,2,...,n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,beta,pi)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em pi} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha, beta, pi}. Note: The permutation {\\em pi} of {\\em {1,2,...,n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em pi} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) NIL NIL -(-1023 T$) +(-1022 T$) ((|constructor| (NIL "This domain implements semigroup operations.")) (|semiGroupOperation| (($ (|Mapping| |#1| |#1| |#1|)) "\\spad{semiGroupOperation f} constructs a semigroup operation out of a binary homogeneous mapping known to be associative."))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-1024 T$) +(-1023 T$) ((|constructor| (NIL "This is the category of all domains that implement semigroup operations"))) -(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3057 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) +(((|%Rule| |associativity| (|%Forall| (|%Sequence| (|:| |f| $) (|:| |x| |#1|) (|:| |y| |#1|) (|:| |z| |#1|)) (-3056 (|f| (|f| |x| |y|) |z|) (|f| |x| (|f| |y| |z|))))) . T)) NIL -(-1025 S) +(-1024 S) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1026) +(-1025) ((|constructor| (NIL "the class of all multiplicative semigroups,{} \\spadignore{i.e.} a set with an associative operation \\spadop{*}. \\blankline")) (** (($ $ (|PositiveInteger|)) "\\spad{x**n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (* (($ $ $) "\\spad{x*y} returns the product of \\spad{x} and \\spad{y}."))) NIL NIL -(-1027 |dimtot| |dim1| S) +(-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 \\spad{dim1} parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-3990 |has| |#3| (-962)) (-3991 |has| |#3| (-962)) (-3993 |has| |#3| (-6 -3993)) (-3996 . 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If \\spad{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 c_{+}-c_{-} where c_{+} is the number of real roots of \\spad{p1} with \\spad{p2>0} and c_{-} is the number of real roots of \\spad{p1} with \\spad{p2<0}. If \\spad{p2=1} what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-392)))) -(-1029) +(-1028) ((|constructor| (NIL "This is the datatype for operation signatures as \\indented{2}{used by the compiler and the interpreter.\\space{2}Note that this domain} \\indented{2}{differs from SignatureAst.} See also: ConstructorCall,{} Domain.")) (|source| (((|List| (|Syntax|)) $) "\\spad{source(s)} returns the list of parameter types of `s'.")) (|target| (((|Syntax|) $) "\\spad{target(s)} returns the target type of the signature `s'.")) (|signature| (($ (|List| (|Syntax|)) (|Syntax|)) "\\spad{signature(s,t)} constructs a Signature object with parameter types indicaded by `s',{} and return type indicated by `t'."))) NIL NIL -(-1030) +(-1029) ((|constructor| (NIL "This domain represents a signature AST. A signature AST \\indented{2}{is a description of an exported operation,{} \\spadignore{e.g.} its name,{} result} \\indented{2}{type,{} and the list of its argument types.}")) (|signature| (((|Signature|) $) "\\spad{signature(s)} returns AST of the declared signature for `s'.")) (|name| (((|Identifier|) $) "\\spad{name(s)} returns the name of the signature `s'.")) (|signatureAst| (($ (|Identifier|) (|Signature|)) "\\spad{signatureAst(n,s,t)} builds the signature AST n: \\spad{s} -> \\spad{t}"))) NIL NIL -(-1031 R -3093) +(-1030 R -3092) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) #1#) |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1032 R) +(-1031 R) ((|constructor| (NIL "Find the sign of a rational function around a point or infinity.")) (|sign| (((|Union| (|Integer|) #1="failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|)) (|String|)) "\\spad{sign(f, x, a, s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from the left (below) if \\spad{s} is the string \\spad{\"left\"},{} or from the right (above) if \\spad{s} is the string \\spad{\"right\"}.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|OrderedCompletion| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sign(f, x, a)} returns the sign of \\spad{f} as \\spad{x} approaches \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) #1#) (|Fraction| (|Polynomial| |#1|))) "\\spad{sign f} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL -(-1033) +(-1032) ((|constructor| (NIL "\\indented{1}{Package to allow simplify to be called on AlgebraicNumbers} by converting to EXPR(INT)")) (|simplify| (((|Expression| (|Integer|)) (|AlgebraicNumber|)) "\\spad{simplify(an)} applies simplifications to \\spad{an}"))) NIL NIL -(-1034) +(-1033) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|xor| (($ $ $) "\\spad{xor(n,m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-3984 . T) (-3988 . T) (-3983 . T) (-3994 . T) (-3995 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3983 . T) (-3987 . T) (-3982 . T) (-3993 . T) (-3994 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1035 S) +(-1034 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}) = \\#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| $) "\\spad{push!(x,s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-3996 . T) (-3997 . T)) +((-3995 . T) (-3996 . T)) NIL -(-1036 S) +(-1035 S) ((|constructor| (NIL "This category describes the class of homogeneous aggregates that support in place mutation that do not change their general shapes.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,u)} destructively replaces each element \\spad{x} of \\spad{u} by \\spad{f(x)}"))) +((-3996 . T)) NIL -NIL -(-1037 S |ndim| R |Row| |Col|) +(-1036 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}'s on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3998 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) -(-1038 |ndim| R |Row| |Col|) +((|HasCategory| |#3| (QUOTE (-312))) (|HasAttribute| |#3| (QUOTE (-3997 "*"))) (|HasCategory| |#3| (QUOTE (-146)))) +(-1037 |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}'s on the diagonal and zeroes elsewhere."))) -((-3996 . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3995 . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1039 R |Row| |Col| M) +(-1038 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{SmithNormalForm} is a package which provides some standard canonical forms for matrices.")) (|diophantineSystem| (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{diophantineSystem(A,B)} returns a particular integer solution and an integer basis of the equation \\spad{AX = B}.")) (|completeSmith| (((|Record| (|:| |Smith| |#4|) (|:| |leftEqMat| |#4|) (|:| |rightEqMat| |#4|)) |#4|) "\\spad{completeSmith} returns a record that contains the Smith normal form \\spad{H} of the matrix and the left and right equivalence matrices \\spad{U} and \\spad{V} such that U*m*v = \\spad{H}")) (|smith| ((|#4| |#4|) "\\spad{smith(m)} returns the Smith Normal form of the matrix \\spad{m}.")) (|completeHermite| (((|Record| (|:| |Hermite| |#4|) (|:| |eqMat| |#4|)) |#4|) "\\spad{completeHermite} returns a record that contains the Hermite normal form \\spad{H} of the matrix and the equivalence matrix \\spad{U} such that U*m = \\spad{H}")) (|hermite| ((|#4| |#4|) "\\spad{hermite(m)} returns the Hermite normal form of the matrix \\spad{m}."))) NIL NIL -(-1040 R |VarSet|) +(-1039 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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| |#2| (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| |#2| (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| |#2| (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1041 |Coef| |Var| SMP) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| |#2| (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| |#2| (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| |#2| (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1040 |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 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| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial SMP.")) (|coerce| (($ |#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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1042 R E V P) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312)))) +(-1041 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}"))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-1043 UP -3093) +(-1042 UP -3092) ((|constructor| (NIL "This package factors the formulas out of the general solve code,{} allowing their recursive use over different domains. Care is taken to introduce few radicals so that radical extension domains can more easily simplify the results.")) (|aQuartic| ((|#2| |#2| |#2| |#2| |#2| |#2|) "\\spad{aQuartic(f,g,h,i,k)} \\undocumented")) (|aCubic| ((|#2| |#2| |#2| |#2| |#2|) "\\spad{aCubic(f,g,h,j)} \\undocumented")) (|aQuadratic| ((|#2| |#2| |#2| |#2|) "\\spad{aQuadratic(f,g,h)} \\undocumented")) (|aLinear| ((|#2| |#2| |#2|) "\\spad{aLinear(f,g)} \\undocumented")) (|quartic| (((|List| |#2|) |#2| |#2| |#2| |#2| |#2|) "\\spad{quartic(f,g,h,i,j)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quartic(u)} \\undocumented")) (|cubic| (((|List| |#2|) |#2| |#2| |#2| |#2|) "\\spad{cubic(f,g,h,i)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{cubic(u)} \\undocumented")) (|quadratic| (((|List| |#2|) |#2| |#2| |#2|) "\\spad{quadratic(f,g,h)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{quadratic(u)} \\undocumented")) (|linear| (((|List| |#2|) |#2| |#2|) "\\spad{linear(f,g)} \\undocumented") (((|List| |#2|) |#1|) "\\spad{linear(u)} \\undocumented")) (|mapSolve| (((|Record| (|:| |solns| (|List| |#2|)) (|:| |maps| (|List| (|Record| (|:| |arg| |#2|) (|:| |res| |#2|))))) |#1| (|Mapping| |#2| |#2|)) "\\spad{mapSolve(u,f)} \\undocumented")) (|particularSolution| ((|#2| |#1|) "\\spad{particularSolution(u)} \\undocumented")) (|solve| (((|List| |#2|) |#1|) "\\spad{solve(u)} \\undocumented"))) NIL NIL -(-1044 R) +(-1043 R) ((|constructor| (NIL "This package tries to find solutions expressed in terms of radicals for systems of equations of rational functions with coefficients in an integral domain \\spad{R}.")) (|contractSolve| (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{contractSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function. The result contains new symbols for common subexpressions in order to reduce the size of the output.") (((|SuchThat| (|List| (|Expression| |#1|)) (|List| (|Equation| (|Expression| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{contractSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}. The result contains new symbols for common subexpressions in order to reduce the size of the output.")) (|radicalRoots| (((|List| (|List| (|Expression| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalRoots(lrf,lvar)} finds the roots expressed in terms of radicals of the list of rational functions \\spad{lrf} with respect to the list of symbols \\spad{lvar}.") (((|List| (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalRoots(rf,x)} finds the roots expressed in terms of radicals of the rational function \\spad{rf} with respect to the symbol \\spad{x}.")) (|radicalSolve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{radicalSolve(leq)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the unique symbol \\spad{x} appearing in \\spad{leq}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{radicalSolve(leq,lvar)} finds the solutions expressed in terms of radicals of the system of equations of rational functions \\spad{leq} with respect to the list of symbols \\spad{lvar}.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(lrf)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0,{} where \\spad{lrf} is a system of univariate rational functions.") (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{radicalSolve(lrf,lvar)} finds the solutions expressed in terms of radicals of the system of equations \\spad{lrf} = 0 with respect to the list of symbols \\spad{lvar},{} where \\spad{lrf} is a list of rational functions.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{radicalSolve(eq)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{radicalSolve(eq,x)} finds the solutions expressed in terms of radicals of the equation of rational functions \\spad{eq} with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|))) "\\spad{radicalSolve(rf)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0,{} where \\spad{rf} is a univariate rational function.") (((|List| (|Equation| (|Expression| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{radicalSolve(rf,x)} finds the solutions expressed in terms of radicals of the equation \\spad{rf} = 0 with respect to the symbol \\spad{x},{} where \\spad{rf} is a rational function."))) NIL NIL -(-1045 R) +(-1044 R) ((|constructor| (NIL "This package finds the function \\spad{func3} where \\spad{func1} and \\spad{func2} \\indented{1}{are given and\\space{2}\\spad{func1} = \\spad{func3}(\\spad{func2}) .\\space{2}If there is no solution then} \\indented{1}{function \\spad{func1} will be returned.} \\indented{1}{An example would be\\space{2}\\spad{func1:= 8*X**3+32*X**2-14*X ::EXPR INT} and} \\indented{1}{\\spad{func2:=2*X ::EXPR INT} convert them via univariate} \\indented{1}{to FRAC SUP EXPR INT and then the solution is \\spad{func3:=X**3+X**2-X}} \\indented{1}{of type FRAC SUP EXPR INT}")) (|unvectorise| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Vector| (|Expression| |#1|)) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Integer|)) "\\spad{unvectorise(vect, var, n)} returns \\spad{vect(1) + vect(2)*var + ... + vect(n+1)*var**(n)} where \\spad{vect} is the vector of the coefficients of the polynomail ,{} \\spad{var} the new variable and \\spad{n} the degree.")) (|decomposeFunc| (((|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|))) (|Fraction| (|SparseUnivariatePolynomial| (|Expression| |#1|)))) "\\spad{decomposeFunc(func1, func2, newvar)} returns a function \\spad{func3} where \\spad{func1} = \\spad{func3}(\\spad{func2}) and expresses it in the new variable newvar. If there is no solution then \\spad{func1} will be returned."))) NIL NIL -(-1046 R) +(-1045 R) ((|constructor| (NIL "This package tries to find solutions of equations of type Expression(\\spad{R}). This means expressions involving transcendental,{} exponential,{} logarithmic and nthRoot functions. After trying to transform different kernels to one kernel by applying several rules,{} it calls zerosOf for the SparseUnivariatePolynomial in the remaining kernel. For example the expression \\spad{sin(x)*cos(x)-2} will be transformed to \\indented{3}{\\spad{-2 tan(x/2)**4 -2 tan(x/2)**3 -4 tan(x/2)**2 +2 tan(x/2) -2}} by using the function normalize and then to \\indented{3}{\\spad{-2 tan(x)**2 + tan(x) -2}} with help of subsTan. This function tries to express the given function in terms of \\spad{tan(x/2)} to express in terms of \\spad{tan(x)} . Other examples are the expressions \\spad{sqrt(x+1)+sqrt(x+7)+1} or \\indented{1}{\\spad{sqrt(sin(x))+1} .}")) (|solve| (((|List| (|List| (|Equation| (|Expression| |#1|)))) (|List| (|Equation| (|Expression| |#1|))) (|List| (|Symbol|))) "\\spad{solve(leqs, lvar)} returns a list of solutions to the list of equations \\spad{leqs} with respect to the list of symbols lvar.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|) (|Symbol|)) "\\spad{solve(expr,x)} finds the solutions of the equation \\spad{expr} = 0 with respect to the symbol \\spad{x} where \\spad{expr} is a function of type Expression(\\spad{R}).") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|)) (|Symbol|)) "\\spad{solve(eq,x)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the symbol \\spad{x}.") (((|List| (|Equation| (|Expression| |#1|))) (|Equation| (|Expression| |#1|))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} where \\spad{eq} is an equation of functions of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in \\spad{eq}.") (((|List| (|Equation| (|Expression| |#1|))) (|Expression| |#1|)) "\\spad{solve(expr)} finds the solutions of the equation \\spad{expr} = 0 where \\spad{expr} is a function of type Expression(\\spad{R}) with respect to the unique symbol \\spad{x} appearing in eq."))) NIL NIL -(-1047 S A) +(-1046 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 (-757)))) -(-1048 R) +((|HasCategory| |#1| (QUOTE (-756)))) +(-1047 R) ((|constructor| (NIL "The domain ThreeSpace is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them."))) NIL NIL -(-1049 R) +(-1048 R) ((|constructor| (NIL "The category ThreeSpaceCategory is used for creating three dimensional objects using functions for defining points,{} curves,{} polygons,{} constructs and the subspaces containing them.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(s)} returns the \\spadtype{ThreeSpace} \\spad{s} to Output format.")) (|subspace| (((|SubSpace| 3 |#1|) $) "\\spad{subspace(s)} returns the \\spadtype{SubSpace} which holds all the point information in the \\spadtype{ThreeSpace},{} \\spad{s}.")) (|check| (($ $) "\\spad{check(s)} returns lllpt,{} list of lists of lists of point information about the \\spadtype{ThreeSpace} \\spad{s}.")) (|objects| (((|Record| (|:| |points| (|NonNegativeInteger|)) (|:| |curves| (|NonNegativeInteger|)) (|:| |polygons| (|NonNegativeInteger|)) (|:| |constructs| (|NonNegativeInteger|))) $) "\\spad{objects(s)} returns the \\spadtype{ThreeSpace},{} \\spad{s},{} in the form of a 3D object record containing information on the number of points,{} curves,{} polygons and constructs comprising the \\spadtype{ThreeSpace}..")) (|lprop| (((|List| (|SubSpaceComponentProperty|)) $) "\\spad{lprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of subspace component properties,{} and if so,{} returns the list; An error is signaled otherwise.")) (|llprop| (((|List| (|List| (|SubSpaceComponentProperty|))) $) "\\spad{llprop(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of curves which are lists of the subspace component properties of the curves,{} and if so,{} returns the list of lists; An error is signaled otherwise.")) (|lllp| (((|List| (|List| (|List| (|Point| |#1|)))) $) "\\spad{lllp(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lllip| (((|List| (|List| (|List| (|NonNegativeInteger|)))) $) "\\spad{lllip(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a list of components,{} which are lists of curves,{} which are lists of indices to points,{} and if so,{} returns the list of lists of lists; An error is signaled otherwise.")) (|lp| (((|List| (|Point| |#1|)) $) "\\spad{lp(s)} returns the list of points component which the \\spadtype{ThreeSpace},{} \\spad{s},{} contains; these points are used by reference,{} \\spadignore{i.e.} the component holds indices referring to the points rather than the points themselves. This allows for sharing of the points.")) (|mesh?| (((|Boolean|) $) "\\spad{mesh?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} is composed of one component,{} a mesh comprising a list of curves which are lists of points,{} or returns \\spad{false} if otherwise")) (|mesh| (((|List| (|List| (|Point| |#1|))) $) "\\spad{mesh(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single surface component defined by a list curves which contain lists of points,{} and if so,{} returns the list of lists of points; An error is signaled otherwise.") (($ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh([[p0],[p1],...,[pn]], close1, close2)} creates a surface defined over a list of curves,{} \\spad{p0} through pn,{} which are lists of points; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: \\spad{close1} set to \\spad{true} means that each individual list (a curve) is to be closed (that is,{} the last point of the list is to be connected to the first point); \\spad{close2} set to \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)); the \\spadtype{ThreeSpace} containing this surface is returned.") (($ (|List| (|List| (|Point| |#1|)))) "\\spad{mesh([[p0],[p1],...,[pn]])} creates a surface defined by a list of curves which are lists,{} \\spad{p0} through pn,{} of points,{} and returns a \\spadtype{ThreeSpace} whose component is the surface.") (($ $ (|List| (|List| (|List| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; the booleans \\spad{close1} and \\spad{close2} indicate how the surface is to be closed: if \\spad{close1} is \\spad{true} this means that each individual list (a curve) is to be closed (\\spadignore{i.e.} the last point of the list is to be connected to the first point); if \\spad{close2} is \\spad{true},{} this means that the boundary at one end of the surface is to be connected to the boundary at the other end (the boundaries are defined as the first list of points (curve) and the last list of points (curve)).") (($ $ (|List| (|List| (|Point| |#1|))) (|Boolean|) (|Boolean|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]], close1, close2)} adds a surface component to the \\spadtype{ThreeSpace},{} which is defined over a list of curves,{} in which each of these curves is a list of points. The boolean arguments \\spad{close1} and \\spad{close2} indicate how the surface is to be closed. Argument \\spad{close1} equal \\spad{true} means that each individual list (a curve) is to be closed,{} \\spadignore{i.e.} the last point of the list is to be connected to the first point. Argument \\spad{close2} equal \\spad{true} means that the boundary at one end of the surface is to be connected to the boundary at the other end,{} \\spadignore{i.e.} the boundaries are defined as the first list of points (curve) and the last list of points (curve).") (($ $ (|List| (|List| (|List| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)} adds a surface component to the \\spadtype{ThreeSpace} \\spad{s},{} which is defined over a rectangular domain of size WxH where \\spad{W} is the number of lists of points from the domain \\spad{PointDomain(R)} and \\spad{H} is the number of elements in each of those lists; lprops is the list of the subspace component properties for each curve list,{} and prop is the subspace component property by which the points are defined.") (($ $ (|List| (|List| (|Point| |#1|))) (|List| (|SubSpaceComponentProperty|)) (|SubSpaceComponentProperty|)) "\\spad{mesh(s,[[p0],[p1],...,[pn]],[props],prop)} adds a surface component,{} defined over a list curves which contains lists of points,{} to the \\spadtype{ThreeSpace} \\spad{s}; props is a list which contains the subspace component properties for each surface parameter,{} and \\spad{prop} is the subspace component property by which the points are defined.")) (|polygon?| (((|Boolean|) $) "\\spad{polygon?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single polygon component,{} or \\spad{false} otherwise.")) (|polygon| (((|List| (|Point| |#1|)) $) "\\spad{polygon(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single polygon component defined by a list of points,{} and if so,{} returns the list of points; An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{polygon([p0,p1,...,pn])} creates a polygon defined by a list of points,{} \\spad{p0} through pn,{} and returns a \\spadtype{ThreeSpace} whose component is the polygon.") (($ $ (|List| (|List| |#1|))) "\\spad{polygon(s,[[r0],[r1],...,[rn]])} adds a polygon component defined by a list of points \\spad{r0} through \\spad{rn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)} to the \\spadtype{ThreeSpace} \\spad{s},{} where \\spad{m} is the dimension of the points and \\spad{R} is the \\spadtype{Ring} over which the points are defined.") (($ $ (|List| (|Point| |#1|))) "\\spad{polygon(s,[p0,p1,...,pn])} adds a polygon component defined by a list of points,{} \\spad{p0} throught pn,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|closedCurve?| (((|Boolean|) $) "\\spad{closedCurve?(s)} returns \\spad{true} if the \\spadtype{ThreeSpace} \\spad{s} contains a single closed curve component,{} \\spadignore{i.e.} the first element of the curve is also the last element,{} or \\spad{false} otherwise.")) (|closedCurve| (((|List| (|Point| |#1|)) $) "\\spad{closedCurve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single closed curve component defined by a list of points in which the first point is also the last point,{} all of which are from the domain \\spad{PointDomain(m,R)} and if so,{} returns the list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{closedCurve(lp)} sets a list of points defined by the first element of \\spad{lp} through the last element of \\spad{lp} and back to the first elelment again and returns a \\spadtype{ThreeSpace} whose component is the closed curve defined by \\spad{lp}.") (($ $ (|List| (|List| |#1|))) "\\spad{closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]])} adds a closed curve component defined by a list of points \\spad{lr0} through \\spad{lrn},{} which are lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} in which the last element of the list of points contains a copy of the first element list,{} \\spad{lr0}. The closed curve is added to the \\spadtype{ThreeSpace},{} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{closedCurve(s,[p0,p1,...,pn,p0])} adds a closed curve component which is a list of points defined by the first element \\spad{p0} through the last element \\spad{pn} and back to the first element \\spad{p0} again,{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|curve?| (((|Boolean|) $) "\\spad{curve?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is a curve,{} \\spadignore{i.e.} has one component,{} a list of list of points,{} and returns \\spad{true} if it is,{} or \\spad{false} otherwise.")) (|curve| (((|List| (|Point| |#1|)) $) "\\spad{curve(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single curve defined by a list of points and if so,{} returns the curve,{} \\spadignore{i.e.} list of points. An error is signaled otherwise.") (($ (|List| (|Point| |#1|))) "\\spad{curve([p0,p1,p2,...,pn])} creates a space curve defined by the list of points \\spad{p0} through \\spad{pn},{} and returns the \\spadtype{ThreeSpace} whose component is the curve.") (($ $ (|List| (|List| |#1|))) "\\spad{curve(s,[[p0],[p1],...,[pn]])} adds a space curve which is a list of points \\spad{p0} through pn defined by lists of elements from the domain \\spad{PointDomain(m,R)},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined and \\spad{m} is the dimension of the points,{} to the \\spadtype{ThreeSpace} \\spad{s}.") (($ $ (|List| (|Point| |#1|))) "\\spad{curve(s,[p0,p1,...,pn])} adds a space curve component defined by a list of points \\spad{p0} through \\spad{pn},{} to the \\spadtype{ThreeSpace} \\spad{s}.")) (|point?| (((|Boolean|) $) "\\spad{point?(s)} queries whether the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of a single component which is a point and returns the boolean result.")) (|point| (((|Point| |#1|) $) "\\spad{point(s)} checks to see if the \\spadtype{ThreeSpace},{} \\spad{s},{} is composed of only a single point and if so,{} returns the point. An error is signaled otherwise.") (($ (|Point| |#1|)) "\\spad{point(p)} returns a \\spadtype{ThreeSpace} object which is composed of one component,{} the point \\spad{p}.") (($ $ (|NonNegativeInteger|)) "\\spad{point(s,i)} adds a point component which is placed into a component list of the \\spadtype{ThreeSpace},{} \\spad{s},{} at the index given by \\spad{i}.") (($ $ (|List| |#1|)) "\\spad{point(s,[x,y,z])} adds a point component defined by a list of elements which are from the \\spad{PointDomain(R)} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point elements are defined.") (($ $ (|Point| |#1|)) "\\spad{point(s,p)} adds a point component defined by the point,{} \\spad{p},{} specified as a list from \\spad{List(R)},{} to the \\spadtype{ThreeSpace},{} \\spad{s},{} where \\spad{R} is the \\spadtype{Ring} over which the point is defined.")) (|modifyPointData| (($ $ (|NonNegativeInteger|) (|Point| |#1|)) "\\spad{modifyPointData(s,i,p)} changes the point at the indexed location \\spad{i} in the \\spadtype{ThreeSpace},{} \\spad{s},{} to that of point \\spad{p}. This is useful for making changes to a point which has been transformed.")) (|enterPointData| (((|NonNegativeInteger|) $ (|List| (|Point| |#1|))) "\\spad{enterPointData(s,[p0,p1,...,pn])} adds a list of points from \\spad{p0} through pn to the \\spadtype{ThreeSpace},{} \\spad{s},{} and returns the index,{} to the starting point of the list.")) (|copy| (($ $) "\\spad{copy(s)} returns a new \\spadtype{ThreeSpace} that is an exact copy of \\spad{s}.")) (|composites| (((|List| $) $) "\\spad{composites(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single composite of \\spad{s}. If \\spad{s} has no composites defined (composites need to be explicitly created),{} the list returned is empty. Note that not all the components need to be part of a composite.")) (|components| (((|List| $) $) "\\spad{components(s)} takes the \\spadtype{ThreeSpace} \\spad{s},{} and creates a list containing a unique \\spadtype{ThreeSpace} for each single component of \\spad{s}. If \\spad{s} has no components defined,{} the list returned is empty.")) (|composite| (($ (|List| $)) "\\spad{composite([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that is a union of all the components from each \\spadtype{ThreeSpace} in the parameter list,{} grouped as a composite.")) (|merge| (($ $ $) "\\spad{merge(s1,s2)} will create a new \\spadtype{ThreeSpace} that has the components of \\spad{s1} and \\spad{s2}; Groupings of components into composites are maintained.") (($ (|List| $)) "\\spad{merge([s1,s2,...,sn])} will create a new \\spadtype{ThreeSpace} that has the components of all the ones in the list; Groupings of components into composites are maintained.")) (|numberOfComposites| (((|NonNegativeInteger|) $) "\\spad{numberOfComposites(s)} returns the number of supercomponents,{} or composites,{} in the \\spadtype{ThreeSpace},{} \\spad{s}; Composites are arbitrary groupings of otherwise distinct and unrelated components; A \\spadtype{ThreeSpace} need not have any composites defined at all and,{} outside of the requirement that no component can belong to more than one composite at a time,{} the definition and interpretation of composites are unrestricted.")) (|numberOfComponents| (((|NonNegativeInteger|) $) "\\spad{numberOfComponents(s)} returns the number of distinct object components in the indicated \\spadtype{ThreeSpace},{} \\spad{s},{} such as points,{} curves,{} polygons,{} and constructs.")) (|create3Space| (($ (|SubSpace| 3 |#1|)) "\\spad{create3Space(s)} creates a \\spadtype{ThreeSpace} object containing objects pre-defined within some \\spadtype{SubSpace} \\spad{s}.") (($) "\\spad{create3Space()} creates a \\spadtype{ThreeSpace} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1050) +(-1049) ((|constructor| (NIL "This domain represents a kind of base domain \\indented{2}{for Spad syntax domain.\\space{2}It merely exists as a kind of} \\indented{2}{of abstract base in object-oriented programming language.} \\indented{2}{However,{} this is not an abstract class.}"))) NIL NIL -(-1051) +(-1050) ((|constructor| (NIL "\\indented{1}{This package provides a simple Spad algebra parser.} Related Constructors: Syntax. See Also: Syntax.")) (|parse| (((|List| (|Syntax|)) (|String|)) "\\spad{parse(f)} parses the source file \\spad{f} (supposedly containing Spad algebras) and returns a List Syntax. The filename \\spad{f} is supposed to have the proper extension. Note that this function has the side effect of executing any system command contained in the file \\spad{f},{} even if it might not be meaningful."))) NIL NIL -(-1052) +(-1051) ((|constructor| (NIL "This category describes the exported \\indented{2}{signatures of the SpadAst domain.}")) (|autoCoerce| (((|Integer|) $) "\\spad{autoCoerce(s)} returns the Integer view of `s'. Left at the discretion of the compiler.") (((|String|) $) "\\spad{autoCoerce(s)} returns the String view of `s'. Left at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} returns the Identifier view of `s'. Left at the discretion of the compiler.") (((|IsAst|) $) "\\spad{autoCoerce(s)} returns the IsAst view of `s'. Left at the discretion of the compiler.") (((|HasAst|) $) "\\spad{autoCoerce(s)} returns the HasAst view of `s'. Left at the discretion of the compiler.") (((|CaseAst|) $) "\\spad{autoCoerce(s)} returns the CaseAst view of `s'. Left at the discretion of the compiler.") (((|ColonAst|) $) "\\spad{autoCoerce(s)} returns the ColoonAst view of `s'. Left at the discretion of the compiler.") (((|SuchThatAst|) $) "\\spad{autoCoerce(s)} returns the SuchThatAst view of `s'. Left at the discretion of the compiler.") (((|LetAst|) $) "\\spad{autoCoerce(s)} returns the LetAst view of `s'. Left at the discretion of the compiler.") (((|SequenceAst|) $) "\\spad{autoCoerce(s)} returns the SequenceAst view of `s'. Left at the discretion of the compiler.") (((|SegmentAst|) $) "\\spad{autoCoerce(s)} returns the SegmentAst view of `s'. Left at the discretion of the compiler.") (((|RestrictAst|) $) "\\spad{autoCoerce(s)} returns the RestrictAst view of `s'. Left at the discretion of the compiler.") (((|PretendAst|) $) "\\spad{autoCoerce(s)} returns the PretendAst view of `s'. Left at the discretion of the compiler.") (((|CoerceAst|) $) "\\spad{autoCoerce(s)} returns the CoerceAst view of `s'. Left at the discretion of the compiler.") (((|ReturnAst|) $) "\\spad{autoCoerce(s)} returns the ReturnAst view of `s'. Left at the discretion of the compiler.") (((|ExitAst|) $) "\\spad{autoCoerce(s)} returns the ExitAst view of `s'. Left at the discretion of the compiler.") (((|ConstructAst|) $) "\\spad{autoCoerce(s)} returns the ConstructAst view of `s'. Left at the discretion of the compiler.") (((|CollectAst|) $) "\\spad{autoCoerce(s)} returns the CollectAst view of `s'. Left at the discretion of the compiler.") (((|StepAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of \\spad{s}. Left at the discretion of the compiler.") (((|InAst|) $) "\\spad{autoCoerce(s)} returns the InAst view of `s'. Left at the discretion of the compiler.") (((|WhileAst|) $) "\\spad{autoCoerce(s)} returns the WhileAst view of `s'. Left at the discretion of the compiler.") (((|RepeatAst|) $) "\\spad{autoCoerce(s)} returns the RepeatAst view of `s'. Left at the discretion of the compiler.") (((|IfAst|) $) "\\spad{autoCoerce(s)} returns the IfAst view of `s'. Left at the discretion of the compiler.") (((|MappingAst|) $) "\\spad{autoCoerce(s)} returns the MappingAst view of `s'. Left at the discretion of the compiler.") (((|AttributeAst|) $) "\\spad{autoCoerce(s)} returns the AttributeAst view of `s'. Left at the discretion of the compiler.") (((|SignatureAst|) $) "\\spad{autoCoerce(s)} returns the SignatureAst view of `s'. Left at the discretion of the compiler.") (((|CapsuleAst|) $) "\\spad{autoCoerce(s)} returns the CapsuleAst view of `s'. Left at the discretion of the compiler.") (((|JoinAst|) $) "\\spad{autoCoerce(s)} returns the \\spadype{JoinAst} view of of the AST object \\spad{s}. Left at the discretion of the compiler.") (((|CategoryAst|) $) "\\spad{autoCoerce(s)} returns the CategoryAst view of `s'. Left at the discretion of the compiler.") (((|WhereAst|) $) "\\spad{autoCoerce(s)} returns the WhereAst view of `s'. Left at the discretion of the compiler.") (((|MacroAst|) $) "\\spad{autoCoerce(s)} returns the MacroAst view of `s'. Left at the discretion of the compiler.") (((|DefinitionAst|) $) "\\spad{autoCoerce(s)} returns the DefinitionAst view of `s'. Left at the discretion of the compiler.") (((|ImportAst|) $) "\\spad{autoCoerce(s)} returns the ImportAst view of `s'. Left at the discretion of the compiler.")) (|case| (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{s case Integer} holds if `s' represents an integer literal.") (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{s case String} holds if `s' represents a string literal.") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{s case Identifier} holds if `s' represents an identifier.") (((|Boolean|) $ (|[\|\|]| (|IsAst|))) "\\spad{s case IsAst} holds if `s' represents an is-expression.") (((|Boolean|) $ (|[\|\|]| (|HasAst|))) "\\spad{s case HasAst} holds if `s' represents a has-expression.") (((|Boolean|) $ (|[\|\|]| (|CaseAst|))) "\\spad{s case CaseAst} holds if `s' represents a case-expression.") (((|Boolean|) $ (|[\|\|]| (|ColonAst|))) "\\spad{s case ColonAst} holds if `s' represents a colon-expression.") (((|Boolean|) $ (|[\|\|]| (|SuchThatAst|))) "\\spad{s case SuchThatAst} holds if `s' represents a qualified-expression.") (((|Boolean|) $ (|[\|\|]| (|LetAst|))) "\\spad{s case LetAst} holds if `s' represents an assignment-expression.") (((|Boolean|) $ (|[\|\|]| (|SequenceAst|))) "\\spad{s case SequenceAst} holds if `s' represents a sequence-of-statements.") (((|Boolean|) $ (|[\|\|]| (|SegmentAst|))) "\\spad{s case SegmentAst} holds if `s' represents a segment-expression.") (((|Boolean|) $ (|[\|\|]| (|RestrictAst|))) "\\spad{s case RestrictAst} holds if `s' represents a restrict-expression.") (((|Boolean|) $ (|[\|\|]| (|PretendAst|))) "\\spad{s case PretendAst} holds if `s' represents a pretend-expression.") (((|Boolean|) $ (|[\|\|]| (|CoerceAst|))) "\\spad{s case ReturnAst} holds if `s' represents a coerce-expression.") (((|Boolean|) $ (|[\|\|]| (|ReturnAst|))) "\\spad{s case ReturnAst} holds if `s' represents a return-statement.") (((|Boolean|) $ (|[\|\|]| (|ExitAst|))) "\\spad{s case ExitAst} holds if `s' represents an exit-expression.") (((|Boolean|) $ (|[\|\|]| (|ConstructAst|))) "\\spad{s case ConstructAst} holds if `s' represents a list-expression.") (((|Boolean|) $ (|[\|\|]| (|CollectAst|))) "\\spad{s case CollectAst} holds if `s' represents a list-comprehension.") (((|Boolean|) $ (|[\|\|]| (|StepAst|))) "\\spad{s case StepAst} holds if \\spad{s} represents an arithmetic progression iterator.") (((|Boolean|) $ (|[\|\|]| (|InAst|))) "\\spad{s case InAst} holds if `s' represents a in-iterator") (((|Boolean|) $ (|[\|\|]| (|WhileAst|))) "\\spad{s case WhileAst} holds if `s' represents a while-iterator") (((|Boolean|) $ (|[\|\|]| (|RepeatAst|))) "\\spad{s case RepeatAst} holds if `s' represents an repeat-loop.") (((|Boolean|) $ (|[\|\|]| (|IfAst|))) "\\spad{s case IfAst} holds if `s' represents an if-statement.") (((|Boolean|) $ (|[\|\|]| (|MappingAst|))) "\\spad{s case MappingAst} holds if `s' represents a mapping type.") (((|Boolean|) $ (|[\|\|]| (|AttributeAst|))) "\\spad{s case AttributeAst} holds if `s' represents an attribute.") (((|Boolean|) $ (|[\|\|]| (|SignatureAst|))) "\\spad{s case SignatureAst} holds if `s' represents a signature export.") (((|Boolean|) $ (|[\|\|]| (|CapsuleAst|))) "\\spad{s case CapsuleAst} holds if `s' represents a domain capsule.") (((|Boolean|) $ (|[\|\|]| (|JoinAst|))) "\\spad{s case JoinAst} holds is the syntax object \\spad{s} denotes the join of several categories.") (((|Boolean|) $ (|[\|\|]| (|CategoryAst|))) "\\spad{s case CategoryAst} holds if `s' represents an unnamed category.") (((|Boolean|) $ (|[\|\|]| (|WhereAst|))) "\\spad{s case WhereAst} holds if `s' represents an expression with local definitions.") (((|Boolean|) $ (|[\|\|]| (|MacroAst|))) "\\spad{s case MacroAst} holds if `s' represents a macro definition.") (((|Boolean|) $ (|[\|\|]| (|DefinitionAst|))) "\\spad{s case DefinitionAst} holds if `s' represents a definition.") (((|Boolean|) $ (|[\|\|]| (|ImportAst|))) "\\spad{s case ImportAst} holds if `s' represents an `import' statement."))) NIL NIL -(-1053) +(-1052) ((|constructor| (NIL "SpecialOutputPackage allows FORTRAN,{} Tex and \\indented{2}{Script Formula Formatter output from programs.}")) (|outputAsTex| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsTex(l)} sends (for each expression in the list \\spad{l}) output in Tex format to the destination as defined by \\spadsyscom{set output tex}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsTex(o)} sends output \\spad{o} in Tex format to the destination defined by \\spadsyscom{set output tex}.")) (|outputAsScript| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsScript(l)} sends (for each expression in the list \\spad{l}) output in Script Formula Formatter format to the destination defined. by \\spadsyscom{set output forumula}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsScript(o)} sends output \\spad{o} in Script Formula Formatter format to the destination defined by \\spadsyscom{set output formula}.")) (|outputAsFortran| (((|Void|) (|List| (|OutputForm|))) "\\spad{outputAsFortran(l)} sends (for each expression in the list \\spad{l}) output in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}.") (((|Void|) (|OutputForm|)) "\\spad{outputAsFortran(o)} sends output \\spad{o} in FORTRAN format.") (((|Void|) (|String|) (|OutputForm|)) "\\spad{outputAsFortran(v,o)} sends output \\spad{v} = \\spad{o} in FORTRAN format to the destination defined by \\spadsyscom{set output fortran}."))) NIL NIL -(-1054) +(-1053) ((|constructor| (NIL "Category for the other special functions.")) (|airyBi| (($ $) "\\spad{airyBi(x)} is the Airy function \\spad{Bi(x)}.")) (|airyAi| (($ $) "\\spad{airyAi(x)} is the Airy function \\spad{Ai(x)}.")) (|besselK| (($ $ $) "\\spad{besselK(v,z)} is the modified Bessel function of the second kind.")) (|besselI| (($ $ $) "\\spad{besselI(v,z)} is the modified Bessel function of the first kind.")) (|besselY| (($ $ $) "\\spad{besselY(v,z)} is the Bessel function of the second kind.")) (|besselJ| (($ $ $) "\\spad{besselJ(v,z)} is the Bessel function of the first kind.")) (|polygamma| (($ $ $) "\\spad{polygamma(k,x)} is the \\spad{k-th} derivative of \\spad{digamma(x)},{} (often written \\spad{psi(k,x)} in the literature).")) (|digamma| (($ $) "\\spad{digamma(x)} is the logarithmic derivative of \\spad{Gamma(x)} (often written \\spad{psi(x)} in the literature).")) (|Beta| (($ $ $) "\\spad{Beta(x,y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $ $) "\\spad{Gamma(a,x)} is the incomplete Gamma function.") (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}."))) NIL NIL -(-1055 V C) +(-1054 V C) ((|constructor| (NIL "This domain exports a modest implementation for the vertices of splitting trees. These vertices are called here splitting nodes. Every of these nodes store 3 informations. The first one is its value,{} that is the current expression to evaluate. The second one is its condition,{} that is the hypothesis under which the value has to be evaluated. The last one is its status,{} that is a boolean flag which is \\spad{true} iff the value is the result of its evaluation under its condition. Two splitting vertices are equal iff they have the sane values and the same conditions (so their status do not matter).")) (|subNode?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNode?(\\spad{n1},{}\\spad{n2},{}\\spad{o2})} returns \\spad{true} iff \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}")) (|infLex?| (((|Boolean|) $ $ (|Mapping| (|Boolean|) |#1| |#1|) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{infLex?(\\spad{n1},{}\\spad{n2},{}\\spad{o1},{}\\spad{o2})} returns \\spad{true} iff \\axiom{\\spad{o1}(value(\\spad{n1}),{}value(\\spad{n2}))} or \\axiom{value(\\spad{n1}) = value(\\spad{n2})} and \\axiom{\\spad{o2}(condition(\\spad{n1}),{}condition(\\spad{n2}))}.")) (|setEmpty!| (($ $) "\\axiom{setEmpty!(\\spad{n})} replaces \\spad{n} by \\axiom{empty()\\$\\%}.")) (|setStatus!| (($ $ (|Boolean|)) "\\axiom{setStatus!(\\spad{n},{}\\spad{b})} returns \\spad{n} whose status has been replaced by \\spad{b} if it is not empty,{} else an error is produced.")) (|setCondition!| (($ $ |#2|) "\\axiom{setCondition!(\\spad{n},{}\\spad{t})} returns \\spad{n} whose condition has been replaced by \\spad{t} if it is not empty,{} else an error is produced.")) (|setValue!| (($ $ |#1|) "\\axiom{setValue!(\\spad{n},{}\\spad{v})} returns \\spad{n} whose value has been replaced by \\spad{v} if it is not empty,{} else an error is produced.")) (|copy| (($ $) "\\axiom{copy(\\spad{n})} returns a copy of \\spad{n}.")) (|construct| (((|List| $) |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v},{}lt)} returns the same as \\axiom{[construct(\\spad{v},{}\\spad{t}) for \\spad{t} in lt]}") (((|List| $) (|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|)))) "\\axiom{construct(lvt)} returns the same as \\axiom{[construct(vt.val,{}vt.tower) for vt in lvt]}") (($ (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) "\\axiom{construct(vt)} returns the same as \\axiom{construct(vt.val,{}vt.tower)}") (($ |#1| |#2|) "\\axiom{construct(\\spad{v},{}\\spad{t})} returns the same as \\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{false})}") (($ |#1| |#2| (|Boolean|)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{b})} returns the non-empty node with value \\spad{v},{} condition \\spad{t} and flag \\spad{b}")) (|status| (((|Boolean|) $) "\\axiom{status(\\spad{n})} returns the status of the node \\spad{n}.")) (|condition| ((|#2| $) "\\axiom{condition(\\spad{n})} returns the condition of the node \\spad{n}.")) (|value| ((|#1| $) "\\axiom{value(\\spad{n})} returns the value of the node \\spad{n}.")) (|empty?| (((|Boolean|) $) "\\axiom{empty?(\\spad{n})} returns \\spad{true} iff the node \\spad{n} is \\axiom{empty()\\$\\%}.")) (|empty| (($) "\\axiom{empty()} returns the same as \\axiom{[empty()\\$\\spad{V},{}empty()\\$\\spad{C},{}\\spad{false}]\\$\\%}"))) NIL NIL -(-1056 V C) +(-1055 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,{}ls,{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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,{}ls)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in 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|))) $) "\\axiom{result(a)} where \\axiom{ls} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$VT for \\spad{s} in 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},{}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 ls]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}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 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") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| (-1055 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1055) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014))) (OR (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-1014)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-553 (-773)))) (|HasCategory| (-1055 |#1| |#2|) (QUOTE (-72)))) -(-1057 |ndim| R) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| (-1054 |#1| |#2|) (|%list| (QUOTE -260) (|%list| (QUOTE -1054) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013))) (OR (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-1013)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-552 (-772)))) (|HasCategory| (-1054 |#1| |#2|) (QUOTE (-72)))) +(-1056 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}.")) (|new| (($ |#2|) "\\spad{new(c)} constructs a new \\spadtype{SquareMatrix} object of dimension \\spad{ndim} with initial entries equal to \\spad{c}."))) -((-3993 . T) (-3985 |has| |#2| (-6 (-3998 "*"))) (-3996 . T) (-3990 . T) (-3991 . T)) -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (QUOTE (-812 (-1091)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3998 #1="*"))) (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-951 (-485)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-581 (-485)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-554 (-474)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3998 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-810 (-1091))))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) -(-1058 S) +((-3992 . T) (-3984 |has| |#2| (-6 (-3997 "*"))) (-3995 . T) (-3989 . T) (-3990 . T)) +((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-189))) (|HasAttribute| |#2| (QUOTE (-3997 #1="*"))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|))))) (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| |#2| (QUOTE (-258))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-312))) (OR (|HasAttribute| |#2| (QUOTE (-3997 #1#))) (|HasCategory| |#2| (QUOTE (-190))) (|HasCategory| |#2| (QUOTE (-809 (-1090))))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| |#2| (QUOTE (-146)))) +(-1057 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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL -(-1059) +(-1058) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|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{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{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\",{}\"*\")} 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}) == 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|) $ $) "\\spad{prefix?(s,t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) == reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-1060 R E V P TS) +(-1059 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'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{TS}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) NIL NIL -(-1061 R E V P) +(-1060 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(lp,{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(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(lp,{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(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},{}ts,{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) -(-1062) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-1061) ((|constructor| (NIL "The category of all semiring structures,{} \\spadignore{e.g.} triples (\\spad{D},{}+,{}*) such that (\\spad{D},{}+) is an Abelian monoid and (\\spad{D},{}*) is a monoid with the following laws:"))) NIL NIL -(-1063 S) +(-1062 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}."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1064 A S) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1063 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}.")) (|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.")) (|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 -(-1065 S) +(-1064 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}.")) (|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.")) (|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 -(-1066 |Key| |Ent| |dent|) +(-1065 |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."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) -(-1067) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772))))) +(-1066) ((|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 non-fiinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline")) (|nextItem| (((|Maybe| $) $) "\\spad{nextItem(x)} returns the next item,{} or \\spad{failed} if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL NIL -(-1068) +(-1067) ((|constructor| (NIL "This domain represents an arithmetic progression iterator syntax.")) (|step| (((|SpadAst|) $) "\\spad{step(i)} returns the Spad AST denoting the step of the arithmetic progression represented by the iterator \\spad{i}.")) (|upperBound| (((|Maybe| (|SpadAst|)) $) "If the set of values assumed by the iteration variable is bounded from above,{} \\spad{upperBound(i)} returns the upper bound. Otherwise,{} its returns \\spad{nothing}.")) (|lowerBound| (((|SpadAst|) $) "\\spad{lowerBound(i)} returns the lower bound on the values assumed by the iteration variable.")) (|iterationVar| (((|Identifier|) $) "\\spad{iterationVar(i)} returns the name of the iterating variable of the arithmetic progression iterator \\spad{i}."))) NIL NIL -(-1069 |Coef|) +(-1068 |Coef|) ((|constructor| (NIL "This package computes infinite products of Taylor series over an integral domain of characteristic 0. Here Taylor series are represented by streams of Taylor coefficients.")) (|generalInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),a,d)} computes \\spad{product(n=a,a+d,a+2*d,...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,3,5...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,4,6...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,2,3...,f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-1070 S) +(-1069 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,s)} returns \\spad{[x0,x1,...,x(n)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,s)} returns \\spad{[x0,x1,...,x(n-1)]} where \\spad{s = [x0,x1,x2,..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,x) = [x,f(x),f(f(x)),...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),f(),f(),...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,n,y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,s) = concat(a,s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-3997 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1071 S) +((-3996 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1070 S) ((|constructor| (NIL "Functions defined on streams with entries in one set.")) (|concat| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{concat(u)} returns the left-to-right concatentation of the streams in \\spad{u}. Note: \\spad{concat(u) = reduce(concat,u)}."))) NIL NIL -(-1072 A B) +(-1071 A B) ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|reduce| ((|#2| |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{reduce(b,f,u)},{} where \\spad{u} is a finite stream \\spad{[x0,x1,...,xn]},{} returns the value \\spad{r(n)} computed as follows: \\spad{r0 = f(x0,b), r1 = f(x1,r0),..., r(n) = f(xn,r(n-1))}.")) (|scan| (((|Stream| |#2|) |#2| (|Mapping| |#2| |#1| |#2|) (|Stream| |#1|)) "\\spad{scan(b,h,[x0,x1,x2,...])} returns \\spad{[y0,y1,y2,...]},{} where \\spad{y0 = h(x0,b)},{} \\spad{y1 = h(x1,y0)},{}\\spad{...} \\spad{yn = h(xn,y(n-1))}.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|Stream| |#1|)) "\\spad{map(f,s)} returns a stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{s}. Note: \\spad{map(f,[x0,x1,x2,...]) = [f(x0),f(x1),f(x2),..]}."))) NIL NIL -(-1073 A B C) +(-1072 A B C) ((|constructor| (NIL "Functions defined on streams with entries in three sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|Stream| |#2|)) "\\spad{map(f,st1,st2)} returns the stream whose elements are the function \\spad{f} applied to the corresponding elements of \\spad{st1} and \\spad{st2}. Note: \\spad{map(f,[x0,x1,x2,..],[y0,y1,y2,..]) = [f(x0,y0),f(x1,y1),..]}."))) NIL NIL -(-1074) +(-1073) ((|constructor| (NIL "This is the domain of character strings.")) (|string| (($ (|Identifier|)) "\\spad{string id} is the string representation of the identifier \\spad{id}") (($ (|DoubleFloat|)) "\\spad{string f} returns the decimal representation of \\spad{f} in a string") (($ (|Integer|)) "\\spad{string i} returns the decimal representation of \\spad{i} in a string"))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-757)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) (|HasCategory| (-117) (QUOTE (-553 (-773)))) (|HasCategory| (-117) (QUOTE (-554 (-474)))) (OR (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-117) (QUOTE (-757))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| (-117) (QUOTE (-1014))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1014))))) -(-1075 |Entry|) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-756)))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) (|HasCategory| (-117) (QUOTE (-552 (-772)))) (|HasCategory| (-117) (QUOTE (-553 (-473)))) (OR (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-117) (QUOTE (-756))) (OR (|HasCategory| (-117) (QUOTE (-72))) (|HasCategory| (-117) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| (-117) (QUOTE (-1013))) (|HasCategory| (-117) (QUOTE (-72))) (-12 (|HasCategory| (-117) (QUOTE (-260 (-117)))) (|HasCategory| (-117) (QUOTE (-1013))))) +(-1074 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3861 (-1074))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-1014))) (|HasCategory| (-1074) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 (-1074)) (|:| |entry| |#1|)) (QUOTE (-553 (-773))))) -(-1076 A) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (QUOTE (|:| -3860 (-1073))) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#1|))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-1013))) (|HasCategory| (-1073) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-72))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-72)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 (-1073)) (|:| |entry| |#1|)) (QUOTE (-552 (-772))))) +(-1075 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,r,g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,a1,..],[b0,b1,..])} returns \\spad{[a0/b0,a1/b1,..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,0>,b<0,1>,...],[b<1,0>,b<1,1>,.],...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,j=0 to infinity,b<i,j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,[a0,a1,a2,...]) = [a,a0,a1/2,a2/3,...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,b,st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,b,st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,0>,a<0,1>,..],[a<1,0>,a<1,1>,..],[a<2,0>,a<2,1>,..],..]} and \\spad{addiag(x) = [b<0,b<1>,...], then b<k> = sum(i+j=k,a<i,j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient should be invertible.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,[a0,a1,a2,..])} returns \\spad{[f(0)*a0,f(1)*a1,f(2)*a2,..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,a1,a2,...])} returns \\spad{[a1,2 a2,3 a3,...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,a1,..],[b0,b1,..])} returns \\spad{[a0*b0,a1*b1,..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,n+2,n+4,...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,n+1,n+2,...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by 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 b: \\spad{[a0,a1,...] * [b0,b1,...] = [c0,c1,...]} where \\spad{ck = sum(i + j = k,ai * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,a1,...] = [- a0,- a1,...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] - [b0,b1,..] = [a0 - b0,a1 - b1,..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,a1,..] + [b0,b1,..] = [a0 + b0,a1 + b1,..]}"))) NIL -((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) -(-1077 |Coef|) +((|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) +(-1076 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctions implements transcendental functions on Taylor series,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|sinhcosh| (((|Record| (|:| |sinh| (|Stream| |#1|)) (|:| |cosh| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sinhcosh(st)} returns a record containing the hyperbolic sine and cosine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (|sincos| (((|Record| (|:| |sin| (|Stream| |#1|)) (|:| |cos| (|Stream| |#1|))) (|Stream| |#1|)) "\\spad{sincos(st)} returns a record containing the sine and cosine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1078 |Coef|) +(-1077 |Coef|) ((|constructor| (NIL "StreamTranscendentalFunctionsNonCommutative implements transcendental functions on Taylor series over a non-commutative ring,{} where a Taylor series is represented by a stream of its coefficients.")) (|acsch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsch(st)} computes the inverse hyperbolic cosecant of a power series \\spad{st}.")) (|asech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asech(st)} computes the inverse hyperbolic secant of a power series \\spad{st}.")) (|acoth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acoth(st)} computes the inverse hyperbolic cotangent of a power series \\spad{st}.")) (|atanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atanh(st)} computes the inverse hyperbolic tangent of a power series \\spad{st}.")) (|acosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acosh(st)} computes the inverse hyperbolic cosine of a power series \\spad{st}.")) (|asinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asinh(st)} computes the inverse hyperbolic sine of a power series \\spad{st}.")) (|csch| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csch(st)} computes the hyperbolic cosecant of a power series \\spad{st}.")) (|sech| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sech(st)} computes the hyperbolic secant of a power series \\spad{st}.")) (|coth| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{coth(st)} computes the hyperbolic cotangent of a power series \\spad{st}.")) (|tanh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tanh(st)} computes the hyperbolic tangent of a power series \\spad{st}.")) (|cosh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cosh(st)} computes the hyperbolic cosine of a power series \\spad{st}.")) (|sinh| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sinh(st)} computes the hyperbolic sine of a power series \\spad{st}.")) (|acsc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acsc(st)} computes arccosecant of a power series \\spad{st}.")) (|asec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asec(st)} computes arcsecant of a power series \\spad{st}.")) (|acot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acot(st)} computes arccotangent of a power series \\spad{st}.")) (|atan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{atan(st)} computes arctangent of a power series \\spad{st}.")) (|acos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{acos(st)} computes arccosine of a power series \\spad{st}.")) (|asin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{asin(st)} computes arcsine of a power series \\spad{st}.")) (|csc| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{csc(st)} computes cosecant of a power series \\spad{st}.")) (|sec| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sec(st)} computes secant of a power series \\spad{st}.")) (|cot| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cot(st)} computes cotangent of a power series \\spad{st}.")) (|tan| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{tan(st)} computes tangent of a power series \\spad{st}.")) (|cos| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{cos(st)} computes cosine of a power series \\spad{st}.")) (|sin| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{sin(st)} computes sine of a power series \\spad{st}.")) (** (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{st1 ** st2} computes the power of a power series \\spad{st1} by another power series \\spad{st2}.")) (|log| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{log(st)} computes the log of a power series.")) (|exp| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{exp(st)} computes the exponential of a power series \\spad{st}."))) NIL NIL -(-1079 R UP) +(-1078 R UP) ((|constructor| (NIL "This package computes the subresultants of two polynomials which is needed for the `Lazard Rioboo' enhancement to Tragers integrations formula For efficiency reasons this has been rewritten to call Lionel Ducos package which is currently the best one. \\blankline")) (|primitivePart| ((|#2| |#2| |#1|) "\\spad{primitivePart(p, q)} reduces the coefficient of \\spad{p} modulo \\spad{q},{} takes the primitive part of the result,{} and ensures that the leading coefficient of that result is monic.")) (|subresultantVector| (((|PrimitiveArray| |#2|) |#2| |#2|) "\\spad{subresultantVector(p, q)} returns \\spad{[p0,...,pn]} where \\spad{pi} is the \\spad{i}-th subresultant of \\spad{p} and \\spad{q}. In particular,{} \\spad{p0 = resultant(p, q)}."))) NIL ((|HasCategory| |#1| (QUOTE (-258)))) -(-1080 |n| R) +(-1079 |n| R) ((|constructor| (NIL "This domain \\undocumented")) (|pointData| (((|List| (|Point| |#2|)) $) "\\spad{pointData(s)} returns the list of points from the point data field of the 3 dimensional subspace \\spad{s}.")) (|parent| (($ $) "\\spad{parent(s)} returns the subspace which is the parent of the indicated 3 dimensional subspace \\spad{s}. If \\spad{s} is the top level subspace an error message is returned.")) (|level| (((|NonNegativeInteger|) $) "\\spad{level(s)} returns a non negative integer which is the current level field of the indicated 3 dimensional subspace \\spad{s}.")) (|extractProperty| (((|SubSpaceComponentProperty|) $) "\\spad{extractProperty(s)} returns the property of domain \\spadtype{SubSpaceComponentProperty} of the indicated 3 dimensional subspace \\spad{s}.")) (|extractClosed| (((|Boolean|) $) "\\spad{extractClosed(s)} returns the \\spadtype{Boolean} value of the closed property for the indicated 3 dimensional subspace \\spad{s}. If the property is closed,{} \\spad{True} is returned,{} otherwise \\spad{False} is returned.")) (|extractIndex| (((|NonNegativeInteger|) $) "\\spad{extractIndex(s)} returns a non negative integer which is the current index of the 3 dimensional subspace \\spad{s}.")) (|extractPoint| (((|Point| |#2|) $) "\\spad{extractPoint(s)} returns the point which is given by the current index location into the point data field of the 3 dimensional subspace \\spad{s}.")) (|traverse| (($ $ (|List| (|NonNegativeInteger|))) "\\spad{traverse(s,li)} follows the branch list of the 3 dimensional subspace,{} \\spad{s},{} along the path dictated by the list of non negative integers,{} \\spad{li},{} which points to the component which has been traversed to. The subspace,{} \\spad{s},{} is returned,{} where \\spad{s} is now the subspace pointed to by \\spad{li}.")) (|defineProperty| (($ $ (|List| (|NonNegativeInteger|)) (|SubSpaceComponentProperty|)) "\\spad{defineProperty(s,li,p)} defines the component property in the 3 dimensional subspace,{} \\spad{s},{} to be that of \\spad{p},{} where \\spad{p} is of the domain \\spadtype{SubSpaceComponentProperty}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose property is being defined. The subspace,{} \\spad{s},{} is returned with the component property definition.")) (|closeComponent| (($ $ (|List| (|NonNegativeInteger|)) (|Boolean|)) "\\spad{closeComponent(s,li,b)} sets the property of the component in the 3 dimensional subspace,{} \\spad{s},{} to be closed if \\spad{b} is \\spad{true},{} or open if \\spad{b} is \\spad{false}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component whose closed property is to be set. The subspace,{} \\spad{s},{} is returned with the component property modification.")) (|modifyPoint| (($ $ (|NonNegativeInteger|) (|Point| |#2|)) "\\spad{modifyPoint(s,ind,p)} modifies the point referenced by the index location,{} \\spad{ind},{} by replacing it with the point,{} \\spad{p} in the 3 dimensional subspace,{} \\spad{s}. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{modifyPoint(s,li,i)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point indicated by the index location,{} \\spad{i}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{modifyPoint(s,li,p)} replaces an existing point in the 3 dimensional subspace,{} \\spad{s},{} with the 4 dimensional point,{} \\spad{p}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the existing point is to be modified. An error message occurs if \\spad{s} is empty,{} otherwise the subspace \\spad{s} is returned with the point modification.")) (|addPointLast| (($ $ $ (|Point| |#2|) (|NonNegativeInteger|)) "\\spad{addPointLast(s,s2,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. \\spad{s2} point to the end of the subspace \\spad{s}. \\spad{n} is the path in the \\spad{s2} component. The subspace \\spad{s} is returned with the additional point.")) (|addPoint2| (($ $ (|Point| |#2|)) "\\spad{addPoint2(s,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The subspace \\spad{s} is returned with the additional point.")) (|addPoint| (((|NonNegativeInteger|) $ (|Point| |#2|)) "\\spad{addPoint(s,p)} adds the point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s},{} and returns the new total number of points in \\spad{s}.") (($ $ (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{addPoint(s,li,i)} adds the 4 dimensional point indicated by the index location,{} \\spad{i},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.") (($ $ (|List| (|NonNegativeInteger|)) (|Point| |#2|)) "\\spad{addPoint(s,li,p)} adds the 4 dimensional point,{} \\spad{p},{} to the 3 dimensional subspace,{} \\spad{s}. The list of non negative integers,{} \\spad{li},{} dictates the path to follow,{} or,{} to look at it another way,{} points to the component in which the point is to be added. It's length should range from 0 to \\spad{n - 1} where \\spad{n} is the dimension of the subspace. If the length is \\spad{n - 1},{} then a specific lowest level component is being referenced. If it is less than \\spad{n - 1},{} then some higher level component (0 indicates top level component) is being referenced and a component of that level with the desired point is created. The subspace \\spad{s} is returned with the additional point.")) (|separate| (((|List| $) $) "\\spad{separate(s)} makes each of the components of the \\spadtype{SubSpace},{} \\spad{s},{} into a list of separate and distinct subspaces and returns the list.")) (|merge| (($ (|List| $)) "\\spad{merge(ls)} a list of subspaces,{} \\spad{ls},{} into one subspace.") (($ $ $) "\\spad{merge(s1,s2)} the subspaces \\spad{s1} and \\spad{s2} into a single subspace.")) 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(|sum| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{sum(f(n), n = a..b)} returns \\spad{f}(a) + \\spad{f}(\\spad{a+1}) + ... + \\spad{f}(\\spad{b}).") ((|#2| |#2| (|Symbol|)) "\\spad{sum(a(n), n)} returns A(\\spad{n}) such that A(\\spad{n+1}) - A(\\spad{n}) = a(\\spad{n})."))) NIL NIL -(-1085 R) +(-1084 R) ((|constructor| (NIL "Computes sums of rational functions.")) (|sum| (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|SegmentBinding| (|Fraction| (|Polynomial| |#1|)))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|SegmentBinding| (|Polynomial| |#1|))) "\\spad{sum(f(n), n = a..b)} returns \\spad{f(a) + f(a+1) + ... f(b)}.") (((|Union| (|Fraction| (|Polynomial| |#1|)) (|Expression| |#1|)) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}.") (((|Fraction| (|Polynomial| |#1|)) (|Polynomial| |#1|) (|Symbol|)) "\\spad{sum(a(n), n)} returns \\spad{A} which is the indefinite sum of \\spad{a} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{A(n+1) - A(n) = a(n)}."))) NIL NIL -(-1086 R) +(-1085 R) ((|constructor| (NIL "This domain represents univariate polynomials over arbitrary (not necessarily commutative) coefficient rings. The variable is unspecified so that the variable displays as \\spad{?} on output. If it is necessary to specify the variable name,{} use type \\spadtype{UnivariatePolynomial}. The representation is sparse in the sense that only non-zero terms are represented.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\spad{fmecg(p1,e,r,p2)} finds \\spad{X} : \\spad{p1} - \\spad{r} * X**e * \\spad{p2}")) (|outputForm| (((|OutputForm|) $ (|OutputForm|)) "\\spad{outputForm(p,var)} converts the SparseUnivariatePolynomial \\spad{p} to an output form (see \\spadtype{OutputForm}) printed as a polynomial in the output form variable."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-330)))) (|HasCategory| (-995) (QUOTE (-797 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-797 (-485)))) (|HasCategory| (-995) (QUOTE (-797 (-485))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-330))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-801 (-485))))) (|HasCategory| (-995) (QUOTE (-554 (-801 (-485)))))) (-12 (|HasCategory| |#1| (QUOTE (-554 (-474)))) (|HasCategory| (-995) (QUOTE (-554 (-474))))) (|HasCategory| |#1| (QUOTE (-581 (-485)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-822)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-822)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1067))) (|HasCategory| |#1| (QUOTE (-812 (-1091)))) (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3994)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-822))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) -(-1087 R S) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3991 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#1| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#1| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#1| (QUOTE (-580 (-484)))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-821)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (|HasCategory| |#1| (QUOTE (-821)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-1066))) (|HasCategory| |#1| (QUOTE (-811 (-1090)))) (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasCategory| |#1| (QUOTE (-189))) (|HasCategory| |#1| (QUOTE (-190))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#1| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#1| (QUOTE (-118))))) +(-1086 R S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from sparse univariate polynomial over \\spad{R} to a sparse univariate polynomial over \\spad{S}. Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|SparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1088 E OV R P) +(-1087 E OV R P) ((|constructor| (NIL "\\indented{1}{SupFractionFactorize} contains the factor function for univariate polynomials over the quotient field of a ring \\spad{S} such that the package MultivariateFactorize works for \\spad{S}")) (|squareFree| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{squareFree(p)} returns the square-free factorization of the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}. Each factor has no repeated roots and the factors are pairwise relatively prime.")) (|factor| (((|Factored| (|SparseUnivariatePolynomial| (|Fraction| |#4|))) (|SparseUnivariatePolynomial| (|Fraction| |#4|))) "\\spad{factor(p)} factors the univariate polynomial \\spad{p} with coefficients which are fractions of polynomials over \\spad{R}."))) NIL NIL -(-1089 |Coef| |var| |cen|) +(-1088 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Puiseux series in one variable \\indented{2}{\\spadtype{SparseUnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) -(-1090 |Coef| |var| |cen|) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) +(-1089 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Taylor series in one variable \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries} is a domain representing Taylor} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spadtype{SparseUnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor} \\indented{2}{series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) -(-1091) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) +(-1090) ((|constructor| (NIL "Basic and scripted symbols.")) (|sample| (($) "\\spad{sample()} returns a sample of \\%")) (|list| (((|List| $) $) "\\spad{list(sy)} takes a scripted symbol and produces a list of the name followed by the scripts.")) (|string| (((|String|) $) "\\spad{string(s)} converts the symbol \\spad{s} to a string. Error: if the symbol is subscripted.")) (|elt| (($ $ (|List| (|OutputForm|))) "\\spad{elt(s,[a1,...,an])} or \\spad{s}([\\spad{a1},{}...,{}an]) returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|argscript| (($ $ (|List| (|OutputForm|))) "\\spad{argscript(s, [a1,...,an])} returns \\spad{s} arg-scripted by \\spad{[a1,...,an]}.")) (|superscript| (($ $ (|List| (|OutputForm|))) "\\spad{superscript(s, [a1,...,an])} returns \\spad{s} superscripted by \\spad{[a1,...,an]}.")) (|subscript| (($ $ (|List| (|OutputForm|))) "\\spad{subscript(s, [a1,...,an])} returns \\spad{s} subscripted by \\spad{[a1,...,an]}.")) (|script| (($ $ (|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|))))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}.") (($ $ (|List| (|List| (|OutputForm|)))) "\\spad{script(s, [a,b,c,d,e])} returns \\spad{s} with subscripts a,{} superscripts \\spad{b},{} pre-superscripts \\spad{c},{} pre-subscripts \\spad{d},{} and argument-scripts \\spad{e}. Omitted components are taken to be empty. For example,{} \\spad{script(s, [a,b,c])} is equivalent to \\spad{script(s,[a,b,c,[],[]])}.")) (|scripts| (((|Record| (|:| |sub| (|List| (|OutputForm|))) (|:| |sup| (|List| (|OutputForm|))) (|:| |presup| (|List| (|OutputForm|))) (|:| |presub| (|List| (|OutputForm|))) (|:| |args| (|List| (|OutputForm|)))) $) "\\spad{scripts(s)} returns all the scripts of \\spad{s}.")) (|scripted?| (((|Boolean|) $) "\\spad{scripted?(s)} is \\spad{true} if \\spad{s} has been given any scripts.")) (|name| (($ $) "\\spad{name(s)} returns \\spad{s} without its scripts.")) (|resetNew| (((|Void|)) "\\spad{resetNew()} resets the internals counters that new() and new(\\spad{s}) use to return distinct symbols every time.")) (|new| (($ $) "\\spad{new(s)} returns a new symbol whose name starts with \\%\\spad{s}.") (($) "\\spad{new()} returns a new symbol whose name starts with \\%."))) NIL NIL -(-1092 R) +(-1091 R) ((|constructor| (NIL "Computes all the symmetric functions in \\spad{n} variables.")) (|symFunc| (((|Vector| |#1|) |#1| (|PositiveInteger|)) "\\spad{symFunc(r, n)} returns the vector of the elementary symmetric functions in \\spad{[r,r,...,r]} \\spad{n} times.") (((|Vector| |#1|) (|List| |#1|)) "\\spad{symFunc([r1,...,rn])} returns the vector of the elementary symmetric functions in the \\spad{ri's}: \\spad{[r1 + ... + rn, r1 r2 + ... + r(n-1) rn, ..., r1 r2 ... rn]}."))) NIL NIL -(-1093 R) +(-1092 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-6 -3994)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485)))))) (|HasCategory| |#1| (QUOTE (-951 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-951 (-485)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| (-885) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3994))) -(-1094) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-6 -3993)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (OR (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#1| (QUOTE (-950 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-950 (-484)))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-392))) (-12 (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| (-884) (QUOTE (-104)))) (|HasAttribute| |#1| (QUOTE -3993))) +(-1093) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1="void")) (|Symbol|) $) "\\spad{returnTypeOf(f,tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#))) "\\spad{returnType!(f,t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| #1#)) $) "\\spad{returnType!(f,t,tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,l,tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,t,asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,t,asp,tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL NIL -(-1095) +(-1094) ((|constructor| (NIL "Create and manipulate a symbol table for generated FORTRAN code")) (|symbolTable| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| (|FortranType|))))) "\\spad{symbolTable(l)} creates a symbol table from the elements of \\spad{l}.")) (|printTypes| (((|Void|) $) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|newTypeLists| (((|SExpression|) $) "\\spad{newTypeLists(x)} \\undocumented")) (|typeLists| (((|List| (|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|))))))))) $) "\\spad{typeLists(tab)} returns a list of lists of types of objects in \\spad{tab}")) (|externalList| (((|List| (|Symbol|)) $) "\\spad{externalList(tab)} returns a list of all the external symbols in \\spad{tab}")) (|typeList| (((|List| (|Union| (|:| |name| (|Symbol|)) (|:| |bounds| (|List| (|Union| (|:| S (|Symbol|)) (|:| P (|Polynomial| (|Integer|)))))))) (|FortranScalarType|) $) "\\spad{typeList(t,tab)} returns a list of all the objects of type \\spad{t} in \\spad{tab}")) (|parametersOf| (((|List| (|Symbol|)) $) "\\spad{parametersOf(tab)} returns a list of all the symbols declared in \\spad{tab}")) (|fortranTypeOf| (((|FortranType|) (|Symbol|) $) "\\spad{fortranTypeOf(u,tab)} returns the type of \\spad{u} in \\spad{tab}")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) $) "\\spad{declare!(u,t,tab)} creates a new entry in \\spad{tab},{} declaring \\spad{u} to be of type \\spad{t}") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) $) "\\spad{declare!(l,t,tab)} creates new entrys in \\spad{tab},{} declaring each of \\spad{l} to be of type \\spad{t}")) (|empty| (($) "\\spad{empty()} returns a new,{} empty symbol table")) (|coerce| (((|Table| (|Symbol|) (|FortranType|)) $) "\\spad{coerce(x)} returns a table view of \\spad{x}"))) NIL NIL -(-1096) +(-1095) ((|constructor| (NIL "\\indented{1}{This domain provides a simple domain,{} general enough for} \\indented{2}{building complete representation of Spad programs as objects} \\indented{2}{of a term algebra built from ground terms of type integers,{} foats,{}} \\indented{2}{identifiers,{} and strings.} \\indented{2}{This domain differs from InputForm in that it represents} \\indented{2}{any entity in a Spad program,{} not just expressions.\\space{2}Furthermore,{}} \\indented{2}{while InputForm may contain atoms like vectors and other Lisp} \\indented{2}{objects,{} the Syntax domain is supposed to contain only that} \\indented{2}{initial algebra build from the primitives listed above.} Related Constructors: \\indented{2}{Integer,{} DoubleFloat,{} Identifier,{} String,{} SExpression.} See Also: SExpression,{} InputForm. The equality supported by this domain is structural.")) (|case| (((|Boolean|) $ (|[\|\|]| (|String|))) "\\spad{x case String} is \\spad{true} if `x' really is a String") (((|Boolean|) $ (|[\|\|]| (|Identifier|))) "\\spad{x case Identifier} is \\spad{true} if `x' really is an Identifier") (((|Boolean|) $ (|[\|\|]| (|DoubleFloat|))) "\\spad{x case DoubleFloat} is \\spad{true} if `x' really is a DoubleFloat") (((|Boolean|) $ (|[\|\|]| (|Integer|))) "\\spad{x case Integer} is \\spad{true} if `x' really is an Integer")) (|compound?| (((|Boolean|) $) "\\spad{compound? x} is \\spad{true} when `x' is not an atomic syntax.")) (|getOperands| (((|List| $) $) "\\spad{getOperands(x)} returns the list of operands to the operator in `x'.")) (|getOperator| (((|Union| (|Integer|) (|DoubleFloat|) (|Identifier|) (|String|) $) $) "\\spad{getOperator(x)} returns the operator,{} or tag,{} of the syntax `x'. The value returned is itself a syntax if `x' really is an application of a function symbol as opposed to being an atomic ground term.")) (|nil?| (((|Boolean|) $) "\\spad{nil?(s)} is \\spad{true} when `s' is a syntax for the constant nil.")) (|buildSyntax| (($ $ (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).") (($ (|Identifier|) (|List| $)) "\\spad{buildSyntax(op, [a1, ..., an])} builds a syntax object for \\spad{op}(\\spad{a1},{}...,{}an).")) (|autoCoerce| (((|String|) $) "\\spad{autoCoerce(s)} forcibly extracts a string value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.") (((|Identifier|) $) "\\spad{autoCoerce(s)} forcibly extracts an identifier from the Syntax domain `s'; no check performed. To be called only at at the discretion of the compiler.") (((|DoubleFloat|) $) "\\spad{autoCoerce(s)} forcibly extracts a float value from the syntax `s'; no check performed. To be called only at the discretion of the compiler") (((|Integer|) $) "\\spad{autoCoerce(s)} forcibly extracts an integer value from the syntax `s'; no check performed. To be called only at the discretion of the compiler.")) (|coerce| (((|String|) $) "\\spad{coerce(s)} extracts a string value from the syntax `s'.") (((|Identifier|) $) "\\spad{coerce(s)} extracts an identifier from the syntax `s'.") (((|DoubleFloat|) $) "\\spad{coerce(s)} extracts a float value from the syntax `s'.") (((|Integer|) $) "\\spad{coerce(s)} extracts and integer value from the syntax `s'")) (|convert| (($ (|SExpression|)) "\\spad{convert(s)} converts an \\spad{s}-expression to Syntax. Note,{} when `s' is not an atom,{} it is expected that it designates a proper list,{} \\spadignore{e.g.} a sequence of cons cells ending with nil.") (((|SExpression|) $) "\\spad{convert(s)} returns the \\spad{s}-expression representation of a syntax."))) NIL NIL -(-1097 N) +(-1096 N) ((|constructor| (NIL "This domain implements sized (signed) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of this type."))) NIL NIL -(-1098 N) +(-1097 N) ((|constructor| (NIL "This domain implements sized (unsigned) integer datatypes parameterized by the precision (or width) of the underlying representation. The intent is that they map directly to the hosting hardware natural integer datatypes. Consequently,{} natural values for \\spad{N} are: 8,{} 16,{} 32,{} 64,{} etc. These datatypes are mostly useful for system programming tasks,{} \\spadignore{i.e.} interfacting with the hosting operating system,{} reading/writing external binary format files.")) (|sample| (($) "\\spad{sample} gives a sample datum of type Byte.")) (|bitior| (($ $ $) "\\spad{bitior(x,y)} returns the bitwise `inclusive or' of `x' and `y'.")) (|bitand| (($ $ $) "\\spad{bitand(x,y)} returns the bitwise `and' of `x' and `y'."))) NIL NIL -(-1099) +(-1098) ((|constructor| (NIL "This domain is a datatype system-level pointer values."))) NIL NIL -(-1100 R) +(-1099 R) ((|triangularSystems| (((|List| (|List| (|Polynomial| |#1|))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{triangularSystems(lf,lv)} solves the system of equations defined by \\spad{lf} with respect to the list of symbols \\spad{lv}; the system of equations is obtaining by equating to zero the list of rational functions \\spad{lf}. The output is a list of solutions where each solution is expressed as a \"reduced\" triangular system of polynomials.")) (|solve| (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(eq)} finds the solutions of the equation \\spad{eq} with respect to the unique variable appearing in \\spad{eq}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|))) "\\spad{solve(p)} finds the solution of a rational function \\spad{p} = 0 with respect to the unique variable appearing in \\spad{p}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Equation| (|Fraction| (|Polynomial| |#1|))) (|Symbol|)) "\\spad{solve(eq,v)} finds the solutions of the equation \\spad{eq} with respect to the variable \\spad{v}.") (((|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{solve(p,v)} solves the equation \\spad{p=0},{} where \\spad{p} is a rational function with respect to the variable \\spad{v}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) "\\spad{solve(le)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to all symbols appearing in \\spad{le}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{solve(lp)} finds the solutions of the list \\spad{lp} of rational functions with respect to all symbols appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| |#1|)))) (|List| (|Symbol|))) "\\spad{solve(le,lv)} finds the solutions of the list \\spad{le} of equations of rational functions with respect to the list of symbols \\spad{lv}.") (((|List| (|List| (|Equation| (|Fraction| (|Polynomial| |#1|))))) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{solve(lp,lv)} finds the solutions of the list \\spad{lp} of rational functions with respect to the list of symbols \\spad{lv}."))) NIL NIL -(-1101) +(-1100) ((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension} is a string representation of a filename extension for native modules.")) (|hostByteOrder| (((|ByteOrder|)) "\\sapd{hostByteOrder}")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform} is a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL -(-1102 S) +(-1101 S) ((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,b,c,d,e)} is an auxiliary function for mr")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{\\spad{ListFunctions3}}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{\\spad{tab1}}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation \\spad{bat1} is the inverse of \\spad{tab1}.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,pr,t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,pr,r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) NIL NIL -(-1103 |Key| |Entry|) +(-1102 |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}"))) -((-3996 . T) (-3997 . T)) -((-12 (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3861) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014)))) (OR (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773)))) (|HasCategory| |#2| (QUOTE (-553 (-773))))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-554 (-474)))) (-12 (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#2| (QUOTE (-1014))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-553 (-773)))) (|HasCategory| (-2 (|:| -3861 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-773))))) -(-1104 S) +((-3995 . T) (-3996 . T)) +((-12 (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (|%list| (QUOTE -260) (|%list| (QUOTE -2) (|%list| (QUOTE |:|) (QUOTE -3860) (|devaluate| |#1|)) (|%list| (QUOTE |:|) (QUOTE |entry|) (|devaluate| |#2|))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013)))) (OR (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772)))) (|HasCategory| |#2| (QUOTE (-552 (-772))))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-553 (-473)))) (-12 (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (|%list| (QUOTE -260) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#2| (QUOTE (-1013))) (|HasCategory| |#2| (QUOTE (-72))) (OR (|HasCategory| |#2| (QUOTE (-72))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-72)))) (|HasCategory| |#2| (QUOTE (-552 (-772)))) (|HasCategory| (-2 (|:| -3860 |#1|) (|:| |entry| |#2|)) (QUOTE (-552 (-772))))) +(-1103 S) ((|constructor| (NIL "\\indented{1}{The tableau domain is for printing Young tableaux,{} and} coercions to and from List List \\spad{S} where \\spad{S} is a set.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(t)} converts a tableau \\spad{t} to an output form.")) (|listOfLists| (((|List| (|List| |#1|)) $) "\\spad{listOfLists t} converts a tableau \\spad{t} to a list of lists.")) (|tableau| (($ (|List| (|List| |#1|))) "\\spad{tableau(ll)} converts a list of lists \\spad{ll} to a tableau."))) NIL NIL -(-1105 S) +(-1104 S) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: April 17,{} 2010 Date Last Modified: April 17,{} 2010")) (|operator| (($ |#1| (|Arity|)) "\\spad{operator(n,a)} returns an operator named \\spad{n} and with arity \\spad{a}."))) NIL NIL -(-1106 R) +(-1105 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a, n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a, n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,...,an])} returns \\spad{f(a1,...,an)} such that if \\spad{ai = tan(ui)} then \\spad{f(a1,...,an) = tan(u1 + ... + un)}."))) NIL NIL -(-1107 S |Key| |Entry|) +(-1106 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,t1,t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,y,...,z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}."))) NIL NIL -(-1108 |Key| |Entry|) +(-1107 |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}."))) -((-3996 . T) (-3997 . T)) +((-3995 . T) (-3996 . T)) NIL -(-1109 |Key| |Entry|) +(-1108 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key -> Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1110) +(-1109) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain ``\\verb+\\[+'' and ``\\verb+\\]+'',{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,step,type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers."))) NIL NIL -(-1111 S) +(-1110 S) ((|constructor| (NIL "\\spadtype{TexFormat1} provides a utility coercion for changing to TeX format anything that has a coercion to the standard output format.")) (|coerce| (((|TexFormat|) |#1|) "\\spad{coerce(s)} provides a direct coercion from a domain \\spad{S} to TeX format. This allows the user to skip the step of first manually coercing the object to standard output format before it is coerced to TeX format."))) NIL NIL -(-1112) +(-1111) ((|constructor| (NIL "This domain provides an implementation of text files. Text is stored in these files using the native character set of the computer.")) (|endOfFile?| (((|Boolean|) $) "\\spad{endOfFile?(f)} tests whether the file \\spad{f} is positioned after the end of all text. If the file is open for output,{} then this test is always \\spad{true}.")) (|readIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLineIfCan!| (((|Union| (|String|) "failed") $) "\\spad{readLineIfCan!(f)} returns a string of the contents of a line from file \\spad{f},{} if possible. If \\spad{f} is not readable or if it is positioned at the end of file,{} then \\spad{\"failed\"} is returned.")) (|readLine!| (((|String|) $) "\\spad{readLine!(f)} returns a string of the contents of a line from the file \\spad{f}.")) (|writeLine!| (((|String|) $) "\\spad{writeLine!(f)} finishes the current line in the file \\spad{f}. An empty string is returned. The call \\spad{writeLine!(f)} is equivalent to \\spad{writeLine!(f,\"\")}.") (((|String|) $ (|String|)) "\\spad{writeLine!(f,s)} writes the contents of the string \\spad{s} and finishes the current line in the file \\spad{f}. The value of \\spad{s} is returned."))) NIL NIL -(-1113 R) +(-1112 R) ((|constructor| (NIL "Tools for the sign finding utilities.")) (|direction| (((|Integer|) (|String|)) "\\spad{direction(s)} \\undocumented")) (|nonQsign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{nonQsign(r)} \\undocumented")) (|sign| (((|Union| (|Integer|) "failed") |#1|) "\\spad{sign(r)} \\undocumented"))) NIL NIL -(-1114) +(-1113) ((|constructor| (NIL "This package exports a function for making a \\spadtype{ThreeSpace}")) (|createThreeSpace| (((|ThreeSpace| (|DoubleFloat|))) "\\spad{createThreeSpace()} creates a \\spadtype{ThreeSpace(DoubleFloat)} object capable of holding point,{} curve,{} mesh components and any combination."))) NIL NIL -(-1115 S) +(-1114 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1116) +(-1115) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{pi()} returns the constant \\spad{pi}."))) NIL NIL -(-1117 S) +(-1116 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| $)) "\\spad{tree(nd,ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1014))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-72)))) -(-1118 S) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1013))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-72)))) +(-1117 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1119) +(-1118) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1120 R -3093) +(-1119 R -3092) ((|constructor| (NIL "\\spadtype{TrigonometricManipulations} provides transformations from trigonometric functions to complex exponentials and logarithms,{} and back.")) (|complexForm| (((|Complex| |#2|) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f, imag f]}.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| ((|#2| |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| ((|#2| |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f, x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log, exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f, x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL -(-1121 R |Row| |Col| M) +(-1120 R |Row| |Col| M) ((|constructor| (NIL "This package provides functions that compute \"fraction-free\" inverses of upper and lower triangular matrices over a integral domain. By \"fraction-free inverses\" we mean the following: given a matrix \\spad{B} with entries in \\spad{R} and an element \\spad{d} of \\spad{R} such that \\spad{d} * inv(\\spad{B}) also has entries in \\spad{R},{} we return \\spad{d} * inv(\\spad{B}). Thus,{} it is not necessary to pass to the quotient field in any of our computations.")) (|LowTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{LowTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular lower triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}.")) (|UpTriBddDenomInv| ((|#4| |#4| |#1|) "\\spad{UpTriBddDenomInv(B,d)} returns \\spad{M},{} where \\spad{B} is a non-singular upper triangular matrix and \\spad{d} is an element of \\spad{R} such that \\spad{M = d * inv(B)} has entries in \\spad{R}."))) NIL NIL -(-1122 R -3093) +(-1121 R -3092) ((|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 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 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 -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -797) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -554) (|%list| (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -797) (|devaluate| |#1|))))) -(-1123 |Coef|) +((-12 (|HasCategory| |#1| (|%list| (QUOTE -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#1| (|%list| (QUOTE -796) (|devaluate| |#1|))) (|HasCategory| |#2| (|%list| (QUOTE -553) (|%list| (QUOTE -800) (|devaluate| |#1|)))) (|HasCategory| |#2| (|%list| (QUOTE -796) (|devaluate| |#1|))))) +(-1122 |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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1124 S R E V P) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-120))) (|HasCategory| |#1| (QUOTE (-118))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-312)))) +(-1123 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} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#5|) "\\axiom{extend(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{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(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{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(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{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},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{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},{}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{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},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{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 (-320)))) -(-1125 R E V P) +(-1124 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} < ... < Xn}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}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|) $) "\\axiom{coHeight(ts)} returns \\axiom{size()\\$\\spad{V}} minus \\axiom{\\#ts}.")) (|extend| (($ $ |#4|) "\\axiom{extend(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{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(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{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(ts,{}\\spad{v})} returns the polynomial of \\axiom{ts} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}ts)} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{ts}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(ts)} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{ts}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(ts)} returns the polynomials of \\axiom{ts} with smaller main variable than \\axiom{mvar(ts)} if \\axiom{ts} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(ts)} returns the polynomial of \\axiom{ts} with smallest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(ts)} returns the polynomial of \\axiom{ts} with greatest main variable if \\axiom{ts} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(lp)} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[tsn,{}qsn]]} such that the zero set of \\axiom{lp} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{ts} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(lp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{lp} is the union of the closures of the regular zero sets of the members of \\axiom{lts}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}ts)} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(ts)).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(ts)} returns the subset of \\axiom{ts} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}ts)} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{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},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}ts)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}ts)} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{ts}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(lp,{}ts,{}redOp,{}redOp?)} returns a list \\axiom{lq} of polynomials such that \\axiom{[reduce(\\spad{p},{}ts,{}redOp,{}redOp?) for \\spad{p} in lp]} and \\axiom{lp} have the same zeros inside the regular zero set of \\axiom{ts}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{lq} and every polynomial \\axiom{\\spad{t}} in \\axiom{ts} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{lp} and a product \\axiom{\\spad{h}} of \\axiom{initials(ts)} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}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{ts} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{ts} such that \\axiom{h*p - \\spad{r}} lies in the ideal generated by \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(ts,{}redOp?)} returns \\spad{true} iff every element of \\axiom{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},{}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{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},{}ts)} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(ts)} returns \\spad{true} iff every element of \\axiom{ts} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{ts}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}ts)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{ts}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}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{ts} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(ts)} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{ts} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(ts,{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}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{ts}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(ts)} returns \\axiom{[lp,{}lq]} where \\axiom{lp} is the list of the members of \\axiom{ts} and \\axiom{lq}is \\axiom{initials(ts)}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(ts)} returns the product of main degrees of the members of \\axiom{ts}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(ts)} returns the list of the non-constant initials of the members of \\axiom{ts}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(qs,{}redOp?)} where \\axiom{qs} consists of the polynomials of \\axiom{ps} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(ps,{}redOp?)} returns \\axiom{[bs,{}ts]} where \\axiom{concat(bs,{}ts)} is \\axiom{ps} and \\axiom{bs} is a basic set in Wu Wen Tsun sense of \\axiom{ps} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{ps},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-1126 |Curve|) +(-1125 |Curve|) ((|constructor| (NIL "\\indented{2}{Package for constructing tubes around 3-dimensional parametric curves.} Domain of tubes around 3-dimensional parametric curves.")) (|tube| (($ |#1| (|List| (|List| (|Point| (|DoubleFloat|)))) (|Boolean|)) "\\spad{tube(c,ll,b)} creates a tube of the domain \\spadtype{TubePlot} from a space curve \\spad{c} of the category \\spadtype{PlottableSpaceCurveCategory},{} a list of lists of points (loops) \\spad{ll} and a boolean \\spad{b} which if \\spad{true} indicates a closed tube,{} or if \\spad{false} an open tube.")) (|setClosed| (((|Boolean|) $ (|Boolean|)) "\\spad{setClosed(t,b)} declares the given tube plot \\spad{t} to be closed if \\spad{b} is \\spad{true},{} or if \\spad{b} is \\spad{false},{} \\spad{t} is set to be open.")) (|open?| (((|Boolean|) $) "\\spad{open?(t)} tests whether the given tube plot \\spad{t} is open.")) (|closed?| (((|Boolean|) $) "\\spad{closed?(t)} tests whether the given tube plot \\spad{t} is closed.")) (|listLoops| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listLoops(t)} returns the list of lists of points,{} or the 'loops',{} of the given tube plot \\spad{t}.")) (|getCurve| ((|#1| $) "\\spad{getCurve(t)} returns the \\spadtype{PlottableSpaceCurveCategory} representing the parametric curve of the given tube plot \\spad{t}."))) NIL NIL -(-1127) +(-1126) ((|constructor| (NIL "Tools for constructing tubes around 3-dimensional parametric curves.")) (|loopPoints| (((|List| (|Point| (|DoubleFloat|))) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|List| (|List| (|DoubleFloat|)))) "\\spad{loopPoints(p,n,b,r,lls)} creates and returns a list of points which form the loop with radius \\spad{r},{} around the center point indicated by the point \\spad{p},{} with the principal normal vector of the space curve at point \\spad{p} given by the point(vector) \\spad{n},{} and the binormal vector given by the point(vector) \\spad{b},{} and a list of lists,{} \\spad{lls},{} which is the \\spadfun{cosSinInfo} of the number of points defining the loop.")) (|cosSinInfo| (((|List| (|List| (|DoubleFloat|))) (|Integer|)) "\\spad{cosSinInfo(n)} returns the list of lists of values for \\spad{n},{} in the form: \\spad{[[cos(n - 1) a,sin(n - 1) a],...,[cos 2 a,sin 2 a],[cos a,sin a]]} where \\spad{a = 2 pi/n}. Note: \\spad{n} should be greater than 2.")) (|unitVector| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{unitVector(p)} creates the unit vector of the point \\spad{p} and returns the result as a point. Note: \\spad{unitVector(p) = p/|p|}.")) (|cross| (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{cross(p,q)} computes the cross product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and keeping the color of the first point \\spad{p}. The result is returned as a point.")) (|dot| (((|DoubleFloat|) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{dot(p,q)} computes the dot product of the two points \\spad{p} and \\spad{q} using only the first three coordinates,{} and returns the resulting \\spadtype{DoubleFloat}.")) (- (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p - q} computes and returns a point whose coordinates are the differences of the coordinates of two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (+ (((|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|)) (|Point| (|DoubleFloat|))) "\\spad{p + q} computes and returns a point whose coordinates are the sums of the coordinates of the two points \\spad{p} and \\spad{q},{} using the color,{} or fourth coordinate,{} of the first point \\spad{p} as the color also of the point \\spad{q}.")) (* (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|Point| (|DoubleFloat|))) "\\spad{s * p} returns a point whose coordinates are the scalar multiple of the point \\spad{p} by the scalar \\spad{s},{} preserving the color,{} or fourth coordinate,{} of \\spad{p}.")) (|point| (((|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{point(x1,x2,x3,c)} creates and returns a point from the three specified coordinates \\spad{x1},{} \\spad{x2},{} \\spad{x3},{} and also a fourth coordinate,{} \\spad{c},{} which is generally used to specify the color of the point."))) NIL NIL -(-1128 S) +(-1127 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter's notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based"))) NIL -((|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-553 (-773))))) -(-1129 -3093) +((|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-552 (-772))))) +(-1128 -3092) ((|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 -(-1130) +(-1129) ((|constructor| (NIL "The fundamental Type."))) NIL NIL -(-1131) +(-1130) ((|constructor| (NIL "This domain represents a type AST."))) NIL NIL -(-1132 S) +(-1131 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 fn.")) 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The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,...,bm], [a1,...,an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,...,bm], [a1,...,an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,...,bm], [a1,...,an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,...,an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1134 S) +(-1133 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) 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A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-312)))) -(-1144 |Coef| UTS) +(-1143 |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)}.")) 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The factorization is done by \"lifting\" (HENSEL) the factorization over a finite field.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(m,flag)} returns the factorization of \\spad{m},{} FinalFact is a Record \\spad{s}.\\spad{t}. FinalFact.contp=content \\spad{m},{} FinalFact.factors=List of irreducible factors of \\spad{m} with exponent ,{} if \\spad{flag} =true the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(m)} returns the factorization of \\spad{m} square free polynomial")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(m)} returns the factorization of \\spad{m}"))) NIL NIL -(-1147 S) +(-1146 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 (-756))) (|HasCategory| |#1| (QUOTE (-1014)))) -(-1148 R S) +((|HasCategory| |#1| (QUOTE (-755))) (|HasCategory| |#1| (QUOTE (-1013)))) +(-1147 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.") 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T)) +((|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-495)))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-330)))) (|HasCategory| (-994) (QUOTE (-796 (-330))))) (-12 (|HasCategory| |#2| (QUOTE (-796 (-484)))) (|HasCategory| (-994) (QUOTE (-796 (-484))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-330))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-330)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-800 (-484))))) (|HasCategory| (-994) (QUOTE (-553 (-800 (-484)))))) (-12 (|HasCategory| |#2| (QUOTE (-553 (-473)))) (|HasCategory| (-994) (QUOTE (-553 (-473))))) (|HasCategory| |#2| (QUOTE (-580 (-484)))) (|HasCategory| |#2| (QUOTE (-120))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-484)))) (OR (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484)))))) (|HasCategory| |#2| (QUOTE (-950 (-350 (-484))))) (OR (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-821)))) (OR (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-821)))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-1066))) (|HasCategory| |#2| (QUOTE (-811 (-1090)))) (|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|HasCategory| |#2| (QUOTE (-189))) (|HasCategory| |#2| (QUOTE (-190))) (|HasAttribute| |#2| (QUOTE -3993)) (|HasCategory| |#2| (QUOTE (-392))) (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (OR (-12 (|HasCategory| |#2| (QUOTE (-821))) (|HasCategory| $ (QUOTE (-118)))) (|HasCategory| |#2| (QUOTE (-118))))) +(-1149 |x| R |y| S) ((|constructor| (NIL "This package lifts a mapping from coefficient rings \\spad{R} to \\spad{S} to a mapping from \\spadtype{UnivariatePolynomial}(\\spad{x},{}\\spad{R}) to \\spadtype{UnivariatePolynomial}(\\spad{y},{}\\spad{S}). Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|UnivariatePolynomial| |#3| |#4|) (|Mapping| |#4| |#2|) (|UnivariatePolynomial| |#1| |#2|)) "\\spad{map(func, poly)} creates a new polynomial by applying \\spad{func} to every non-zero coefficient of the polynomial poly."))) NIL NIL -(-1151 R Q UP) +(-1150 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a gcd domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p, d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1152 R UP) +(-1151 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} fn ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} fn).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,d,c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1153 R UP) +(-1152 R UP) ((|constructor| (NIL "UnivariatePolynomialDivisionPackage provides a division for non monic univarite polynomials with coefficients in an \\spad{IntegralDomain}.")) (|divideIfCan| (((|Union| (|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) "failed") |#2| |#2|) "\\spad{divideIfCan(f,g)} returns quotient and remainder of the division of \\spad{f} by \\spad{g} or \"failed\" if it has not succeeded."))) NIL NIL -(-1154 R U) +(-1153 R U) ((|constructor| (NIL "This package implements Karatsuba's trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,b,l,k)} returns \\spad{a*b} by applying Karatsuba's trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,b)} returns \\spad{a*b} by applying Karatsuba's trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,b)} returns \\spad{a*b} without using Karatsuba's trick at all."))) NIL NIL -(-1155 S R) +(-1154 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL -((|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-496))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1067)))) -(-1156 R) +((|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312))) (|HasCategory| |#2| (QUOTE (-392))) (|HasCategory| |#2| (QUOTE (-495))) (|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-1066)))) +(-1155 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p, q)} returns \\spad{[a, b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,q)} returns \\spad{[c, q, r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f, q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p, q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,q)} computes the gcd of the polynomials \\spad{p} and \\spad{q} using the SubResultant GCD algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p, q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p, d, x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where Dx is given by x',{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,n)} returns \\spad{p * monomial(1,n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,n)} returns \\spad{monicDivide(p,monomial(1,n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,n)} returns the same as \\spad{monicDivide(p,monomial(1,n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient, remainder]}. Error: if \\spad{q} isn't monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p, n)} returns \\spad{[a0,...,a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3992 |has| |#1| (-312)) (-3994 |has| |#1| (-6 -3994)) (-3991 . T) (-3990 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3991 |has| |#1| (-312)) (-3993 |has| |#1| (-6 -3993)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL -(-1157 R PR S PS) +(-1156 R PR S PS) ((|constructor| (NIL "Mapping from polynomials over \\spad{R} to polynomials over \\spad{S} given a map from \\spad{R} to \\spad{S} assumed to send zero to zero.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f, p)} takes a function \\spad{f} from \\spad{R} to \\spad{S},{} and applies it to each (non-zero) coefficient of a polynomial \\spad{p} over \\spad{R},{} getting a new polynomial over \\spad{S}. Note: since the map is not applied to zero elements,{} it may map zero to zero."))) NIL NIL -(-1158 S |Coef| |Expon|) +(-1157 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{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (QUOTE (-810 (-1091)))) (|HasSignature| |#2| (|%list| (QUOTE *) (|%list| (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1026))) (|HasSignature| |#2| (|%list| (QUOTE **) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#2|) (QUOTE (-1091)))))) -(-1159 |Coef| |Expon|) +((|HasCategory| |#2| (QUOTE (-809 (-1090)))) (|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 -3946) (|%list| (|devaluate| |#2|) (QUOTE (-1090)))))) +(-1158 |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{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,k1,k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,n) = min(m,n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1160 RC P) +(-1159 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| #1="nil" #2="sqfr" #3="irred" #4="prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| #1# #2# #3# #4#)) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1161 |Coef| |var| |cen|) +(-1160 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,x,3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) -(-1162 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) +(-1161 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1163 |Coef|) +(-1162 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),var)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{var}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by rational numbers.")) (|multiplyExponents| (($ $ (|Fraction| (|Integer|))) "\\spad{multiplyExponents(f,r)} multiplies all exponents of the power series \\spad{f} by the positive rational number \\spad{r}.")) (|series| (($ (|NonNegativeInteger|) (|Stream| (|Record| (|:| |k| (|Fraction| (|Integer|))) (|:| |c| |#1|)))) "\\spad{series(n,st)} creates a series from a common denomiator and a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents and \\spad{n} should be a common denominator for the exponents in the stream of terms."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1164 S |Coef| ULS) +(-1163 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1165 |Coef| ULS) +(-1164 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,f(x))} returns \\spad{f(x^r)}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1166 |Coef| ULS) +(-1165 |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)}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3994 |has| |#1| (-312)) (-3988 |has| |#1| (-312)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-485)) (QUOTE (-1026))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-496)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-485)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-485)))))) -(-1167 R FE |var| |cen|) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3993 |has| |#1| (-312)) (-3987 |has| |#1| (-312)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#1| (QUOTE (-146))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484))) (|devaluate| |#1|)))) (|HasCategory| (-350 (-484)) (QUOTE (-1025))) (|HasCategory| |#1| (QUOTE (-312))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (OR (|HasCategory| |#1| (QUOTE (-312))) (|HasCategory| |#1| (QUOTE (-495)))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (|%list| (QUOTE -350) (QUOTE (-484)))))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (QUOTE (-38 (-350 (-484)))))) +(-1166 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))}."))) -(((-3998 "*") |has| (-1161 |#2| |#3| |#4|) (-146)) (-3989 |has| (-1161 |#2| |#3| |#4|) (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) -((|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485)))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-350 (-485))))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-951 (-485)))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1161 |#2| |#3| |#4|) (QUOTE (-496)))) -(-1168 A S) +(((-3997 "*") |has| (-1160 |#2| |#3| |#4|) (-146)) (-3988 |has| (-1160 |#2| |#3| |#4|) (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-118))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-120))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-146))) (OR (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-38 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-350 (-484)))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-350 (-484))))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-950 (-484)))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-312))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-392))) (|HasCategory| (-1160 |#2| |#3| |#4|) (QUOTE (-495)))) +(-1167 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,\"last\",x)} (also written: \\axiom{\\spad{u}.last := \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,\"first\",x)} (also written: \\axiom{\\spad{u}.first := \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} >= 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,n)} returns the \\axiom{\\spad{n}}th (\\spad{n} >= 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} >= 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -3997))) -(-1169 S) +((|HasAttribute| |#1| (QUOTE -3996))) +(-1168 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|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{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,\"rest\",v)} (also written: \\axiom{\\spad{u}.rest := \\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{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} >= 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} >= 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} >= 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL NIL -(-1170 |Coef| |var| |cen|) +(-1169 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,b,f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,b,f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and invertible 1st order coefficient.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),a,d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|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}."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . 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T)) -((|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-496))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-496)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-810 (-1091)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-695)) (|devaluate| |#1|)))) (|HasCategory| (-695) (QUOTE (-1026))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasSignature| |#1| (|%list| (QUOTE -3947) (|%list| (|devaluate| |#1|) (QUOTE (-1091)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-695))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#1| (QUOTE (-29 (-485)))) (|HasCategory| |#1| (QUOTE (-872))) (|HasCategory| |#1| (QUOTE (-1116)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-485))))) (|HasSignature| |#1| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1091))))) (|HasSignature| |#1| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#1|))))))) -(-1171 |Coef1| |Coef2| UTS1 UTS2) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-495))) (OR (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-495)))) (|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-118))) (|HasCategory| |#1| (QUOTE (-120))) (-12 (|HasCategory| |#1| (QUOTE (-809 (-1090)))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|))))) (|HasSignature| |#1| (|%list| (QUOTE *) (|%list| (|devaluate| |#1|) (QUOTE (-694)) (|devaluate| |#1|)))) (|HasCategory| (-694) (QUOTE (-1025))) (-12 (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasSignature| |#1| (|%list| (QUOTE -3946) (|%list| (|devaluate| |#1|) (QUOTE (-1090)))))) (|HasSignature| |#1| (|%list| (QUOTE **) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-694))))) (|HasCategory| |#1| (QUOTE (-312))) (OR (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#1| (QUOTE (-29 (-484)))) (|HasCategory| |#1| (QUOTE (-871))) (|HasCategory| |#1| (QUOTE (-1115)))) (-12 (|HasCategory| |#1| (QUOTE (-38 (-350 (-484))))) (|HasSignature| |#1| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1090))))) (|HasSignature| |#1| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#1|))))))) +(-1170 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1172 S |Coef|) +(-1171 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| (QUOTE (-29 (-485)))) (|HasCategory| |#2| (QUOTE (-872))) (|HasCategory| |#2| (QUOTE (-1116))) (|HasSignature| |#2| (|%list| (QUOTE -3082) (|%list| (|%list| (QUOTE -584) (QUOTE (-1091))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3813) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1091))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-485))))) (|HasCategory| |#2| (QUOTE (-312)))) -(-1173 |Coef|) +((|HasCategory| |#2| (QUOTE (-29 (-484)))) (|HasCategory| |#2| (QUOTE (-871))) (|HasCategory| |#2| (QUOTE (-1115))) (|HasSignature| |#2| (|%list| (QUOTE -3081) (|%list| (|%list| (QUOTE -583) (QUOTE (-1090))) (|devaluate| |#2|)))) (|HasSignature| |#2| (|%list| (QUOTE -3812) (|%list| (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1090))))) (|HasCategory| |#2| (QUOTE (-38 (-350 (-484))))) (|HasCategory| |#2| (QUOTE (-312)))) +(-1172 |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."))) -(((-3998 "*") |has| |#1| (-146)) (-3989 |has| |#1| (-496)) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") |has| |#1| (-146)) (-3988 |has| |#1| (-495)) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1174 |Coef| UTS) +(-1173 |Coef| UTS) ((|constructor| (NIL "\\indented{1}{This package provides Taylor series solutions to regular} linear or non-linear ordinary differential equations of arbitrary order.")) (|mpsode| (((|List| |#2|) (|List| |#1|) (|List| (|Mapping| |#2| (|List| |#2|)))) "\\spad{mpsode(r,f)} solves the system of differential equations \\spad{dy[i]/dx =f[i] [x,y[1],y[2],...,y[n]]},{} \\spad{y[i](a) = r[i]} for \\spad{i} in 1..\\spad{n}.")) (|ode| ((|#2| (|Mapping| |#2| (|List| |#2|)) (|List| |#1|)) "\\spad{ode(f,cl)} is the solution to \\spad{y<n>=f(y,y',..,y<n-1>)} such that \\spad{y<i>(a) = cl.i} for \\spad{i} in 1..\\spad{n}.")) (|ode2| ((|#2| (|Mapping| |#2| |#2| |#2|) |#1| |#1|) "\\spad{ode2(f,c0,c1)} is the solution to \\spad{y'' = f(y,y')} such that \\spad{y(a) = c0} and \\spad{y'(a) = c1}.")) (|ode1| ((|#2| (|Mapping| |#2| |#2|) |#1|) "\\spad{ode1(f,c)} is the solution to \\spad{y' = f(y)} such that \\spad{y(a) = c}.")) (|fixedPointExquo| ((|#2| |#2| |#2|) "\\spad{fixedPointExquo(f,g)} computes the exact quotient of \\spad{f} and \\spad{g} using a fixed point computation.")) (|stFuncN| (((|Mapping| (|Stream| |#1|) (|List| (|Stream| |#1|))) (|Mapping| |#2| (|List| |#2|))) "\\spad{stFuncN(f)} is a local function xported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc2| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2| |#2|)) "\\spad{stFunc2(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user.")) (|stFunc1| (((|Mapping| (|Stream| |#1|) (|Stream| |#1|)) (|Mapping| |#2| |#2|)) "\\spad{stFunc1(f)} is a local function exported due to compiler problem. This function is of no interest to the top-level user."))) NIL NIL -(-1175 -3093 UP L UTS) +(-1174 -3092 UP L UTS) ((|constructor| (NIL "\\spad{RUTSodetools} provides tools to interface with the series \\indented{1}{ODE solver when presented with linear ODEs.}")) (RF2UTS ((|#4| (|Fraction| |#2|)) "\\spad{RF2UTS(f)} converts \\spad{f} to a Taylor series.")) (LODO2FUN (((|Mapping| |#4| (|List| |#4|)) |#3|) "\\spad{LODO2FUN(op)} returns the function to pass to the series ODE solver in order to solve \\spad{op y = 0}.")) (UTS2UP ((|#2| |#4| (|NonNegativeInteger|)) "\\spad{UTS2UP(s, n)} converts the first \\spad{n} terms of \\spad{s} to a univariate polynomial.")) (UP2UTS ((|#4| |#2|) "\\spad{UP2UTS(p)} converts \\spad{p} to a Taylor series."))) NIL -((|HasCategory| |#1| (QUOTE (-496)))) -(-1176) +((|HasCategory| |#1| (QUOTE (-495)))) +(-1175) ((|constructor| (NIL "The category of domains that act like unions. UnionType,{} like Type or Category,{} acts mostly as a take that communicates `union-like' intended semantics to the compiler. A domain \\spad{D} that satifies UnionType should provide definitions for `case' operators,{} with corresponding `autoCoerce' operators."))) NIL NIL -(-1177 |sym|) +(-1176 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1178 S R) +(-1177 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})*v(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL -((|HasCategory| |#2| (QUOTE (-916))) (|HasCategory| |#2| (QUOTE (-962))) (|HasCategory| |#2| (QUOTE (-664))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1179 R) +((|HasCategory| |#2| (QUOTE (-915))) (|HasCategory| |#2| (QUOTE (-961))) (|HasCategory| |#2| (QUOTE (-663))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) +(-1178 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})*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}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-3997 . T) (-3996 . T)) +((-3996 . T) (-3995 . T)) NIL -(-1180 R) +(-1179 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-3997 . T) (-3996 . T)) -((OR (-12 (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-553 (-773)))) (|HasCategory| |#1| (QUOTE (-554 (-474)))) (OR (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| |#1| (QUOTE (-757))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014)))) (|HasCategory| (-485) (QUOTE (-757))) (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-664))) (|HasCategory| |#1| (QUOTE (-962))) (-12 (|HasCategory| |#1| (QUOTE (-916))) (|HasCategory| |#1| (QUOTE (-962)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1014))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) -(-1181 A B) +((-3996 . T) (-3995 . T)) +((OR (-12 (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-552 (-772)))) (|HasCategory| |#1| (QUOTE (-553 (-473)))) (OR (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| |#1| (QUOTE (-756))) (OR (|HasCategory| |#1| (QUOTE (-72))) (|HasCategory| |#1| (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013)))) (|HasCategory| (-484) (QUOTE (-756))) (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-663))) (|HasCategory| |#1| (QUOTE (-961))) (-12 (|HasCategory| |#1| (QUOTE (-915))) (|HasCategory| |#1| (QUOTE (-961)))) (|HasCategory| |#1| (QUOTE (-72))) (-12 (|HasCategory| |#1| (QUOTE (-1013))) (|HasCategory| |#1| (|%list| (QUOTE -260) (|devaluate| |#1|))))) +(-1180 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f, v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,vec,ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,vec,ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1182) +(-1181) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(gi)} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],[p1],...,[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through pn.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],[p1],...,[pn]],ptColor,lineColor,ptSize,[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught pn,{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1183) +(-1182) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,gr,n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,n,s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,n,dx,dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,n,sx,sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,n,s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,n,s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,n,s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,n,c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,n,s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,n,c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,n,s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,gi,n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{gi} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{gi} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,num,sX,sY,dX,dY,pts,lns,box,axes,axesC,un,unC,cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it's draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(gi,lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{gi},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1184) +(-1183) ((|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and terminates the corresponding process ID.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,s,lf)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,s,f)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,s)} takes the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data file for \\spad{v}.")) (|colorDef| (((|Void|) $ (|Color|) (|Color|)) "\\spad{colorDef(v,c1,c2)} sets the range of colors along the colormap so that the lower end of the colormap is defined by \\spad{c1} and the top end of the colormap is defined by \\spad{c2},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} back to their initial settings.")) (|intensity| (((|Void|) $ (|Float|)) "\\spad{intensity(v,i)} sets the intensity of the light source to \\spad{i},{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|lighting| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{lighting(v,x,y,z)} sets the position of the light source to the coordinates \\spad{x},{} \\spad{y},{} and \\spad{z} and displays the graph for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|clipSurface| (((|Void|) $ (|String|)) "\\spad{clipSurface(v,s)} displays the graph with the specified clipping region removed if \\spad{s} is \"on\",{} or displays the graph without clipping implemented if \\spad{s} is \"off\",{} for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|showClipRegion| (((|Void|) $ (|String|)) "\\spad{showClipRegion(v,s)} displays the clipping region of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the region if \\spad{s} is \"off\".")) (|showRegion| (((|Void|) $ (|String|)) "\\spad{showRegion(v,s)} displays the bounding box of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the box if \\spad{s} is \"off\".")) (|hitherPlane| (((|Void|) $ (|Float|)) "\\spad{hitherPlane(v,h)} sets the hither clipping plane of the graph to \\spad{h},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|eyeDistance| (((|Void|) $ (|Float|)) "\\spad{eyeDistance(v,d)} sets the distance of the observer from the center of the graph to \\spad{d},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|perspective| (((|Void|) $ (|String|)) "\\spad{perspective(v,s)} displays the graph in perspective if \\spad{s} is \"on\",{} or does not display perspective if \\spad{s} is \"off\" for the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport}.")) (|translate| (((|Void|) $ (|Float|) (|Float|)) "\\spad{translate(v,dx,dy)} sets the horizontal viewport offset to \\spad{dx} and the vertical viewport offset to \\spad{dy},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|zoom| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{zoom(v,sx,sy,sz)} sets the graph scaling factors for the \\spad{x}-coordinate axis to \\spad{sx},{} the \\spad{y}-coordinate axis to \\spad{sy} and the \\spad{z}-coordinate axis to \\spad{sz} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.") (((|Void|) $ (|Float|)) "\\spad{zoom(v,s)} sets the graph scaling factor to \\spad{s},{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|rotate| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} degrees and the latitudinal view angle \\spad{phi} degrees for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new rotation position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{rotate(v,th,phi)} rotates the graph to the longitudinal view angle \\spad{th} radians and the latitudinal view angle \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}.")) (|drawStyle| (((|Void|) $ (|String|)) "\\spad{drawStyle(v,s)} displays the surface for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport} in the style of drawing indicated by \\spad{s}. If \\spad{s} is not a valid drawing style the style is wireframe by default. Possible styles are \\spad{\"shade\"},{} \\spad{\"solid\"} or \\spad{\"opaque\"},{} \\spad{\"smooth\"},{} and \\spad{\"wireMesh\"}.")) (|outlineRender| (((|Void|) $ (|String|)) "\\spad{outlineRender(v,s)} displays the polygon outline showing either triangularized surface or a quadrilateral surface outline depending on the whether the \\spadfun{diagonals} function has been set,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the polygon outline if \\spad{s} is \"off\".")) (|diagonals| (((|Void|) $ (|String|)) "\\spad{diagonals(v,s)} displays the diagonals of the polygon outline showing a triangularized surface instead of a quadrilateral surface outline,{} for the given three-dimensional viewport \\spad{v} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the diagonals if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|String|)) "\\spad{axes(v,s)} displays the axes of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,s)} displays the control panel of the given three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|viewpoint| (((|Void|) $ (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,rotx,roty,rotz)} sets the rotation about the \\spad{x}-axis to be \\spad{rotx} radians,{} sets the rotation about the \\spad{y}-axis to be \\spad{roty} radians,{} and sets the rotation about the \\spad{z}-axis to be \\spad{rotz} radians,{} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and displays \\spad{v} with the new view position.") (((|Void|) $ (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi)} sets the longitudinal view angle to \\spad{th} radians and the latitudinal view angle to \\spad{phi} radians for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Integer|) (|Integer|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} degrees,{} the latitudinal view angle to \\spad{phi} degrees,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.") (((|Void|) $ (|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)))) "\\spad{viewpoint(v,viewpt)} sets the viewpoint for the viewport. The viewport record consists of the latitudal and longitudal angles,{} the zoom factor,{} the \\spad{X},{} \\spad{Y},{} and \\spad{Z} scales,{} and the \\spad{X} and \\spad{Y} displacements.") (((|Record| (|:| |theta| (|DoubleFloat|)) (|:| |phi| (|DoubleFloat|)) (|:| |scale| (|DoubleFloat|)) (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |scaleZ| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|))) $) "\\spad{viewpoint(v)} returns the current viewpoint setting of the given viewport,{} \\spad{v}. This function is useful in the situation where the user has created a viewport,{} proceeded to interact with it via the control panel and desires to save the values of the viewpoint as the default settings for another viewport to be created using the system.") (((|Void|) $ (|Float|) (|Float|) (|Float|) (|Float|) (|Float|)) "\\spad{viewpoint(v,th,phi,s,dx,dy)} sets the longitudinal view angle to \\spad{th} radians,{} the latitudinal view angle to \\spad{phi} radians,{} the scale factor to \\spad{s},{} the horizontal viewport offset to \\spad{dx},{} and the vertical viewport offset to \\spad{dy} for the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport}. The new viewpoint position is not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,x,y,width,height)} sets the position of the upper left-hand corner of the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport3D} is executed again for \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,s)} changes the title which is shown in the three-dimensional viewport window,{} \\spad{v} of domain \\spadtype{ThreeDimensionalViewport}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,w,h)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,x,y)} displays the three-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{ThreeDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,lopt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and sets the draw options being used by \\spad{v} to those indicated in the list,{} \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport} and returns a list of all the draw options from the domain \\spad{DrawOption} which are being used by \\spad{v}.")) (|modifyPointData| (((|Void|) $ (|NonNegativeInteger|) (|Point| (|DoubleFloat|))) "\\spad{modifyPointData(v,ind,pt)} takes the viewport,{} \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} and places the data point,{} \\spad{pt} into the list of points database of \\spad{v} at the index location given by \\spad{ind}.")) (|subspace| (($ $ (|ThreeSpace| (|DoubleFloat|))) "\\spad{subspace(v,sp)} places the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} in the subspace \\spad{sp},{} which is of the domain \\spad{ThreeSpace}.") (((|ThreeSpace| (|DoubleFloat|)) $) "\\spad{subspace(v)} returns the contents of the viewport \\spad{v},{} which is of the domain \\spadtype{ThreeDimensionalViewport},{} as a subspace of the domain \\spad{ThreeSpace}.")) (|makeViewport3D| (($ (|ThreeSpace| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{makeViewport3D(sp,lopt)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose draw options are indicated by the list \\spad{lopt},{} which is a list of options from the domain \\spad{DrawOption}.") (($ (|ThreeSpace| (|DoubleFloat|)) (|String|)) "\\spad{makeViewport3D(sp,s)} takes the given space,{} \\spad{sp} which is of the domain \\spadtype{ThreeSpace} and displays a viewport window on the screen which contains the contents of \\spad{sp},{} and whose title is given by \\spad{s}.") (($ $) "\\spad{makeViewport3D(v)} takes the given three-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{ThreeDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport3D| (($) "\\spad{viewport3D()} returns an undefined three-dimensional viewport of the domain \\spadtype{ThreeDimensionalViewport} whose contents are empty.")) (|viewDeltaYDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaYDefault(dy)} sets the current default vertical offset from the center of the viewport window to be \\spad{dy} and returns \\spad{dy}.") (((|Float|)) "\\spad{viewDeltaYDefault()} returns the current default vertical offset from the center of the viewport window.")) (|viewDeltaXDefault| (((|Float|) (|Float|)) "\\spad{viewDeltaXDefault(dx)} sets the current default horizontal offset from the center of the viewport window to be \\spad{dx} and returns \\spad{dx}.") (((|Float|)) "\\spad{viewDeltaXDefault()} returns the current default horizontal offset from the center of the viewport window.")) (|viewZoomDefault| (((|Float|) (|Float|)) "\\spad{viewZoomDefault(s)} sets the current default graph scaling value to \\spad{s} and returns \\spad{s}.") (((|Float|)) "\\spad{viewZoomDefault()} returns the current default graph scaling value.")) (|viewPhiDefault| (((|Float|) (|Float|)) "\\spad{viewPhiDefault(p)} sets the current default latitudinal view angle in radians to the value \\spad{p} and returns \\spad{p}.") (((|Float|)) "\\spad{viewPhiDefault()} returns the current default latitudinal view angle in radians.")) (|viewThetaDefault| (((|Float|) (|Float|)) "\\spad{viewThetaDefault(t)} sets the current default longitudinal view angle in radians to the value \\spad{t} and returns \\spad{t}.") (((|Float|)) "\\spad{viewThetaDefault()} returns the current default longitudinal view angle in radians."))) NIL NIL -(-1185) +(-1184) ((|constructor| (NIL "ViewportDefaultsPackage describes default and user definable values for graphics")) (|tubeRadiusDefault| (((|DoubleFloat|)) "\\spad{tubeRadiusDefault()} returns the radius used for a 3D tube plot.") (((|DoubleFloat|) (|Float|)) "\\spad{tubeRadiusDefault(r)} sets the default radius for a 3D tube plot to \\spad{r}.")) (|tubePointsDefault| (((|PositiveInteger|)) "\\spad{tubePointsDefault()} returns the number of points to be used when creating the circle to be used in creating a 3D tube plot.") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{tubePointsDefault(i)} sets the number of points to use when creating the circle to be used in creating a 3D tube plot to \\spad{i}.")) (|var2StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var2StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var2StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|var1StepsDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{var1StepsDefault(i)} sets the number of steps to take when creating a 3D mesh in the direction of the first defined free variable to \\spad{i} (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).") (((|PositiveInteger|)) "\\spad{var1StepsDefault()} is the current setting for the number of steps to take when creating a 3D mesh in the direction of the first defined free variable (a free variable is considered defined when its range is specified (\\spadignore{e.g.} \\spad{x=0}..10)).")) (|viewWriteAvailable| (((|List| (|String|))) "\\spad{viewWriteAvailable()} returns a list of available methods for writing,{} such as BITMAP,{} POSTSCRIPT,{} etc.")) (|viewWriteDefault| (((|List| (|String|)) (|List| (|String|))) "\\spad{viewWriteDefault(l)} sets the default list of things to write in a viewport data file to the strings in \\spad{l}; a viewAlone file is always genereated.") (((|List| (|String|))) "\\spad{viewWriteDefault()} returns the list of things to write in a viewport data file; a viewAlone file is always generated.")) (|viewDefaults| (((|Void|)) "\\spad{viewDefaults()} resets all the default graphics settings.")) (|viewSizeDefault| (((|List| (|PositiveInteger|)) (|List| (|PositiveInteger|))) "\\spad{viewSizeDefault([w,h])} sets the default viewport width to \\spad{w} and height to \\spad{h}.") (((|List| (|PositiveInteger|))) "\\spad{viewSizeDefault()} returns the default viewport width and height.")) (|viewPosDefault| (((|List| (|NonNegativeInteger|)) (|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault([x,y])} sets the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have th \\spad{X} and \\spad{Y} coordinates \\spad{x},{} \\spad{y}.") (((|List| (|NonNegativeInteger|))) "\\spad{viewPosDefault()} returns the default \\spad{X} and \\spad{Y} position of a viewport window unless overriden explicityly,{} newly created viewports will have this \\spad{X} and \\spad{Y} coordinate.")) (|pointSizeDefault| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{pointSizeDefault(i)} sets the default size of the points in a 2D viewport to \\spad{i}.") (((|PositiveInteger|)) "\\spad{pointSizeDefault()} returns the default size of the points in a 2D viewport.")) (|unitsColorDefault| (((|Palette|) (|Palette|)) "\\spad{unitsColorDefault(p)} sets the default color of the unit ticks in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{unitsColorDefault()} returns the default color of the unit ticks in a 2D viewport.")) (|axesColorDefault| (((|Palette|) (|Palette|)) "\\spad{axesColorDefault(p)} sets the default color of the axes in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{axesColorDefault()} returns the default color of the axes in a 2D viewport.")) (|lineColorDefault| (((|Palette|) (|Palette|)) "\\spad{lineColorDefault(p)} sets the default color of lines connecting points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{lineColorDefault()} returns the default color of lines connecting points in a 2D viewport.")) (|pointColorDefault| (((|Palette|) (|Palette|)) "\\spad{pointColorDefault(p)} sets the default color of points in a 2D viewport to the palette \\spad{p}.") (((|Palette|)) "\\spad{pointColorDefault()} returns the default color of points in a 2D viewport."))) NIL NIL -(-1186) +(-1185) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1187 A S) +(-1186 A S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#2|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) NIL NIL -(-1188 S) +(-1187 S) ((|constructor| (NIL "Vector Spaces (not necessarily finite dimensional) over a field.")) (|dimension| (((|CardinalNumber|)) "\\spad{dimension()} returns the dimensionality of the vector space.")) (/ (($ $ |#1|) "\\spad{x/y} divides the vector \\spad{x} by the scalar \\spad{y}."))) -((-3991 . T) (-3990 . T)) +((-3990 . T) (-3989 . T)) NIL -(-1189 R) +(-1188 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]*v + A[2]\\spad{*v**2} + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,s,st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1190 K R UP -3093) +(-1189 K R UP -3092) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,basisDen,basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,w2,...,wn}. If \\spad{basis} is the matrix \\spad{(aij, i = 1..n, j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{vi = (1/basisDen) * sum(aij * wj, j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{wi} with respect to the basis \\spad{v1,...,vn}: if \\spad{basisInv} is the matrix \\spad{(bij, i = 1..n, j = 1..n)},{} then \\spad{wi = sum(bij * vj, j = 1..n)}."))) NIL NIL -(-1191) +(-1190) ((|constructor| (NIL "This domain represents the syntax of a `where' expression.")) (|qualifier| (((|SpadAst|) $) "\\spad{qualifier(e)} returns the qualifier of the expression `e'.")) (|mainExpression| (((|SpadAst|) $) "\\spad{mainExpression(e)} returns the main expression of the `where' expression `e'."))) NIL NIL -(-1192) +(-1191) ((|constructor| (NIL "This domain represents the `while' iterator syntax.")) (|condition| (((|SpadAst|) $) "\\spad{condition(i)} returns the condition of the while iterator `i'."))) NIL NIL -(-1193 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1192 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: 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)"))) -((-3991 |has| |#1| (-146)) (-3990 |has| |#1| (-146)) (-3993 . T)) +((-3990 |has| |#1| (-146)) (-3989 |has| |#1| (-146)) (-3992 . T)) ((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312)))) -(-1194 R E V P) +(-1193 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}{MM Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. \\spad{DISCO'92}. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(ps)} returns the same as \\axiom{characteristicSerie(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(ps,{}redOp?,{}redOp)} returns a list \\axiom{lts} of triangular sets such that the zero set of \\axiom{ps} is the union of the regular zero sets of the members of \\axiom{lts}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(ps,{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(ps)} returns the same as \\axiom{characteristicSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(ps,{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{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 = f*q + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(ps)} returns the same as \\axiom{medialSet(ps,{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(ps,{}redOp?,{}redOp)} returns \\axiom{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{ps} (with rank not higher than any basic set of \\axiom{ps}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{bs} has to be understood as a candidate for being a characteristic set of \\axiom{ps}. In the original algorithm,{} \\axiom{bs} is simply a basic set of \\axiom{ps}."))) -((-3997 . T) (-3996 . T)) -((-12 (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-554 (-474)))) (|HasCategory| |#4| (QUOTE (-1014))) (|HasCategory| |#1| (QUOTE (-496))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-553 (-773)))) (|HasCategory| |#4| (QUOTE (-72)))) -(-1195 R) +((-3996 . T) (-3995 . T)) +((-12 (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#4| (|%list| (QUOTE -260) (|devaluate| |#4|)))) (|HasCategory| |#4| (QUOTE (-553 (-473)))) (|HasCategory| |#4| (QUOTE (-1013))) (|HasCategory| |#1| (QUOTE (-495))) (|HasCategory| |#3| (QUOTE (-320))) (|HasCategory| |#4| (QUOTE (-552 (-772)))) (|HasCategory| |#4| (QUOTE (-72)))) +(-1194 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.fr)"))) -((-3990 . T) (-3991 . T) (-3993 . T)) +((-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1196 |vl| R) +(-1195 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables do not commute. The coefficient ring may be non-commutative too. However,{} coefficients and variables commute."))) -((-3993 . T) (-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) -(-1197 R |VarSet| XPOLY) +((-3992 . T) (-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3988))) +(-1196 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1198 S -3093) +(-1197 S -3092) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-320))) (|HasCategory| |#2| (QUOTE (-118))) (|HasCategory| |#2| (QUOTE (-120)))) -(-1199 -3093) +(-1198 -3092) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|NonNegativeInteger|)) "\\spad{Frobenius(a,s)} returns \\spad{a**(q**s)} where \\spad{q} is the size()\\$\\spad{F}.") (($ $) "\\spad{Frobenius(a)} returns \\spad{a ** q} where \\spad{q} is the \\spad{size()\\$F}.")) (|transcendenceDegree| (((|NonNegativeInteger|)) "\\spad{transcendenceDegree()} returns the transcendence degree of the field extension,{} 0 if the extension is algebraic.")) (|extensionDegree| (((|OnePointCompletion| (|PositiveInteger|))) "\\spad{extensionDegree()} returns the degree of the field extension if the extension is algebraic,{} and \\spad{infinity} if it is not.")) (|degree| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{degree(a)} returns the degree of minimal polynomial of an element \\spad{a} if \\spad{a} is algebraic with respect to the ground field \\spad{F},{} and \\spad{infinity} otherwise.")) (|inGroundField?| (((|Boolean|) $) "\\spad{inGroundField?(a)} tests whether an element \\spad{a} is already in the ground field \\spad{F}.")) (|transcendent?| (((|Boolean|) $) "\\spad{transcendent?(a)} tests whether an element \\spad{a} is transcendent with respect to the ground field \\spad{F}.")) (|algebraic?| (((|Boolean|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-3988 . T) (-3994 . T) (-3989 . T) ((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +((-3987 . T) (-3993 . T) (-3988 . T) ((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL -(-1200 |vl| R) +(-1199 |vl| R) ((|constructor| (NIL "This category specifies opeations for polynomials and formal series with non-commutative variables.")) (|varList| (((|List| |#1|) $) "\\spad{varList(x)} returns the list of variables which appear in \\spad{x}.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|sh| (($ $ (|NonNegativeInteger|)) "\\spad{sh(x,n)} returns the shuffle power of \\spad{x} to the \\spad{n}.") (($ $ $) "\\spad{sh(x,y)} returns the shuffle-product of \\spad{x} by \\spad{y}. This multiplication is associative and commutative.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(x)} is zero.")) (|constant| ((|#2| $) "\\spad{constant(x)} returns the constant term of \\spad{x}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(x)} returns \\spad{true} if \\spad{x} is constant.")) (|coerce| (($ |#1|) "\\spad{coerce(v)} returns \\spad{v}.")) (|mirror| (($ $) "\\spad{mirror(x)} returns \\spad{Sum(r_i mirror(w_i))} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} is a monomial")) (|monom| (($ (|OrderedFreeMonoid| |#1|) |#2|) "\\spad{monom(w,r)} returns the product of the word \\spad{w} by the coefficient \\spad{r}.")) (|rquo| (($ $ $) "\\spad{rquo(x,y)} returns the right simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{rquo(x,w)} returns the right simplification of \\spad{x} by \\spad{w}.") (($ $ |#1|) "\\spad{rquo(x,v)} returns the right simplification of \\spad{x} by the variable \\spad{v}.")) (|lquo| (($ $ $) "\\spad{lquo(x,y)} returns the left simplification of \\spad{x} by \\spad{y}.") (($ $ (|OrderedFreeMonoid| |#1|)) "\\spad{lquo(x,w)} returns the left simplification of \\spad{x} by the word \\spad{w}.") (($ $ |#1|) "\\spad{lquo(x,v)} returns the left simplification of \\spad{x} by the variable \\spad{v}.")) (|coef| ((|#2| $ $) "\\spad{coef(x,y)} returns scalar product of \\spad{x} by \\spad{y},{} the set of words being regarded as an orthogonal basis.") ((|#2| $ (|OrderedFreeMonoid| |#1|)) "\\spad{coef(x,w)} returns the coefficient of the word \\spad{w} in \\spad{x}.")) (|mindegTerm| (((|Record| (|:| |k| (|OrderedFreeMonoid| |#1|)) (|:| |c| |#2|)) $) "\\spad{mindegTerm(x)} returns the term whose word is \\spad{mindeg(x)}.")) (|mindeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{mindeg(x)} returns the little word which appears in \\spad{x}. Error if \\spad{x=0}.")) (* (($ $ |#2|) "\\spad{x * r} returns the product of \\spad{x} by \\spad{r}. Usefull if \\spad{R} is a non-commutative Ring.") (($ |#1| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) +((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL -(-1201 |VarSet| R) +(-1200 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.fr).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-655 (-350 (-485))))) (|HasAttribute| |#2| (QUOTE -3989))) -(-1202 R) +((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasCategory| |#2| (QUOTE (-654 (-350 (-484))))) (|HasAttribute| |#2| (QUOTE -3988))) +(-1201 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3989))) -(-1203 |vl| R) +((-3988 |has| |#1| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasAttribute| |#1| (QUOTE -3988))) +(-1202 |vl| R) ((|constructor| (NIL "The Category of polynomial rings with non-commutative variables. The coefficient ring may be non-commutative too. However coefficients commute with vaiables.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\spad{trunc(p,n)} returns the polynomial \\spad{p} truncated at order \\spad{n}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} returns the degree of \\spad{p}. \\indented{1}{Note that the degree of a word is its length.}")) (|maxdeg| (((|OrderedFreeMonoid| |#1|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) +((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) NIL -(-1204 R E) +(-1203 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-3993 . T) (-3994 |has| |#1| (-6 -3994)) (-3989 |has| |#1| (-6 -3989)) (-3991 . T) (-3990 . T)) -((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3994)) (|HasAttribute| |#1| (QUOTE -3989))) -(-1205 |VarSet| R) +((-3992 . T) (-3993 |has| |#1| (-6 -3993)) (-3988 |has| |#1| (-6 -3988)) (-3990 . T) (-3989 . T)) +((|HasCategory| |#1| (QUOTE (-146))) (|HasCategory| |#1| (QUOTE (-312))) (|HasAttribute| |#1| (QUOTE -3992)) (|HasAttribute| |#1| (QUOTE -3993)) (|HasAttribute| |#1| (QUOTE -3988))) +(-1204 |VarSet| R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose variables do not commute. The representation is recursive. The coefficient ring may be non-commutative. Coefficients and variables commute.")) (|RemainderList| (((|List| (|Record| (|:| |k| |#1|) (|:| |c| $))) $) "\\spad{RemainderList(p)} returns the regular part of \\spad{p} as a list of terms.")) (|unexpand| (($ (|XDistributedPolynomial| |#1| |#2|)) "\\spad{unexpand(p)} returns \\spad{p} in recursive form.")) (|expand| (((|XDistributedPolynomial| |#1| |#2|) $) "\\spad{expand(p)} returns \\spad{p} in distributed form."))) -((-3989 |has| |#2| (-6 -3989)) (-3991 . T) (-3990 . T) (-3993 . T)) -((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3989))) -(-1206) +((-3988 |has| |#2| (-6 -3988)) (-3990 . T) (-3989 . T) (-3992 . T)) +((|HasCategory| |#2| (QUOTE (-146))) (|HasAttribute| |#2| (QUOTE -3988))) +(-1205) ((|constructor| (NIL "This domain provides representations of Young diagrams.")) (|shape| (((|Partition|) $) "\\spad{shape x} returns the partition shaping \\spad{x}.")) (|youngDiagram| (($ (|List| (|PositiveInteger|))) "\\spad{youngDiagram l} returns an object representing a Young diagram with shape given by the list of integers \\spad{l}"))) NIL NIL -(-1207 A) +(-1206 A) ((|constructor| (NIL "This package implements fixed-point computations on streams.")) (Y (((|List| (|Stream| |#1|)) (|Mapping| (|List| (|Stream| |#1|)) (|List| (|Stream| |#1|))) (|Integer|)) "\\spad{Y(g,n)} computes a fixed point of the function \\spad{g},{} where \\spad{g} takes a list of \\spad{n} streams and returns a list of \\spad{n} streams.") (((|Stream| |#1|) (|Mapping| (|Stream| |#1|) (|Stream| |#1|))) "\\spad{Y(f)} computes a fixed point of the function \\spad{f}."))) NIL NIL -(-1208 R |ls| |ls2|) +(-1207 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,info?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,info?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,info?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,false,false,false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,info?)} returns the same as \\spad{realSolve(ts,info?,false,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?)} returns the same as \\spad{realSolve(ts,info?,check?,false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,info?,check?,lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(lp,{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,info?,check?,lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,false,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,info?)} returns the same as \\spad{univariateSolve(lp,info?,false,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?)} returns the same as \\spad{univariateSolve(lp,info?,check?,false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,info?,check?,lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(lp,{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,false,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,info?)} returns the same as \\spad{triangSolve(lp,false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,info?,lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1209 R) +(-1208 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,...,vn], u)} returns \\spad{[c1,...,cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}'s exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,...,vn])} returns \\spad{[c1,...,cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}'s are 0,{} \"failed\" if the \\spad{vi}'s are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,...,vn])} returns \\spad{true} if the \\spad{vi}'s are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1210 |p|) +(-1209 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-3998 "*") . T) (-3990 . T) (-3991 . T) (-3993 . T)) +(((-3997 "*") . T) (-3989 . T) (-3990 . T) (-3992 . T)) NIL NIL NIL @@ -4788,4 +4784,4 @@ NIL NIL NIL NIL -((-3 NIL 1963082 1963087 1963092 1963097) (-2 NIL 1963062 1963067 1963072 1963077) (-1 NIL 1963042 1963047 1963052 1963057) (0 NIL 1963022 1963027 1963032 1963037) (-1210 "ZMOD.spad" 1962831 1962844 1962960 1963017) (-1209 "ZLINDEP.spad" 1961929 1961940 1962821 1962826) (-1208 "ZDSOLVE.spad" 1951890 1951912 1961919 1961924) (-1207 "YSTREAM.spad" 1951385 1951396 1951880 1951885) (-1206 "YDIAGRAM.spad" 1951019 1951028 1951375 1951380) (-1205 "XRPOLY.spad" 1950239 1950259 1950875 1950944) (-1204 "XPR.spad" 1948034 1948047 1949957 1950056) (-1203 "XPOLYC.spad" 1947353 1947369 1947960 1948029) (-1202 "XPOLY.spad" 1946908 1946919 1947209 1947278) (-1201 "XPBWPOLY.spad" 1945379 1945399 1946714 1946783) (-1200 "XFALG.spad" 1942427 1942443 1945305 1945374) (-1199 "XF.spad" 1940890 1940905 1942329 1942422) (-1198 "XF.spad" 1939333 1939350 1940774 1940779) (-1197 "XEXPPKG.spad" 1938592 1938618 1939323 1939328) (-1196 "XDPOLY.spad" 1938206 1938222 1938448 1938517) (-1195 "XALG.spad" 1937874 1937885 1938162 1938201) (-1194 "WUTSET.spad" 1933877 1933894 1937508 1937535) (-1193 "WP.spad" 1933084 1933128 1933735 1933802) (-1192 "WHILEAST.spad" 1932882 1932891 1933074 1933079) (-1191 "WHEREAST.spad" 1932553 1932562 1932872 1932877) (-1190 "WFFINTBS.spad" 1930216 1930238 1932543 1932548) (-1189 "WEIER.spad" 1928438 1928449 1930206 1930211) (-1188 "VSPACE.spad" 1928111 1928122 1928406 1928433) (-1187 "VSPACE.spad" 1927804 1927817 1928101 1928106) (-1186 "VOID.spad" 1927481 1927490 1927794 1927799) (-1185 "VIEWDEF.spad" 1922682 1922691 1927471 1927476) (-1184 "VIEW3D.spad" 1906643 1906652 1922672 1922677) (-1183 "VIEW2D.spad" 1894542 1894551 1906633 1906638) (-1182 "VIEW.spad" 1892262 1892271 1894532 1894537) (-1181 "VECTOR2.spad" 1890901 1890914 1892252 1892257) (-1180 "VECTOR.spad" 1889620 1889631 1889871 1889898) (-1179 "VECTCAT.spad" 1887532 1887543 1889588 1889615) (-1178 "VECTCAT.spad" 1885253 1885266 1887311 1887316) (-1177 "VARIABLE.spad" 1885033 1885048 1885243 1885248) (-1176 "UTYPE.spad" 1884677 1884686 1885023 1885028) (-1175 "UTSODETL.spad" 1883972 1883996 1884633 1884638) (-1174 "UTSODE.spad" 1882188 1882208 1883962 1883967) (-1173 "UTSCAT.spad" 1879667 1879683 1882086 1882183) (-1172 "UTSCAT.spad" 1876814 1876832 1879235 1879240) (-1171 "UTS2.spad" 1876409 1876444 1876804 1876809) (-1170 "UTS.spad" 1871421 1871449 1874941 1875038) (-1169 "URAGG.spad" 1866142 1866153 1871411 1871416) (-1168 "URAGG.spad" 1860827 1860840 1866098 1866103) (-1167 "UPXSSING.spad" 1858595 1858621 1860031 1860164) (-1166 "UPXSCONS.spad" 1856413 1856433 1856786 1856935) (-1165 "UPXSCCA.spad" 1854984 1855004 1856259 1856408) (-1164 "UPXSCCA.spad" 1853697 1853719 1854974 1854979) (-1163 "UPXSCAT.spad" 1852286 1852302 1853543 1853692) (-1162 "UPXS2.spad" 1851829 1851882 1852276 1852281) (-1161 "UPXS.spad" 1849184 1849212 1850020 1850169) (-1160 "UPSQFREE.spad" 1847599 1847613 1849174 1849179) (-1159 "UPSCAT.spad" 1845394 1845418 1847497 1847594) (-1158 "UPSCAT.spad" 1842890 1842916 1844995 1845000) (-1157 "UPOLYC2.spad" 1842361 1842380 1842880 1842885) (-1156 "UPOLYC.spad" 1837441 1837452 1842203 1842356) (-1155 "UPOLYC.spad" 1832439 1832452 1837203 1837208) (-1154 "UPMP.spad" 1831371 1831384 1832429 1832434) (-1153 "UPDIVP.spad" 1830936 1830950 1831361 1831366) (-1152 "UPDECOMP.spad" 1829197 1829211 1830926 1830931) (-1151 "UPCDEN.spad" 1828414 1828430 1829187 1829192) (-1150 "UP2.spad" 1827778 1827799 1828404 1828409) (-1149 "UP.spad" 1825248 1825263 1825635 1825788) (-1148 "UNISEG2.spad" 1824745 1824758 1825204 1825209) (-1147 "UNISEG.spad" 1824098 1824109 1824664 1824669) (-1146 "UNIFACT.spad" 1823201 1823213 1824088 1824093) (-1145 "ULSCONS.spad" 1817047 1817067 1817417 1817566) (-1144 "ULSCCAT.spad" 1814784 1814804 1816893 1817042) (-1143 "ULSCCAT.spad" 1812629 1812651 1814740 1814745) (-1142 "ULSCAT.spad" 1810869 1810885 1812475 1812624) (-1141 "ULS2.spad" 1810383 1810436 1810859 1810864) (-1140 "ULS.spad" 1802416 1802444 1803361 1803784) (-1139 "UINT8.spad" 1802293 1802302 1802406 1802411) (-1138 "UINT64.spad" 1802169 1802178 1802283 1802288) (-1137 "UINT32.spad" 1802045 1802054 1802159 1802164) (-1136 "UINT16.spad" 1801921 1801930 1802035 1802040) (-1135 "UFD.spad" 1800986 1800995 1801847 1801916) (-1134 "UFD.spad" 1800113 1800124 1800976 1800981) (-1133 "UDVO.spad" 1798994 1799003 1800103 1800108) (-1132 "UDPO.spad" 1796575 1796586 1798950 1798955) (-1131 "TYPEAST.spad" 1796494 1796503 1796565 1796570) (-1130 "TYPE.spad" 1796426 1796435 1796484 1796489) (-1129 "TWOFACT.spad" 1795078 1795093 1796416 1796421) (-1128 "TUPLE.spad" 1794585 1794596 1794990 1794995) (-1127 "TUBETOOL.spad" 1791452 1791461 1794575 1794580) (-1126 "TUBE.spad" 1790099 1790116 1791442 1791447) (-1125 "TSETCAT.spad" 1778170 1778187 1790067 1790094) (-1124 "TSETCAT.spad" 1766227 1766246 1778126 1778131) (-1123 "TS.spad" 1764855 1764871 1765821 1765918) (-1122 "TRMANIP.spad" 1759219 1759236 1764543 1764548) (-1121 "TRIMAT.spad" 1758182 1758207 1759209 1759214) (-1120 "TRIGMNIP.spad" 1756709 1756726 1758172 1758177) (-1119 "TRIGCAT.spad" 1756221 1756230 1756699 1756704) (-1118 "TRIGCAT.spad" 1755731 1755742 1756211 1756216) (-1117 "TREE.spad" 1754371 1754382 1755403 1755430) (-1116 "TRANFUN.spad" 1754210 1754219 1754361 1754366) (-1115 "TRANFUN.spad" 1754047 1754058 1754200 1754205) (-1114 "TOPSP.spad" 1753721 1753730 1754037 1754042) (-1113 "TOOLSIGN.spad" 1753384 1753395 1753711 1753716) (-1112 "TEXTFILE.spad" 1751945 1751954 1753374 1753379) (-1111 "TEX1.spad" 1751501 1751512 1751935 1751940) (-1110 "TEX.spad" 1748695 1748704 1751491 1751496) (-1109 "TBCMPPK.spad" 1746796 1746819 1748685 1748690) (-1108 "TBAGG.spad" 1746039 1746062 1746764 1746791) (-1107 "TBAGG.spad" 1745302 1745327 1746029 1746034) (-1106 "TANEXP.spad" 1744710 1744721 1745292 1745297) (-1105 "TALGOP.spad" 1744434 1744445 1744700 1744705) (-1104 "TABLEAU.spad" 1743915 1743926 1744424 1744429) (-1103 "TABLE.spad" 1742190 1742213 1742460 1742487) (-1102 "TABLBUMP.spad" 1738969 1738980 1742180 1742185) (-1101 "SYSTEM.spad" 1738197 1738206 1738959 1738964) (-1100 "SYSSOLP.spad" 1735680 1735691 1738187 1738192) (-1099 "SYSPTR.spad" 1735579 1735588 1735670 1735675) (-1098 "SYSNNI.spad" 1734802 1734813 1735569 1735574) (-1097 "SYSINT.spad" 1734206 1734217 1734792 1734797) (-1096 "SYNTAX.spad" 1730540 1730549 1734196 1734201) (-1095 "SYMTAB.spad" 1728608 1728617 1730530 1730535) (-1094 "SYMS.spad" 1724637 1724646 1728598 1728603) (-1093 "SYMPOLY.spad" 1723770 1723781 1723852 1723979) (-1092 "SYMFUNC.spad" 1723271 1723282 1723760 1723765) (-1091 "SYMBOL.spad" 1720766 1720775 1723261 1723266) (-1090 "SUTS.spad" 1717879 1717907 1719298 1719395) (-1089 "SUPXS.spad" 1715221 1715249 1716070 1716219) (-1088 "SUPFRACF.spad" 1714326 1714344 1715211 1715216) (-1087 "SUP2.spad" 1713718 1713731 1714316 1714321) (-1086 "SUP.spad" 1710802 1710813 1711575 1711728) (-1085 "SUMRF.spad" 1709776 1709787 1710792 1710797) (-1084 "SUMFS.spad" 1709405 1709422 1709766 1709771) (-1083 "SULS.spad" 1701425 1701453 1702383 1702806) (-1082 "syntax.spad" 1701194 1701203 1701415 1701420) (-1081 "SUCH.spad" 1700884 1700899 1701184 1701189) (-1080 "SUBSPACE.spad" 1693015 1693030 1700874 1700879) (-1079 "SUBRESP.spad" 1692185 1692199 1692971 1692976) (-1078 "STTFNC.spad" 1688653 1688669 1692175 1692180) (-1077 "STTF.spad" 1684752 1684768 1688643 1688648) (-1076 "STTAYLOR.spad" 1677429 1677440 1684659 1684664) (-1075 "STRTBL.spad" 1675816 1675833 1675965 1675992) (-1074 "STRING.spad" 1674684 1674693 1675069 1675096) (-1073 "STREAM3.spad" 1674257 1674272 1674674 1674679) (-1072 "STREAM2.spad" 1673385 1673398 1674247 1674252) (-1071 "STREAM1.spad" 1673091 1673102 1673375 1673380) (-1070 "STREAM.spad" 1670087 1670098 1672694 1672709) (-1069 "STINPROD.spad" 1669023 1669039 1670077 1670082) (-1068 "STEPAST.spad" 1668257 1668266 1669013 1669018) (-1067 "STEP.spad" 1667574 1667583 1668247 1668252) (-1066 "STBL.spad" 1665952 1665980 1666119 1666146) (-1065 "STAGG.spad" 1664651 1664662 1665942 1665947) (-1064 "STAGG.spad" 1663348 1663361 1664641 1664646) (-1063 "STACK.spad" 1662770 1662781 1663020 1663047) (-1062 "SRING.spad" 1662530 1662539 1662760 1662765) (-1061 "SREGSET.spad" 1660262 1660279 1662164 1662191) (-1060 "SRDCMPK.spad" 1658839 1658859 1660252 1660257) (-1059 "SRAGG.spad" 1654022 1654031 1658807 1658834) (-1058 "SRAGG.spad" 1649225 1649236 1654012 1654017) (-1057 "SQMATRIX.spad" 1646902 1646920 1647818 1647905) (-1056 "SPLTREE.spad" 1641644 1641657 1646440 1646467) (-1055 "SPLNODE.spad" 1638264 1638277 1641634 1641639) (-1054 "SPFCAT.spad" 1637073 1637082 1638254 1638259) (-1053 "SPECOUT.spad" 1635625 1635634 1637063 1637068) (-1052 "SPADXPT.spad" 1627716 1627725 1635615 1635620) (-1051 "spad-parser.spad" 1627181 1627190 1627706 1627711) (-1050 "SPADAST.spad" 1626882 1626891 1627171 1627176) (-1049 "SPACEC.spad" 1611097 1611108 1626872 1626877) (-1048 "SPACE3.spad" 1610873 1610884 1611087 1611092) (-1047 "SORTPAK.spad" 1610422 1610435 1610829 1610834) (-1046 "SOLVETRA.spad" 1608185 1608196 1610412 1610417) (-1045 "SOLVESER.spad" 1606641 1606652 1608175 1608180) (-1044 "SOLVERAD.spad" 1602667 1602678 1606631 1606636) (-1043 "SOLVEFOR.spad" 1601129 1601147 1602657 1602662) (-1042 "SNTSCAT.spad" 1600729 1600746 1601097 1601124) (-1041 "SMTS.spad" 1599046 1599072 1600323 1600420) (-1040 "SMP.spad" 1596854 1596874 1597244 1597371) (-1039 "SMITH.spad" 1595699 1595724 1596844 1596849) (-1038 "SMATCAT.spad" 1593817 1593847 1595643 1595694) (-1037 "SMATCAT.spad" 1591867 1591899 1593695 1593700) (-1036 "aggcat.spad" 1591553 1591564 1591857 1591862) (-1035 "SKAGG.spad" 1590522 1590533 1591521 1591548) (-1034 "SINT.spad" 1589821 1589830 1590388 1590517) (-1033 "SIMPAN.spad" 1589549 1589558 1589811 1589816) (-1032 "SIGNRF.spad" 1588674 1588685 1589539 1589544) (-1031 "SIGNEF.spad" 1587960 1587977 1588664 1588669) (-1030 "syntax.spad" 1587377 1587386 1587950 1587955) (-1029 "SIG.spad" 1586739 1586748 1587367 1587372) (-1028 "SHP.spad" 1584683 1584698 1586695 1586700) (-1027 "SHDP.spad" 1574176 1574203 1574693 1574790) (-1026 "SGROUP.spad" 1573784 1573793 1574166 1574171) (-1025 "SGROUP.spad" 1573390 1573401 1573774 1573779) (-1024 "catdef.spad" 1573100 1573112 1573211 1573385) (-1023 "catdef.spad" 1572656 1572668 1572921 1573095) (-1022 "SGCF.spad" 1565795 1565804 1572646 1572651) (-1021 "SFRTCAT.spad" 1564741 1564758 1565763 1565790) (-1020 "SFRGCD.spad" 1563804 1563824 1564731 1564736) (-1019 "SFQCMPK.spad" 1558617 1558637 1563794 1563799) (-1018 "SEXOF.spad" 1558460 1558500 1558607 1558612) (-1017 "SEXCAT.spad" 1556288 1556328 1558450 1558455) (-1016 "SEX.spad" 1556180 1556189 1556278 1556283) (-1015 "SETMN.spad" 1554640 1554657 1556170 1556175) (-1014 "SETCAT.spad" 1554125 1554134 1554630 1554635) (-1013 "SETCAT.spad" 1553608 1553619 1554115 1554120) (-1012 "SETAGG.spad" 1550157 1550168 1553588 1553603) (-1011 "SETAGG.spad" 1546714 1546727 1550147 1550152) (-1010 "SET.spad" 1545023 1545034 1546120 1546159) (-1009 "syntax.spad" 1544726 1544735 1545013 1545018) (-1008 "SEGXCAT.spad" 1543882 1543895 1544716 1544721) (-1007 "SEGCAT.spad" 1542807 1542818 1543872 1543877) (-1006 "SEGBIND2.spad" 1542505 1542518 1542797 1542802) (-1005 "SEGBIND.spad" 1542263 1542274 1542452 1542457) (-1004 "SEGAST.spad" 1541993 1542002 1542253 1542258) (-1003 "SEG2.spad" 1541428 1541441 1541949 1541954) (-1002 "SEG.spad" 1541241 1541252 1541347 1541352) (-1001 "SDVAR.spad" 1540517 1540528 1541231 1541236) (-1000 "SDPOL.spad" 1538209 1538220 1538500 1538627) (-999 "SCPKG.spad" 1536299 1536309 1538199 1538204) (-998 "SCOPE.spad" 1535477 1535485 1536289 1536294) (-997 "SCACHE.spad" 1534174 1534184 1535467 1535472) (-996 "SASTCAT.spad" 1534084 1534092 1534164 1534169) (-995 "SAOS.spad" 1533957 1533965 1534074 1534079) (-994 "SAERFFC.spad" 1533671 1533690 1533947 1533952) (-993 "SAEFACT.spad" 1533373 1533392 1533661 1533666) (-992 "SAE.spad" 1531024 1531039 1531634 1531769) (-991 "RURPK.spad" 1528684 1528699 1531014 1531019) (-990 "RULESET.spad" 1528138 1528161 1528674 1528679) (-989 "RULECOLD.spad" 1527991 1528003 1528128 1528133) (-988 "RULE.spad" 1526240 1526263 1527981 1527986) (-987 "RTVALUE.spad" 1525976 1525984 1526230 1526235) (-986 "syntax.spad" 1525694 1525702 1525966 1525971) (-985 "RSETGCD.spad" 1522137 1522156 1525684 1525689) (-984 "RSETCAT.spad" 1512106 1512122 1522105 1522132) (-983 "RSETCAT.spad" 1502095 1502113 1512096 1512101) (-982 "RSDCMPK.spad" 1500596 1500615 1502085 1502090) (-981 "RRCC.spad" 1498981 1499010 1500586 1500591) (-980 "RRCC.spad" 1497364 1497395 1498971 1498976) (-979 "RPTAST.spad" 1497067 1497075 1497354 1497359) (-978 "RPOLCAT.spad" 1476572 1476586 1496935 1497062) (-977 "RPOLCAT.spad" 1455870 1455886 1476235 1476240) (-976 "ROMAN.spad" 1455199 1455207 1455736 1455865) (-975 "ROIRC.spad" 1454280 1454311 1455189 1455194) (-974 "RNS.spad" 1453257 1453265 1454182 1454275) (-973 "RNS.spad" 1452320 1452330 1453247 1453252) (-972 "RNGBIND.spad" 1451481 1451494 1452275 1452280) (-971 "RNG.spad" 1451090 1451098 1451471 1451476) (-970 "RNG.spad" 1450697 1450707 1451080 1451085) (-969 "RMODULE.spad" 1450479 1450489 1450687 1450692) (-968 "RMCAT2.spad" 1449900 1449956 1450469 1450474) (-967 "RMATRIX.spad" 1448710 1448728 1449052 1449091) (-966 "RMATCAT.spad" 1444348 1444378 1448666 1448705) (-965 "RMATCAT.spad" 1439876 1439908 1444196 1444201) (-964 "RLINSET.spad" 1439581 1439591 1439866 1439871) (-963 "RINTERP.spad" 1439470 1439489 1439571 1439576) (-962 "RING.spad" 1438941 1438949 1439450 1439465) (-961 "RING.spad" 1438420 1438430 1438931 1438936) (-960 "RIDIST.spad" 1437813 1437821 1438410 1438415) (-959 "RGCHAIN.spad" 1436368 1436383 1437261 1437288) (-958 "RGBCSPC.spad" 1436158 1436169 1436358 1436363) (-957 "RGBCMDL.spad" 1435721 1435732 1436148 1436153) (-956 "RFFACTOR.spad" 1435184 1435194 1435711 1435716) (-955 "RFFACT.spad" 1434920 1434931 1435174 1435179) (-954 "RFDIST.spad" 1433917 1433925 1434910 1434915) (-953 "RF.spad" 1431592 1431602 1433907 1433912) (-952 "RETSOL.spad" 1431012 1431024 1431582 1431587) (-951 "RETRACT.spad" 1430441 1430451 1431002 1431007) (-950 "RETRACT.spad" 1429868 1429880 1430431 1430436) (-949 "RETAST.spad" 1429681 1429689 1429858 1429863) (-948 "RESRING.spad" 1429029 1429075 1429619 1429676) (-947 "RESLATC.spad" 1428354 1428364 1429019 1429024) (-946 "REPSQ.spad" 1428086 1428096 1428344 1428349) (-945 "REPDB.spad" 1427794 1427804 1428076 1428081) (-944 "REP2.spad" 1417509 1417519 1427636 1427641) (-943 "REP1.spad" 1411730 1411740 1417459 1417464) (-942 "REP.spad" 1409285 1409293 1411720 1411725) (-941 "REGSET.spad" 1407111 1407127 1408919 1408946) (-940 "REF.spad" 1406630 1406640 1407101 1407106) (-939 "REDORDER.spad" 1405837 1405853 1406620 1406625) (-938 "RECLOS.spad" 1404734 1404753 1405437 1405530) (-937 "REALSOLV.spad" 1403875 1403883 1404724 1404729) (-936 "REAL0Q.spad" 1401174 1401188 1403865 1403870) (-935 "REAL0.spad" 1398019 1398033 1401164 1401169) (-934 "REAL.spad" 1397892 1397900 1398009 1398014) (-933 "RDUCEAST.spad" 1397614 1397622 1397882 1397887) (-932 "RDIV.spad" 1397270 1397294 1397604 1397609) (-931 "RDIST.spad" 1396838 1396848 1397260 1397265) (-930 "RDETRS.spad" 1395703 1395720 1396828 1396833) (-929 "RDETR.spad" 1393843 1393860 1395693 1395698) (-928 "RDEEFS.spad" 1392943 1392959 1393833 1393838) (-927 "RDEEF.spad" 1391954 1391970 1392933 1392938) (-926 "RCFIELD.spad" 1389173 1389181 1391856 1391949) (-925 "RCFIELD.spad" 1386478 1386488 1389163 1389168) (-924 "RCAGG.spad" 1384415 1384425 1386468 1386473) (-923 "RCAGG.spad" 1382279 1382291 1384334 1384339) (-922 "RATRET.spad" 1381640 1381650 1382269 1382274) (-921 "RATFACT.spad" 1381333 1381344 1381630 1381635) (-920 "RANDSRC.spad" 1380653 1380661 1381323 1381328) (-919 "RADUTIL.spad" 1380410 1380418 1380643 1380648) (-918 "RADIX.spad" 1377455 1377468 1379000 1379093) (-917 "RADFF.spad" 1375372 1375408 1375490 1375646) (-916 "RADCAT.spad" 1374968 1374976 1375362 1375367) (-915 "RADCAT.spad" 1374562 1374572 1374958 1374963) (-914 "QUEUE.spad" 1373976 1373986 1374234 1374261) (-913 "QUATCT2.spad" 1373597 1373615 1373966 1373971) (-912 "QUATCAT.spad" 1371768 1371778 1373527 1373592) (-911 "QUATCAT.spad" 1369704 1369716 1371465 1371470) (-910 "QUAT.spad" 1368311 1368321 1368653 1368718) (-909 "QUAGG.spad" 1367145 1367155 1368279 1368306) (-908 "QQUTAST.spad" 1366914 1366922 1367135 1367140) (-907 "QFORM.spad" 1366533 1366547 1366904 1366909) (-906 "QFCAT2.spad" 1366226 1366242 1366523 1366528) (-905 "QFCAT.spad" 1364929 1364939 1366128 1366221) (-904 "QFCAT.spad" 1363265 1363277 1364466 1364471) (-903 "QEQUAT.spad" 1362824 1362832 1363255 1363260) (-902 "QCMPACK.spad" 1357739 1357758 1362814 1362819) (-901 "QALGSET2.spad" 1355735 1355753 1357729 1357734) (-900 "QALGSET.spad" 1351840 1351872 1355649 1355654) (-899 "PWFFINTB.spad" 1349256 1349277 1351830 1351835) (-898 "PUSHVAR.spad" 1348595 1348614 1349246 1349251) (-897 "PTRANFN.spad" 1344731 1344741 1348585 1348590) (-896 "PTPACK.spad" 1341819 1341829 1344721 1344726) (-895 "PTFUNC2.spad" 1341642 1341656 1341809 1341814) (-894 "PTCAT.spad" 1340897 1340907 1341610 1341637) (-893 "PSQFR.spad" 1340212 1340236 1340887 1340892) (-892 "PSEUDLIN.spad" 1339098 1339108 1340202 1340207) (-891 "PSETPK.spad" 1325803 1325819 1338976 1338981) (-890 "PSETCAT.spad" 1320203 1320226 1325783 1325798) (-889 "PSETCAT.spad" 1314577 1314602 1320159 1320164) (-888 "PSCURVE.spad" 1313576 1313584 1314567 1314572) (-887 "PSCAT.spad" 1312359 1312388 1313474 1313571) (-886 "PSCAT.spad" 1311232 1311263 1312349 1312354) (-885 "PRTITION.spad" 1309930 1309938 1311222 1311227) (-884 "PRTDAST.spad" 1309649 1309657 1309920 1309925) (-883 "PRS.spad" 1299267 1299284 1309605 1309610) (-882 "PRQAGG.spad" 1298702 1298712 1299235 1299262) (-881 "PROPLOG.spad" 1298306 1298314 1298692 1298697) (-880 "PROPFUN2.spad" 1297929 1297942 1298296 1298301) (-879 "PROPFUN1.spad" 1297335 1297346 1297919 1297924) (-878 "PROPFRML.spad" 1295903 1295914 1297325 1297330) (-877 "PROPERTY.spad" 1295399 1295407 1295893 1295898) (-876 "PRODUCT.spad" 1293096 1293108 1293380 1293435) (-875 "PRINT.spad" 1292848 1292856 1293086 1293091) (-874 "PRIMES.spad" 1291109 1291119 1292838 1292843) (-873 "PRIMELT.spad" 1289230 1289244 1291099 1291104) (-872 "PRIMCAT.spad" 1288873 1288881 1289220 1289225) (-871 "PRIMARR2.spad" 1287640 1287652 1288863 1288868) (-870 "PRIMARR.spad" 1286695 1286705 1286865 1286892) (-869 "PREASSOC.spad" 1286077 1286089 1286685 1286690) (-868 "PR.spad" 1284595 1284607 1285294 1285421) (-867 "PPCURVE.spad" 1283732 1283740 1284585 1284590) (-866 "PORTNUM.spad" 1283523 1283531 1283722 1283727) (-865 "POLYROOT.spad" 1282372 1282394 1283479 1283484) (-864 "POLYLIFT.spad" 1281637 1281660 1282362 1282367) (-863 "POLYCATQ.spad" 1279763 1279785 1281627 1281632) (-862 "POLYCAT.spad" 1273265 1273286 1279631 1279758) (-861 "POLYCAT.spad" 1266287 1266310 1272655 1272660) (-860 "POLY2UP.spad" 1265739 1265753 1266277 1266282) (-859 "POLY2.spad" 1265336 1265348 1265729 1265734) (-858 "POLY.spad" 1263004 1263014 1263519 1263646) (-857 "POLUTIL.spad" 1261969 1261998 1262960 1262965) (-856 "POLTOPOL.spad" 1260717 1260732 1261959 1261964) (-855 "POINT.spad" 1259600 1259610 1259687 1259714) (-854 "PNTHEORY.spad" 1256302 1256310 1259590 1259595) (-853 "PMTOOLS.spad" 1255077 1255091 1256292 1256297) (-852 "PMSYM.spad" 1254626 1254636 1255067 1255072) (-851 "PMQFCAT.spad" 1254217 1254231 1254616 1254621) (-850 "PMPREDFS.spad" 1253679 1253701 1254207 1254212) (-849 "PMPRED.spad" 1253166 1253180 1253669 1253674) (-848 "PMPLCAT.spad" 1252243 1252261 1253095 1253100) (-847 "PMLSAGG.spad" 1251828 1251842 1252233 1252238) (-846 "PMKERNEL.spad" 1251407 1251419 1251818 1251823) (-845 "PMINS.spad" 1250987 1250997 1251397 1251402) (-844 "PMFS.spad" 1250564 1250582 1250977 1250982) (-843 "PMDOWN.spad" 1249854 1249868 1250554 1250559) (-842 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"ELTAGG.spad" 328171 328192 329909 329914) (-241 "ELTAB.spad" 327646 327659 328161 328166) (-240 "ELFUTS.spad" 327081 327100 327636 327641) (-239 "ELEMFUN.spad" 326770 326778 327071 327076) (-238 "ELEMFUN.spad" 326457 326467 326760 326765) (-237 "ELAGG.spad" 324428 324438 326437 326452) (-236 "ELAGG.spad" 322336 322348 324347 324352) (-235 "ELABOR.spad" 321682 321690 322326 322331) (-234 "ELABEXPR.spad" 320614 320622 321672 321677) (-233 "EFUPXS.spad" 317390 317420 320570 320575) (-232 "EFULS.spad" 314226 314249 317346 317351) (-231 "EFSTRUC.spad" 312241 312257 314216 314221) (-230 "EF.spad" 307017 307033 312231 312236) (-229 "EAB.spad" 305317 305325 307007 307012) (-228 "DVARCAT.spad" 302323 302333 305307 305312) (-227 "DVARCAT.spad" 299327 299339 302313 302318) (-226 "DSMP.spad" 297060 297074 297365 297492) (-225 "DSEXT.spad" 296362 296372 297050 297055) (-224 "DSEXT.spad" 295584 295596 296274 296279) (-223 "DROPT1.spad" 295249 295259 295574 295579) (-222 "DROPT0.spad" 290114 290122 295239 295244) (-221 "DROPT.spad" 284073 284081 290104 290109) (-220 "DRAWPT.spad" 282246 282254 284063 284068) (-219 "DRAWHACK.spad" 281554 281564 282236 282241) (-218 "DRAWCX.spad" 279032 279040 281544 281549) (-217 "DRAWCURV.spad" 278579 278594 279022 279027) (-216 "DRAWCFUN.spad" 268111 268119 278569 278574) (-215 "DRAW.spad" 260987 261000 268101 268106) (-214 "DQAGG.spad" 259165 259175 260955 260982) (-213 "DPOLCAT.spad" 254522 254538 259033 259160) (-212 "DPOLCAT.spad" 249965 249983 254478 254483) (-211 "DPMO.spad" 242668 242684 242806 243012) (-210 "DPMM.spad" 235384 235402 235509 235715) (-209 "DOMTMPLT.spad" 235155 235163 235374 235379) (-208 "DOMCTOR.spad" 234910 234918 235145 235150) (-207 "DOMAIN.spad" 234021 234029 234900 234905) (-206 "DMP.spad" 231614 231629 232184 232311) (-205 "DMEXT.spad" 231481 231491 231582 231609) (-204 "DLP.spad" 230841 230851 231471 231476) (-203 "DLIST.spad" 229462 229472 230066 230093) (-202 "DLAGG.spad" 227879 227889 229452 229457) (-201 "DIVRING.spad" 227421 227429 227823 227874) (-200 "DIVRING.spad" 227007 227017 227411 227416) (-199 "DISPLAY.spad" 225197 225205 226997 227002) (-198 "DIRPROD2.spad" 224015 224033 225187 225192) (-197 "DIRPROD.spad" 213385 213401 214025 214122) (-196 "DIRPCAT.spad" 212668 212684 213283 213380) (-195 "DIRPCAT.spad" 211577 211595 212194 212199) (-194 "DIOSP.spad" 210402 210410 211567 211572) (-193 "DIOPS.spad" 209398 209408 210382 210397) (-192 "DIOPS.spad" 208368 208380 209354 209359) (-191 "catdef.spad" 208226 208234 208358 208363) (-190 "DIFRING.spad" 208064 208072 208206 208221) (-189 "DIFFSPC.spad" 207643 207651 208054 208059) (-188 "DIFFSPC.spad" 207220 207230 207633 207638) (-187 "DIFFMOD.spad" 206709 206719 207188 207215) (-186 "DIFFDOM.spad" 205874 205885 206699 206704) (-185 "DIFFDOM.spad" 205037 205050 205864 205869) (-184 "DIFEXT.spad" 204856 204866 205017 205032) (-183 "DIAGG.spad" 204486 204496 204836 204851) (-182 "DIAGG.spad" 204124 204136 204476 204481) (-181 "DHMATRIX.spad" 202501 202511 203646 203673) (-180 "DFSFUN.spad" 196141 196149 202491 202496) (-179 "DFLOAT.spad" 192748 192756 196031 196136) (-178 "DFINTTLS.spad" 190979 190995 192738 192743) (-177 "DERHAM.spad" 188893 188925 190959 190974) (-176 "DEQUEUE.spad" 188282 188292 188565 188592) (-175 "DEGRED.spad" 187899 187913 188272 188277) (-174 "DEFINTRF.spad" 185481 185491 187889 187894) (-173 "DEFINTEF.spad" 184019 184035 185471 185476) (-172 "DEFAST.spad" 183403 183411 184009 184014) (-171 "DECIMAL.spad" 181632 181640 181993 182086) (-170 "DDFACT.spad" 179453 179470 181622 181627) (-169 "DBLRESP.spad" 179053 179077 179443 179448) (-168 "DBASIS.spad" 178679 178694 179043 179048) (-167 "DBASE.spad" 177343 177353 178669 178674) (-166 "DATAARY.spad" 176829 176842 177333 177338) (-165 "CYCLOTOM.spad" 176335 176343 176819 176824) (-164 "CYCLES.spad" 173127 173135 176325 176330) (-163 "CVMP.spad" 172544 172554 173117 173122) (-162 "CTRIGMNP.spad" 171044 171060 172534 172539) (-161 "CTORKIND.spad" 170647 170655 171034 171039) (-160 "CTORCAT.spad" 169888 169896 170637 170642) (-159 "CTORCAT.spad" 169127 169137 169878 169883) (-158 "CTORCALL.spad" 168716 168726 169117 169122) (-157 "CTOR.spad" 168407 168415 168706 168711) (-156 "CSTTOOLS.spad" 167652 167665 168397 168402) (-155 "CRFP.spad" 161424 161437 167642 167647) (-154 "CRCEAST.spad" 161144 161152 161414 161419) (-153 "CRAPACK.spad" 160211 160221 161134 161139) (-152 "CPMATCH.spad" 159712 159727 160133 160138) (-151 "CPIMA.spad" 159417 159436 159702 159707) (-150 "COORDSYS.spad" 154426 154436 159407 159412) (-149 "CONTOUR.spad" 153853 153861 154416 154421) (-148 "CONTFRAC.spad" 149603 149613 153755 153848) (-147 "CONDUIT.spad" 149361 149369 149593 149598) (-146 "COMRING.spad" 149035 149043 149299 149356) (-145 "COMPPROP.spad" 148553 148561 149025 149030) (-144 "COMPLPAT.spad" 148320 148335 148543 148548) (-143 "COMPLEX2.spad" 148035 148047 148310 148315) (-142 "COMPLEX.spad" 143741 143751 143985 144243) (-141 "COMPILER.spad" 143290 143298 143731 143736) (-140 "COMPFACT.spad" 142892 142906 143280 143285) (-139 "COMPCAT.spad" 140967 140977 142629 142887) (-138 "COMPCAT.spad" 138783 138795 140447 140452) (-137 "COMMUPC.spad" 138531 138549 138773 138778) (-136 "COMMONOP.spad" 138064 138072 138521 138526) (-135 "COMMAAST.spad" 137827 137835 138054 138059) (-134 "COMM.spad" 137638 137646 137817 137822) (-133 "COMBOPC.spad" 136561 136569 137628 137633) (-132 "COMBINAT.spad" 135328 135338 136551 136556) (-131 "COMBF.spad" 132750 132766 135318 135323) (-130 "COLOR.spad" 131587 131595 132740 132745) (-129 "COLONAST.spad" 131253 131261 131577 131582) (-128 "CMPLXRT.spad" 130964 130981 131243 131248) (-127 "CLLCTAST.spad" 130626 130634 130954 130959) (-126 "CLIP.spad" 126734 126742 130616 130621) (-125 "CLIF.spad" 125389 125405 126690 126729) (-124 "CLAGG.spad" 121926 121936 125379 125384) (-123 "CLAGG.spad" 118347 118359 121802 121807) (-122 "CINTSLPE.spad" 117702 117715 118337 118342) (-121 "CHVAR.spad" 115840 115862 117692 117697) (-120 "CHARZ.spad" 115755 115763 115820 115835) (-119 "CHARPOL.spad" 115281 115291 115745 115750) (-118 "CHARNZ.spad" 115043 115051 115261 115276) (-117 "CHAR.spad" 112411 112419 115033 115038) (-116 "CFCAT.spad" 111739 111747 112401 112406) (-115 "CDEN.spad" 110959 110973 111729 111734) (-114 "CCLASS.spad" 109139 109147 110401 110440) (-113 "CATEGORY.spad" 108213 108221 109129 109134) (-112 "CATCTOR.spad" 108104 108112 108203 108208) (-111 "CATAST.spad" 107730 107738 108094 108099) (-110 "CASEAST.spad" 107444 107452 107720 107725) (-109 "CARTEN2.spad" 106834 106861 107434 107439) (-108 "CARTEN.spad" 102586 102610 106824 106829) (-107 "CARD.spad" 99881 99889 102560 102581) (-106 "CAPSLAST.spad" 99663 99671 99871 99876) (-105 "CACHSET.spad" 99287 99295 99653 99658) (-104 "CABMON.spad" 98842 98850 99277 99282) (-103 "BYTEORD.spad" 98517 98525 98832 98837) (-102 "BYTEBUF.spad" 96564 96572 97770 97797) (-101 "BYTE.spad" 96039 96047 96554 96559) (-100 "BTREE.spad" 95177 95187 95711 95738) (-99 "BTOURN.spad" 94248 94257 94849 94876) (-98 "BTCAT.spad" 93727 93736 94216 94243) (-97 "BTCAT.spad" 93226 93237 93717 93722) (-96 "BTAGG.spad" 92693 92700 93194 93221) (-95 "BTAGG.spad" 92180 92189 92683 92688) (-94 "BSTREE.spad" 90987 90996 91852 91879) (-93 "BRILL.spad" 89193 89203 90977 90982) (-92 "BRAGG.spad" 88150 88159 89183 89188) (-91 "BRAGG.spad" 87071 87082 88106 88111) (-90 "BPADICRT.spad" 85131 85142 85377 85470) (-89 "BPADIC.spad" 84804 84815 85057 85126) (-88 "BOUNDZRO.spad" 84461 84477 84794 84799) (-87 "BOP1.spad" 81920 81929 84451 84456) (-86 "BOP.spad" 77063 77070 81910 81915) (-85 "BOOLEAN.spad" 76612 76619 77053 77058) (-84 "BOOLE.spad" 76263 76270 76602 76607) (-83 "BOOLE.spad" 75912 75921 76253 76258) (-82 "BMODULE.spad" 75625 75636 75880 75907) (-81 "BITS.spad" 75057 75064 75271 75298) (-80 "catdef.spad" 74940 74950 75047 75052) (-79 "catdef.spad" 74691 74701 74930 74935) (-78 "BINDING.spad" 74113 74120 74681 74686) (-77 "BINARY.spad" 72348 72355 72703 72796) (-76 "BGAGG.spad" 71554 71563 72328 72343) (-75 "BGAGG.spad" 70768 70779 71544 71549) (-74 "BEZOUT.spad" 69909 69935 70718 70723) (-73 "BBTREE.spad" 66852 66861 69581 69608) (-72 "BASTYPE.spad" 66352 66359 66842 66847) (-71 "BASTYPE.spad" 65850 65859 66342 66347) (-70 "BALFACT.spad" 65310 65322 65840 65845) (-69 "AUTOMOR.spad" 64761 64770 65290 65305) (-68 "ATTREG.spad" 61484 61491 64513 64756) (-67 "ATTRAST.spad" 61201 61208 61474 61479) (-66 "ATRIG.spad" 60671 60678 61191 61196) (-65 "ATRIG.spad" 60139 60148 60661 60666) (-64 "ASTCAT.spad" 60043 60050 60129 60134) (-63 "ASTCAT.spad" 59945 59954 60033 60038) (-62 "ASTACK.spad" 59349 59358 59617 59644) (-61 "ASSOCEQ.spad" 58183 58194 59305 59310) (-60 "ARRAY2.spad" 57706 57715 57855 57882) (-59 "ARRAY12.spad" 56419 56430 57696 57701) (-58 "ARRAY1.spad" 55298 55307 55644 55671) (-57 "ARR2CAT.spad" 51264 51285 55266 55293) (-56 "ARR2CAT.spad" 47250 47273 51254 51259) (-55 "ARITY.spad" 46622 46629 47240 47245) (-54 "APPRULE.spad" 45906 45928 46612 46617) (-53 "APPLYORE.spad" 45525 45538 45896 45901) (-52 "ANY1.spad" 44596 44605 45515 45520) (-51 "ANY.spad" 43447 43454 44586 44591) (-50 "ANTISYM.spad" 41892 41908 43427 43442) (-49 "ANON.spad" 41601 41608 41882 41887) (-48 "AN.spad" 40069 40076 41432 41525) (-47 "AMR.spad" 38254 38265 39967 40064) (-46 "AMR.spad" 36302 36315 38017 38022) (-45 "ALIST.spad" 33540 33561 33890 33917) (-44 "ALGSC.spad" 32675 32701 33412 33465) (-43 "ALGPKG.spad" 28458 28469 32631 32636) (-42 "ALGMFACT.spad" 27651 27665 28448 28453) (-41 "ALGMANIP.spad" 25152 25167 27495 27500) (-40 "ALGFF.spad" 22970 22997 23187 23343) (-39 "ALGFACT.spad" 22089 22099 22960 22965) (-38 "ALGEBRA.spad" 21922 21931 22045 22084) (-37 "ALGEBRA.spad" 21787 21798 21912 21917) (-36 "ALAGG.spad" 21303 21324 21755 21782) (-35 "AHYP.spad" 20684 20691 21293 21298) (-34 "AGG.spad" 19393 19400 20674 20679) (-33 "AGG.spad" 18066 18075 19349 19354) (-32 "AF.spad" 16511 16526 18015 18020) (-31 "ADDAST.spad" 16197 16204 16501 16506) (-30 "ACPLOT.spad" 15074 15081 16187 16192) (-29 "ACFS.spad" 12931 12940 14976 15069) (-28 "ACFS.spad" 10874 10885 12921 12926) (-27 "ACF.spad" 7628 7635 10776 10869) (-26 "ACF.spad" 4468 4477 7618 7623) (-25 "ABELSG.spad" 4009 4016 4458 4463) (-24 "ABELSG.spad" 3548 3557 3999 4004) (-23 "ABELMON.spad" 2976 2983 3538 3543) (-22 "ABELMON.spad" 2402 2411 2966 2971) (-21 "ABELGRP.spad" 2067 2074 2392 2397) (-20 "ABELGRP.spad" 1730 1739 2057 2062) (-19 "A1AGG.spad" 870 879 1698 1725) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 1961955 1961960 1961965 1961970) (-2 NIL 1961935 1961940 1961945 1961950) (-1 NIL 1961915 1961920 1961925 1961930) (0 NIL 1961895 1961900 1961905 1961910) (-1209 "ZMOD.spad" 1961704 1961717 1961833 1961890) (-1208 "ZLINDEP.spad" 1960802 1960813 1961694 1961699) (-1207 "ZDSOLVE.spad" 1950763 1950785 1960792 1960797) (-1206 "YSTREAM.spad" 1950258 1950269 1950753 1950758) (-1205 "YDIAGRAM.spad" 1949892 1949901 1950248 1950253) (-1204 "XRPOLY.spad" 1949112 1949132 1949748 1949817) (-1203 "XPR.spad" 1946907 1946920 1948830 1948929) (-1202 "XPOLYC.spad" 1946226 1946242 1946833 1946902) (-1201 "XPOLY.spad" 1945781 1945792 1946082 1946151) (-1200 "XPBWPOLY.spad" 1944252 1944272 1945587 1945656) (-1199 "XFALG.spad" 1941300 1941316 1944178 1944247) (-1198 "XF.spad" 1939763 1939778 1941202 1941295) (-1197 "XF.spad" 1938206 1938223 1939647 1939652) (-1196 "XEXPPKG.spad" 1937465 1937491 1938196 1938201) (-1195 "XDPOLY.spad" 1937079 1937095 1937321 1937390) (-1194 "XALG.spad" 1936747 1936758 1937035 1937074) (-1193 "WUTSET.spad" 1932750 1932767 1936381 1936408) (-1192 "WP.spad" 1931957 1932001 1932608 1932675) (-1191 "WHILEAST.spad" 1931755 1931764 1931947 1931952) (-1190 "WHEREAST.spad" 1931426 1931435 1931745 1931750) (-1189 "WFFINTBS.spad" 1929089 1929111 1931416 1931421) (-1188 "WEIER.spad" 1927311 1927322 1929079 1929084) (-1187 "VSPACE.spad" 1926984 1926995 1927279 1927306) (-1186 "VSPACE.spad" 1926677 1926690 1926974 1926979) (-1185 "VOID.spad" 1926354 1926363 1926667 1926672) (-1184 "VIEWDEF.spad" 1921555 1921564 1926344 1926349) (-1183 "VIEW3D.spad" 1905516 1905525 1921545 1921550) (-1182 "VIEW2D.spad" 1893415 1893424 1905506 1905511) (-1181 "VIEW.spad" 1891135 1891144 1893405 1893410) (-1180 "VECTOR2.spad" 1889774 1889787 1891125 1891130) (-1179 "VECTOR.spad" 1888493 1888504 1888744 1888771) (-1178 "VECTCAT.spad" 1886405 1886416 1888461 1888488) (-1177 "VECTCAT.spad" 1884126 1884139 1886184 1886189) (-1176 "VARIABLE.spad" 1883906 1883921 1884116 1884121) (-1175 "UTYPE.spad" 1883550 1883559 1883896 1883901) (-1174 "UTSODETL.spad" 1882845 1882869 1883506 1883511) (-1173 "UTSODE.spad" 1881061 1881081 1882835 1882840) (-1172 "UTSCAT.spad" 1878540 1878556 1880959 1881056) (-1171 "UTSCAT.spad" 1875687 1875705 1878108 1878113) (-1170 "UTS2.spad" 1875282 1875317 1875677 1875682) (-1169 "UTS.spad" 1870294 1870322 1873814 1873911) (-1168 "URAGG.spad" 1865015 1865026 1870284 1870289) (-1167 "URAGG.spad" 1859700 1859713 1864971 1864976) (-1166 "UPXSSING.spad" 1857468 1857494 1858904 1859037) (-1165 "UPXSCONS.spad" 1855286 1855306 1855659 1855808) (-1164 "UPXSCCA.spad" 1853857 1853877 1855132 1855281) (-1163 "UPXSCCA.spad" 1852570 1852592 1853847 1853852) (-1162 "UPXSCAT.spad" 1851159 1851175 1852416 1852565) (-1161 "UPXS2.spad" 1850702 1850755 1851149 1851154) (-1160 "UPXS.spad" 1848057 1848085 1848893 1849042) (-1159 "UPSQFREE.spad" 1846472 1846486 1848047 1848052) (-1158 "UPSCAT.spad" 1844267 1844291 1846370 1846467) (-1157 "UPSCAT.spad" 1841763 1841789 1843868 1843873) (-1156 "UPOLYC2.spad" 1841234 1841253 1841753 1841758) (-1155 "UPOLYC.spad" 1836314 1836325 1841076 1841229) (-1154 "UPOLYC.spad" 1831312 1831325 1836076 1836081) (-1153 "UPMP.spad" 1830244 1830257 1831302 1831307) (-1152 "UPDIVP.spad" 1829809 1829823 1830234 1830239) (-1151 "UPDECOMP.spad" 1828070 1828084 1829799 1829804) (-1150 "UPCDEN.spad" 1827287 1827303 1828060 1828065) (-1149 "UP2.spad" 1826651 1826672 1827277 1827282) (-1148 "UP.spad" 1824121 1824136 1824508 1824661) (-1147 "UNISEG2.spad" 1823618 1823631 1824077 1824082) (-1146 "UNISEG.spad" 1822971 1822982 1823537 1823542) (-1145 "UNIFACT.spad" 1822074 1822086 1822961 1822966) (-1144 "ULSCONS.spad" 1815920 1815940 1816290 1816439) (-1143 "ULSCCAT.spad" 1813657 1813677 1815766 1815915) (-1142 "ULSCCAT.spad" 1811502 1811524 1813613 1813618) (-1141 "ULSCAT.spad" 1809742 1809758 1811348 1811497) (-1140 "ULS2.spad" 1809256 1809309 1809732 1809737) (-1139 "ULS.spad" 1801289 1801317 1802234 1802657) (-1138 "UINT8.spad" 1801166 1801175 1801279 1801284) (-1137 "UINT64.spad" 1801042 1801051 1801156 1801161) (-1136 "UINT32.spad" 1800918 1800927 1801032 1801037) (-1135 "UINT16.spad" 1800794 1800803 1800908 1800913) (-1134 "UFD.spad" 1799859 1799868 1800720 1800789) (-1133 "UFD.spad" 1798986 1798997 1799849 1799854) (-1132 "UDVO.spad" 1797867 1797876 1798976 1798981) (-1131 "UDPO.spad" 1795448 1795459 1797823 1797828) (-1130 "TYPEAST.spad" 1795367 1795376 1795438 1795443) (-1129 "TYPE.spad" 1795299 1795308 1795357 1795362) (-1128 "TWOFACT.spad" 1793951 1793966 1795289 1795294) (-1127 "TUPLE.spad" 1793458 1793469 1793863 1793868) (-1126 "TUBETOOL.spad" 1790325 1790334 1793448 1793453) (-1125 "TUBE.spad" 1788972 1788989 1790315 1790320) (-1124 "TSETCAT.spad" 1777043 1777060 1788940 1788967) (-1123 "TSETCAT.spad" 1765100 1765119 1776999 1777004) (-1122 "TS.spad" 1763728 1763744 1764694 1764791) (-1121 "TRMANIP.spad" 1758092 1758109 1763416 1763421) (-1120 "TRIMAT.spad" 1757055 1757080 1758082 1758087) (-1119 "TRIGMNIP.spad" 1755582 1755599 1757045 1757050) (-1118 "TRIGCAT.spad" 1755094 1755103 1755572 1755577) (-1117 "TRIGCAT.spad" 1754604 1754615 1755084 1755089) (-1116 "TREE.spad" 1753244 1753255 1754276 1754303) (-1115 "TRANFUN.spad" 1753083 1753092 1753234 1753239) (-1114 "TRANFUN.spad" 1752920 1752931 1753073 1753078) (-1113 "TOPSP.spad" 1752594 1752603 1752910 1752915) (-1112 "TOOLSIGN.spad" 1752257 1752268 1752584 1752589) (-1111 "TEXTFILE.spad" 1750818 1750827 1752247 1752252) (-1110 "TEX1.spad" 1750374 1750385 1750808 1750813) (-1109 "TEX.spad" 1747568 1747577 1750364 1750369) (-1108 "TBCMPPK.spad" 1745669 1745692 1747558 1747563) (-1107 "TBAGG.spad" 1744912 1744935 1745637 1745664) (-1106 "TBAGG.spad" 1744175 1744200 1744902 1744907) (-1105 "TANEXP.spad" 1743583 1743594 1744165 1744170) (-1104 "TALGOP.spad" 1743307 1743318 1743573 1743578) (-1103 "TABLEAU.spad" 1742788 1742799 1743297 1743302) (-1102 "TABLE.spad" 1741063 1741086 1741333 1741360) (-1101 "TABLBUMP.spad" 1737842 1737853 1741053 1741058) (-1100 "SYSTEM.spad" 1737070 1737079 1737832 1737837) (-1099 "SYSSOLP.spad" 1734553 1734564 1737060 1737065) (-1098 "SYSPTR.spad" 1734452 1734461 1734543 1734548) (-1097 "SYSNNI.spad" 1733675 1733686 1734442 1734447) (-1096 "SYSINT.spad" 1733079 1733090 1733665 1733670) (-1095 "SYNTAX.spad" 1729413 1729422 1733069 1733074) (-1094 "SYMTAB.spad" 1727481 1727490 1729403 1729408) (-1093 "SYMS.spad" 1723510 1723519 1727471 1727476) (-1092 "SYMPOLY.spad" 1722643 1722654 1722725 1722852) (-1091 "SYMFUNC.spad" 1722144 1722155 1722633 1722638) (-1090 "SYMBOL.spad" 1719639 1719648 1722134 1722139) (-1089 "SUTS.spad" 1716752 1716780 1718171 1718268) (-1088 "SUPXS.spad" 1714094 1714122 1714943 1715092) (-1087 "SUPFRACF.spad" 1713199 1713217 1714084 1714089) (-1086 "SUP2.spad" 1712591 1712604 1713189 1713194) (-1085 "SUP.spad" 1709675 1709686 1710448 1710601) (-1084 "SUMRF.spad" 1708649 1708660 1709665 1709670) (-1083 "SUMFS.spad" 1708278 1708295 1708639 1708644) (-1082 "SULS.spad" 1700298 1700326 1701256 1701679) (-1081 "syntax.spad" 1700067 1700076 1700288 1700293) (-1080 "SUCH.spad" 1699757 1699772 1700057 1700062) (-1079 "SUBSPACE.spad" 1691888 1691903 1699747 1699752) (-1078 "SUBRESP.spad" 1691058 1691072 1691844 1691849) (-1077 "STTFNC.spad" 1687526 1687542 1691048 1691053) (-1076 "STTF.spad" 1683625 1683641 1687516 1687521) (-1075 "STTAYLOR.spad" 1676302 1676313 1683532 1683537) (-1074 "STRTBL.spad" 1674689 1674706 1674838 1674865) (-1073 "STRING.spad" 1673557 1673566 1673942 1673969) (-1072 "STREAM3.spad" 1673130 1673145 1673547 1673552) (-1071 "STREAM2.spad" 1672258 1672271 1673120 1673125) (-1070 "STREAM1.spad" 1671964 1671975 1672248 1672253) (-1069 "STREAM.spad" 1668960 1668971 1671567 1671582) (-1068 "STINPROD.spad" 1667896 1667912 1668950 1668955) (-1067 "STEPAST.spad" 1667130 1667139 1667886 1667891) (-1066 "STEP.spad" 1666447 1666456 1667120 1667125) (-1065 "STBL.spad" 1664825 1664853 1664992 1665019) (-1064 "STAGG.spad" 1663524 1663535 1664815 1664820) (-1063 "STAGG.spad" 1662221 1662234 1663514 1663519) (-1062 "STACK.spad" 1661643 1661654 1661893 1661920) (-1061 "SRING.spad" 1661403 1661412 1661633 1661638) (-1060 "SREGSET.spad" 1659135 1659152 1661037 1661064) (-1059 "SRDCMPK.spad" 1657712 1657732 1659125 1659130) (-1058 "SRAGG.spad" 1652895 1652904 1657680 1657707) (-1057 "SRAGG.spad" 1648098 1648109 1652885 1652890) (-1056 "SQMATRIX.spad" 1645775 1645793 1646691 1646778) (-1055 "SPLTREE.spad" 1640517 1640530 1645313 1645340) (-1054 "SPLNODE.spad" 1637137 1637150 1640507 1640512) (-1053 "SPFCAT.spad" 1635946 1635955 1637127 1637132) (-1052 "SPECOUT.spad" 1634498 1634507 1635936 1635941) (-1051 "SPADXPT.spad" 1626589 1626598 1634488 1634493) (-1050 "spad-parser.spad" 1626054 1626063 1626579 1626584) (-1049 "SPADAST.spad" 1625755 1625764 1626044 1626049) (-1048 "SPACEC.spad" 1609970 1609981 1625745 1625750) (-1047 "SPACE3.spad" 1609746 1609757 1609960 1609965) (-1046 "SORTPAK.spad" 1609295 1609308 1609702 1609707) (-1045 "SOLVETRA.spad" 1607058 1607069 1609285 1609290) (-1044 "SOLVESER.spad" 1605514 1605525 1607048 1607053) (-1043 "SOLVERAD.spad" 1601540 1601551 1605504 1605509) (-1042 "SOLVEFOR.spad" 1600002 1600020 1601530 1601535) (-1041 "SNTSCAT.spad" 1599602 1599619 1599970 1599997) (-1040 "SMTS.spad" 1597919 1597945 1599196 1599293) (-1039 "SMP.spad" 1595727 1595747 1596117 1596244) (-1038 "SMITH.spad" 1594572 1594597 1595717 1595722) (-1037 "SMATCAT.spad" 1592690 1592720 1594516 1594567) (-1036 "SMATCAT.spad" 1590740 1590772 1592568 1592573) (-1035 "aggcat.spad" 1590416 1590427 1590720 1590735) (-1034 "SKAGG.spad" 1589385 1589396 1590384 1590411) (-1033 "SINT.spad" 1588684 1588693 1589251 1589380) (-1032 "SIMPAN.spad" 1588412 1588421 1588674 1588679) (-1031 "SIGNRF.spad" 1587537 1587548 1588402 1588407) (-1030 "SIGNEF.spad" 1586823 1586840 1587527 1587532) (-1029 "syntax.spad" 1586240 1586249 1586813 1586818) (-1028 "SIG.spad" 1585602 1585611 1586230 1586235) (-1027 "SHP.spad" 1583546 1583561 1585558 1585563) (-1026 "SHDP.spad" 1573039 1573066 1573556 1573653) (-1025 "SGROUP.spad" 1572647 1572656 1573029 1573034) (-1024 "SGROUP.spad" 1572253 1572264 1572637 1572642) (-1023 "catdef.spad" 1571963 1571975 1572074 1572248) (-1022 "catdef.spad" 1571519 1571531 1571784 1571958) (-1021 "SGCF.spad" 1564658 1564667 1571509 1571514) (-1020 "SFRTCAT.spad" 1563604 1563621 1564626 1564653) (-1019 "SFRGCD.spad" 1562667 1562687 1563594 1563599) (-1018 "SFQCMPK.spad" 1557480 1557500 1562657 1562662) (-1017 "SEXOF.spad" 1557323 1557363 1557470 1557475) (-1016 "SEXCAT.spad" 1555151 1555191 1557313 1557318) (-1015 "SEX.spad" 1555043 1555052 1555141 1555146) (-1014 "SETMN.spad" 1553503 1553520 1555033 1555038) (-1013 "SETCAT.spad" 1552988 1552997 1553493 1553498) (-1012 "SETCAT.spad" 1552471 1552482 1552978 1552983) (-1011 "SETAGG.spad" 1549020 1549031 1552451 1552466) (-1010 "SETAGG.spad" 1545577 1545590 1549010 1549015) (-1009 "SET.spad" 1543886 1543897 1544983 1545022) (-1008 "syntax.spad" 1543589 1543598 1543876 1543881) (-1007 "SEGXCAT.spad" 1542745 1542758 1543579 1543584) (-1006 "SEGCAT.spad" 1541670 1541681 1542735 1542740) (-1005 "SEGBIND2.spad" 1541368 1541381 1541660 1541665) (-1004 "SEGBIND.spad" 1541126 1541137 1541315 1541320) (-1003 "SEGAST.spad" 1540856 1540865 1541116 1541121) (-1002 "SEG2.spad" 1540291 1540304 1540812 1540817) (-1001 "SEG.spad" 1540104 1540115 1540210 1540215) (-1000 "SDVAR.spad" 1539380 1539391 1540094 1540099) (-999 "SDPOL.spad" 1537073 1537083 1537363 1537490) (-998 "SCPKG.spad" 1535163 1535173 1537063 1537068) (-997 "SCOPE.spad" 1534341 1534349 1535153 1535158) (-996 "SCACHE.spad" 1533038 1533048 1534331 1534336) (-995 "SASTCAT.spad" 1532948 1532956 1533028 1533033) (-994 "SAOS.spad" 1532821 1532829 1532938 1532943) (-993 "SAERFFC.spad" 1532535 1532554 1532811 1532816) (-992 "SAEFACT.spad" 1532237 1532256 1532525 1532530) (-991 "SAE.spad" 1529888 1529903 1530498 1530633) (-990 "RURPK.spad" 1527548 1527563 1529878 1529883) (-989 "RULESET.spad" 1527002 1527025 1527538 1527543) (-988 "RULECOLD.spad" 1526855 1526867 1526992 1526997) (-987 "RULE.spad" 1525104 1525127 1526845 1526850) (-986 "RTVALUE.spad" 1524840 1524848 1525094 1525099) (-985 "syntax.spad" 1524558 1524566 1524830 1524835) (-984 "RSETGCD.spad" 1521001 1521020 1524548 1524553) (-983 "RSETCAT.spad" 1510970 1510986 1520969 1520996) (-982 "RSETCAT.spad" 1500959 1500977 1510960 1510965) (-981 "RSDCMPK.spad" 1499460 1499479 1500949 1500954) (-980 "RRCC.spad" 1497845 1497874 1499450 1499455) (-979 "RRCC.spad" 1496228 1496259 1497835 1497840) (-978 "RPTAST.spad" 1495931 1495939 1496218 1496223) (-977 "RPOLCAT.spad" 1475436 1475450 1495799 1495926) (-976 "RPOLCAT.spad" 1454734 1454750 1475099 1475104) (-975 "ROMAN.spad" 1454063 1454071 1454600 1454729) (-974 "ROIRC.spad" 1453144 1453175 1454053 1454058) (-973 "RNS.spad" 1452121 1452129 1453046 1453139) (-972 "RNS.spad" 1451184 1451194 1452111 1452116) (-971 "RNGBIND.spad" 1450345 1450358 1451139 1451144) (-970 "RNG.spad" 1449954 1449962 1450335 1450340) (-969 "RNG.spad" 1449561 1449571 1449944 1449949) (-968 "RMODULE.spad" 1449343 1449353 1449551 1449556) (-967 "RMCAT2.spad" 1448764 1448820 1449333 1449338) (-966 "RMATRIX.spad" 1447574 1447592 1447916 1447955) (-965 "RMATCAT.spad" 1443212 1443242 1447530 1447569) (-964 "RMATCAT.spad" 1438740 1438772 1443060 1443065) (-963 "RLINSET.spad" 1438445 1438455 1438730 1438735) (-962 "RINTERP.spad" 1438334 1438353 1438435 1438440) (-961 "RING.spad" 1437805 1437813 1438314 1438329) (-960 "RING.spad" 1437284 1437294 1437795 1437800) (-959 "RIDIST.spad" 1436677 1436685 1437274 1437279) (-958 "RGCHAIN.spad" 1435232 1435247 1436125 1436152) (-957 "RGBCSPC.spad" 1435022 1435033 1435222 1435227) (-956 "RGBCMDL.spad" 1434585 1434596 1435012 1435017) (-955 "RFFACTOR.spad" 1434048 1434058 1434575 1434580) (-954 "RFFACT.spad" 1433784 1433795 1434038 1434043) (-953 "RFDIST.spad" 1432781 1432789 1433774 1433779) (-952 "RF.spad" 1430456 1430466 1432771 1432776) (-951 "RETSOL.spad" 1429876 1429888 1430446 1430451) (-950 "RETRACT.spad" 1429305 1429315 1429866 1429871) (-949 "RETRACT.spad" 1428732 1428744 1429295 1429300) (-948 "RETAST.spad" 1428545 1428553 1428722 1428727) (-947 "RESRING.spad" 1427893 1427939 1428483 1428540) (-946 "RESLATC.spad" 1427218 1427228 1427883 1427888) (-945 "REPSQ.spad" 1426950 1426960 1427208 1427213) (-944 "REPDB.spad" 1426658 1426668 1426940 1426945) (-943 "REP2.spad" 1416373 1416383 1426500 1426505) (-942 "REP1.spad" 1410594 1410604 1416323 1416328) (-941 "REP.spad" 1408149 1408157 1410584 1410589) (-940 "REGSET.spad" 1405975 1405991 1407783 1407810) (-939 "REF.spad" 1405494 1405504 1405965 1405970) (-938 "REDORDER.spad" 1404701 1404717 1405484 1405489) (-937 "RECLOS.spad" 1403598 1403617 1404301 1404394) (-936 "REALSOLV.spad" 1402739 1402747 1403588 1403593) (-935 "REAL0Q.spad" 1400038 1400052 1402729 1402734) (-934 "REAL0.spad" 1396883 1396897 1400028 1400033) (-933 "REAL.spad" 1396756 1396764 1396873 1396878) (-932 "RDUCEAST.spad" 1396478 1396486 1396746 1396751) (-931 "RDIV.spad" 1396134 1396158 1396468 1396473) (-930 "RDIST.spad" 1395702 1395712 1396124 1396129) (-929 "RDETRS.spad" 1394567 1394584 1395692 1395697) (-928 "RDETR.spad" 1392707 1392724 1394557 1394562) (-927 "RDEEFS.spad" 1391807 1391823 1392697 1392702) (-926 "RDEEF.spad" 1390818 1390834 1391797 1391802) (-925 "RCFIELD.spad" 1388037 1388045 1390720 1390813) (-924 "RCFIELD.spad" 1385342 1385352 1388027 1388032) (-923 "RCAGG.spad" 1383279 1383289 1385332 1385337) (-922 "RCAGG.spad" 1381143 1381155 1383198 1383203) (-921 "RATRET.spad" 1380504 1380514 1381133 1381138) (-920 "RATFACT.spad" 1380197 1380208 1380494 1380499) (-919 "RANDSRC.spad" 1379517 1379525 1380187 1380192) (-918 "RADUTIL.spad" 1379274 1379282 1379507 1379512) (-917 "RADIX.spad" 1376319 1376332 1377864 1377957) (-916 "RADFF.spad" 1374236 1374272 1374354 1374510) (-915 "RADCAT.spad" 1373832 1373840 1374226 1374231) (-914 "RADCAT.spad" 1373426 1373436 1373822 1373827) (-913 "QUEUE.spad" 1372840 1372850 1373098 1373125) (-912 "QUATCT2.spad" 1372461 1372479 1372830 1372835) (-911 "QUATCAT.spad" 1370632 1370642 1372391 1372456) (-910 "QUATCAT.spad" 1368568 1368580 1370329 1370334) (-909 "QUAT.spad" 1367175 1367185 1367517 1367582) (-908 "QUAGG.spad" 1366009 1366019 1367143 1367170) (-907 "QQUTAST.spad" 1365778 1365786 1365999 1366004) (-906 "QFORM.spad" 1365397 1365411 1365768 1365773) (-905 "QFCAT2.spad" 1365090 1365106 1365387 1365392) (-904 "QFCAT.spad" 1363793 1363803 1364992 1365085) (-903 "QFCAT.spad" 1362129 1362141 1363330 1363335) (-902 "QEQUAT.spad" 1361688 1361696 1362119 1362124) (-901 "QCMPACK.spad" 1356603 1356622 1361678 1361683) (-900 "QALGSET2.spad" 1354599 1354617 1356593 1356598) (-899 "QALGSET.spad" 1350704 1350736 1354513 1354518) (-898 "PWFFINTB.spad" 1348120 1348141 1350694 1350699) (-897 "PUSHVAR.spad" 1347459 1347478 1348110 1348115) (-896 "PTRANFN.spad" 1343595 1343605 1347449 1347454) (-895 "PTPACK.spad" 1340683 1340693 1343585 1343590) (-894 "PTFUNC2.spad" 1340506 1340520 1340673 1340678) (-893 "PTCAT.spad" 1339761 1339771 1340474 1340501) (-892 "PSQFR.spad" 1339076 1339100 1339751 1339756) (-891 "PSEUDLIN.spad" 1337962 1337972 1339066 1339071) (-890 "PSETPK.spad" 1324667 1324683 1337840 1337845) (-889 "PSETCAT.spad" 1319067 1319090 1324647 1324662) (-888 "PSETCAT.spad" 1313441 1313466 1319023 1319028) (-887 "PSCURVE.spad" 1312440 1312448 1313431 1313436) (-886 "PSCAT.spad" 1311223 1311252 1312338 1312435) (-885 "PSCAT.spad" 1310096 1310127 1311213 1311218) (-884 "PRTITION.spad" 1308794 1308802 1310086 1310091) (-883 "PRTDAST.spad" 1308513 1308521 1308784 1308789) (-882 "PRS.spad" 1298131 1298148 1308469 1308474) (-881 "PRQAGG.spad" 1297566 1297576 1298099 1298126) (-880 "PROPLOG.spad" 1297170 1297178 1297556 1297561) (-879 "PROPFUN2.spad" 1296793 1296806 1297160 1297165) (-878 "PROPFUN1.spad" 1296199 1296210 1296783 1296788) (-877 "PROPFRML.spad" 1294767 1294778 1296189 1296194) (-876 "PROPERTY.spad" 1294263 1294271 1294757 1294762) (-875 "PRODUCT.spad" 1291960 1291972 1292244 1292299) (-874 "PRINT.spad" 1291712 1291720 1291950 1291955) (-873 "PRIMES.spad" 1289973 1289983 1291702 1291707) (-872 "PRIMELT.spad" 1288094 1288108 1289963 1289968) (-871 "PRIMCAT.spad" 1287737 1287745 1288084 1288089) (-870 "PRIMARR2.spad" 1286504 1286516 1287727 1287732) (-869 "PRIMARR.spad" 1285559 1285569 1285729 1285756) (-868 "PREASSOC.spad" 1284941 1284953 1285549 1285554) (-867 "PR.spad" 1283459 1283471 1284158 1284285) (-866 "PPCURVE.spad" 1282596 1282604 1283449 1283454) (-865 "PORTNUM.spad" 1282387 1282395 1282586 1282591) (-864 "POLYROOT.spad" 1281236 1281258 1282343 1282348) (-863 "POLYLIFT.spad" 1280501 1280524 1281226 1281231) (-862 "POLYCATQ.spad" 1278627 1278649 1280491 1280496) (-861 "POLYCAT.spad" 1272129 1272150 1278495 1278622) (-860 "POLYCAT.spad" 1265151 1265174 1271519 1271524) (-859 "POLY2UP.spad" 1264603 1264617 1265141 1265146) (-858 "POLY2.spad" 1264200 1264212 1264593 1264598) (-857 "POLY.spad" 1261868 1261878 1262383 1262510) (-856 "POLUTIL.spad" 1260833 1260862 1261824 1261829) (-855 "POLTOPOL.spad" 1259581 1259596 1260823 1260828) (-854 "POINT.spad" 1258464 1258474 1258551 1258578) (-853 "PNTHEORY.spad" 1255166 1255174 1258454 1258459) (-852 "PMTOOLS.spad" 1253941 1253955 1255156 1255161) (-851 "PMSYM.spad" 1253490 1253500 1253931 1253936) (-850 "PMQFCAT.spad" 1253081 1253095 1253480 1253485) (-849 "PMPREDFS.spad" 1252543 1252565 1253071 1253076) (-848 "PMPRED.spad" 1252030 1252044 1252533 1252538) (-847 "PMPLCAT.spad" 1251107 1251125 1251959 1251964) (-846 "PMLSAGG.spad" 1250692 1250706 1251097 1251102) (-845 "PMKERNEL.spad" 1250271 1250283 1250682 1250687) (-844 "PMINS.spad" 1249851 1249861 1250261 1250266) (-843 "PMFS.spad" 1249428 1249446 1249841 1249846) (-842 "PMDOWN.spad" 1248718 1248732 1249418 1249423) (-841 "PMASSFS.spad" 1247693 1247709 1248708 1248713) (-840 "PMASS.spad" 1246711 1246719 1247683 1247688) (-839 "PLOTTOOL.spad" 1246491 1246499 1246701 1246706) (-838 "PLOT3D.spad" 1242955 1242963 1246481 1246486) (-837 "PLOT1.spad" 1242128 1242138 1242945 1242950) (-836 "PLOT.spad" 1237051 1237059 1242118 1242123) (-835 "PLEQN.spad" 1224453 1224480 1237041 1237046) (-834 "PINTERPA.spad" 1224237 1224253 1224443 1224448) (-833 "PINTERP.spad" 1223859 1223878 1224227 1224232) (-832 "PID.spad" 1222833 1222841 1223785 1223854) (-831 "PICOERCE.spad" 1222490 1222500 1222823 1222828) (-830 "PI.spad" 1222107 1222115 1222464 1222485) (-829 "PGROEB.spad" 1220716 1220730 1222097 1222102) (-828 "PGE.spad" 1212389 1212397 1220706 1220711) (-827 "PGCD.spad" 1211343 1211360 1212379 1212384) (-826 "PFRPAC.spad" 1210492 1210502 1211333 1211338) (-825 "PFR.spad" 1207195 1207205 1210394 1210487) (-824 "PFOTOOLS.spad" 1206453 1206469 1207185 1207190) (-823 "PFOQ.spad" 1205823 1205841 1206443 1206448) (-822 "PFO.spad" 1205242 1205269 1205813 1205818) (-821 "PFECAT.spad" 1202952 1202960 1205168 1205237) (-820 "PFECAT.spad" 1200690 1200700 1202908 1202913) (-819 "PFBRU.spad" 1198578 1198590 1200680 1200685) (-818 "PFBR.spad" 1196138 1196161 1198568 1198573) (-817 "PF.spad" 1195712 1195724 1195943 1196036) (-816 "PERMGRP.spad" 1190482 1190492 1195702 1195707) (-815 "PERMCAT.spad" 1189143 1189153 1190462 1190477) (-814 "PERMAN.spad" 1187699 1187713 1189133 1189138) (-813 "PERM.spad" 1183509 1183519 1187532 1187547) (-812 "PENDTREE.spad" 1182923 1182933 1183203 1183208) (-811 "PDSPC.spad" 1181736 1181746 1182913 1182918) (-810 "PDSPC.spad" 1180547 1180559 1181726 1181731) (-809 "PDRING.spad" 1180389 1180399 1180527 1180542) (-808 "PDMOD.spad" 1180205 1180217 1180357 1180384) (-807 "PDECOMP.spad" 1179675 1179692 1180195 1180200) (-806 "PDDOM.spad" 1179113 1179126 1179665 1179670) (-805 "PDDOM.spad" 1178549 1178564 1179103 1179108) (-804 "PCOMP.spad" 1178402 1178415 1178539 1178544) (-803 "PBWLB.spad" 1177000 1177017 1178392 1178397) (-802 "PATTERN2.spad" 1176738 1176750 1176990 1176995) (-801 "PATTERN1.spad" 1175082 1175098 1176728 1176733) (-800 "PATTERN.spad" 1169657 1169667 1175072 1175077) (-799 "PATRES2.spad" 1169329 1169343 1169647 1169652) (-798 "PATRES.spad" 1166912 1166924 1169319 1169324) (-797 "PATMATCH.spad" 1165153 1165184 1166664 1166669) (-796 "PATMAB.spad" 1164582 1164592 1165143 1165148) (-795 "PATLRES.spad" 1163668 1163682 1164572 1164577) (-794 "PATAB.spad" 1163432 1163442 1163658 1163663) (-793 "PARTPERM.spad" 1161488 1161496 1163422 1163427) (-792 "PARSURF.spad" 1160922 1160950 1161478 1161483) (-791 "PARSU2.spad" 1160719 1160735 1160912 1160917) (-790 "script-parser.spad" 1160239 1160247 1160709 1160714) (-789 "PARSCURV.spad" 1159673 1159701 1160229 1160234) (-788 "PARSC2.spad" 1159464 1159480 1159663 1159668) (-787 "PARPCURV.spad" 1158926 1158954 1159454 1159459) (-786 "PARPC2.spad" 1158717 1158733 1158916 1158921) (-785 "PARAMAST.spad" 1157845 1157853 1158707 1158712) (-784 "PAN2EXPR.spad" 1157257 1157265 1157835 1157840) (-783 "PALETTE.spad" 1156371 1156379 1157247 1157252) (-782 "PAIR.spad" 1155445 1155458 1156014 1156019) (-781 "PADICRC.spad" 1152850 1152868 1154013 1154106) (-780 "PADICRAT.spad" 1150910 1150922 1151123 1151216) (-779 "PADICCT.spad" 1149459 1149471 1150836 1150905) (-778 "PADIC.spad" 1149162 1149174 1149385 1149454) (-777 "PADEPAC.spad" 1147851 1147870 1149152 1149157) (-776 "PADE.spad" 1146603 1146619 1147841 1147846) (-775 "OWP.spad" 1145851 1145881 1146461 1146528) (-774 "OVERSET.spad" 1145424 1145432 1145841 1145846) (-773 "OVAR.spad" 1145205 1145228 1145414 1145419) (-772 "OUTFORM.spad" 1134613 1134621 1145195 1145200) (-771 "OUTBFILE.spad" 1134047 1134055 1134603 1134608) (-770 "OUTBCON.spad" 1133117 1133125 1134037 1134042) (-769 "OUTBCON.spad" 1132185 1132195 1133107 1133112) (-768 "OUT.spad" 1131303 1131311 1132175 1132180) (-767 "OSI.spad" 1130778 1130786 1131293 1131298) (-766 "OSGROUP.spad" 1130696 1130704 1130768 1130773) 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"FLAGG.spad" 501859 501871 504775 504780) (-322 "FINRALG.spad" 499944 499957 501815 501854) (-321 "FINRALG.spad" 497955 497970 499828 499833) (-320 "FINITE.spad" 497107 497115 497945 497950) (-319 "FINITE.spad" 496257 496267 497097 497102) (-318 "aggcat.spad" 494423 494433 496237 496252) (-317 "FINAGG.spad" 492564 492576 494380 494385) (-316 "FINAALG.spad" 481749 481759 492506 492559) (-315 "FINAALG.spad" 470946 470958 481705 481710) (-314 "FILECAT.spad" 469480 469497 470936 470941) (-313 "FILE.spad" 469063 469073 469470 469475) (-312 "FIELD.spad" 468469 468477 468965 469058) (-311 "FIELD.spad" 467961 467971 468459 468464) (-310 "FGROUP.spad" 466624 466634 467941 467956) (-309 "FGLMICPK.spad" 465419 465434 466614 466619) (-308 "FFX.spad" 464805 464820 465138 465231) (-307 "FFSLPE.spad" 464316 464337 464795 464800) (-306 "FFPOLY2.spad" 463376 463393 464306 464311) (-305 "FFPOLY.spad" 454718 454729 463366 463371) (-304 "FFP.spad" 454126 454146 454437 454530) (-303 "FFNBX.spad" 452649 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T) (((-485)) . T) ((|#2|) . T)) +((((-772)) . T)) +((($) . T) (((-484)) . T) ((|#2|) . T)) ((($) . T) ((|#2|) . T)) (((|#2|) |has| |#2| (-146))) (((|#2|) |has| |#2| (-146))) -((((-740 |#1|)) . T)) -(((|#2|) . T) (((-485)) . T) (((-740 |#1|)) . T)) -(((|#2| (-740 |#1|)) . T)) -(((|#2| (-804 |#1|)) . T)) +((((-739 |#1|)) . T)) +(((|#2|) . T) (((-484)) . T) (((-739 |#1|)) . T)) +(((|#2| (-739 |#1|)) . T)) +(((|#2| (-803 |#1|)) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-146))) (((|#2| |#2|) . T)) @@ -4020,12 +4045,12 @@ (((|#2|) |has| |#2| (-146))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((-773)) . T)) -(((|#2|) . T) (($) . T) (((-485)) . T)) -((((-804 |#1|)) . T) ((|#2|) . T) (((-485)) . T) (((-740 |#1|)) . T)) -((((-804 |#1|)) . T) (((-740 |#1|)) . T)) +((((-772)) . T)) +(((|#2|) . T) (($) . T) (((-484)) . T)) +((((-803 |#1|)) . T) ((|#2|) . T) (((-484)) . T) (((-739 |#1|)) . T)) +((((-803 |#1|)) . T) (((-739 |#1|)) . T)) (((|#1| |#2|) . T)) -((((-1091) |#1|) . T)) +((((-1090) |#1|) . T)) (((|#1|) |has| |#1| (-146))) (((|#1| |#1|) . T)) (((|#1|) . T)) @@ -4034,11 +4059,11 @@ (((|#1|) |has| |#1| (-146))) (((|#1|) . T)) (((|#1|) . T) (($) . T)) -((((-773)) . T)) -(((|#1|) . T) (($) . T) (((-485)) . T)) -(((|#1|) . T) (((-485)) . T) (((-740 (-1091))) . T)) -((((-740 (-1091))) . T)) -((((-1091) |#1|) . T)) +((((-772)) . T)) +(((|#1|) . T) (($) . T) (((-484)) . T)) +(((|#1|) . T) (((-484)) . T) (((-739 (-1090))) . T)) +((((-739 (-1090))) . T)) +((((-1090) |#1|) . T)) (((|#2|) . T)) (((|#1| |#2|) . T)) (((|#1|) |has| |#1| (-146))) @@ -4048,10 +4073,10 @@ (((|#1|) |has| |#1| (-146))) (((|#1|) |has| |#1| (-146))) (((|#1|) . T)) -(((|#2|) . T) ((|#1|) . T) (((-485)) . T)) +(((|#2|) . T) ((|#1|) . T) (((-484)) . T)) (((|#1|) . T) (($) . T)) -((((-773)) . T)) -(((|#1|) . T) (($) . T) (((-485)) . T)) +((((-772)) . T)) +(((|#1|) . T) (($) . T) (((-484)) . T)) (((|#1| |#2|) . T)) (((|#2|) |has| |#2| (-146))) (((|#2| |#2|) . T)) @@ -4061,20 +4086,20 @@ (((|#2|) |has| |#2| (-146))) (((|#2|) . T)) (((|#2|) . T) (($) . T)) -((((-773)) . T)) -(((|#2|) . T) (($) . T) (((-485)) . T)) -(((|#2|) . T) (((-485)) . T) (((-740 |#1|)) . T)) -((((-740 |#1|)) . T)) +((((-772)) . T)) +(((|#2|) . T) (($) . T) (((-484)) . T)) +(((|#2|) . T) (((-484)) . T) (((-739 |#1|)) . T)) +((((-739 |#1|)) . T)) (((|#1| |#2|) . T)) -((((-885)) . T)) -((((-885)) . T)) -((((-885)) . T) (((-773)) . T)) -((((-485)) . T)) +((((-884)) . T)) +((((-884)) . T)) +((((-884)) . T) (((-772)) . T)) +((((-484)) . T)) ((($ $) . T)) ((($) . T)) ((($) . T)) -((((-773)) . T)) -((((-485)) . T) (($) . T)) +((((-772)) . T)) +((((-484)) . T) (($) . T)) ((($) . T)) -((((-485)) . T)) -(((-1210 . -146) T) ((-1210 . -556) 199769) ((-1210 . -971) T) ((-1210 . -1026) T) ((-1210 . -1062) T) ((-1210 . -664) T) ((-1210 . -962) T) ((-1210 . -591) 199756) ((-1210 . -589) 199728) ((-1210 . -104) T) ((-1210 . -25) T) ((-1210 . -72) T) ((-1210 . -13) T) ((-1210 . -1130) T) ((-1210 . -553) 199710) ((-1210 . -1014) T) ((-1210 . -23) T) ((-1210 . -21) T) ((-1210 . -969) 199697) ((-1210 . -964) 199684) ((-1210 . -82) 199669) ((-1210 . -320) T) ((-1210 . -554) 199651) ((-1210 . -1067) T) ((-1206 . -1014) T) ((-1206 . -553) 199618) ((-1206 . -1130) T) ((-1206 . -13) T) ((-1206 . -72) T) ((-1206 . -430) 199600) ((-1206 . -556) 199582) ((-1205 . -1203) 199561) ((-1205 . -951) 199538) ((-1205 . -556) 199487) ((-1205 . -962) T) ((-1205 . -664) T) ((-1205 . -1062) T) ((-1205 . -1026) T) ((-1205 . -971) T) ((-1205 . -21) T) ((-1205 . -589) 199446) ((-1205 . -23) T) ((-1205 . -1014) T) ((-1205 . -553) 199428) ((-1205 . -1130) T) ((-1205 . -13) T) ((-1205 . -72) T) ((-1205 . -25) T) ((-1205 . -104) T) ((-1205 . -591) 199402) ((-1205 . -1195) 199386) ((-1205 . -655) 199356) ((-1205 . -583) 199326) ((-1205 . -969) 199310) ((-1205 . -964) 199294) ((-1205 . -82) 199273) ((-1205 . -38) 199243) ((-1205 . -1200) 199222) ((-1204 . -962) T) ((-1204 . -664) T) ((-1204 . -1062) T) ((-1204 . -1026) T) ((-1204 . -971) T) ((-1204 . -21) T) ((-1204 . -589) 199181) ((-1204 . -23) T) ((-1204 . -1014) T) ((-1204 . -553) 199163) ((-1204 . -1130) T) ((-1204 . -13) T) ((-1204 . -72) T) ((-1204 . -25) T) ((-1204 . -104) T) ((-1204 . -591) 199137) ((-1204 . -556) 199093) ((-1204 . -1195) 199077) ((-1204 . -655) 199047) ((-1204 . -583) 199017) ((-1204 . -969) 199001) ((-1204 . -964) 198985) ((-1204 . -82) 198964) ((-1204 . -38) 198934) ((-1204 . -335) 198913) ((-1204 . -951) 198897) ((-1202 . -1203) 198873) ((-1202 . -951) 198847) ((-1202 . -556) 198793) ((-1202 . -962) T) ((-1202 . -664) T) ((-1202 . -1062) T) ((-1202 . -1026) T) ((-1202 . -971) T) ((-1202 . -21) T) ((-1202 . -589) 198752) ((-1202 . -23) T) ((-1202 . -1014) T) ((-1202 . -553) 198734) ((-1202 . -1130) T) ((-1202 . -13) T) ((-1202 . -72) T) ((-1202 . -25) T) ((-1202 . -104) T) ((-1202 . -591) 198708) ((-1202 . -1195) 198692) ((-1202 . -655) 198662) ((-1202 . -583) 198632) ((-1202 . -969) 198616) ((-1202 . -964) 198600) ((-1202 . -82) 198579) ((-1202 . -38) 198549) ((-1202 . -1200) 198525) ((-1201 . -1203) 198504) ((-1201 . -951) 198461) ((-1201 . -556) 198390) ((-1201 . -962) T) ((-1201 . -664) T) ((-1201 . -1062) T) ((-1201 . -1026) T) ((-1201 . -971) T) ((-1201 . -21) T) ((-1201 . -589) 198349) ((-1201 . -23) T) ((-1201 . -1014) T) ((-1201 . -553) 198331) ((-1201 . -1130) T) ((-1201 . -13) T) ((-1201 . -72) T) ((-1201 . -25) T) ((-1201 . -104) T) ((-1201 . -591) 198305) ((-1201 . -1195) 198289) ((-1201 . -655) 198259) ((-1201 . -583) 198229) ((-1201 . -969) 198213) ((-1201 . -964) 198197) ((-1201 . -82) 198176) ((-1201 . -38) 198146) ((-1201 . -1200) 198125) ((-1201 . -335) 198097) ((-1196 . -335) 198069) ((-1196 . -556) 198018) ((-1196 . -951) 197995) ((-1196 . -583) 197965) ((-1196 . -655) 197935) ((-1196 . -591) 197909) ((-1196 . -589) 197868) ((-1196 . -104) T) ((-1196 . -25) T) ((-1196 . -72) T) ((-1196 . -13) T) ((-1196 . -1130) T) ((-1196 . -553) 197850) ((-1196 . -1014) T) ((-1196 . -23) T) ((-1196 . -21) T) ((-1196 . -969) 197834) ((-1196 . -964) 197818) ((-1196 . -82) 197797) ((-1196 . -1203) 197776) ((-1196 . -962) T) ((-1196 . -664) T) ((-1196 . -1062) T) ((-1196 . -1026) T) ((-1196 . -971) T) ((-1196 . -1195) 197760) ((-1196 . -38) 197730) ((-1196 . -1200) 197709) ((-1194 . -1125) 197678) ((-1194 . -553) 197640) ((-1194 . -124) 197624) ((-1194 . -34) T) ((-1194 . -13) T) ((-1194 . -1130) T) ((-1194 . -72) T) ((-1194 . -260) 197562) ((-1194 . -456) 197495) ((-1194 . -1014) T) ((-1194 . -429) 197479) ((-1194 . -554) 197440) ((-1194 . -318) 197424) ((-1194 . -890) 197393) ((-1193 . -962) T) ((-1193 . -664) T) ((-1193 . -1062) T) ((-1193 . -1026) T) ((-1193 . -971) T) ((-1193 . -21) T) ((-1193 . -589) 197338) ((-1193 . -23) T) ((-1193 . -1014) T) ((-1193 . -553) 197307) ((-1193 . -1130) T) ((-1193 . -13) T) ((-1193 . -72) T) ((-1193 . -25) T) ((-1193 . -104) T) ((-1193 . -591) 197267) ((-1193 . -556) 197209) ((-1193 . -430) 197193) ((-1193 . -38) 197163) ((-1193 . -82) 197128) ((-1193 . -964) 197098) ((-1193 . -969) 197068) ((-1193 . -583) 197038) ((-1193 . -655) 197008) ((-1192 . -996) T) ((-1192 . -430) 196989) ((-1192 . -553) 196955) ((-1192 . -556) 196936) ((-1192 . -1014) T) ((-1192 . -1130) T) ((-1192 . -13) T) ((-1192 . -72) T) ((-1192 . -64) T) ((-1191 . -996) T) ((-1191 . -430) 196917) ((-1191 . -553) 196883) ((-1191 . -556) 196864) ((-1191 . -1014) T) ((-1191 . -1130) T) ((-1191 . -13) T) ((-1191 . -72) T) ((-1191 . -64) T) ((-1186 . -553) 196846) ((-1184 . -1014) T) ((-1184 . -553) 196828) ((-1184 . -1130) T) ((-1184 . -13) T) ((-1184 . -72) T) ((-1183 . -1014) T) ((-1183 . -553) 196810) ((-1183 . -1130) T) ((-1183 . -13) T) ((-1183 . -72) T) ((-1180 . -1179) 196794) ((-1180 . -324) 196778) ((-1180 . -760) 196757) ((-1180 . -757) 196736) ((-1180 . -124) 196720) ((-1180 . -554) 196681) ((-1180 . -241) 196633) ((-1180 . -539) 196610) ((-1180 . -243) 196587) ((-1180 . -594) 196571) ((-1180 . -429) 196555) ((-1180 . -1014) 196508) ((-1180 . -456) 196441) ((-1180 . -260) 196379) ((-1180 . -553) 196294) ((-1180 . -72) 196228) ((-1180 . -1130) T) ((-1180 . -13) T) ((-1180 . -34) T) ((-1180 . -318) 196212) ((-1180 . -19) 196196) ((-1177 . -1014) T) ((-1177 . -553) 196162) ((-1177 . -1130) T) ((-1177 . -13) T) ((-1177 . -72) T) ((-1170 . -1173) 196146) ((-1170 . -190) 196105) ((-1170 . -556) 195987) ((-1170 . -591) 195912) ((-1170 . -589) 195822) ((-1170 . -104) T) ((-1170 . -25) T) ((-1170 . -72) T) ((-1170 . -553) 195804) ((-1170 . -1014) T) ((-1170 . -23) T) ((-1170 . -21) T) ((-1170 . -971) T) ((-1170 . -1026) T) ((-1170 . -1062) T) ((-1170 . -664) T) ((-1170 . -962) T) ((-1170 . -186) 195757) ((-1170 . -13) T) ((-1170 . -1130) T) ((-1170 . -189) 195716) ((-1170 . -241) 195681) ((-1170 . -810) 195594) ((-1170 . -807) 195482) ((-1170 . -812) 195395) ((-1170 . -887) 195365) ((-1170 . -38) 195262) ((-1170 . -82) 195127) ((-1170 . -964) 195013) ((-1170 . -969) 194899) ((-1170 . -583) 194796) ((-1170 . -655) 194693) ((-1170 . -118) 194672) ((-1170 . -120) 194651) ((-1170 . -146) 194605) ((-1170 . -496) 194584) ((-1170 . -246) 194563) ((-1170 . -47) 194540) ((-1170 . -1159) 194517) ((-1170 . -35) 194483) ((-1170 . -66) 194449) ((-1170 . -239) 194415) ((-1170 . -433) 194381) ((-1170 . -1119) 194347) ((-1170 . -1116) 194313) ((-1170 . -916) 194279) ((-1167 . -277) 194223) ((-1167 . -951) 194189) ((-1167 . -355) 194155) ((-1167 . -38) 194012) ((-1167 . -556) 193886) ((-1167 . -591) 193775) ((-1167 . -589) 193649) ((-1167 . -971) T) ((-1167 . -1026) T) ((-1167 . -1062) T) ((-1167 . -664) T) ((-1167 . -962) T) ((-1167 . -82) 193499) ((-1167 . -964) 193388) ((-1167 . -969) 193277) ((-1167 . -21) T) ((-1167 . -23) T) ((-1167 . -1014) T) ((-1167 . -553) 193259) ((-1167 . -1130) T) ((-1167 . -13) T) ((-1167 . -72) T) ((-1167 . -25) T) ((-1167 . -104) T) ((-1167 . -583) 193116) ((-1167 . -655) 192973) ((-1167 . -118) 192934) ((-1167 . -120) 192895) ((-1167 . -146) T) ((-1167 . -496) T) ((-1167 . -246) T) ((-1167 . -47) 192839) ((-1166 . -1165) 192818) ((-1166 . -312) 192797) ((-1166 . -1135) 192776) ((-1166 . -833) 192755) ((-1166 . -496) 192709) ((-1166 . -146) 192643) ((-1166 . -556) 192462) ((-1166 . -655) 192309) ((-1166 . -583) 192156) ((-1166 . -38) 192003) ((-1166 . -392) 191982) ((-1166 . -258) 191961) ((-1166 . -591) 191861) ((-1166 . -589) 191746) ((-1166 . -971) T) ((-1166 . -1026) T) ((-1166 . -1062) T) ((-1166 . -664) T) ((-1166 . -962) T) ((-1166 . -82) 191566) ((-1166 . -964) 191407) ((-1166 . -969) 191248) ((-1166 . -21) T) ((-1166 . -23) T) ((-1166 . -1014) T) ((-1166 . -553) 191230) ((-1166 . -1130) T) ((-1166 . -13) T) ((-1166 . -72) T) ((-1166 . -25) T) ((-1166 . -104) T) ((-1166 . -246) 191184) ((-1166 . -201) 191163) ((-1166 . -916) 191129) ((-1166 . -1116) 191095) ((-1166 . -1119) 191061) ((-1166 . -433) 191027) ((-1166 . -239) 190993) ((-1166 . -66) 190959) ((-1166 . -35) 190925) ((-1166 . -1159) 190895) ((-1166 . -47) 190865) ((-1166 . -120) 190844) ((-1166 . -118) 190823) ((-1166 . -887) 190786) ((-1166 . -812) 190692) ((-1166 . -807) 190596) ((-1166 . -810) 190502) ((-1166 . -241) 190460) ((-1166 . -189) 190412) ((-1166 . -186) 190358) ((-1166 . -190) 190310) ((-1166 . -1163) 190294) ((-1166 . -951) 190278) ((-1161 . -1165) 190239) ((-1161 . -312) 190218) ((-1161 . -1135) 190197) ((-1161 . -833) 190176) ((-1161 . -496) 190130) ((-1161 . -146) 190064) ((-1161 . -556) 189813) ((-1161 . -655) 189660) ((-1161 . -583) 189507) ((-1161 . -38) 189354) ((-1161 . -392) 189333) ((-1161 . -258) 189312) ((-1161 . -591) 189212) ((-1161 . -589) 189097) ((-1161 . -971) T) ((-1161 . -1026) T) ((-1161 . -1062) T) ((-1161 . -664) T) ((-1161 . -962) T) ((-1161 . -82) 188917) ((-1161 . -964) 188758) ((-1161 . -969) 188599) ((-1161 . -21) T) ((-1161 . -23) T) ((-1161 . -1014) T) ((-1161 . -553) 188581) ((-1161 . -1130) T) ((-1161 . -13) T) ((-1161 . -72) T) ((-1161 . -25) T) ((-1161 . -104) T) ((-1161 . -246) 188535) ((-1161 . -201) 188514) ((-1161 . -916) 188480) ((-1161 . -1116) 188446) ((-1161 . -1119) 188412) ((-1161 . -433) 188378) ((-1161 . -239) 188344) ((-1161 . -66) 188310) ((-1161 . -35) 188276) ((-1161 . -1159) 188246) ((-1161 . -47) 188216) ((-1161 . -120) 188195) ((-1161 . -118) 188174) ((-1161 . -887) 188137) ((-1161 . -812) 188043) ((-1161 . -807) 187924) ((-1161 . -810) 187830) ((-1161 . -241) 187788) ((-1161 . -189) 187740) ((-1161 . -186) 187686) ((-1161 . -190) 187638) ((-1161 . -1163) 187622) ((-1161 . -951) 187557) ((-1149 . -1156) 187541) ((-1149 . -1067) 187519) ((-1149 . -554) NIL) ((-1149 . -260) 187506) ((-1149 . -456) 187454) ((-1149 . -277) 187431) ((-1149 . -951) 187314) ((-1149 . -355) 187298) ((-1149 . -38) 187130) ((-1149 . -82) 186935) ((-1149 . -964) 186761) ((-1149 . -969) 186587) ((-1149 . -589) 186497) ((-1149 . -591) 186386) ((-1149 . -583) 186218) ((-1149 . -655) 186050) ((-1149 . -556) 185806) ((-1149 . -118) 185785) ((-1149 . -120) 185764) ((-1149 . -47) 185741) ((-1149 . -329) 185725) ((-1149 . -581) 185673) ((-1149 . -810) 185617) ((-1149 . -807) 185524) ((-1149 . -812) 185435) ((-1149 . -797) NIL) ((-1149 . -822) 185414) ((-1149 . -1135) 185393) ((-1149 . -862) 185363) ((-1149 . -833) 185342) ((-1149 . -496) 185256) ((-1149 . -246) 185170) ((-1149 . -146) 185064) ((-1149 . -392) 184998) ((-1149 . -258) 184977) ((-1149 . -241) 184904) ((-1149 . -190) T) ((-1149 . -104) T) ((-1149 . -25) T) ((-1149 . -72) T) ((-1149 . -553) 184886) ((-1149 . -1014) T) ((-1149 . -23) T) ((-1149 . -21) T) ((-1149 . -971) T) ((-1149 . -1026) T) ((-1149 . -1062) T) ((-1149 . -664) T) ((-1149 . -962) T) ((-1149 . -186) 184873) ((-1149 . -13) T) ((-1149 . -1130) T) ((-1149 . -189) T) ((-1149 . -225) 184857) ((-1149 . -184) 184841) ((-1147 . -1007) 184825) ((-1147 . -558) 184809) ((-1147 . -1014) 184787) ((-1147 . -553) 184754) ((-1147 . -1130) 184732) ((-1147 . -13) 184710) ((-1147 . -72) 184688) ((-1147 . -1008) 184645) ((-1145 . -1144) 184624) ((-1145 . -916) 184590) ((-1145 . -1116) 184556) ((-1145 . -1119) 184522) ((-1145 . -433) 184488) ((-1145 . -239) 184454) ((-1145 . -66) 184420) ((-1145 . -35) 184386) ((-1145 . -1159) 184363) ((-1145 . -47) 184340) ((-1145 . -556) 184095) ((-1145 . -655) 183915) ((-1145 . -583) 183735) ((-1145 . -591) 183546) ((-1145 . -589) 183404) ((-1145 . -969) 183218) ((-1145 . -964) 183032) ((-1145 . -82) 182820) ((-1145 . -38) 182640) ((-1145 . -887) 182610) ((-1145 . -241) 182510) ((-1145 . -1142) 182494) ((-1145 . -971) T) ((-1145 . -1026) T) ((-1145 . -1062) T) ((-1145 . -664) T) ((-1145 . -962) T) ((-1145 . -21) T) ((-1145 . -23) T) ((-1145 . -1014) T) ((-1145 . -553) 182476) ((-1145 . -1130) T) ((-1145 . -13) T) ((-1145 . -72) T) ((-1145 . -25) T) ((-1145 . -104) T) ((-1145 . -118) 182404) ((-1145 . -120) 182286) ((-1145 . -554) 181959) ((-1145 . -184) 181929) ((-1145 . -810) 181783) ((-1145 . -812) 181583) ((-1145 . -807) 181381) ((-1145 . -225) 181351) ((-1145 . -189) 181213) ((-1145 . -186) 181069) ((-1145 . -190) 180977) ((-1145 . -312) 180956) ((-1145 . -1135) 180935) ((-1145 . -833) 180914) ((-1145 . -496) 180868) ((-1145 . -146) 180802) ((-1145 . -392) 180781) ((-1145 . -258) 180760) ((-1145 . -246) 180714) ((-1145 . -201) 180693) ((-1145 . -288) 180663) ((-1145 . -456) 180523) ((-1145 . -260) 180462) ((-1145 . -329) 180432) ((-1145 . -581) 180340) ((-1145 . -343) 180310) ((-1145 . -797) 180183) ((-1145 . -741) 180136) ((-1145 . -715) 180089) ((-1145 . -717) 180042) ((-1145 . -757) 179944) ((-1145 . -760) 179846) ((-1145 . -719) 179799) ((-1145 . -722) 179752) ((-1145 . -756) 179705) ((-1145 . -795) 179675) ((-1145 . -822) 179628) ((-1145 . -934) 179581) ((-1145 . -951) 179370) ((-1145 . -1067) 179322) ((-1145 . -905) 179292) ((-1140 . -1144) 179253) ((-1140 . -916) 179219) ((-1140 . -1116) 179185) ((-1140 . -1119) 179151) ((-1140 . -433) 179117) ((-1140 . -239) 179083) ((-1140 . -66) 179049) ((-1140 . -35) 179015) ((-1140 . -1159) 178992) ((-1140 . -47) 178969) ((-1140 . -556) 178770) ((-1140 . -655) 178572) ((-1140 . -583) 178374) ((-1140 . -591) 178229) ((-1140 . -589) 178069) ((-1140 . -969) 177865) ((-1140 . -964) 177661) ((-1140 . -82) 177413) ((-1140 . -38) 177215) ((-1140 . -887) 177185) ((-1140 . -241) 177013) ((-1140 . -1142) 176997) ((-1140 . -971) T) ((-1140 . -1026) T) ((-1140 . -1062) T) ((-1140 . -664) T) ((-1140 . -962) T) ((-1140 . -21) T) ((-1140 . -23) T) ((-1140 . -1014) T) ((-1140 . -553) 176979) ((-1140 . -1130) T) ((-1140 . -13) T) ((-1140 . -72) T) ((-1140 . -25) T) ((-1140 . -104) T) ((-1140 . -118) 176889) ((-1140 . -120) 176799) ((-1140 . -554) NIL) ((-1140 . -184) 176751) ((-1140 . -810) 176587) ((-1140 . -812) 176351) ((-1140 . -807) 176090) ((-1140 . -225) 176042) ((-1140 . -189) 175868) ((-1140 . -186) 175688) ((-1140 . -190) 175578) ((-1140 . -312) 175557) ((-1140 . -1135) 175536) ((-1140 . -833) 175515) ((-1140 . -496) 175469) ((-1140 . -146) 175403) ((-1140 . -392) 175382) ((-1140 . -258) 175361) ((-1140 . -246) 175315) ((-1140 . -201) 175294) ((-1140 . -288) 175246) ((-1140 . -456) 174980) ((-1140 . -260) 174865) ((-1140 . -329) 174817) ((-1140 . -581) 174769) ((-1140 . -343) 174721) ((-1140 . -797) NIL) ((-1140 . -741) NIL) ((-1140 . -715) NIL) ((-1140 . -717) NIL) ((-1140 . -757) NIL) ((-1140 . -760) NIL) ((-1140 . -719) NIL) ((-1140 . -722) NIL) ((-1140 . -756) NIL) ((-1140 . -795) 174673) ((-1140 . -822) NIL) ((-1140 . -934) NIL) ((-1140 . -951) 174639) ((-1140 . -1067) NIL) ((-1140 . -905) 174591) ((-1139 . -753) T) ((-1139 . -760) T) ((-1139 . -757) T) ((-1139 . -1014) T) ((-1139 . -553) 174573) ((-1139 . -1130) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -320) T) ((-1139 . -605) T) ((-1138 . -753) T) ((-1138 . -760) T) ((-1138 . -757) T) ((-1138 . -1014) T) ((-1138 . -553) 174555) ((-1138 . -1130) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -605) T) ((-1137 . -753) T) ((-1137 . -760) T) ((-1137 . -757) T) ((-1137 . -1014) T) ((-1137 . -553) 174537) ((-1137 . -1130) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -605) T) ((-1136 . -753) T) ((-1136 . -760) T) ((-1136 . -757) T) ((-1136 . -1014) T) ((-1136 . -553) 174519) ((-1136 . -1130) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -320) T) ((-1136 . -605) T) ((-1131 . -996) T) ((-1131 . -430) 174500) ((-1131 . -553) 174466) ((-1131 . -556) 174447) ((-1131 . -1014) T) ((-1131 . -1130) T) ((-1131 . -13) T) ((-1131 . -72) T) ((-1131 . -64) T) ((-1128 . -430) 174424) ((-1128 . -553) 174365) ((-1128 . -556) 174342) ((-1128 . -1014) 174320) ((-1128 . -1130) 174298) ((-1128 . -13) 174276) ((-1128 . -72) 174254) ((-1123 . -680) 174230) ((-1123 . -35) 174196) ((-1123 . -66) 174162) ((-1123 . -239) 174128) ((-1123 . -433) 174094) ((-1123 . -1119) 174060) ((-1123 . -1116) 174026) ((-1123 . -916) 173992) ((-1123 . -47) 173961) ((-1123 . -38) 173858) ((-1123 . -583) 173755) ((-1123 . -655) 173652) ((-1123 . -556) 173534) ((-1123 . -246) 173513) ((-1123 . -496) 173492) ((-1123 . -82) 173357) ((-1123 . -964) 173243) ((-1123 . -969) 173129) ((-1123 . -146) 173083) ((-1123 . -120) 173062) ((-1123 . -118) 173041) ((-1123 . -591) 172966) ((-1123 . -589) 172876) ((-1123 . -887) 172837) ((-1123 . -812) 172818) ((-1123 . -1130) T) ((-1123 . -13) T) ((-1123 . -807) 172797) ((-1123 . -962) T) ((-1123 . -664) T) ((-1123 . -1062) T) ((-1123 . -1026) T) ((-1123 . -971) T) ((-1123 . -21) T) ((-1123 . -23) T) ((-1123 . -1014) T) ((-1123 . -553) 172779) ((-1123 . -72) T) ((-1123 . -25) T) ((-1123 . -104) T) ((-1123 . -810) 172760) ((-1123 . -456) 172727) ((-1123 . -260) 172714) ((-1117 . -924) 172698) ((-1117 . -34) T) ((-1117 . -13) T) ((-1117 . -1130) T) ((-1117 . -72) 172652) ((-1117 . -553) 172587) ((-1117 . -260) 172525) ((-1117 . -456) 172458) ((-1117 . -1014) 172436) ((-1117 . -429) 172420) ((-1117 . -318) 172404) ((-1112 . -314) 172378) ((-1112 . -72) T) ((-1112 . -13) T) ((-1112 . -1130) T) ((-1112 . -553) 172360) ((-1112 . -1014) T) ((-1110 . -1014) T) ((-1110 . -553) 172342) ((-1110 . -1130) T) ((-1110 . -13) T) ((-1110 . -72) T) ((-1110 . -556) 172324) ((-1105 . -748) 172308) ((-1105 . -72) T) ((-1105 . -13) T) ((-1105 . -1130) T) ((-1105 . -553) 172290) ((-1105 . -1014) T) ((-1103 . -1108) 172269) ((-1103 . -183) 172217) ((-1103 . -76) 172165) ((-1103 . -124) 172113) ((-1103 . -554) NIL) ((-1103 . -193) 172061) ((-1103 . -539) 172040) ((-1103 . -260) 171838) ((-1103 . -456) 171590) ((-1103 . -429) 171525) ((-1103 . -241) 171504) ((-1103 . -243) 171483) ((-1103 . -550) 171462) ((-1103 . -1014) T) ((-1103 . -553) 171444) ((-1103 . -72) T) ((-1103 . -1130) T) ((-1103 . -13) T) ((-1103 . -34) T) ((-1103 . -318) 171392) ((-1099 . -1014) T) ((-1099 . -553) 171374) ((-1099 . -1130) T) ((-1099 . -13) T) ((-1099 . -72) T) ((-1098 . -753) T) ((-1098 . -760) T) ((-1098 . -757) T) ((-1098 . -1014) T) ((-1098 . -553) 171356) ((-1098 . -1130) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1098 . -320) T) ((-1098 . -605) T) ((-1097 . -753) T) ((-1097 . -760) T) ((-1097 . -757) T) ((-1097 . -1014) T) ((-1097 . -553) 171338) ((-1097 . -1130) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -320) T) ((-1096 . -1176) T) ((-1096 . -1014) T) ((-1096 . -553) 171305) ((-1096 . -1130) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -951) 171241) ((-1096 . -556) 171177) ((-1095 . -553) 171159) ((-1094 . -553) 171141) ((-1093 . -277) 171118) ((-1093 . -951) 171016) ((-1093 . -355) 171000) ((-1093 . -38) 170897) ((-1093 . -556) 170754) ((-1093 . -591) 170679) ((-1093 . -589) 170589) ((-1093 . -971) T) ((-1093 . -1026) T) ((-1093 . -1062) T) ((-1093 . -664) T) ((-1093 . -962) T) ((-1093 . -82) 170454) ((-1093 . -964) 170340) ((-1093 . -969) 170226) ((-1093 . -21) T) ((-1093 . -23) T) ((-1093 . -1014) T) ((-1093 . -553) 170208) ((-1093 . -1130) T) ((-1093 . -13) T) ((-1093 . -72) T) ((-1093 . -25) T) ((-1093 . -104) T) ((-1093 . -583) 170105) ((-1093 . -655) 170002) ((-1093 . -118) 169981) ((-1093 . -120) 169960) ((-1093 . -146) 169914) ((-1093 . -496) 169893) ((-1093 . -246) 169872) ((-1093 . -47) 169849) ((-1091 . -757) T) ((-1091 . -553) 169831) ((-1091 . -1014) T) ((-1091 . -72) T) ((-1091 . -13) T) ((-1091 . -1130) T) ((-1091 . -760) T) ((-1091 . -554) 169753) ((-1091 . -556) 169719) ((-1091 . -951) 169701) ((-1091 . -797) 169668) ((-1090 . -1173) 169652) ((-1090 . -190) 169611) ((-1090 . -556) 169493) ((-1090 . -591) 169418) ((-1090 . -589) 169328) ((-1090 . -104) T) ((-1090 . -25) T) ((-1090 . -72) T) ((-1090 . -553) 169310) ((-1090 . -1014) T) ((-1090 . -23) T) ((-1090 . -21) T) ((-1090 . -971) T) ((-1090 . -1026) T) ((-1090 . -1062) T) ((-1090 . -664) T) ((-1090 . -962) T) ((-1090 . -186) 169263) ((-1090 . -13) T) ((-1090 . -1130) T) ((-1090 . -189) 169222) ((-1090 . -241) 169187) ((-1090 . -810) 169100) ((-1090 . -807) 168988) ((-1090 . -812) 168901) ((-1090 . -887) 168871) ((-1090 . -38) 168768) ((-1090 . -82) 168633) ((-1090 . -964) 168519) ((-1090 . -969) 168405) ((-1090 . -583) 168302) ((-1090 . -655) 168199) ((-1090 . -118) 168178) ((-1090 . -120) 168157) ((-1090 . -146) 168111) ((-1090 . -496) 168090) ((-1090 . -246) 168069) ((-1090 . -47) 168046) ((-1090 . -1159) 168023) ((-1090 . -35) 167989) ((-1090 . -66) 167955) ((-1090 . -239) 167921) ((-1090 . -433) 167887) ((-1090 . -1119) 167853) ((-1090 . -1116) 167819) ((-1090 . -916) 167785) ((-1089 . -1165) 167746) ((-1089 . -312) 167725) ((-1089 . -1135) 167704) ((-1089 . -833) 167683) ((-1089 . -496) 167637) ((-1089 . -146) 167571) ((-1089 . -556) 167320) ((-1089 . -655) 167167) ((-1089 . -583) 167014) ((-1089 . -38) 166861) ((-1089 . -392) 166840) ((-1089 . -258) 166819) ((-1089 . -591) 166719) ((-1089 . -589) 166604) ((-1089 . -971) T) ((-1089 . -1026) T) ((-1089 . -1062) T) ((-1089 . -664) T) ((-1089 . -962) T) ((-1089 . -82) 166424) ((-1089 . -964) 166265) ((-1089 . -969) 166106) ((-1089 . -21) T) ((-1089 . -23) T) ((-1089 . -1014) T) ((-1089 . -553) 166088) ((-1089 . -1130) T) ((-1089 . -13) T) ((-1089 . -72) T) ((-1089 . -25) T) ((-1089 . -104) T) ((-1089 . -246) 166042) ((-1089 . -201) 166021) ((-1089 . -916) 165987) ((-1089 . -1116) 165953) ((-1089 . -1119) 165919) ((-1089 . -433) 165885) ((-1089 . -239) 165851) ((-1089 . -66) 165817) ((-1089 . -35) 165783) ((-1089 . -1159) 165753) ((-1089 . -47) 165723) ((-1089 . -120) 165702) ((-1089 . -118) 165681) ((-1089 . -887) 165644) ((-1089 . -812) 165550) ((-1089 . -807) 165431) ((-1089 . -810) 165337) ((-1089 . -241) 165295) ((-1089 . -189) 165247) ((-1089 . -186) 165193) ((-1089 . -190) 165145) ((-1089 . -1163) 165129) ((-1089 . -951) 165064) ((-1086 . -1156) 165048) ((-1086 . -1067) 165026) ((-1086 . -554) NIL) ((-1086 . -260) 165013) ((-1086 . -456) 164961) ((-1086 . -277) 164938) ((-1086 . -951) 164821) ((-1086 . -355) 164805) ((-1086 . -38) 164637) ((-1086 . -82) 164442) ((-1086 . -964) 164268) ((-1086 . -969) 164094) ((-1086 . -589) 164004) ((-1086 . -591) 163893) ((-1086 . -583) 163725) ((-1086 . -655) 163557) ((-1086 . -556) 163334) ((-1086 . -118) 163313) ((-1086 . -120) 163292) ((-1086 . -47) 163269) ((-1086 . -329) 163253) ((-1086 . -581) 163201) ((-1086 . -810) 163145) ((-1086 . -807) 163052) ((-1086 . -812) 162963) ((-1086 . -797) NIL) ((-1086 . -822) 162942) ((-1086 . -1135) 162921) ((-1086 . -862) 162891) ((-1086 . -833) 162870) ((-1086 . -496) 162784) ((-1086 . -246) 162698) ((-1086 . -146) 162592) ((-1086 . -392) 162526) ((-1086 . -258) 162505) ((-1086 . -241) 162432) ((-1086 . -190) T) ((-1086 . -104) T) ((-1086 . -25) T) ((-1086 . -72) T) ((-1086 . -553) 162414) ((-1086 . -1014) T) ((-1086 . -23) T) ((-1086 . -21) T) ((-1086 . -971) T) ((-1086 . -1026) T) ((-1086 . -1062) T) ((-1086 . -664) T) ((-1086 . -962) T) ((-1086 . -186) 162401) ((-1086 . -13) T) ((-1086 . -1130) T) ((-1086 . -189) T) ((-1086 . -225) 162385) ((-1086 . -184) 162369) ((-1083 . -1144) 162330) ((-1083 . -916) 162296) ((-1083 . -1116) 162262) ((-1083 . -1119) 162228) ((-1083 . -433) 162194) ((-1083 . -239) 162160) ((-1083 . -66) 162126) ((-1083 . -35) 162092) ((-1083 . -1159) 162069) ((-1083 . -47) 162046) ((-1083 . -556) 161847) ((-1083 . -655) 161649) ((-1083 . -583) 161451) ((-1083 . -591) 161306) ((-1083 . -589) 161146) ((-1083 . -969) 160942) ((-1083 . -964) 160738) ((-1083 . -82) 160490) ((-1083 . -38) 160292) ((-1083 . -887) 160262) ((-1083 . -241) 160090) ((-1083 . -1142) 160074) ((-1083 . -971) T) ((-1083 . -1026) T) ((-1083 . -1062) T) ((-1083 . -664) T) ((-1083 . -962) T) ((-1083 . -21) T) ((-1083 . -23) T) ((-1083 . -1014) T) ((-1083 . -553) 160056) ((-1083 . -1130) T) ((-1083 . -13) T) ((-1083 . -72) T) ((-1083 . -25) T) ((-1083 . -104) T) ((-1083 . -118) 159966) ((-1083 . -120) 159876) ((-1083 . -554) NIL) ((-1083 . -184) 159828) ((-1083 . -810) 159664) ((-1083 . -812) 159428) ((-1083 . -807) 159167) ((-1083 . -225) 159119) ((-1083 . -189) 158945) ((-1083 . -186) 158765) ((-1083 . -190) 158655) ((-1083 . -312) 158634) ((-1083 . -1135) 158613) ((-1083 . -833) 158592) ((-1083 . -496) 158546) ((-1083 . -146) 158480) ((-1083 . -392) 158459) ((-1083 . -258) 158438) ((-1083 . -246) 158392) ((-1083 . -201) 158371) ((-1083 . -288) 158323) ((-1083 . -456) 158057) ((-1083 . -260) 157942) ((-1083 . -329) 157894) ((-1083 . -581) 157846) ((-1083 . -343) 157798) ((-1083 . -797) NIL) ((-1083 . -741) NIL) ((-1083 . -715) NIL) ((-1083 . -717) NIL) ((-1083 . -757) NIL) ((-1083 . -760) NIL) ((-1083 . -719) NIL) ((-1083 . -722) NIL) ((-1083 . -756) NIL) ((-1083 . -795) 157750) ((-1083 . -822) NIL) ((-1083 . -934) NIL) ((-1083 . -951) 157716) ((-1083 . -1067) NIL) ((-1083 . -905) 157668) ((-1082 . -996) T) ((-1082 . -430) 157649) ((-1082 . -553) 157615) ((-1082 . -556) 157596) ((-1082 . -1014) T) ((-1082 . -1130) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -64) T) ((-1081 . -1014) T) ((-1081 . -553) 157578) ((-1081 . -1130) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1080 . -1014) T) ((-1080 . -553) 157560) ((-1080 . -1130) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1075 . -1108) 157536) ((-1075 . -183) 157481) ((-1075 . -76) 157426) ((-1075 . -124) 157371) ((-1075 . -554) NIL) ((-1075 . -193) 157316) ((-1075 . -539) 157292) ((-1075 . -260) 157081) ((-1075 . -456) 156821) ((-1075 . -429) 156753) ((-1075 . -241) 156729) ((-1075 . -243) 156705) ((-1075 . -550) 156681) ((-1075 . -1014) T) ((-1075 . -553) 156663) ((-1075 . -72) T) ((-1075 . -1130) T) ((-1075 . -13) T) ((-1075 . -34) T) ((-1075 . -318) 156608) ((-1074 . -1059) T) ((-1074 . -324) 156590) ((-1074 . -760) T) ((-1074 . -757) T) ((-1074 . -124) 156572) ((-1074 . -554) NIL) ((-1074 . -241) 156522) ((-1074 . -539) 156497) ((-1074 . -243) 156472) ((-1074 . -594) 156454) ((-1074 . -429) 156436) ((-1074 . -1014) T) ((-1074 . -456) NIL) ((-1074 . -260) NIL) ((-1074 . -553) 156418) ((-1074 . -72) T) ((-1074 . -1130) T) ((-1074 . -13) T) ((-1074 . -34) T) ((-1074 . -318) 156400) ((-1074 . -19) 156382) ((-1070 . -617) 156366) ((-1070 . -594) 156350) ((-1070 . -243) 156327) ((-1070 . -241) 156279) ((-1070 . -539) 156256) ((-1070 . -554) 156217) ((-1070 . -429) 156201) ((-1070 . -1014) 156179) ((-1070 . -456) 156112) ((-1070 . -260) 156050) ((-1070 . -553) 155985) ((-1070 . -72) 155939) ((-1070 . -1130) T) ((-1070 . -13) T) ((-1070 . -34) T) ((-1070 . -124) 155923) ((-1070 . -1169) 155907) ((-1070 . -924) 155891) ((-1070 . -1065) 155875) ((-1070 . -556) 155852) ((-1068 . -996) T) ((-1068 . -430) 155833) ((-1068 . -553) 155799) ((-1068 . -556) 155780) ((-1068 . -1014) T) ((-1068 . -1130) T) ((-1068 . -13) T) ((-1068 . -72) T) ((-1068 . -64) T) ((-1066 . -1108) 155759) ((-1066 . -183) 155707) ((-1066 . -76) 155655) ((-1066 . -124) 155603) ((-1066 . -554) NIL) ((-1066 . -193) 155551) ((-1066 . -539) 155530) ((-1066 . -260) 155328) ((-1066 . -456) 155080) ((-1066 . -429) 155015) ((-1066 . -241) 154994) ((-1066 . -243) 154973) ((-1066 . -550) 154952) ((-1066 . -1014) T) ((-1066 . -553) 154934) ((-1066 . -72) T) ((-1066 . -1130) T) ((-1066 . -13) T) ((-1066 . -34) T) ((-1066 . -318) 154882) ((-1063 . -1035) 154866) ((-1063 . -318) 154850) ((-1063 . -429) 154834) ((-1063 . -1014) 154812) ((-1063 . -456) 154745) ((-1063 . -260) 154683) ((-1063 . -553) 154618) ((-1063 . -72) 154572) ((-1063 . -1130) T) ((-1063 . -13) T) ((-1063 . -34) T) ((-1063 . -76) 154556) ((-1061 . -1021) 154525) ((-1061 . -1125) 154494) ((-1061 . -553) 154456) ((-1061 . -124) 154440) ((-1061 . -34) T) ((-1061 . -13) T) ((-1061 . -1130) T) ((-1061 . -72) T) ((-1061 . -260) 154378) ((-1061 . -456) 154311) ((-1061 . -1014) T) ((-1061 . -429) 154295) ((-1061 . -554) 154256) ((-1061 . -318) 154240) ((-1061 . -890) 154209) ((-1061 . -984) 154178) ((-1057 . -1038) 154123) ((-1057 . -318) 154107) ((-1057 . -34) T) ((-1057 . -260) 154045) ((-1057 . -456) 153978) ((-1057 . -429) 153962) ((-1057 . -966) 153902) ((-1057 . -951) 153800) ((-1057 . -556) 153719) ((-1057 . -355) 153703) ((-1057 . -581) 153651) ((-1057 . -591) 153589) ((-1057 . -329) 153573) ((-1057 . -190) 153552) ((-1057 . -186) 153500) ((-1057 . -189) 153454) ((-1057 . -225) 153438) ((-1057 . -807) 153362) ((-1057 . -812) 153288) ((-1057 . -810) 153247) ((-1057 . -184) 153231) ((-1057 . -655) 153166) ((-1057 . -583) 153101) ((-1057 . -589) 153060) ((-1057 . -104) T) ((-1057 . -25) T) ((-1057 . -72) T) ((-1057 . -13) T) ((-1057 . -1130) T) ((-1057 . -553) 153022) ((-1057 . -1014) T) ((-1057 . -23) T) ((-1057 . -21) T) ((-1057 . -969) 153006) ((-1057 . -964) 152990) ((-1057 . -82) 152969) ((-1057 . -962) T) ((-1057 . -664) T) ((-1057 . -1062) T) ((-1057 . -1026) T) ((-1057 . -971) T) ((-1057 . -38) 152929) ((-1057 . -554) 152890) ((-1056 . -924) 152861) ((-1056 . -34) T) ((-1056 . -13) T) ((-1056 . -1130) T) ((-1056 . -72) T) ((-1056 . -553) 152843) ((-1056 . -260) 152769) ((-1056 . -456) 152677) ((-1056 . -1014) T) ((-1056 . -429) 152648) ((-1056 . -318) 152619) ((-1055 . -1014) T) ((-1055 . -553) 152601) ((-1055 . -1130) T) ((-1055 . -13) T) ((-1055 . -72) T) ((-1050 . -1052) T) ((-1050 . -1176) T) ((-1050 . -64) T) ((-1050 . -72) T) ((-1050 . -13) T) ((-1050 . -1130) T) ((-1050 . -553) 152567) ((-1050 . -1014) T) ((-1050 . -556) 152548) ((-1050 . -430) 152529) ((-1050 . -996) T) ((-1048 . -1049) 152513) ((-1048 . -72) T) ((-1048 . -13) T) ((-1048 . -1130) T) ((-1048 . -553) 152495) ((-1048 . -1014) T) ((-1041 . -680) 152474) ((-1041 . -35) 152440) ((-1041 . -66) 152406) ((-1041 . -239) 152372) ((-1041 . -433) 152338) ((-1041 . -1119) 152304) ((-1041 . -1116) 152270) ((-1041 . -916) 152236) ((-1041 . -47) 152208) ((-1041 . -38) 152105) ((-1041 . -583) 152002) ((-1041 . -655) 151899) ((-1041 . -556) 151781) ((-1041 . -246) 151760) ((-1041 . -496) 151739) ((-1041 . -82) 151604) ((-1041 . -964) 151490) ((-1041 . -969) 151376) ((-1041 . -146) 151330) ((-1041 . -120) 151309) ((-1041 . -118) 151288) ((-1041 . -591) 151213) ((-1041 . -589) 151123) ((-1041 . -887) 151090) ((-1041 . -812) 151074) ((-1041 . -1130) T) ((-1041 . -13) T) ((-1041 . -807) 151056) ((-1041 . -962) T) ((-1041 . -664) T) ((-1041 . -1062) T) ((-1041 . -1026) T) ((-1041 . -971) T) ((-1041 . -21) T) ((-1041 . -23) T) ((-1041 . -1014) T) ((-1041 . -553) 151038) ((-1041 . -72) T) ((-1041 . -25) T) ((-1041 . -104) T) ((-1041 . -810) 151022) ((-1041 . -456) 150992) ((-1041 . -260) 150979) ((-1040 . -862) 150946) ((-1040 . -556) 150745) ((-1040 . -951) 150630) ((-1040 . -1135) 150609) ((-1040 . -822) 150588) ((-1040 . -797) 150447) ((-1040 . -812) 150431) ((-1040 . -807) 150413) ((-1040 . -810) 150397) ((-1040 . -456) 150349) ((-1040 . -392) 150303) ((-1040 . -581) 150251) ((-1040 . -591) 150140) ((-1040 . -329) 150124) ((-1040 . -47) 150096) ((-1040 . -38) 149948) ((-1040 . -583) 149800) ((-1040 . -655) 149652) ((-1040 . -246) 149586) ((-1040 . -496) 149520) ((-1040 . -82) 149345) ((-1040 . -964) 149191) ((-1040 . -969) 149037) ((-1040 . -146) 148951) ((-1040 . -120) 148930) ((-1040 . -118) 148909) ((-1040 . -589) 148819) ((-1040 . -104) T) ((-1040 . -25) T) ((-1040 . -72) T) ((-1040 . -13) T) ((-1040 . -1130) T) ((-1040 . -553) 148801) ((-1040 . -1014) T) ((-1040 . -23) T) ((-1040 . -21) T) ((-1040 . -962) T) ((-1040 . -664) T) ((-1040 . -1062) T) ((-1040 . -1026) T) ((-1040 . -971) T) ((-1040 . -355) 148785) ((-1040 . -277) 148757) ((-1040 . -260) 148744) ((-1040 . -554) 148492) ((-1034 . -484) T) ((-1034 . -1135) T) ((-1034 . -1067) T) ((-1034 . -951) 148474) ((-1034 . -554) 148389) ((-1034 . -934) T) ((-1034 . -797) 148371) ((-1034 . -756) T) ((-1034 . -722) T) ((-1034 . -719) T) ((-1034 . -760) T) ((-1034 . -757) T) ((-1034 . -717) T) ((-1034 . -715) T) ((-1034 . -741) T) ((-1034 . -591) 148343) ((-1034 . -581) 148325) ((-1034 . -833) T) ((-1034 . -496) T) ((-1034 . -246) T) ((-1034 . -146) T) ((-1034 . -556) 148297) ((-1034 . -655) 148284) ((-1034 . -583) 148271) ((-1034 . -969) 148258) ((-1034 . -964) 148245) ((-1034 . -82) 148230) ((-1034 . -38) 148217) ((-1034 . -392) T) ((-1034 . -258) T) ((-1034 . -189) T) ((-1034 . -186) 148204) ((-1034 . -190) T) ((-1034 . -116) T) ((-1034 . -962) T) ((-1034 . -664) T) ((-1034 . -1062) T) ((-1034 . -1026) T) ((-1034 . -971) T) ((-1034 . -21) T) ((-1034 . -589) 148176) ((-1034 . -23) T) ((-1034 . -1014) T) ((-1034 . -553) 148158) ((-1034 . -1130) T) ((-1034 . -13) T) ((-1034 . -72) T) ((-1034 . -25) T) ((-1034 . -104) T) ((-1034 . -120) T) ((-1034 . -753) T) ((-1034 . -320) T) ((-1034 . -84) T) ((-1034 . -605) T) ((-1030 . -996) T) ((-1030 . -430) 148139) ((-1030 . -553) 148105) ((-1030 . -556) 148086) ((-1030 . -1014) T) ((-1030 . -1130) T) ((-1030 . -13) T) ((-1030 . -72) T) ((-1030 . -64) T) ((-1029 . -1014) T) ((-1029 . -553) 148068) ((-1029 . -1130) T) ((-1029 . -13) T) ((-1029 . -72) T) ((-1027 . -196) 148047) ((-1027 . -1188) 148017) ((-1027 . -722) 147996) ((-1027 . -719) 147975) ((-1027 . -760) 147929) ((-1027 . -757) 147883) ((-1027 . -717) 147862) ((-1027 . -718) 147841) ((-1027 . -655) 147786) ((-1027 . -583) 147711) ((-1027 . -243) 147688) ((-1027 . -241) 147665) ((-1027 . -539) 147642) ((-1027 . -951) 147471) ((-1027 . -556) 147275) ((-1027 . -355) 147244) ((-1027 . -581) 147152) ((-1027 . -591) 146991) ((-1027 . -329) 146961) ((-1027 . -429) 146945) ((-1027 . -456) 146878) ((-1027 . -260) 146816) ((-1027 . -34) T) ((-1027 . -318) 146800) ((-1027 . -320) 146779) ((-1027 . -190) 146732) ((-1027 . -589) 146520) ((-1027 . -971) 146499) ((-1027 . -1026) 146478) ((-1027 . -1062) 146457) ((-1027 . -664) 146436) ((-1027 . -962) 146415) ((-1027 . -186) 146311) ((-1027 . -189) 146213) ((-1027 . -225) 146183) ((-1027 . -807) 146055) ((-1027 . -812) 145929) ((-1027 . -810) 145862) ((-1027 . -184) 145832) ((-1027 . -553) 145529) ((-1027 . -969) 145454) ((-1027 . -964) 145359) ((-1027 . -82) 145279) ((-1027 . -104) 145154) ((-1027 . -25) 144991) ((-1027 . -72) 144728) ((-1027 . -13) T) ((-1027 . -1130) T) ((-1027 . -1014) 144484) ((-1027 . -23) 144340) ((-1027 . -21) 144255) ((-1023 . -1024) 144239) ((-1023 . |MappingCategory|) 144213) ((-1023 . -1130) T) ((-1023 . -80) 144197) ((-1023 . -1014) T) ((-1023 . -553) 144179) ((-1023 . -13) T) ((-1023 . -72) T) ((-1018 . -1017) 144143) ((-1018 . -72) T) ((-1018 . -553) 144125) ((-1018 . -1014) T) ((-1018 . -241) 144081) ((-1018 . -1130) T) ((-1018 . -13) T) ((-1018 . -558) 143996) ((-1016 . -1017) 143948) ((-1016 . -72) T) ((-1016 . -553) 143930) ((-1016 . -1014) T) ((-1016 . -241) 143886) ((-1016 . -1130) T) ((-1016 . -13) T) ((-1016 . -558) 143789) ((-1015 . -320) T) ((-1015 . -72) T) ((-1015 . -13) T) ((-1015 . -1130) T) ((-1015 . -553) 143771) ((-1015 . -1014) T) ((-1010 . -369) 143755) ((-1010 . -1012) 143739) ((-1010 . -318) 143723) ((-1010 . -320) 143702) ((-1010 . -193) 143686) ((-1010 . -554) 143647) ((-1010 . -124) 143631) ((-1010 . -429) 143615) ((-1010 . -1014) T) ((-1010 . -456) 143548) ((-1010 . -260) 143486) ((-1010 . -553) 143468) ((-1010 . -72) T) ((-1010 . -1130) T) ((-1010 . -13) T) ((-1010 . -34) T) ((-1010 . -76) 143452) ((-1010 . -183) 143436) ((-1009 . -996) T) ((-1009 . -430) 143417) ((-1009 . -553) 143383) ((-1009 . -556) 143364) ((-1009 . -1014) T) ((-1009 . -1130) T) ((-1009 . -13) T) ((-1009 . -72) T) ((-1009 . -64) T) ((-1005 . -1130) T) ((-1005 . -13) T) ((-1005 . -1014) 143334) ((-1005 . -553) 143293) ((-1005 . -72) 143263) ((-1004 . -996) T) ((-1004 . -430) 143244) ((-1004 . -553) 143210) ((-1004 . -556) 143191) ((-1004 . -1014) T) ((-1004 . -1130) T) ((-1004 . -13) T) ((-1004 . -72) T) ((-1004 . -64) T) ((-1002 . -1007) 143175) ((-1002 . -558) 143159) ((-1002 . -1014) 143137) ((-1002 . -553) 143104) ((-1002 . -1130) 143082) ((-1002 . -13) 143060) ((-1002 . -72) 143038) ((-1002 . -1008) 142996) ((-1001 . -228) 142980) ((-1001 . -556) 142964) ((-1001 . -951) 142948) ((-1001 . -760) T) ((-1001 . -72) T) ((-1001 . -1014) T) ((-1001 . -553) 142930) ((-1001 . -757) T) ((-1001 . -186) 142917) ((-1001 . -13) T) ((-1001 . -1130) T) ((-1001 . -189) T) ((-1000 . -213) 142854) ((-1000 . -556) 142597) ((-1000 . -951) 142426) ((-1000 . -554) NIL) ((-1000 . -277) 142387) ((-1000 . -355) 142371) ((-1000 . -38) 142223) ((-1000 . -82) 142048) ((-1000 . -964) 141894) ((-1000 . -969) 141740) ((-1000 . -589) 141650) ((-1000 . -591) 141539) ((-1000 . -583) 141391) ((-1000 . -655) 141243) ((-1000 . -118) 141222) ((-1000 . -120) 141201) ((-1000 . -146) 141115) ((-1000 . -496) 141049) ((-1000 . -246) 140983) ((-1000 . -47) 140944) ((-1000 . -329) 140928) ((-1000 . -581) 140876) ((-1000 . -392) 140830) ((-1000 . -456) 140693) ((-1000 . -810) 140628) ((-1000 . -807) 140526) ((-1000 . -812) 140428) ((-1000 . -797) NIL) ((-1000 . -822) 140407) ((-1000 . -1135) 140386) ((-1000 . -862) 140331) ((-1000 . -260) 140318) ((-1000 . -190) 140297) ((-1000 . -104) T) ((-1000 . -25) T) ((-1000 . -72) T) ((-1000 . -553) 140279) ((-1000 . -1014) T) ((-1000 . -23) T) ((-1000 . -21) T) ((-1000 . -971) T) ((-1000 . -1026) T) ((-1000 . -1062) T) ((-1000 . -664) T) ((-1000 . -962) T) ((-1000 . -186) 140227) ((-1000 . -13) T) ((-1000 . -1130) T) ((-1000 . -189) 140181) ((-1000 . -225) 140165) ((-1000 . -184) 140149) ((-998 . -553) 140131) ((-995 . -757) T) ((-995 . -553) 140113) ((-995 . -1014) T) ((-995 . -72) T) ((-995 . -13) T) ((-995 . -1130) T) ((-995 . -760) T) ((-995 . -554) 140094) ((-992 . -662) 140073) ((-992 . -951) 139971) ((-992 . -355) 139955) ((-992 . -581) 139903) ((-992 . -591) 139780) ((-992 . -329) 139764) ((-992 . -322) 139743) ((-992 . -120) 139722) ((-992 . -556) 139547) ((-992 . -655) 139421) ((-992 . -583) 139295) ((-992 . -589) 139193) ((-992 . -969) 139106) ((-992 . -964) 139019) ((-992 . -82) 138911) ((-992 . -38) 138785) ((-992 . -353) 138764) ((-992 . -345) 138743) ((-992 . -118) 138697) ((-992 . -1067) 138676) ((-992 . -299) 138655) ((-992 . -320) 138609) ((-992 . -201) 138563) ((-992 . -246) 138517) ((-992 . -258) 138471) ((-992 . -392) 138425) ((-992 . -496) 138379) ((-992 . -833) 138333) ((-992 . -1135) 138287) ((-992 . -312) 138241) ((-992 . -190) 138169) ((-992 . -186) 138045) ((-992 . -189) 137927) ((-992 . -225) 137897) ((-992 . -807) 137769) ((-992 . -812) 137643) ((-992 . -810) 137576) ((-992 . -184) 137546) ((-992 . -554) 137530) ((-992 . -21) T) ((-992 . -23) T) ((-992 . -1014) T) ((-992 . -553) 137512) ((-992 . -1130) T) ((-992 . -13) T) ((-992 . -72) T) ((-992 . -25) T) ((-992 . -104) T) ((-992 . -962) T) ((-992 . -664) T) ((-992 . -1062) T) ((-992 . -1026) T) ((-992 . -971) T) ((-992 . -146) T) ((-990 . -1014) T) ((-990 . -553) 137494) ((-990 . -1130) T) ((-990 . -13) T) ((-990 . -72) T) ((-990 . -241) 137473) ((-989 . -1014) T) ((-989 . -553) 137455) ((-989 . -1130) T) ((-989 . -13) T) ((-989 . -72) T) ((-988 . -1014) T) ((-988 . -553) 137437) ((-988 . -1130) T) ((-988 . -13) T) ((-988 . -72) T) ((-988 . -241) 137416) ((-988 . -951) 137393) ((-988 . -556) 137370) ((-987 . -1130) T) ((-987 . -13) T) ((-986 . -996) T) ((-986 . -430) 137351) ((-986 . -553) 137317) ((-986 . -556) 137298) ((-986 . -1014) T) ((-986 . -1130) T) ((-986 . -13) T) ((-986 . -72) T) ((-986 . -64) T) ((-979 . -996) T) ((-979 . -430) 137279) ((-979 . -553) 137245) ((-979 . -556) 137226) ((-979 . -1014) T) ((-979 . -1130) T) ((-979 . -13) T) ((-979 . -72) T) ((-979 . -64) T) ((-976 . -484) T) ((-976 . -1135) T) ((-976 . -1067) T) ((-976 . -951) 137208) ((-976 . -554) 137123) ((-976 . -934) T) ((-976 . -797) 137105) ((-976 . -756) T) ((-976 . -722) T) ((-976 . -719) T) ((-976 . -760) T) ((-976 . -757) T) ((-976 . -717) T) ((-976 . -715) T) ((-976 . -741) T) ((-976 . -591) 137077) ((-976 . -581) 137059) ((-976 . -833) T) ((-976 . -496) T) ((-976 . -246) T) ((-976 . -146) T) ((-976 . -556) 137031) ((-976 . -655) 137018) ((-976 . -583) 137005) ((-976 . -969) 136992) ((-976 . -964) 136979) ((-976 . -82) 136964) ((-976 . -38) 136951) ((-976 . -392) T) ((-976 . -258) T) ((-976 . -189) T) ((-976 . -186) 136938) ((-976 . -190) T) ((-976 . -116) T) ((-976 . -962) T) ((-976 . -664) T) ((-976 . -1062) T) ((-976 . -1026) T) ((-976 . -971) T) ((-976 . -21) T) ((-976 . -589) 136910) ((-976 . -23) T) ((-976 . -1014) T) ((-976 . -553) 136892) ((-976 . -1130) T) ((-976 . -13) T) ((-976 . -72) T) ((-976 . -25) T) ((-976 . -104) T) ((-976 . -120) T) ((-976 . -558) 136873) ((-975 . -981) 136852) ((-975 . -72) T) ((-975 . -13) T) ((-975 . -1130) T) ((-975 . -553) 136834) ((-975 . -1014) T) ((-972 . -1130) T) ((-972 . -13) T) ((-972 . -1014) 136812) ((-972 . -553) 136779) ((-972 . -72) 136757) ((-967 . -966) 136697) ((-967 . -583) 136642) ((-967 . -655) 136587) ((-967 . -429) 136571) ((-967 . -456) 136504) ((-967 . -260) 136442) ((-967 . -34) T) ((-967 . -318) 136426) ((-967 . -591) 136410) ((-967 . -589) 136379) ((-967 . -104) T) ((-967 . -25) T) ((-967 . -72) T) ((-967 . -13) T) ((-967 . -1130) T) ((-967 . -553) 136341) ((-967 . -1014) T) ((-967 . -23) T) ((-967 . -21) T) ((-967 . -969) 136325) ((-967 . -964) 136309) ((-967 . -82) 136288) ((-967 . -1188) 136258) ((-967 . -554) 136219) ((-959 . -984) 136148) ((-959 . -890) 136077) ((-959 . -318) 136042) ((-959 . -554) 135984) ((-959 . -429) 135949) ((-959 . -1014) T) ((-959 . -456) 135833) ((-959 . -260) 135741) ((-959 . -553) 135684) ((-959 . -72) T) ((-959 . -1130) T) ((-959 . -13) T) ((-959 . -34) T) ((-959 . -124) 135649) ((-959 . -1125) 135578) ((-949 . -996) T) ((-949 . -430) 135559) ((-949 . -553) 135525) ((-949 . -556) 135506) ((-949 . -1014) T) ((-949 . -1130) T) ((-949 . -13) T) ((-949 . -72) T) ((-949 . -64) T) ((-948 . -146) T) ((-948 . -556) 135475) ((-948 . -971) T) ((-948 . -1026) T) ((-948 . -1062) T) ((-948 . -664) T) ((-948 . -962) T) ((-948 . -591) 135449) ((-948 . -589) 135408) ((-948 . -104) T) ((-948 . -25) T) ((-948 . -72) T) ((-948 . -13) T) ((-948 . -1130) T) ((-948 . -553) 135390) ((-948 . -1014) T) ((-948 . -23) T) ((-948 . -21) T) ((-948 . -969) 135364) ((-948 . -964) 135338) ((-948 . -82) 135305) ((-948 . -38) 135289) ((-948 . -583) 135273) ((-948 . -655) 135257) ((-941 . -984) 135226) ((-941 . -890) 135195) ((-941 . -318) 135179) ((-941 . -554) 135140) ((-941 . -429) 135124) ((-941 . -1014) T) ((-941 . -456) 135057) ((-941 . -260) 134995) ((-941 . -553) 134957) ((-941 . -72) T) ((-941 . -1130) T) ((-941 . -13) T) ((-941 . -34) T) ((-941 . -124) 134941) ((-941 . -1125) 134910) ((-940 . -1014) T) ((-940 . -553) 134892) ((-940 . -1130) T) ((-940 . -13) T) ((-940 . -72) T) ((-938 . -926) T) ((-938 . -916) T) ((-938 . -715) T) ((-938 . -717) T) ((-938 . -757) T) ((-938 . -760) T) ((-938 . -719) T) ((-938 . -722) T) ((-938 . -756) T) ((-938 . -951) 134777) ((-938 . -355) 134739) ((-938 . -201) T) ((-938 . -246) T) ((-938 . -258) T) ((-938 . -392) T) ((-938 . -38) 134676) ((-938 . -583) 134613) ((-938 . -655) 134550) ((-938 . -556) 134487) ((-938 . -496) T) ((-938 . -833) T) ((-938 . -1135) T) ((-938 . -312) T) ((-938 . -82) 134396) ((-938 . -964) 134333) ((-938 . -969) 134270) ((-938 . -146) T) ((-938 . -120) T) ((-938 . -591) 134207) ((-938 . -589) 134144) ((-938 . -104) T) ((-938 . -25) T) ((-938 . -72) T) ((-938 . -13) T) ((-938 . -1130) T) ((-938 . -553) 134126) ((-938 . -1014) T) ((-938 . -23) T) ((-938 . -21) T) ((-938 . -962) T) ((-938 . -664) T) ((-938 . -1062) T) ((-938 . -1026) T) ((-938 . -971) T) ((-933 . -996) T) ((-933 . -430) 134107) ((-933 . -553) 134073) ((-933 . -556) 134054) ((-933 . -1014) T) ((-933 . -1130) T) ((-933 . -13) T) ((-933 . -72) T) ((-933 . -64) T) ((-918 . -905) 134036) ((-918 . -1067) T) ((-918 . -556) 133986) ((-918 . -951) 133946) ((-918 . -554) 133876) ((-918 . -934) T) ((-918 . -822) NIL) ((-918 . -795) 133858) ((-918 . -756) T) ((-918 . -722) T) ((-918 . -719) T) ((-918 . -760) T) ((-918 . -757) T) ((-918 . -717) T) ((-918 . -715) T) ((-918 . -741) T) ((-918 . -797) 133840) ((-918 . -343) 133822) ((-918 . -581) 133804) ((-918 . -329) 133786) ((-918 . -241) NIL) ((-918 . -260) NIL) ((-918 . -456) NIL) ((-918 . -288) 133768) ((-918 . -201) T) ((-918 . -82) 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((-818 . -1014) T) ((-818 . -553) 122270) ((-818 . -72) T) ((-818 . -25) T) ((-818 . -104) T) ((-818 . -190) T) ((-818 . -280) 122257) ((-818 . -120) 122239) ((-818 . -951) 122226) ((-818 . -1188) 122213) ((-818 . -1199) 122200) ((-818 . -554) 122182) ((-817 . -1014) T) ((-817 . -553) 122164) ((-817 . -1130) T) ((-817 . -13) T) ((-817 . -72) T) ((-814 . -816) 122148) ((-814 . -760) 122102) ((-814 . -757) 122056) ((-814 . -664) T) ((-814 . -1014) T) ((-814 . -553) 122038) ((-814 . -72) T) ((-814 . -1026) T) ((-814 . -413) T) ((-814 . -1130) T) ((-814 . -13) T) ((-814 . -241) 122017) ((-813 . -92) 122001) ((-813 . -429) 121985) ((-813 . -1014) 121963) ((-813 . -456) 121896) ((-813 . -260) 121834) ((-813 . -553) 121748) ((-813 . -72) 121702) ((-813 . -1130) T) ((-813 . -13) T) ((-813 . -34) T) ((-813 . -924) 121686) ((-804 . -757) T) ((-804 . -553) 121668) ((-804 . -1014) T) ((-804 . -72) T) ((-804 . -13) T) ((-804 . -1130) T) ((-804 . -760) T) ((-804 . -951) 121645) ((-804 . -556) 121622) ((-801 . -1014) T) ((-801 . -553) 121604) ((-801 . -1130) T) ((-801 . -13) T) ((-801 . -72) T) ((-801 . -951) 121572) ((-801 . -556) 121540) ((-799 . -1014) T) ((-799 . -553) 121522) ((-799 . -1130) T) ((-799 . -13) T) ((-799 . -72) T) ((-796 . -1014) T) ((-796 . -553) 121504) ((-796 . -1130) T) ((-796 . -13) T) ((-796 . -72) T) ((-786 . -996) T) ((-786 . -430) 121485) ((-786 . -553) 121451) ((-786 . -556) 121432) ((-786 . -1014) T) ((-786 . -1130) T) ((-786 . -13) T) ((-786 . -72) T) ((-786 . -64) T) ((-786 . -1176) T) ((-784 . -1014) T) ((-784 . -553) 121414) ((-784 . -1130) T) ((-784 . -13) T) ((-784 . -72) T) ((-784 . -556) 121396) ((-783 . -1130) T) ((-783 . -13) T) ((-783 . -553) 121271) ((-783 . -1014) 121222) ((-783 . -72) 121173) ((-782 . -905) 121157) ((-782 . -1067) 121135) ((-782 . -951) 121002) ((-782 . -556) 120901) ((-782 . -554) 120704) ((-782 . -934) 120683) ((-782 . -822) 120662) ((-782 . -795) 120646) ((-782 . -756) 120625) ((-782 . -722) 120604) ((-782 . -719) 120583) ((-782 . -760) 120537) ((-782 . -757) 120491) ((-782 . -717) 120470) ((-782 . -715) 120449) ((-782 . -741) 120428) ((-782 . -797) 120353) ((-782 . -343) 120337) ((-782 . -581) 120285) ((-782 . -591) 120201) ((-782 . -329) 120185) ((-782 . -241) 120143) ((-782 . -260) 120108) ((-782 . -456) 120020) ((-782 . -288) 120004) ((-782 . -201) T) ((-782 . -82) 119935) ((-782 . -964) 119887) ((-782 . -969) 119839) ((-782 . -246) T) ((-782 . -655) 119791) ((-782 . -583) 119743) ((-782 . -589) 119680) ((-782 . -38) 119632) ((-782 . -258) T) ((-782 . -392) T) ((-782 . -146) T) ((-782 . -496) T) ((-782 . -833) T) ((-782 . -1135) T) ((-782 . -312) T) ((-782 . -190) 119611) ((-782 . -186) 119559) ((-782 . -189) 119513) ((-782 . -225) 119497) ((-782 . -807) 119421) ((-782 . -812) 119347) ((-782 . -810) 119306) ((-782 . -184) 119290) ((-782 . -120) 119244) ((-782 . -118) 119223) ((-782 . -104) T) ((-782 . -25) T) ((-782 . -72) T) ((-782 . -13) T) ((-782 . -1130) T) ((-782 . -553) 119205) ((-782 . -1014) T) ((-782 . -23) T) ((-782 . -21) T) ((-782 . -962) T) ((-782 . -664) T) ((-782 . -1062) T) ((-782 . -1026) T) ((-782 . -971) T) ((-781 . -905) 119182) ((-781 . -1067) NIL) ((-781 . -951) 119159) ((-781 . -556) 119089) ((-781 . -554) NIL) ((-781 . -934) NIL) ((-781 . -822) NIL) ((-781 . -795) 119066) ((-781 . -756) NIL) ((-781 . -722) NIL) ((-781 . -719) NIL) ((-781 . -760) NIL) ((-781 . -757) NIL) ((-781 . -717) NIL) ((-781 . -715) NIL) ((-781 . -741) NIL) ((-781 . -797) NIL) ((-781 . -343) 119043) ((-781 . -581) 119020) ((-781 . -591) 118965) ((-781 . -329) 118942) ((-781 . -241) 118872) ((-781 . -260) 118816) ((-781 . -456) 118679) ((-781 . -288) 118656) ((-781 . -201) T) ((-781 . -82) 118573) ((-781 . -964) 118518) ((-781 . -969) 118463) ((-781 . -246) T) ((-781 . -655) 118408) ((-781 . -583) 118353) ((-781 . -589) 118283) ((-781 . -38) 118228) ((-781 . -258) T) ((-781 . -392) T) ((-781 . -146) T) ((-781 . -496) T) ((-781 . -833) T) ((-781 . -1135) T) ((-781 . -312) T) ((-781 . -190) NIL) ((-781 . -186) NIL) ((-781 . -189) NIL) ((-781 . -225) 118205) ((-781 . -807) NIL) ((-781 . -812) NIL) ((-781 . -810) NIL) ((-781 . -184) 118182) ((-781 . -120) T) ((-781 . -118) NIL) ((-781 . -104) T) ((-781 . -25) T) ((-781 . -72) T) ((-781 . -13) T) ((-781 . -1130) T) ((-781 . -553) 118164) ((-781 . -1014) T) ((-781 . -23) T) ((-781 . -21) T) ((-781 . -962) T) ((-781 . -664) T) ((-781 . -1062) T) ((-781 . -1026) T) ((-781 . -971) T) ((-779 . -780) 118148) ((-779 . -833) T) ((-779 . -496) T) ((-779 . -246) T) ((-779 . -146) T) ((-779 . -556) 118120) ((-779 . -655) 118107) ((-779 . -583) 118094) ((-779 . -969) 118081) ((-779 . -964) 118068) ((-779 . -82) 118053) ((-779 . -38) 118040) ((-779 . -392) T) ((-779 . -258) T) ((-779 . -962) T) ((-779 . -664) T) ((-779 . -1062) T) ((-779 . -1026) T) ((-779 . -971) T) ((-779 . -21) T) ((-779 . -589) 118012) ((-779 . -23) T) ((-779 . -1014) T) ((-779 . -553) 117994) ((-779 . -1130) T) ((-779 . -13) T) ((-779 . -72) T) ((-779 . -25) T) ((-779 . -104) T) ((-779 . -591) 117981) ((-779 . -120) T) ((-776 . -962) T) ((-776 . -664) T) ((-776 . -1062) T) ((-776 . -1026) T) ((-776 . -971) T) ((-776 . -21) T) ((-776 . -589) 117926) ((-776 . -23) T) ((-776 . -1014) T) ((-776 . -553) 117888) ((-776 . -1130) T) ((-776 . -13) T) ((-776 . -72) T) ((-776 . -25) T) ((-776 . -104) T) ((-776 . -591) 117848) ((-776 . -556) 117783) ((-776 . -430) 117760) ((-776 . -38) 117730) ((-776 . -82) 117695) ((-776 . -964) 117665) ((-776 . -969) 117635) ((-776 . -583) 117605) ((-776 . -655) 117575) ((-775 . -1014) T) ((-775 . -553) 117557) ((-775 . -1130) T) ((-775 . -13) T) ((-775 . -72) T) ((-774 . -753) T) ((-774 . -760) T) ((-774 . -757) T) ((-774 . -1014) T) ((-774 . -553) 117539) ((-774 . -1130) T) ((-774 . -13) T) ((-774 . -72) T) ((-774 . -320) T) ((-774 . -554) 117461) ((-773 . -1014) T) ((-773 . -553) 117443) ((-773 . -1130) T) ((-773 . -13) T) ((-773 . -72) T) ((-772 . -771) T) ((-772 . -147) T) ((-772 . -553) 117425) ((-768 . -757) T) ((-768 . -553) 117407) ((-768 . -1014) T) ((-768 . -72) T) ((-768 . -13) T) ((-768 . -1130) T) ((-768 . -760) T) ((-765 . -762) 117391) ((-765 . -951) 117289) ((-765 . -556) 117187) ((-765 . -355) 117171) ((-765 . -655) 117141) ((-765 . -583) 117111) ((-765 . -591) 117085) ((-765 . -589) 117044) ((-765 . -104) T) ((-765 . -25) T) ((-765 . -72) T) ((-765 . -13) T) ((-765 . -1130) T) ((-765 . -553) 117026) ((-765 . -1014) T) ((-765 . -23) T) ((-765 . -21) T) ((-765 . -969) 117010) ((-765 . -964) 116994) ((-765 . -82) 116973) ((-765 . -962) T) ((-765 . -664) T) ((-765 . -1062) T) ((-765 . -1026) T) ((-765 . -971) T) ((-765 . -38) 116943) ((-764 . -762) 116927) ((-764 . -951) 116825) ((-764 . -556) 116744) ((-764 . -355) 116728) ((-764 . -655) 116698) ((-764 . -583) 116668) ((-764 . -591) 116642) ((-764 . -589) 116601) ((-764 . -104) T) ((-764 . -25) T) ((-764 . -72) T) ((-764 . -13) T) ((-764 . -1130) T) ((-764 . -553) 116583) ((-764 . -1014) T) ((-764 . -23) T) ((-764 . -21) T) ((-764 . -969) 116567) ((-764 . -964) 116551) ((-764 . -82) 116530) ((-764 . -962) T) ((-764 . -664) T) ((-764 . -1062) T) ((-764 . -1026) T) ((-764 . -971) T) ((-764 . -38) 116500) ((-758 . -760) T) ((-758 . -1130) T) ((-758 . -13) T) ((-758 . -72) T) ((-758 . -430) 116484) ((-758 . -553) 116432) ((-758 . -556) 116416) ((-751 . -1014) T) ((-751 . -553) 116398) ((-751 . -1130) T) ((-751 . -13) T) ((-751 . -72) T) ((-751 . -355) 116382) ((-751 . -556) 116255) ((-751 . -951) 116153) ((-751 . -21) 116108) ((-751 . -589) 116028) ((-751 . -23) 115983) ((-751 . -25) 115938) ((-751 . -104) 115893) ((-751 . -756) 115872) ((-751 . -722) 115851) ((-751 . -719) 115830) ((-751 . -760) 115809) ((-751 . -757) 115788) ((-751 . -717) 115767) ((-751 . -715) 115746) ((-751 . -962) 115725) ((-751 . -664) 115704) ((-751 . -1062) 115683) ((-751 . -1026) 115662) ((-751 . -971) 115641) ((-751 . -591) 115614) ((-751 . -120) 115593) ((-750 . -748) 115575) ((-750 . -72) T) ((-750 . -13) T) ((-750 . -1130) T) ((-750 . -553) 115557) ((-750 . -1014) T) ((-746 . -962) T) ((-746 . -664) T) ((-746 . -1062) T) ((-746 . -1026) T) ((-746 . -971) T) ((-746 . -21) T) ((-746 . -589) 115502) ((-746 . -23) T) ((-746 . -1014) T) ((-746 . -553) 115484) ((-746 . -1130) T) ((-746 . -13) T) ((-746 . -72) T) ((-746 . -25) T) ((-746 . -104) T) ((-746 . -591) 115444) ((-746 . -556) 115399) ((-746 . -951) 115369) ((-746 . -241) 115348) ((-746 . -120) 115327) ((-746 . -118) 115306) ((-746 . -38) 115276) ((-746 . -82) 115241) ((-746 . -964) 115211) ((-746 . -969) 115181) ((-746 . -583) 115151) ((-746 . -655) 115121) ((-744 . -1014) T) ((-744 . -553) 115103) ((-744 . -1130) T) ((-744 . -13) T) ((-744 . -72) T) ((-744 . -355) 115087) ((-744 . -556) 114960) ((-744 . -951) 114858) ((-744 . -21) 114813) ((-744 . -589) 114733) ((-744 . -23) 114688) ((-744 . -25) 114643) ((-744 . -104) 114598) ((-744 . -756) 114577) ((-744 . -722) 114556) ((-744 . -719) 114535) ((-744 . -760) 114514) ((-744 . -757) 114493) ((-744 . -717) 114472) ((-744 . -715) 114451) ((-744 . -962) 114430) ((-744 . -664) 114409) ((-744 . -1062) 114388) ((-744 . -1026) 114367) ((-744 . -971) 114346) ((-744 . -591) 114319) ((-744 . -120) 114298) ((-742 . -646) 114282) ((-742 . -556) 114237) ((-742 . -655) 114207) ((-742 . -583) 114177) ((-742 . -591) 114151) ((-742 . -589) 114110) ((-742 . -104) T) ((-742 . -25) T) ((-742 . -72) T) ((-742 . -13) T) ((-742 . -1130) T) ((-742 . -553) 114092) ((-742 . -1014) T) ((-742 . -23) T) ((-742 . -21) T) ((-742 . -969) 114076) ((-742 . -964) 114060) ((-742 . -82) 114039) ((-742 . -962) T) ((-742 . -664) T) ((-742 . -1062) T) ((-742 . -1026) T) ((-742 . -971) T) ((-742 . -38) 114009) ((-742 . -190) 113988) ((-742 . -186) 113961) ((-742 . -189) 113940) ((-740 . -336) 113924) ((-740 . -556) 113908) ((-740 . -951) 113892) ((-740 . -760) T) ((-740 . -757) T) ((-740 . -1026) T) ((-740 . -72) T) ((-740 . -13) T) ((-740 . -1130) T) ((-740 . -553) 113874) ((-740 . -1014) T) ((-740 . -664) T) ((-740 . -755) T) ((-740 . -767) T) ((-739 . -228) 113858) ((-739 . -556) 113842) ((-739 . -951) 113826) ((-739 . -760) T) ((-739 . -72) T) ((-739 . -1014) T) ((-739 . -553) 113808) ((-739 . -757) T) ((-739 . -186) 113795) ((-739 . -13) T) ((-739 . -1130) T) ((-739 . -189) T) ((-738 . -82) 113730) ((-738 . -964) 113681) ((-738 . -969) 113632) ((-738 . -21) T) ((-738 . -589) 113568) ((-738 . -23) T) ((-738 . -1014) T) ((-738 . -553) 113537) ((-738 . -1130) T) ((-738 . -13) T) ((-738 . -72) T) ((-738 . -25) T) ((-738 . -104) T) ((-738 . -591) 113488) ((-738 . -190) T) ((-738 . -556) 113397) ((-738 . -971) T) ((-738 . -1026) T) ((-738 . -1062) T) ((-738 . -664) T) ((-738 . -962) T) ((-738 . -186) 113384) ((-738 . -189) T) ((-738 . -430) 113368) ((-738 . -312) 113347) ((-738 . -1135) 113326) ((-738 . -833) 113305) ((-738 . -496) 113284) ((-738 . -146) 113263) ((-738 . -655) 113200) ((-738 . -583) 113137) ((-738 . -38) 113074) ((-738 . -392) 113053) ((-738 . -258) 113032) ((-738 . -246) 113011) ((-738 . -201) 112990) ((-737 . -213) 112929) ((-737 . -556) 112673) ((-737 . -951) 112503) ((-737 . -554) NIL) ((-737 . -277) 112465) ((-737 . -355) 112449) ((-737 . -38) 112301) ((-737 . -82) 112126) ((-737 . -964) 111972) ((-737 . -969) 111818) ((-737 . -589) 111728) ((-737 . -591) 111617) ((-737 . -583) 111469) ((-737 . -655) 111321) ((-737 . -118) 111300) ((-737 . -120) 111279) ((-737 . -146) 111193) ((-737 . -496) 111127) ((-737 . -246) 111061) ((-737 . -47) 111023) ((-737 . -329) 111007) ((-737 . -581) 110955) ((-737 . -392) 110909) ((-737 . -456) 110774) ((-737 . -810) 110710) ((-737 . -807) 110609) ((-737 . -812) 110512) ((-737 . -797) NIL) ((-737 . -822) 110491) ((-737 . -1135) 110470) ((-737 . -862) 110417) ((-737 . -260) 110404) ((-737 . -190) 110383) ((-737 . -104) T) ((-737 . -25) T) ((-737 . -72) T) ((-737 . -553) 110365) ((-737 . -1014) T) ((-737 . -23) T) ((-737 . -21) T) ((-737 . -971) T) ((-737 . -1026) T) ((-737 . -1062) T) ((-737 . -664) T) ((-737 . -962) T) ((-737 . -186) 110313) ((-737 . -13) T) ((-737 . -1130) T) ((-737 . -189) 110267) ((-737 . -225) 110251) ((-737 . -184) 110235) ((-736 . -196) 110214) ((-736 . -1188) 110184) ((-736 . -722) 110163) ((-736 . -719) 110142) ((-736 . -760) 110096) ((-736 . -757) 110050) ((-736 . -717) 110029) ((-736 . -718) 110008) ((-736 . -655) 109953) ((-736 . -583) 109878) ((-736 . -243) 109855) ((-736 . -241) 109832) ((-736 . -539) 109809) ((-736 . -951) 109638) ((-736 . -556) 109442) ((-736 . -355) 109411) ((-736 . -581) 109319) ((-736 . -591) 109158) ((-736 . -329) 109128) ((-736 . -429) 109112) ((-736 . -456) 109045) ((-736 . -260) 108983) ((-736 . -34) T) ((-736 . -318) 108967) ((-736 . -320) 108946) ((-736 . -190) 108899) ((-736 . -589) 108687) ((-736 . -971) 108666) ((-736 . -1026) 108645) ((-736 . -1062) 108624) ((-736 . -664) 108603) ((-736 . -962) 108582) ((-736 . -186) 108478) ((-736 . -189) 108380) ((-736 . -225) 108350) ((-736 . -807) 108222) ((-736 . -812) 108096) ((-736 . -810) 108029) ((-736 . -184) 107999) ((-736 . -553) 107696) ((-736 . -969) 107621) ((-736 . -964) 107526) ((-736 . -82) 107446) ((-736 . -104) 107321) ((-736 . -25) 107158) ((-736 . -72) 106895) ((-736 . -13) T) ((-736 . -1130) T) ((-736 . -1014) 106651) ((-736 . -23) 106507) ((-736 . -21) 106422) ((-723 . -721) 106406) ((-723 . -760) 106385) ((-723 . -757) 106364) ((-723 . -951) 106157) ((-723 . -556) 106010) ((-723 . -355) 105974) ((-723 . -241) 105932) ((-723 . -260) 105897) ((-723 . -456) 105809) ((-723 . -288) 105793) ((-723 . -320) 105772) ((-723 . -554) 105733) ((-723 . -120) 105712) ((-723 . -118) 105691) ((-723 . -655) 105675) ((-723 . -583) 105659) ((-723 . -591) 105633) ((-723 . -589) 105592) ((-723 . -104) T) ((-723 . -25) T) ((-723 . -72) T) ((-723 . -13) T) ((-723 . -1130) T) ((-723 . -553) 105574) ((-723 . -1014) T) ((-723 . -23) T) ((-723 . -21) T) ((-723 . -969) 105558) ((-723 . -964) 105542) ((-723 . -82) 105521) ((-723 . -962) T) ((-723 . -664) T) ((-723 . -1062) T) ((-723 . -1026) T) ((-723 . -971) T) ((-723 . -38) 105505) ((-705 . -1156) 105489) ((-705 . -1067) 105467) ((-705 . -554) NIL) ((-705 . -260) 105454) ((-705 . -456) 105402) ((-705 . -277) 105379) ((-705 . -951) 105241) ((-705 . -355) 105225) ((-705 . -38) 105057) ((-705 . -82) 104862) ((-705 . -964) 104688) ((-705 . -969) 104514) ((-705 . -589) 104424) ((-705 . -591) 104313) ((-705 . -583) 104145) ((-705 . -655) 103977) ((-705 . -556) 103733) ((-705 . -118) 103712) ((-705 . -120) 103691) ((-705 . -47) 103668) ((-705 . -329) 103652) ((-705 . -581) 103600) ((-705 . -810) 103544) ((-705 . -807) 103451) ((-705 . -812) 103362) ((-705 . -797) NIL) ((-705 . -822) 103341) ((-705 . -1135) 103320) ((-705 . -862) 103290) ((-705 . -833) 103269) ((-705 . -496) 103183) ((-705 . -246) 103097) ((-705 . -146) 102991) ((-705 . -392) 102925) ((-705 . -258) 102904) ((-705 . -241) 102831) ((-705 . -190) T) ((-705 . -104) T) ((-705 . -25) T) ((-705 . -72) T) ((-705 . -553) 102792) ((-705 . -1014) T) ((-705 . -23) T) ((-705 . -21) T) ((-705 . -971) T) ((-705 . -1026) T) ((-705 . -1062) T) ((-705 . -664) T) ((-705 . -962) T) ((-705 . -186) 102779) ((-705 . -13) T) ((-705 . -1130) T) ((-705 . -189) T) ((-705 . -225) 102763) ((-705 . -184) 102747) ((-704 . -978) 102714) ((-704 . -554) 102349) ((-704 . -260) 102336) ((-704 . -456) 102288) ((-704 . -277) 102260) ((-704 . -951) 102119) ((-704 . -355) 102103) ((-704 . -38) 101955) ((-704 . -556) 101728) ((-704 . -591) 101617) ((-704 . -589) 101527) ((-704 . -971) T) ((-704 . -1026) T) ((-704 . -1062) T) ((-704 . -664) T) ((-704 . -962) T) ((-704 . -82) 101352) ((-704 . -964) 101198) ((-704 . -969) 101044) ((-704 . -21) T) ((-704 . -23) T) ((-704 . -1014) T) ((-704 . -553) 100958) ((-704 . -1130) T) ((-704 . -13) T) ((-704 . -72) T) ((-704 . -25) T) ((-704 . -104) T) ((-704 . -583) 100810) ((-704 . -655) 100662) ((-704 . -118) 100641) ((-704 . -120) 100620) ((-704 . -146) 100534) ((-704 . -496) 100468) ((-704 . -246) 100402) ((-704 . -47) 100374) ((-704 . -329) 100358) ((-704 . -581) 100306) ((-704 . -392) 100260) ((-704 . -810) 100244) ((-704 . -807) 100226) ((-704 . -812) 100210) ((-704 . -797) 100069) ((-704 . -822) 100048) ((-704 . -1135) 100027) ((-704 . -862) 99994) ((-697 . -1014) T) ((-697 . -553) 99976) ((-697 . -1130) T) ((-697 . -13) T) ((-697 . -72) T) ((-695 . -718) T) ((-695 . -104) T) ((-695 . -25) T) ((-695 . -72) T) ((-695 . -13) T) ((-695 . -1130) T) ((-695 . -553) 99958) ((-695 . -1014) T) ((-695 . -23) T) ((-695 . -717) T) ((-695 . -757) T) ((-695 . -760) T) ((-695 . -719) T) ((-695 . -722) T) ((-695 . -664) T) ((-695 . -1026) T) ((-676 . -677) 99942) ((-676 . -1012) 99926) ((-676 . -193) 99910) ((-676 . -554) 99871) ((-676 . -124) 99855) ((-676 . -429) 99839) ((-676 . -1014) T) ((-676 . -456) 99772) ((-676 . -260) 99710) ((-676 . -553) 99692) ((-676 . -72) T) ((-676 . -1130) T) ((-676 . -13) T) ((-676 . -34) T) ((-676 . -76) 99676) ((-676 . -635) 99660) ((-676 . -318) 99644) ((-675 . -962) T) ((-675 . -664) T) ((-675 . -1062) T) ((-675 . -1026) T) ((-675 . -971) T) ((-675 . -21) T) ((-675 . -589) 99589) ((-675 . -23) T) ((-675 . -1014) T) ((-675 . -553) 99571) ((-675 . -1130) T) ((-675 . -13) T) ((-675 . -72) T) ((-675 . -25) T) ((-675 . -104) T) ((-675 . -591) 99531) ((-675 . -556) 99487) ((-675 . -951) 99458) ((-675 . -120) 99437) ((-675 . -118) 99416) ((-675 . -38) 99386) ((-675 . -82) 99351) ((-675 . -964) 99321) ((-675 . -969) 99291) ((-675 . -583) 99261) ((-675 . -655) 99231) ((-675 . -320) 99184) ((-671 . -862) 99137) ((-671 . -556) 98929) ((-671 . -951) 98807) ((-671 . -1135) 98786) ((-671 . -822) 98765) ((-671 . -797) NIL) ((-671 . -812) 98742) ((-671 . -807) 98717) ((-671 . -810) 98694) ((-671 . -456) 98632) ((-671 . -392) 98586) ((-671 . -581) 98534) ((-671 . -591) 98423) ((-671 . -329) 98407) ((-671 . -47) 98372) ((-671 . -38) 98224) ((-671 . -583) 98076) ((-671 . -655) 97928) ((-671 . -246) 97862) ((-671 . -496) 97796) ((-671 . -82) 97621) ((-671 . -964) 97467) ((-671 . -969) 97313) ((-671 . -146) 97227) ((-671 . -120) 97206) ((-671 . -118) 97185) ((-671 . -589) 97095) ((-671 . -104) T) ((-671 . -25) T) ((-671 . -72) T) ((-671 . -13) T) ((-671 . -1130) T) ((-671 . -553) 97077) ((-671 . -1014) T) ((-671 . -23) T) ((-671 . -21) T) ((-671 . -962) T) ((-671 . -664) T) ((-671 . -1062) T) ((-671 . -1026) T) ((-671 . -971) T) ((-671 . -355) 97061) ((-671 . -277) 97026) ((-671 . -260) 97013) ((-671 . -554) 96874) ((-665 . -666) 96858) ((-665 . -80) 96842) ((-665 . -1130) T) ((-665 . |MappingCategory|) 96816) ((-665 . -1024) 96800) ((-665 . -1014) T) ((-665 . -553) 96761) ((-665 . -13) T) ((-665 . -72) T) ((-656 . -413) T) ((-656 . -1026) T) ((-656 . -72) T) ((-656 . -13) T) ((-656 . -1130) T) ((-656 . -553) 96743) ((-656 . -1014) T) ((-656 . -664) T) ((-653 . -962) T) ((-653 . -664) T) ((-653 . -1062) T) ((-653 . -1026) T) ((-653 . -971) T) ((-653 . -21) T) ((-653 . -589) 96715) ((-653 . -23) T) ((-653 . -1014) T) ((-653 . -553) 96697) ((-653 . -1130) T) ((-653 . -13) T) ((-653 . -72) T) ((-653 . -25) T) ((-653 . -104) T) ((-653 . -591) 96684) ((-653 . -556) 96666) ((-652 . -962) T) ((-652 . -664) T) ((-652 . -1062) T) ((-652 . -1026) T) ((-652 . -971) T) ((-652 . -21) T) ((-652 . -589) 96611) ((-652 . -23) T) ((-652 . -1014) T) ((-652 . -553) 96593) ((-652 . -1130) T) ((-652 . -13) T) ((-652 . -72) T) ((-652 . -25) T) ((-652 . -104) T) ((-652 . -591) 96553) ((-652 . -556) 96508) ((-652 . -951) 96478) ((-652 . -241) 96457) ((-652 . -120) 96436) ((-652 . -118) 96415) ((-652 . -38) 96385) ((-652 . -82) 96350) ((-652 . -964) 96320) ((-652 . -969) 96290) ((-652 . -583) 96260) ((-652 . -655) 96230) ((-651 . -757) T) ((-651 . -553) 96165) ((-651 . -1014) T) ((-651 . -72) T) ((-651 . -13) T) ((-651 . -1130) T) ((-651 . -760) T) ((-651 . -430) 96115) ((-651 . -556) 96065) ((-650 . -1156) 96049) ((-650 . -1067) 96027) ((-650 . -554) NIL) ((-650 . -260) 96014) ((-650 . -456) 95962) ((-650 . -277) 95939) ((-650 . -951) 95822) ((-650 . -355) 95806) ((-650 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. -589) 90818) ((-607 . -104) T) ((-607 . -25) T) ((-607 . -72) T) ((-607 . -13) T) ((-607 . -1130) T) ((-607 . -553) 90800) ((-607 . -1014) T) ((-607 . -23) T) ((-607 . -21) T) ((-607 . -969) 90784) ((-607 . -964) 90768) ((-607 . -82) 90747) ((-607 . -575) 90731) ((-607 . -335) 90703) ((-607 . -556) 90680) ((-607 . -951) 90657) ((-599 . -601) 90641) ((-599 . -38) 90611) ((-599 . -556) 90530) ((-599 . -591) 90504) ((-599 . -589) 90463) ((-599 . -971) T) ((-599 . -1026) T) ((-599 . -1062) T) ((-599 . -664) T) ((-599 . -962) T) ((-599 . -82) 90442) ((-599 . -964) 90426) ((-599 . -969) 90410) ((-599 . -21) T) ((-599 . -23) T) ((-599 . -1014) T) ((-599 . -553) 90392) ((-599 . -72) T) ((-599 . -25) T) ((-599 . -104) T) ((-599 . -583) 90362) ((-599 . -655) 90332) ((-599 . -355) 90316) ((-599 . -951) 90214) ((-599 . -762) 90198) ((-599 . -1130) T) ((-599 . -13) T) ((-599 . -241) 90159) ((-598 . -601) 90143) ((-598 . -38) 90113) ((-598 . -556) 90032) ((-598 . -591) 90006) ((-598 . -589) 89965) 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T) ((-563 . -971) T) ((-563 . -21) T) ((-563 . -589) 85600) ((-563 . -23) T) ((-563 . -1014) T) ((-563 . -553) 85582) ((-563 . -72) T) ((-563 . -25) T) ((-563 . -104) T) ((-563 . -591) 85569) ((-563 . -556) 85465) ((-563 . -190) 85444) ((-563 . -496) T) ((-563 . -246) T) ((-563 . -146) T) ((-563 . -655) 85431) ((-563 . -583) 85418) ((-563 . -969) 85405) ((-563 . -964) 85392) ((-563 . -82) 85377) ((-563 . -38) 85364) ((-563 . -554) 85341) ((-563 . -355) 85325) ((-563 . -951) 85210) ((-563 . -120) 85189) ((-563 . -118) 85168) ((-563 . -258) 85147) ((-563 . -392) 85126) ((-563 . -833) 85105) ((-559 . -38) 85089) ((-559 . -556) 85058) ((-559 . -591) 85032) ((-559 . -589) 84991) ((-559 . -971) T) ((-559 . -1026) T) ((-559 . -1062) T) ((-559 . -664) T) ((-559 . -962) T) ((-559 . -82) 84970) ((-559 . -964) 84954) ((-559 . -969) 84938) ((-559 . -21) T) ((-559 . -23) T) ((-559 . -1014) T) ((-559 . -553) 84920) ((-559 . -1130) T) ((-559 . -13) T) ((-559 . -72) T) ((-559 . -25) T) ((-559 . -104) T) ((-559 . -583) 84904) ((-559 . -655) 84888) ((-559 . -756) 84867) ((-559 . -722) 84846) ((-559 . -719) 84825) ((-559 . -760) 84804) ((-559 . -757) 84783) ((-559 . -717) 84762) ((-559 . -715) 84741) ((-559 . -120) 84720) ((-557 . -881) T) ((-557 . -72) T) ((-557 . -553) 84702) ((-557 . -1014) T) ((-557 . -605) T) ((-557 . -13) T) ((-557 . -1130) T) ((-557 . -84) T) ((-557 . -320) T) ((-551 . -105) T) ((-551 . -72) T) ((-551 . -13) T) ((-551 . -1130) T) ((-551 . -553) 84684) ((-551 . -1014) T) ((-551 . -757) T) ((-551 . -760) T) ((-551 . -795) 84668) ((-551 . -554) 84529) ((-548 . -314) 84467) ((-548 . -72) T) ((-548 . -13) T) ((-548 . -1130) T) ((-548 . -553) 84449) ((-548 . -1014) T) ((-548 . -1108) 84425) ((-548 . -183) 84370) ((-548 . -76) 84315) ((-548 . -124) 84260) ((-548 . -554) NIL) ((-548 . -193) 84205) ((-548 . -539) 84181) ((-548 . -260) 83970) ((-548 . -456) 83710) ((-548 . -429) 83642) ((-548 . -241) 83618) ((-548 . -243) 83594) ((-548 . -550) 83570) ((-548 . -34) T) 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. -1130) T) ((-486 . -13) T) ((-486 . -72) T) ((-486 . -320) T) ((-485 . -484) T) ((-485 . -1135) T) ((-485 . -1067) T) ((-485 . -951) 78438) ((-485 . -554) 78353) ((-485 . -934) T) ((-485 . -797) 78335) ((-485 . -756) T) ((-485 . -722) T) ((-485 . -719) T) ((-485 . -760) T) ((-485 . -757) T) ((-485 . -717) T) ((-485 . -715) T) ((-485 . -741) T) ((-485 . -591) 78307) ((-485 . -581) 78289) ((-485 . -833) T) ((-485 . -496) T) ((-485 . -246) T) ((-485 . -146) T) ((-485 . -556) 78261) ((-485 . -655) 78248) ((-485 . -583) 78235) ((-485 . -969) 78222) ((-485 . -964) 78209) ((-485 . -82) 78194) ((-485 . -38) 78181) ((-485 . -392) T) ((-485 . -258) T) ((-485 . -189) T) ((-485 . -186) 78168) ((-485 . -190) T) ((-485 . -116) T) ((-485 . -962) T) ((-485 . -664) T) ((-485 . -1062) T) ((-485 . -1026) T) ((-485 . -971) T) ((-485 . -21) T) ((-485 . -589) 78140) ((-485 . -23) T) ((-485 . -1014) T) ((-485 . -553) 78122) ((-485 . -1130) T) ((-485 . -13) T) ((-485 . -72) T) ((-485 . -25) T) ((-485 . 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. -38) 73058) ((-427 . -258) T) ((-427 . -392) T) ((-427 . -146) T) ((-427 . -496) T) ((-427 . -833) T) ((-427 . -1135) T) ((-427 . -312) T) ((-427 . -190) T) ((-427 . -186) 73045) ((-427 . -189) T) ((-427 . -225) 73027) ((-427 . -807) NIL) ((-427 . -812) NIL) ((-427 . -810) NIL) ((-427 . -184) 73009) ((-427 . -120) T) ((-427 . -118) NIL) ((-427 . -104) T) ((-427 . -25) T) ((-427 . -72) T) ((-427 . -13) T) ((-427 . -1130) T) ((-427 . -553) 72951) ((-427 . -1014) T) ((-427 . -23) T) ((-427 . -21) T) ((-427 . -962) T) ((-427 . -664) T) ((-427 . -1062) T) ((-427 . -1026) T) ((-427 . -971) T) ((-425 . -286) 72920) ((-425 . -104) T) ((-425 . -25) T) ((-425 . -72) T) ((-425 . -13) T) ((-425 . -1130) T) ((-425 . -553) 72902) ((-425 . -1014) T) ((-425 . -23) T) ((-425 . -589) 72884) ((-425 . -21) T) ((-424 . -882) 72868) ((-424 . -318) 72852) ((-424 . -429) 72836) ((-424 . -1014) 72814) ((-424 . -456) 72747) ((-424 . -260) 72685) ((-424 . -553) 72620) ((-424 . -72) 72574) ((-424 . -1130) T) ((-424 . -13) T) ((-424 . -34) T) ((-424 . -76) 72558) ((-423 . -996) T) ((-423 . -430) 72539) ((-423 . -553) 72505) ((-423 . -556) 72486) ((-423 . -1014) T) ((-423 . -1130) T) ((-423 . -13) T) ((-423 . -72) T) ((-423 . -64) T) ((-422 . -196) 72465) ((-422 . -1188) 72435) ((-422 . -722) 72414) ((-422 . -719) 72393) ((-422 . -760) 72347) ((-422 . -757) 72301) ((-422 . -717) 72280) ((-422 . -718) 72259) ((-422 . -655) 72204) ((-422 . -583) 72129) ((-422 . -243) 72106) ((-422 . -241) 72083) ((-422 . -539) 72060) ((-422 . -951) 71889) ((-422 . -556) 71693) ((-422 . -355) 71662) ((-422 . -581) 71570) ((-422 . -591) 71409) ((-422 . -329) 71379) ((-422 . -429) 71363) ((-422 . -456) 71296) ((-422 . -260) 71234) ((-422 . -34) T) ((-422 . -318) 71218) ((-422 . -320) 71197) ((-422 . -190) 71150) ((-422 . -589) 70938) ((-422 . -971) 70917) ((-422 . -1026) 70896) ((-422 . -1062) 70875) ((-422 . -664) 70854) ((-422 . -962) 70833) ((-422 . -186) 70729) ((-422 . -189) 70631) ((-422 . -225) 70601) 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((-421 . -1130) T) ((-421 . -553) 66550) ((-421 . -1014) T) ((-421 . -23) T) ((-421 . -21) T) ((-421 . -962) T) ((-421 . -664) T) ((-421 . -1062) T) ((-421 . -1026) T) ((-421 . -971) T) ((-421 . -355) 66534) ((-421 . -277) 66491) ((-421 . -260) 66478) ((-421 . -554) 66339) ((-419 . -1108) 66318) ((-419 . -183) 66266) ((-419 . -76) 66214) ((-419 . -124) 66162) ((-419 . -554) NIL) ((-419 . -193) 66110) ((-419 . -539) 66089) ((-419 . -260) 65887) ((-419 . -456) 65639) ((-419 . -429) 65574) ((-419 . -241) 65553) ((-419 . -243) 65532) ((-419 . -550) 65511) ((-419 . -1014) T) ((-419 . -553) 65493) ((-419 . -72) T) ((-419 . -1130) T) ((-419 . -13) T) ((-419 . -34) T) ((-419 . -318) 65441) ((-418 . -996) T) ((-418 . -430) 65422) ((-418 . -553) 65388) ((-418 . -556) 65369) ((-418 . -1014) T) ((-418 . -1130) T) ((-418 . -13) T) ((-418 . -72) T) ((-418 . -64) T) ((-417 . -312) T) ((-417 . -1135) T) ((-417 . -833) T) ((-417 . -496) T) ((-417 . -146) T) ((-417 . -556) 65319) ((-417 . -655) 65284) ((-417 . -583) 65249) ((-417 . -38) 65214) ((-417 . -392) T) ((-417 . -258) T) ((-417 . -591) 65179) ((-417 . -589) 65129) ((-417 . -971) T) ((-417 . -1026) T) ((-417 . -1062) T) ((-417 . -664) T) ((-417 . -962) T) ((-417 . -82) 65078) ((-417 . -964) 65043) ((-417 . -969) 65008) ((-417 . -21) T) ((-417 . -23) T) ((-417 . -1014) T) ((-417 . -553) 64960) ((-417 . -1130) T) ((-417 . -13) T) ((-417 . -72) T) ((-417 . -25) T) ((-417 . -104) T) ((-417 . -246) T) ((-417 . -201) T) ((-417 . -120) T) ((-417 . -951) 64920) ((-417 . -934) T) ((-417 . -554) 64842) ((-416 . -1125) 64811) ((-416 . -553) 64773) ((-416 . -124) 64757) ((-416 . -34) T) ((-416 . -13) T) ((-416 . -1130) T) ((-416 . -72) T) ((-416 . -260) 64695) ((-416 . -456) 64628) ((-416 . -1014) T) ((-416 . -429) 64612) ((-416 . -554) 64573) ((-416 . -318) 64557) ((-416 . -890) 64526) ((-415 . -1108) 64505) ((-415 . -183) 64453) ((-415 . -76) 64401) ((-415 . -124) 64349) ((-415 . -554) NIL) ((-415 . -193) 64297) ((-415 . -539) 64276) 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((-414 . -13) T) ((-414 . -1130) T) ((-414 . -553) 61311) ((-414 . -1014) T) ((-414 . -23) T) ((-414 . -21) T) ((-414 . -962) T) ((-414 . -664) T) ((-414 . -1062) T) ((-414 . -1026) T) ((-414 . -971) T) ((-414 . -258) 61290) ((-414 . -392) 61269) ((-414 . -146) 61203) ((-414 . -496) 61157) ((-414 . -833) 61136) ((-414 . -1135) 61115) ((-414 . -312) 61094) ((-408 . -1014) T) ((-408 . -553) 61076) ((-408 . -1130) T) ((-408 . -13) T) ((-408 . -72) T) ((-403 . -890) 61045) ((-403 . -318) 61029) ((-403 . -554) 60990) ((-403 . -429) 60974) ((-403 . -1014) T) ((-403 . -456) 60907) ((-403 . -260) 60845) ((-403 . -553) 60807) ((-403 . -72) T) ((-403 . -1130) T) ((-403 . -13) T) ((-403 . -34) T) ((-403 . -124) 60791) ((-401 . -655) 60762) ((-401 . -583) 60733) ((-401 . -591) 60704) ((-401 . -589) 60660) ((-401 . -104) T) ((-401 . -25) T) ((-401 . -72) T) ((-401 . -13) T) ((-401 . -1130) T) ((-401 . -553) 60642) ((-401 . -1014) T) ((-401 . -23) T) ((-401 . -21) T) ((-401 . -969) 60613) ((-401 . -964) 60584) ((-401 . -82) 60545) ((-394 . -862) 60512) ((-394 . -556) 60304) ((-394 . -951) 60182) ((-394 . -1135) 60161) ((-394 . -822) 60140) ((-394 . -797) NIL) ((-394 . -812) 60117) ((-394 . -807) 60092) ((-394 . -810) 60069) ((-394 . -456) 60007) ((-394 . -392) 59961) ((-394 . -581) 59909) ((-394 . -591) 59798) ((-394 . -329) 59782) ((-394 . -47) 59761) ((-394 . -38) 59613) ((-394 . -583) 59465) ((-394 . -655) 59317) ((-394 . -246) 59251) ((-394 . -496) 59185) ((-394 . -82) 59010) ((-394 . -964) 58856) ((-394 . -969) 58702) ((-394 . -146) 58616) ((-394 . -120) 58595) ((-394 . -118) 58574) ((-394 . -589) 58484) ((-394 . -104) T) ((-394 . -25) T) ((-394 . -72) T) ((-394 . -13) T) ((-394 . -1130) T) ((-394 . -553) 58466) ((-394 . -1014) T) ((-394 . -23) T) ((-394 . -21) T) ((-394 . -962) T) ((-394 . -664) T) ((-394 . -1062) T) ((-394 . -1026) T) ((-394 . -971) T) ((-394 . -355) 58450) ((-394 . -277) 58429) ((-394 . -260) 58416) ((-394 . -554) 58277) ((-393 . -361) 58247) ((-393 . -684) 58217) ((-393 . -658) T) ((-393 . -686) T) ((-393 . -82) 58168) ((-393 . -964) 58138) ((-393 . -969) 58108) ((-393 . -21) T) ((-393 . -589) 58023) ((-393 . -23) T) ((-393 . -1014) T) ((-393 . -553) 58005) ((-393 . -72) T) ((-393 . -25) T) ((-393 . -104) T) ((-393 . -591) 57935) ((-393 . -583) 57905) ((-393 . -655) 57875) ((-393 . -316) 57845) ((-393 . -1130) T) ((-393 . -13) T) ((-393 . -241) 57808) ((-381 . -1014) T) ((-381 . -553) 57790) ((-381 . -1130) T) ((-381 . -13) T) ((-381 . -72) T) ((-380 . -1014) T) ((-380 . -553) 57772) ((-380 . -1130) T) ((-380 . -13) T) ((-380 . -72) T) ((-379 . -1014) T) ((-379 . -553) 57754) ((-379 . -1130) T) ((-379 . -13) T) ((-379 . -72) T) ((-377 . -553) 57736) ((-372 . -38) 57720) ((-372 . -556) 57689) ((-372 . -591) 57663) ((-372 . -589) 57622) ((-372 . -971) T) ((-372 . -1026) T) ((-372 . -1062) T) ((-372 . -664) T) ((-372 . -962) T) ((-372 . -82) 57601) ((-372 . -964) 57585) ((-372 . -969) 57569) ((-372 . -21) T) ((-372 . -23) T) ((-372 . -1014) T) ((-372 . -553) 57551) ((-372 . -1130) T) ((-372 . -13) T) ((-372 . -72) T) ((-372 . -25) T) ((-372 . -104) T) ((-372 . -583) 57535) ((-372 . -655) 57519) ((-358 . -664) T) ((-358 . -1014) T) ((-358 . -553) 57501) ((-358 . -1130) T) ((-358 . -13) T) ((-358 . -72) T) ((-358 . -1026) T) ((-356 . -413) T) ((-356 . -1026) T) ((-356 . -72) T) ((-356 . -13) T) ((-356 . -1130) T) ((-356 . -553) 57483) ((-356 . -1014) T) ((-356 . -664) T) ((-350 . -905) 57467) ((-350 . -1067) 57445) ((-350 . -951) 57312) ((-350 . -556) 57211) ((-350 . -554) 57014) ((-350 . -934) 56993) ((-350 . -822) 56972) ((-350 . -795) 56956) ((-350 . -756) 56935) ((-350 . -722) 56914) ((-350 . -719) 56893) ((-350 . -760) 56847) ((-350 . -757) 56801) ((-350 . -717) 56780) ((-350 . -715) 56759) ((-350 . -741) 56738) ((-350 . -797) 56663) ((-350 . -343) 56647) ((-350 . -581) 56595) ((-350 . -591) 56511) ((-350 . -329) 56495) ((-350 . -241) 56453) ((-350 . -260) 56418) ((-350 . -456) 56330) ((-350 . -288) 56314) ((-350 . -201) T) ((-350 . -82) 56245) ((-350 . -964) 56197) ((-350 . -969) 56149) ((-350 . -246) T) ((-350 . -655) 56101) ((-350 . -583) 56053) ((-350 . -589) 55990) ((-350 . -38) 55942) ((-350 . -258) T) ((-350 . -392) T) ((-350 . -146) T) ((-350 . -496) T) ((-350 . -833) T) ((-350 . -1135) T) ((-350 . -312) T) ((-350 . -190) 55921) ((-350 . -186) 55869) ((-350 . -189) 55823) ((-350 . -225) 55807) ((-350 . -807) 55731) ((-350 . -812) 55657) ((-350 . -810) 55616) ((-350 . -184) 55600) ((-350 . -120) 55554) ((-350 . -118) 55533) ((-350 . -104) T) ((-350 . -25) T) ((-350 . -72) T) ((-350 . -13) T) ((-350 . -1130) T) ((-350 . -553) 55515) ((-350 . -1014) T) ((-350 . -23) T) ((-350 . -21) T) ((-350 . -962) T) ((-350 . -664) T) ((-350 . -1062) T) ((-350 . -1026) T) ((-350 . -971) T) ((-348 . -496) T) ((-348 . -246) T) ((-348 . -146) T) ((-348 . -556) 55424) ((-348 . -655) 55398) ((-348 . -583) 55372) ((-348 . -591) 55346) ((-348 . -589) 55305) ((-348 . -104) T) ((-348 . -25) T) ((-348 . -72) T) ((-348 . -13) T) ((-348 . -1130) T) ((-348 . -553) 55287) ((-348 . -1014) T) ((-348 . -23) T) ((-348 . -21) T) ((-348 . -969) 55261) ((-348 . -964) 55235) ((-348 . -82) 55202) ((-348 . -962) T) ((-348 . -664) T) ((-348 . -1062) T) ((-348 . -1026) T) ((-348 . -971) T) ((-348 . -38) 55176) ((-348 . -184) 55160) ((-348 . -810) 55119) ((-348 . -812) 55045) ((-348 . -807) 54969) ((-348 . -225) 54953) ((-348 . -189) 54907) ((-348 . -186) 54855) ((-348 . -190) 54834) ((-348 . -288) 54818) ((-348 . -456) 54660) ((-348 . -260) 54599) ((-348 . -241) 54527) ((-348 . -355) 54511) ((-348 . -951) 54409) ((-348 . -392) 54362) ((-348 . -934) 54341) ((-348 . -554) 54244) ((-348 . -1135) 54222) ((-342 . -1014) T) ((-342 . -553) 54204) ((-342 . -1130) T) ((-342 . -13) T) ((-342 . -72) T) ((-342 . -189) T) ((-342 . -186) 54191) ((-342 . -554) 54168) ((-340 . -684) 54152) ((-340 . -658) T) ((-340 . -686) T) ((-340 . -82) 54131) ((-340 . -964) 54115) ((-340 . -969) 54099) ((-340 . -21) T) ((-340 . -589) 54068) ((-340 . -23) T) ((-340 . -1014) T) ((-340 . -553) 54050) ((-340 . -1130) T) ((-340 . -13) T) ((-340 . -72) T) ((-340 . -25) T) ((-340 . -104) T) ((-340 . -591) 54034) ((-340 . -583) 54018) ((-340 . -655) 54002) ((-338 . -339) T) ((-338 . -72) T) ((-338 . -13) T) ((-338 . -1130) T) ((-338 . -553) 53968) ((-338 . -1014) T) ((-338 . -556) 53949) ((-338 . -430) 53930) ((-337 . -336) 53914) ((-337 . -556) 53898) ((-337 . -951) 53882) ((-337 . -760) 53861) ((-337 . -757) 53840) ((-337 . -1026) T) ((-337 . -72) T) ((-337 . -13) T) ((-337 . -1130) T) ((-337 . -553) 53822) ((-337 . -1014) T) ((-337 . -664) T) ((-334 . -335) 53801) ((-334 . -556) 53785) ((-334 . -951) 53769) ((-334 . -583) 53739) ((-334 . -655) 53709) ((-334 . -591) 53693) ((-334 . -589) 53662) ((-334 . -104) T) ((-334 . -25) T) ((-334 . -72) T) ((-334 . -13) T) ((-334 . -1130) T) ((-334 . -553) 53644) ((-334 . -1014) T) ((-334 . -23) T) ((-334 . -21) T) ((-334 . -969) 53628) ((-334 . -964) 53612) ((-334 . -82) 53591) ((-333 . -82) 53570) ((-333 . -964) 53554) ((-333 . -969) 53538) ((-333 . -21) T) ((-333 . -589) 53507) ((-333 . -23) T) ((-333 . -1014) T) ((-333 . -553) 53489) ((-333 . -1130) T) ((-333 . -13) T) ((-333 . -72) T) ((-333 . -25) T) ((-333 . -104) T) ((-333 . -591) 53473) ((-333 . -450) 53452) ((-333 . -558) 53417) ((-333 . -655) 53387) ((-333 . -583) 53357) ((-330 . -347) T) ((-330 . -120) T) ((-330 . -556) 53307) ((-330 . -591) 53272) ((-330 . -589) 53222) ((-330 . -104) T) ((-330 . -25) T) ((-330 . -72) T) ((-330 . -13) T) ((-330 . -1130) T) ((-330 . -553) 53189) ((-330 . -1014) T) ((-330 . -23) T) ((-330 . -21) T) ((-330 . -971) T) ((-330 . -1026) T) ((-330 . -1062) T) ((-330 . -664) T) ((-330 . -962) T) ((-330 . -554) 53103) ((-330 . -312) T) ((-330 . -1135) T) ((-330 . -833) T) ((-330 . -496) T) ((-330 . -146) T) ((-330 . -655) 53068) ((-330 . -583) 53033) ((-330 . -38) 52998) ((-330 . -392) T) ((-330 . -258) T) ((-330 . -82) 52947) ((-330 . -964) 52912) ((-330 . -969) 52877) ((-330 . -246) T) ((-330 . -201) T) ((-330 . -756) T) ((-330 . -722) T) ((-330 . -719) T) ((-330 . -760) T) ((-330 . -757) T) ((-330 . -717) T) ((-330 . -715) T) ((-330 . -797) 52859) ((-330 . -916) T) ((-330 . -934) T) ((-330 . -951) 52819) ((-330 . -974) T) ((-330 . -190) T) ((-330 . -186) 52806) ((-330 . -189) T) ((-330 . -1116) T) ((-330 . -1119) T) ((-330 . -433) T) ((-330 . -239) T) ((-330 . -66) T) ((-330 . -35) T) ((-330 . -558) 52788) ((-313 . -314) 52765) ((-313 . -72) T) ((-313 . -13) T) ((-313 . -1130) T) ((-313 . -553) 52747) ((-313 . -1014) T) ((-310 . -413) T) ((-310 . -1026) T) ((-310 . -72) T) ((-310 . -13) T) ((-310 . -1130) T) ((-310 . -553) 52729) ((-310 . -1014) T) ((-310 . -664) T) ((-310 . -951) 52713) ((-310 . -556) 52697) ((-308 . -280) 52681) ((-308 . -190) 52660) ((-308 . -186) 52633) ((-308 . -189) 52612) ((-308 . -320) 52591) ((-308 . -1067) 52570) ((-308 . -299) 52549) ((-308 . -120) 52528) ((-308 . -556) 52465) ((-308 . -591) 52417) ((-308 . -589) 52354) ((-308 . -104) T) ((-308 . -25) T) ((-308 . -72) T) ((-308 . -13) T) ((-308 . -1130) T) ((-308 . -553) 52336) ((-308 . -1014) T) ((-308 . -23) T) ((-308 . -21) T) ((-308 . -971) T) ((-308 . -1026) T) ((-308 . -1062) T) ((-308 . -664) T) ((-308 . -962) T) ((-308 . -312) T) ((-308 . -1135) T) ((-308 . -833) T) ((-308 . -496) T) ((-308 . -146) T) ((-308 . -655) 52288) ((-308 . -583) 52240) ((-308 . -38) 52205) ((-308 . -392) T) ((-308 . -258) T) ((-308 . -82) 52136) ((-308 . -964) 52088) ((-308 . -969) 52040) ((-308 . -246) T) ((-308 . -201) T) ((-308 . -345) 51994) ((-308 . -118) 51948) ((-308 . -951) 51932) ((-308 . -1188) 51916) ((-308 . -1199) 51900) ((-304 . -280) 51884) ((-304 . -190) 51863) ((-304 . -186) 51836) ((-304 . -189) 51815) ((-304 . -320) 51794) ((-304 . -1067) 51773) ((-304 . -299) 51752) ((-304 . -120) 51731) ((-304 . -556) 51668) ((-304 . -591) 51620) ((-304 . -589) 51557) ((-304 . -104) T) ((-304 . -25) T) ((-304 . -72) T) ((-304 . -13) T) ((-304 . -1130) T) ((-304 . -553) 51539) ((-304 . -1014) T) ((-304 . -23) T) ((-304 . -21) T) ((-304 . -971) T) ((-304 . -1026) T) ((-304 . -1062) T) ((-304 . -664) T) ((-304 . -962) T) ((-304 . -312) T) ((-304 . -1135) T) ((-304 . -833) T) ((-304 . -496) T) ((-304 . -146) T) ((-304 . -655) 51491) ((-304 . -583) 51443) ((-304 . -38) 51408) ((-304 . -392) T) ((-304 . -258) T) ((-304 . -82) 51339) ((-304 . -964) 51291) ((-304 . -969) 51243) ((-304 . -246) T) ((-304 . -201) T) ((-304 . -345) 51197) ((-304 . -118) 51151) ((-304 . -951) 51135) ((-304 . -1188) 51119) ((-304 . -1199) 51103) ((-303 . -280) 51087) ((-303 . -190) 51066) ((-303 . -186) 51039) ((-303 . -189) 51018) ((-303 . -320) 50997) ((-303 . -1067) 50976) ((-303 . -299) 50955) ((-303 . -120) 50934) ((-303 . -556) 50871) ((-303 . -591) 50823) ((-303 . -589) 50760) ((-303 . -104) T) ((-303 . -25) T) ((-303 . -72) T) ((-303 . -13) T) ((-303 . -1130) T) ((-303 . -553) 50742) ((-303 . -1014) T) ((-303 . -23) T) ((-303 . -21) T) ((-303 . -971) T) 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20157) ((-197 . -589) 19945) ((-197 . -971) 19924) ((-197 . -1026) 19903) ((-197 . -1062) 19882) ((-197 . -664) 19861) ((-197 . -962) 19840) ((-197 . -186) 19736) ((-197 . -189) 19638) ((-197 . -225) 19608) ((-197 . -807) 19480) ((-197 . -812) 19354) ((-197 . -810) 19287) ((-197 . -184) 19257) ((-197 . -553) 18954) ((-197 . -969) 18879) ((-197 . -964) 18784) ((-197 . -82) 18704) ((-197 . -104) 18579) ((-197 . -25) 18416) ((-197 . -72) 18153) ((-197 . -13) T) ((-197 . -1130) T) ((-197 . -1014) 17909) ((-197 . -23) 17765) ((-197 . -21) 17680) ((-181 . -628) 17638) ((-181 . -318) 17622) ((-181 . -34) T) ((-181 . -13) T) ((-181 . -1130) T) ((-181 . -72) 17576) ((-181 . -553) 17511) ((-181 . -260) 17449) ((-181 . -456) 17382) ((-181 . -1014) 17360) ((-181 . -429) 17344) ((-181 . -57) 17302) ((-179 . -347) T) ((-179 . -120) T) ((-179 . -556) 17252) ((-179 . -591) 17217) ((-179 . -589) 17167) ((-179 . -104) T) ((-179 . -25) T) ((-179 . -72) T) ((-179 . -13) T) ((-179 . -1130) T) ((-179 . -553) 17149) ((-179 . -1014) T) ((-179 . -23) T) ((-179 . -21) T) ((-179 . -971) T) ((-179 . -1026) T) ((-179 . -1062) T) ((-179 . -664) T) ((-179 . -962) T) ((-179 . -554) 17079) ((-179 . -312) T) ((-179 . -1135) T) ((-179 . -833) T) ((-179 . -496) T) ((-179 . -146) T) ((-179 . -655) 17044) ((-179 . -583) 17009) ((-179 . -38) 16974) ((-179 . -392) T) ((-179 . -258) T) ((-179 . -82) 16923) ((-179 . -964) 16888) ((-179 . -969) 16853) ((-179 . -246) T) ((-179 . -201) T) ((-179 . -756) T) ((-179 . -722) T) ((-179 . -719) T) ((-179 . -760) T) ((-179 . -757) T) ((-179 . -717) T) ((-179 . -715) T) ((-179 . -797) 16835) ((-179 . -916) T) ((-179 . -934) T) ((-179 . -951) 16795) ((-179 . -974) T) ((-179 . -190) T) ((-179 . -186) 16782) ((-179 . -189) T) ((-179 . -1116) T) ((-179 . -1119) T) ((-179 . -433) T) ((-179 . -239) T) ((-179 . -66) T) ((-179 . -35) T) ((-177 . -561) 16759) ((-177 . -556) 16721) ((-177 . -591) 16688) ((-177 . -589) 16640) ((-177 . -971) T) ((-177 . -1026) T) ((-177 . 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10164) ((-111 . -556) 10145) ((-111 . -1014) T) ((-111 . -1130) T) ((-111 . -13) T) ((-111 . -72) T) ((-111 . -64) T) ((-110 . -996) T) ((-110 . -430) 10126) ((-110 . -553) 10092) ((-110 . -556) 10073) ((-110 . -1014) T) ((-110 . -1130) T) ((-110 . -13) T) ((-110 . -72) T) ((-110 . -64) T) ((-108 . -405) 10050) ((-108 . -556) 9946) ((-108 . -951) 9930) ((-108 . -1014) T) ((-108 . -553) 9912) ((-108 . -1130) T) ((-108 . -13) T) ((-108 . -72) T) ((-108 . -410) 9867) ((-108 . -241) 9844) ((-107 . -757) T) ((-107 . -553) 9826) ((-107 . -1014) T) ((-107 . -72) T) ((-107 . -13) T) ((-107 . -1130) T) ((-107 . -760) T) ((-107 . -23) T) ((-107 . -25) T) ((-107 . -664) T) ((-107 . -1026) T) ((-107 . -951) 9808) ((-107 . -556) 9790) ((-106 . -996) T) ((-106 . -430) 9771) ((-106 . -553) 9737) ((-106 . -556) 9718) ((-106 . -1014) T) ((-106 . -1130) T) ((-106 . -13) T) ((-106 . -72) T) ((-106 . -64) T) ((-103 . -1014) T) ((-103 . -553) 9700) ((-103 . -1130) T) ((-103 . -13) T) ((-103 . -72) T) 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8855) ((-99 . -456) 8788) ((-99 . -1014) 8766) ((-99 . -429) 8750) ((-99 . -92) 8734) ((-94 . -98) 8718) ((-94 . -318) 8702) ((-94 . -924) 8686) ((-94 . -34) T) ((-94 . -13) T) ((-94 . -1130) T) ((-94 . -72) 8640) ((-94 . -553) 8575) ((-94 . -260) 8513) ((-94 . -456) 8446) ((-94 . -1014) 8424) ((-94 . -429) 8408) ((-94 . -92) 8392) ((-90 . -905) 8370) ((-90 . -1067) NIL) ((-90 . -951) 8348) ((-90 . -556) 8279) ((-90 . -554) NIL) ((-90 . -934) NIL) ((-90 . -822) NIL) ((-90 . -795) 8257) ((-90 . -756) NIL) ((-90 . -722) NIL) ((-90 . -719) NIL) ((-90 . -760) NIL) ((-90 . -757) NIL) ((-90 . -717) NIL) ((-90 . -715) NIL) ((-90 . -741) NIL) ((-90 . -797) NIL) ((-90 . -343) 8235) ((-90 . -581) 8213) ((-90 . -591) 8159) ((-90 . -329) 8137) ((-90 . -241) 8071) ((-90 . -260) 8018) ((-90 . -456) 7888) ((-90 . -288) 7866) ((-90 . -201) T) ((-90 . -82) 7785) ((-90 . -964) 7731) ((-90 . -969) 7677) ((-90 . -246) T) ((-90 . -655) 7623) ((-90 . -583) 7569) ((-90 . -589) 7500) ((-90 . -38) 7446) ((-90 . -258) T) ((-90 . -392) T) ((-90 . -146) T) ((-90 . -496) T) ((-90 . -833) T) ((-90 . -1135) T) ((-90 . -312) T) ((-90 . -190) NIL) ((-90 . -186) NIL) ((-90 . -189) NIL) ((-90 . -225) 7424) ((-90 . -807) NIL) ((-90 . -812) NIL) ((-90 . -810) NIL) ((-90 . -184) 7402) ((-90 . -120) T) ((-90 . -118) NIL) ((-90 . -104) T) ((-90 . -25) T) ((-90 . -72) T) ((-90 . -13) T) ((-90 . -1130) T) ((-90 . -553) 7384) ((-90 . -1014) T) ((-90 . -23) T) ((-90 . -21) T) ((-90 . -962) T) ((-90 . -664) T) ((-90 . -1062) T) ((-90 . -1026) T) ((-90 . -971) T) ((-89 . -780) 7368) ((-89 . -833) T) ((-89 . -496) T) ((-89 . -246) T) ((-89 . -146) T) ((-89 . -556) 7340) ((-89 . -655) 7327) ((-89 . -583) 7314) ((-89 . -969) 7301) ((-89 . -964) 7288) ((-89 . -82) 7273) ((-89 . -38) 7260) ((-89 . -392) T) ((-89 . -258) T) ((-89 . -962) T) ((-89 . -664) T) ((-89 . -1062) T) ((-89 . -1026) T) ((-89 . -971) T) ((-89 . -21) T) ((-89 . -589) 7232) ((-89 . -23) T) ((-89 . -1014) T) ((-89 . -553) 7214) ((-89 . -1130) T) 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-663) T) ((-1160 . -961) T) ((-1160 . -82) 189619) ((-1160 . -963) 189460) ((-1160 . -968) 189301) ((-1160 . -21) T) ((-1160 . -23) T) ((-1160 . -1013) T) ((-1160 . -552) 189283) ((-1160 . -1129) T) ((-1160 . -13) T) ((-1160 . -72) T) ((-1160 . -25) T) ((-1160 . -104) T) ((-1160 . -246) 189237) ((-1160 . -201) 189216) ((-1160 . -915) 189182) ((-1160 . -1115) 189148) ((-1160 . -1118) 189114) ((-1160 . -433) 189080) ((-1160 . -239) 189046) ((-1160 . -66) 189012) ((-1160 . -35) 188978) ((-1160 . -1158) 188948) ((-1160 . -47) 188918) ((-1160 . -120) 188897) ((-1160 . -118) 188876) ((-1160 . -886) 188839) ((-1160 . -811) 188745) ((-1160 . -806) 188626) ((-1160 . -809) 188532) ((-1160 . -241) 188490) ((-1160 . -189) 188442) ((-1160 . -186) 188388) ((-1160 . -190) 188340) ((-1160 . -1162) 188324) ((-1160 . -950) 188259) ((-1148 . -1155) 188243) ((-1148 . -1066) 188221) ((-1148 . -553) NIL) ((-1148 . -260) 188208) ((-1148 . -455) 188156) ((-1148 . -277) 188133) ((-1148 . -950) 188016) ((-1148 . -355) 188000) ((-1148 . -38) 187832) ((-1148 . -82) 187637) ((-1148 . -963) 187463) ((-1148 . -968) 187289) ((-1148 . -588) 187199) ((-1148 . -590) 187088) ((-1148 . -582) 186920) ((-1148 . -654) 186752) ((-1148 . -555) 186508) ((-1148 . -118) 186487) ((-1148 . -120) 186466) ((-1148 . -47) 186443) ((-1148 . -329) 186427) ((-1148 . -580) 186375) ((-1148 . -809) 186319) ((-1148 . -806) 186226) ((-1148 . -811) 186137) ((-1148 . -796) NIL) ((-1148 . -821) 186116) ((-1148 . -1134) 186095) ((-1148 . -861) 186065) ((-1148 . -832) 186044) ((-1148 . -495) 185958) ((-1148 . -246) 185872) ((-1148 . -146) 185766) ((-1148 . -392) 185700) ((-1148 . -258) 185679) ((-1148 . -241) 185606) ((-1148 . -190) T) ((-1148 . -104) T) ((-1148 . -25) T) ((-1148 . -72) T) ((-1148 . -552) 185588) ((-1148 . -1013) T) ((-1148 . -23) T) ((-1148 . -21) T) ((-1148 . -970) T) ((-1148 . -1025) T) ((-1148 . -1061) T) ((-1148 . -663) T) ((-1148 . -961) T) ((-1148 . -186) 185575) ((-1148 . -13) T) ((-1148 . -1129) T) ((-1148 . -189) T) ((-1148 . -225) 185559) ((-1148 . -184) 185543) ((-1146 . -1006) 185527) ((-1146 . -557) 185511) ((-1146 . -1013) 185489) ((-1146 . -552) 185456) ((-1146 . -1129) 185434) ((-1146 . -13) 185412) ((-1146 . -72) 185390) ((-1146 . -1007) 185347) ((-1144 . -1143) 185326) ((-1144 . -915) 185292) ((-1144 . -1115) 185258) ((-1144 . -1118) 185224) ((-1144 . -433) 185190) ((-1144 . -239) 185156) ((-1144 . -66) 185122) ((-1144 . -35) 185088) ((-1144 . -1158) 185065) ((-1144 . -47) 185042) ((-1144 . -555) 184797) ((-1144 . -654) 184617) ((-1144 . -582) 184437) ((-1144 . -590) 184248) ((-1144 . -588) 184106) ((-1144 . -968) 183920) ((-1144 . -963) 183734) ((-1144 . -82) 183522) ((-1144 . -38) 183342) ((-1144 . -886) 183312) ((-1144 . -241) 183212) ((-1144 . -1141) 183196) ((-1144 . -970) T) ((-1144 . -1025) T) ((-1144 . -1061) T) ((-1144 . -663) T) ((-1144 . -961) T) ((-1144 . -21) T) ((-1144 . -23) T) ((-1144 . -1013) T) ((-1144 . -552) 183178) ((-1144 . -1129) T) ((-1144 . -13) T) ((-1144 . -72) T) ((-1144 . -25) T) ((-1144 . -104) T) ((-1144 . -118) 183106) ((-1144 . -120) 182988) ((-1144 . -553) 182661) ((-1144 . -184) 182631) ((-1144 . -809) 182485) ((-1144 . -811) 182285) ((-1144 . -806) 182083) ((-1144 . -225) 182053) ((-1144 . -189) 181915) ((-1144 . -186) 181771) ((-1144 . -190) 181679) ((-1144 . -312) 181658) ((-1144 . -1134) 181637) ((-1144 . -832) 181616) ((-1144 . -495) 181570) ((-1144 . -146) 181504) ((-1144 . -392) 181483) ((-1144 . -258) 181462) ((-1144 . -246) 181416) ((-1144 . -201) 181395) ((-1144 . -288) 181365) ((-1144 . -455) 181225) ((-1144 . -260) 181164) ((-1144 . -329) 181134) ((-1144 . -580) 181042) ((-1144 . -343) 181012) ((-1144 . -796) 180885) ((-1144 . -740) 180838) ((-1144 . -714) 180791) ((-1144 . -716) 180744) ((-1144 . -756) 180646) ((-1144 . -759) 180548) ((-1144 . -718) 180501) ((-1144 . -721) 180454) ((-1144 . -755) 180407) ((-1144 . -794) 180377) ((-1144 . -821) 180330) ((-1144 . -933) 180283) ((-1144 . -950) 180072) ((-1144 . -1066) 180024) ((-1144 . -904) 179994) ((-1139 . -1143) 179955) ((-1139 . -915) 179921) ((-1139 . -1115) 179887) ((-1139 . -1118) 179853) ((-1139 . -433) 179819) ((-1139 . -239) 179785) ((-1139 . -66) 179751) ((-1139 . -35) 179717) ((-1139 . -1158) 179694) ((-1139 . -47) 179671) ((-1139 . -555) 179472) ((-1139 . -654) 179274) ((-1139 . -582) 179076) ((-1139 . -590) 178931) ((-1139 . -588) 178771) ((-1139 . -968) 178567) ((-1139 . -963) 178363) ((-1139 . -82) 178115) ((-1139 . -38) 177917) ((-1139 . -886) 177887) ((-1139 . -241) 177715) ((-1139 . -1141) 177699) ((-1139 . -970) T) ((-1139 . -1025) T) ((-1139 . -1061) T) ((-1139 . -663) T) ((-1139 . -961) T) ((-1139 . -21) T) ((-1139 . -23) T) ((-1139 . -1013) T) ((-1139 . -552) 177681) ((-1139 . -1129) T) ((-1139 . -13) T) ((-1139 . -72) T) ((-1139 . -25) T) ((-1139 . -104) T) ((-1139 . -118) 177591) ((-1139 . -120) 177501) ((-1139 . -553) NIL) ((-1139 . -184) 177453) ((-1139 . -809) 177289) ((-1139 . -811) 177053) ((-1139 . -806) 176792) ((-1139 . -225) 176744) ((-1139 . -189) 176570) ((-1139 . -186) 176390) ((-1139 . -190) 176280) ((-1139 . -312) 176259) ((-1139 . -1134) 176238) ((-1139 . -832) 176217) ((-1139 . -495) 176171) ((-1139 . -146) 176105) ((-1139 . -392) 176084) ((-1139 . -258) 176063) ((-1139 . -246) 176017) ((-1139 . -201) 175996) ((-1139 . -288) 175948) ((-1139 . -455) 175682) ((-1139 . -260) 175567) ((-1139 . -329) 175519) ((-1139 . -580) 175471) ((-1139 . -343) 175423) ((-1139 . -796) NIL) ((-1139 . -740) NIL) ((-1139 . -714) NIL) ((-1139 . -716) NIL) ((-1139 . -756) NIL) ((-1139 . -759) NIL) ((-1139 . -718) NIL) ((-1139 . -721) NIL) ((-1139 . -755) NIL) ((-1139 . -794) 175375) ((-1139 . -821) NIL) ((-1139 . -933) NIL) ((-1139 . -950) 175341) ((-1139 . -1066) NIL) ((-1139 . -904) 175293) ((-1138 . -752) T) ((-1138 . -759) T) ((-1138 . -756) T) ((-1138 . -1013) T) ((-1138 . -552) 175275) ((-1138 . -1129) T) ((-1138 . -13) T) ((-1138 . -72) T) ((-1138 . -320) T) ((-1138 . -604) T) ((-1137 . -752) T) ((-1137 . -759) T) ((-1137 . -756) T) ((-1137 . -1013) T) ((-1137 . -552) 175257) ((-1137 . -1129) T) ((-1137 . -13) T) ((-1137 . -72) T) ((-1137 . -320) T) ((-1137 . -604) T) ((-1136 . -752) T) ((-1136 . -759) T) ((-1136 . -756) T) ((-1136 . -1013) T) ((-1136 . -552) 175239) ((-1136 . -1129) T) ((-1136 . -13) T) ((-1136 . -72) T) ((-1136 . -320) T) ((-1136 . -604) T) ((-1135 . -752) T) ((-1135 . -759) T) ((-1135 . -756) T) ((-1135 . -1013) T) ((-1135 . -552) 175221) ((-1135 . -1129) T) ((-1135 . -13) T) ((-1135 . -72) T) ((-1135 . -320) T) ((-1135 . -604) T) ((-1130 . -995) T) ((-1130 . -430) 175202) ((-1130 . -552) 175168) ((-1130 . -555) 175149) ((-1130 . -1013) T) ((-1130 . -1129) T) ((-1130 . -13) T) ((-1130 . -72) T) ((-1130 . -64) T) ((-1127 . -430) 175126) ((-1127 . -552) 175067) ((-1127 . -555) 175044) ((-1127 . -1013) 175022) ((-1127 . -1129) 175000) ((-1127 . -13) 174978) ((-1127 . -72) 174956) ((-1122 . -679) 174932) ((-1122 . -35) 174898) ((-1122 . -66) 174864) ((-1122 . -239) 174830) ((-1122 . -433) 174796) ((-1122 . -1118) 174762) ((-1122 . -1115) 174728) ((-1122 . -915) 174694) ((-1122 . -47) 174663) ((-1122 . -38) 174560) ((-1122 . -582) 174457) ((-1122 . -654) 174354) ((-1122 . -555) 174236) ((-1122 . -246) 174215) ((-1122 . -495) 174194) ((-1122 . -82) 174059) ((-1122 . -963) 173945) ((-1122 . -968) 173831) ((-1122 . -146) 173785) ((-1122 . -120) 173764) ((-1122 . -118) 173743) ((-1122 . -590) 173668) ((-1122 . -588) 173578) ((-1122 . -886) 173539) ((-1122 . -811) 173520) ((-1122 . -1129) T) ((-1122 . -13) T) ((-1122 . -806) 173499) ((-1122 . -961) T) ((-1122 . -663) T) ((-1122 . -1061) T) ((-1122 . -1025) T) ((-1122 . -970) T) ((-1122 . -21) T) ((-1122 . -23) T) ((-1122 . -1013) T) ((-1122 . -552) 173481) ((-1122 . -72) T) ((-1122 . -25) T) ((-1122 . -104) T) ((-1122 . -809) 173462) ((-1122 . -455) 173429) ((-1122 . -260) 173416) ((-1116 . -923) 173400) ((-1116 . -34) T) ((-1116 . -13) T) ((-1116 . -1129) T) ((-1116 . -72) 173354) ((-1116 . -552) 173289) ((-1116 . -260) 173227) ((-1116 . -455) 173160) ((-1116 . -1013) 173138) ((-1116 . -429) 173122) ((-1116 . -318) 173106) ((-1116 . -1035) 173090) ((-1111 . -314) 173064) ((-1111 . -72) T) ((-1111 . -13) T) ((-1111 . -1129) T) ((-1111 . -552) 173046) ((-1111 . -1013) T) ((-1109 . -1013) T) ((-1109 . -552) 173028) ((-1109 . -1129) T) ((-1109 . -13) T) ((-1109 . -72) T) ((-1109 . -555) 173010) ((-1104 . -747) 172994) ((-1104 . -72) T) ((-1104 . -13) T) ((-1104 . -1129) T) ((-1104 . -552) 172976) ((-1104 . -1013) T) ((-1102 . -1107) 172955) ((-1102 . -183) 172903) ((-1102 . -76) 172851) ((-1102 . -1035) 172799) ((-1102 . -124) 172747) ((-1102 . -553) NIL) ((-1102 . -193) 172695) ((-1102 . -538) 172674) ((-1102 . -260) 172472) ((-1102 . -455) 172224) ((-1102 . -429) 172159) ((-1102 . -241) 172138) ((-1102 . -243) 172117) ((-1102 . -549) 172096) ((-1102 . -1013) T) ((-1102 . -552) 172078) ((-1102 . -72) T) ((-1102 . -1129) T) ((-1102 . -13) T) ((-1102 . -34) T) ((-1102 . -318) 172026) ((-1098 . -1013) T) ((-1098 . -552) 172008) ((-1098 . -1129) T) ((-1098 . -13) T) ((-1098 . -72) T) ((-1097 . -752) T) ((-1097 . -759) T) ((-1097 . -756) T) ((-1097 . -1013) T) ((-1097 . -552) 171990) ((-1097 . -1129) T) ((-1097 . -13) T) ((-1097 . -72) T) ((-1097 . -320) T) ((-1097 . -604) T) ((-1096 . -752) T) ((-1096 . -759) T) ((-1096 . -756) T) ((-1096 . -1013) T) ((-1096 . -552) 171972) ((-1096 . -1129) T) ((-1096 . -13) T) ((-1096 . -72) T) ((-1096 . -320) T) ((-1095 . -1175) T) ((-1095 . -1013) T) ((-1095 . -552) 171939) ((-1095 . -1129) T) ((-1095 . -13) T) ((-1095 . -72) T) ((-1095 . -950) 171875) ((-1095 . -555) 171811) ((-1094 . -552) 171793) ((-1093 . -552) 171775) ((-1092 . -277) 171752) ((-1092 . -950) 171650) ((-1092 . -355) 171634) ((-1092 . -38) 171531) ((-1092 . -555) 171388) ((-1092 . -590) 171313) ((-1092 . -588) 171223) ((-1092 . -970) T) ((-1092 . -1025) T) ((-1092 . -1061) T) ((-1092 . -663) T) ((-1092 . -961) T) ((-1092 . -82) 171088) ((-1092 . -963) 170974) ((-1092 . -968) 170860) ((-1092 . -21) T) ((-1092 . -23) T) ((-1092 . -1013) T) ((-1092 . -552) 170842) ((-1092 . -1129) T) ((-1092 . -13) T) ((-1092 . -72) T) ((-1092 . -25) T) ((-1092 . -104) T) ((-1092 . -582) 170739) ((-1092 . -654) 170636) ((-1092 . -118) 170615) ((-1092 . -120) 170594) ((-1092 . -146) 170548) ((-1092 . -495) 170527) ((-1092 . -246) 170506) ((-1092 . -47) 170483) ((-1090 . -756) T) ((-1090 . -552) 170465) ((-1090 . -1013) T) ((-1090 . -72) T) ((-1090 . -13) T) ((-1090 . -1129) T) ((-1090 . -759) T) ((-1090 . -553) 170387) ((-1090 . -555) 170353) ((-1090 . -950) 170335) ((-1090 . -796) 170302) ((-1089 . -1172) 170286) ((-1089 . -190) 170245) ((-1089 . -555) 170127) ((-1089 . -590) 170052) ((-1089 . -588) 169962) ((-1089 . -104) T) ((-1089 . -25) T) ((-1089 . -72) T) ((-1089 . -552) 169944) ((-1089 . -1013) T) ((-1089 . -23) T) ((-1089 . -21) T) ((-1089 . -970) T) ((-1089 . -1025) T) ((-1089 . -1061) T) ((-1089 . -663) T) ((-1089 . -961) T) ((-1089 . -186) 169897) ((-1089 . -13) T) ((-1089 . -1129) T) ((-1089 . -189) 169856) ((-1089 . -241) 169821) ((-1089 . -809) 169734) ((-1089 . -806) 169622) ((-1089 . -811) 169535) ((-1089 . -886) 169505) ((-1089 . -38) 169402) ((-1089 . -82) 169267) ((-1089 . -963) 169153) ((-1089 . -968) 169039) ((-1089 . -582) 168936) ((-1089 . -654) 168833) ((-1089 . -118) 168812) ((-1089 . -120) 168791) ((-1089 . -146) 168745) ((-1089 . -495) 168724) ((-1089 . -246) 168703) ((-1089 . -47) 168680) ((-1089 . -1158) 168657) ((-1089 . -35) 168623) ((-1089 . -66) 168589) ((-1089 . -239) 168555) ((-1089 . -433) 168521) ((-1089 . -1118) 168487) ((-1089 . -1115) 168453) ((-1089 . -915) 168419) ((-1088 . -1164) 168380) ((-1088 . -312) 168359) ((-1088 . -1134) 168338) ((-1088 . -832) 168317) ((-1088 . -495) 168271) ((-1088 . -146) 168205) ((-1088 . -555) 167954) ((-1088 . -654) 167801) ((-1088 . -582) 167648) ((-1088 . -38) 167495) ((-1088 . -392) 167474) ((-1088 . -258) 167453) ((-1088 . -590) 167353) ((-1088 . -588) 167238) ((-1088 . -970) T) ((-1088 . -1025) T) ((-1088 . -1061) T) ((-1088 . -663) T) ((-1088 . -961) T) ((-1088 . -82) 167058) ((-1088 . -963) 166899) ((-1088 . -968) 166740) ((-1088 . -21) T) ((-1088 . -23) T) ((-1088 . -1013) T) ((-1088 . -552) 166722) ((-1088 . -1129) T) ((-1088 . -13) T) ((-1088 . -72) T) ((-1088 . -25) T) ((-1088 . -104) T) ((-1088 . -246) 166676) ((-1088 . -201) 166655) ((-1088 . -915) 166621) ((-1088 . -1115) 166587) ((-1088 . -1118) 166553) ((-1088 . -433) 166519) ((-1088 . -239) 166485) ((-1088 . -66) 166451) ((-1088 . -35) 166417) ((-1088 . -1158) 166387) ((-1088 . -47) 166357) ((-1088 . -120) 166336) ((-1088 . -118) 166315) ((-1088 . -886) 166278) ((-1088 . -811) 166184) ((-1088 . -806) 166065) ((-1088 . -809) 165971) ((-1088 . -241) 165929) ((-1088 . -189) 165881) ((-1088 . -186) 165827) ((-1088 . -190) 165779) ((-1088 . -1162) 165763) ((-1088 . -950) 165698) ((-1085 . -1155) 165682) ((-1085 . -1066) 165660) ((-1085 . -553) NIL) ((-1085 . -260) 165647) ((-1085 . -455) 165595) ((-1085 . -277) 165572) ((-1085 . -950) 165455) ((-1085 . -355) 165439) ((-1085 . -38) 165271) ((-1085 . -82) 165076) ((-1085 . -963) 164902) ((-1085 . -968) 164728) ((-1085 . -588) 164638) ((-1085 . -590) 164527) ((-1085 . -582) 164359) ((-1085 . -654) 164191) ((-1085 . -555) 163968) ((-1085 . -118) 163947) ((-1085 . -120) 163926) ((-1085 . -47) 163903) ((-1085 . -329) 163887) ((-1085 . -580) 163835) ((-1085 . -809) 163779) ((-1085 . -806) 163686) ((-1085 . -811) 163597) ((-1085 . -796) NIL) ((-1085 . -821) 163576) ((-1085 . -1134) 163555) ((-1085 . -861) 163525) ((-1085 . -832) 163504) ((-1085 . -495) 163418) ((-1085 . -246) 163332) ((-1085 . -146) 163226) ((-1085 . -392) 163160) ((-1085 . -258) 163139) ((-1085 . -241) 163066) ((-1085 . -190) T) ((-1085 . -104) T) ((-1085 . -25) T) ((-1085 . -72) T) ((-1085 . -552) 163048) ((-1085 . -1013) T) ((-1085 . -23) T) ((-1085 . -21) T) ((-1085 . -970) T) ((-1085 . -1025) T) ((-1085 . -1061) T) ((-1085 . -663) T) ((-1085 . -961) T) ((-1085 . -186) 163035) ((-1085 . -13) T) ((-1085 . -1129) T) ((-1085 . -189) T) ((-1085 . -225) 163019) ((-1085 . -184) 163003) ((-1082 . -1143) 162964) ((-1082 . -915) 162930) ((-1082 . -1115) 162896) ((-1082 . -1118) 162862) ((-1082 . -433) 162828) ((-1082 . -239) 162794) ((-1082 . -66) 162760) ((-1082 . -35) 162726) ((-1082 . -1158) 162703) ((-1082 . -47) 162680) ((-1082 . -555) 162481) ((-1082 . -654) 162283) ((-1082 . -582) 162085) ((-1082 . -590) 161940) ((-1082 . -588) 161780) ((-1082 . -968) 161576) ((-1082 . -963) 161372) ((-1082 . -82) 161124) ((-1082 . -38) 160926) ((-1082 . -886) 160896) ((-1082 . -241) 160724) ((-1082 . -1141) 160708) ((-1082 . -970) T) ((-1082 . -1025) T) ((-1082 . -1061) T) ((-1082 . -663) T) ((-1082 . -961) T) ((-1082 . -21) T) ((-1082 . -23) T) ((-1082 . -1013) T) ((-1082 . -552) 160690) ((-1082 . -1129) T) ((-1082 . -13) T) ((-1082 . -72) T) ((-1082 . -25) T) ((-1082 . -104) T) ((-1082 . -118) 160600) ((-1082 . -120) 160510) ((-1082 . -553) NIL) ((-1082 . -184) 160462) ((-1082 . -809) 160298) ((-1082 . -811) 160062) ((-1082 . -806) 159801) ((-1082 . -225) 159753) ((-1082 . -189) 159579) ((-1082 . -186) 159399) ((-1082 . -190) 159289) ((-1082 . -312) 159268) ((-1082 . -1134) 159247) ((-1082 . -832) 159226) ((-1082 . -495) 159180) ((-1082 . -146) 159114) ((-1082 . -392) 159093) ((-1082 . -258) 159072) ((-1082 . -246) 159026) ((-1082 . -201) 159005) ((-1082 . -288) 158957) ((-1082 . -455) 158691) ((-1082 . -260) 158576) ((-1082 . -329) 158528) ((-1082 . -580) 158480) ((-1082 . -343) 158432) ((-1082 . -796) NIL) ((-1082 . -740) NIL) ((-1082 . -714) NIL) ((-1082 . -716) NIL) ((-1082 . -756) NIL) ((-1082 . -759) NIL) ((-1082 . -718) NIL) ((-1082 . -721) NIL) ((-1082 . -755) NIL) ((-1082 . -794) 158384) ((-1082 . -821) NIL) ((-1082 . -933) NIL) ((-1082 . -950) 158350) ((-1082 . -1066) NIL) ((-1082 . -904) 158302) ((-1081 . -995) T) ((-1081 . -430) 158283) ((-1081 . -552) 158249) ((-1081 . -555) 158230) ((-1081 . -1013) T) ((-1081 . -1129) T) ((-1081 . -13) T) ((-1081 . -72) T) ((-1081 . -64) T) ((-1080 . -1013) T) ((-1080 . -552) 158212) ((-1080 . -1129) T) ((-1080 . -13) T) ((-1080 . -72) T) ((-1079 . -1013) T) ((-1079 . -552) 158194) ((-1079 . -1129) T) ((-1079 . -13) T) ((-1079 . -72) T) ((-1074 . -1107) 158170) ((-1074 . -183) 158115) ((-1074 . -76) 158060) ((-1074 . -1035) 158005) ((-1074 . -124) 157950) ((-1074 . -553) NIL) ((-1074 . -193) 157895) ((-1074 . -538) 157871) ((-1074 . -260) 157660) ((-1074 . -455) 157400) ((-1074 . -429) 157332) ((-1074 . -241) 157308) ((-1074 . -243) 157284) ((-1074 . -549) 157260) ((-1074 . -1013) T) ((-1074 . -552) 157242) ((-1074 . -72) T) ((-1074 . -1129) T) ((-1074 . -13) T) ((-1074 . -34) T) ((-1074 . -318) 157187) ((-1073 . -1058) T) ((-1073 . -324) 157169) ((-1073 . -759) T) ((-1073 . -756) T) ((-1073 . -124) 157151) ((-1073 . -553) NIL) ((-1073 . -241) 157101) ((-1073 . -538) 157076) ((-1073 . -243) 157051) ((-1073 . -593) 157033) ((-1073 . -429) 157015) ((-1073 . -1013) T) ((-1073 . -455) NIL) ((-1073 . -260) NIL) ((-1073 . -552) 156997) ((-1073 . -72) T) ((-1073 . -1129) T) ((-1073 . -13) T) ((-1073 . -34) T) ((-1073 . -318) 156979) ((-1073 . -1035) 156961) ((-1073 . -19) 156943) ((-1069 . -616) 156927) ((-1069 . -593) 156911) ((-1069 . -243) 156888) ((-1069 . -241) 156840) ((-1069 . -538) 156817) ((-1069 . -553) 156778) ((-1069 . -429) 156762) ((-1069 . -1013) 156740) ((-1069 . -455) 156673) ((-1069 . -260) 156611) ((-1069 . -552) 156546) ((-1069 . -72) 156500) ((-1069 . -1129) T) ((-1069 . -13) T) ((-1069 . -34) T) ((-1069 . -124) 156484) ((-1069 . -1168) 156468) ((-1069 . -923) 156452) ((-1069 . -1064) 156436) ((-1069 . -555) 156413) ((-1067 . -995) T) ((-1067 . -430) 156394) ((-1067 . -552) 156360) ((-1067 . -555) 156341) ((-1067 . -1013) T) ((-1067 . -1129) T) ((-1067 . -13) T) ((-1067 . -72) T) ((-1067 . -64) T) ((-1065 . -1107) 156320) ((-1065 . -183) 156268) ((-1065 . -76) 156216) ((-1065 . -1035) 156164) ((-1065 . -124) 156112) ((-1065 . -553) NIL) ((-1065 . -193) 156060) ((-1065 . -538) 156039) ((-1065 . -260) 155837) ((-1065 . -455) 155589) ((-1065 . -429) 155524) ((-1065 . -241) 155503) ((-1065 . -243) 155482) ((-1065 . -549) 155461) ((-1065 . -1013) T) ((-1065 . -552) 155443) ((-1065 . -72) T) ((-1065 . -1129) T) ((-1065 . -13) T) ((-1065 . -34) T) ((-1065 . -318) 155391) ((-1062 . -1034) 155375) ((-1062 . -318) 155359) ((-1062 . -1035) 155343) ((-1062 . -34) T) ((-1062 . -13) T) ((-1062 . -1129) T) ((-1062 . -72) 155297) ((-1062 . -552) 155232) ((-1062 . -260) 155170) ((-1062 . -455) 155103) ((-1062 . -1013) 155081) ((-1062 . -429) 155065) ((-1062 . -76) 155049) ((-1060 . -1020) 155018) ((-1060 . -1124) 154987) ((-1060 . -552) 154949) ((-1060 . -124) 154933) ((-1060 . -34) T) ((-1060 . -13) T) ((-1060 . -1129) T) ((-1060 . -72) T) ((-1060 . -260) 154871) ((-1060 . -455) 154804) ((-1060 . -1013) T) ((-1060 . -429) 154788) ((-1060 . -553) 154749) ((-1060 . -318) 154733) ((-1060 . -889) 154702) ((-1060 . -983) 154671) ((-1056 . -1037) 154616) ((-1056 . -318) 154600) ((-1056 . -34) T) ((-1056 . -260) 154538) ((-1056 . -455) 154471) ((-1056 . -429) 154455) ((-1056 . -965) 154395) ((-1056 . -950) 154293) ((-1056 . -555) 154212) ((-1056 . -355) 154196) ((-1056 . -580) 154144) ((-1056 . -590) 154082) ((-1056 . -329) 154066) ((-1056 . -190) 154045) ((-1056 . -186) 153993) ((-1056 . -189) 153947) ((-1056 . -225) 153931) ((-1056 . -806) 153855) ((-1056 . -811) 153781) ((-1056 . -809) 153740) ((-1056 . -184) 153724) ((-1056 . -654) 153659) ((-1056 . -582) 153594) ((-1056 . -588) 153553) ((-1056 . -104) T) ((-1056 . -25) T) ((-1056 . -72) T) ((-1056 . -13) T) ((-1056 . -1129) T) ((-1056 . -552) 153515) ((-1056 . -1013) T) ((-1056 . -23) T) ((-1056 . -21) T) ((-1056 . -968) 153499) ((-1056 . -963) 153483) ((-1056 . -82) 153462) ((-1056 . -961) T) ((-1056 . -663) T) ((-1056 . -1061) T) ((-1056 . -1025) T) ((-1056 . -970) T) ((-1056 . -38) 153422) ((-1056 . -553) 153383) ((-1055 . -923) 153354) ((-1055 . -34) T) ((-1055 . -13) T) ((-1055 . -1129) T) ((-1055 . -72) T) ((-1055 . -552) 153336) ((-1055 . -260) 153262) ((-1055 . -455) 153170) ((-1055 . -1013) T) ((-1055 . -429) 153141) ((-1055 . -318) 153112) ((-1054 . -1013) T) ((-1054 . -552) 153094) ((-1054 . -1129) T) ((-1054 . -13) T) ((-1054 . -72) T) ((-1049 . -1051) T) ((-1049 . -1175) T) ((-1049 . -64) T) ((-1049 . -72) T) ((-1049 . -13) T) ((-1049 . -1129) T) ((-1049 . -552) 153060) ((-1049 . -1013) T) ((-1049 . -555) 153041) ((-1049 . -430) 153022) ((-1049 . -995) T) ((-1047 . -1048) 153006) ((-1047 . -72) T) ((-1047 . -13) T) ((-1047 . -1129) T) ((-1047 . -552) 152988) ((-1047 . -1013) T) ((-1040 . -679) 152967) ((-1040 . -35) 152933) ((-1040 . -66) 152899) ((-1040 . -239) 152865) ((-1040 . -433) 152831) ((-1040 . -1118) 152797) ((-1040 . -1115) 152763) ((-1040 . -915) 152729) ((-1040 . -47) 152701) ((-1040 . -38) 152598) ((-1040 . -582) 152495) ((-1040 . -654) 152392) ((-1040 . -555) 152274) 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-47) 150589) ((-1039 . -38) 150441) ((-1039 . -582) 150293) ((-1039 . -654) 150145) ((-1039 . -246) 150079) ((-1039 . -495) 150013) ((-1039 . -82) 149838) ((-1039 . -963) 149684) ((-1039 . -968) 149530) ((-1039 . -146) 149444) ((-1039 . -120) 149423) ((-1039 . -118) 149402) ((-1039 . -588) 149312) ((-1039 . -104) T) ((-1039 . -25) T) ((-1039 . -72) T) ((-1039 . -13) T) ((-1039 . -1129) T) ((-1039 . -552) 149294) ((-1039 . -1013) T) ((-1039 . -23) T) ((-1039 . -21) T) ((-1039 . -961) T) ((-1039 . -663) T) ((-1039 . -1061) T) ((-1039 . -1025) T) ((-1039 . -970) T) ((-1039 . -355) 149278) ((-1039 . -277) 149250) ((-1039 . -260) 149237) ((-1039 . -553) 148985) ((-1033 . -483) T) ((-1033 . -1134) T) ((-1033 . -1066) T) ((-1033 . -950) 148967) ((-1033 . -553) 148882) ((-1033 . -933) T) ((-1033 . -796) 148864) ((-1033 . -755) T) ((-1033 . -721) T) ((-1033 . -718) T) ((-1033 . -759) T) ((-1033 . -756) T) ((-1033 . -716) T) ((-1033 . -714) T) ((-1033 . -740) T) ((-1033 . -590) 148836) ((-1033 . 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. -1129) T) ((-1028 . -13) T) ((-1028 . -72) T) ((-1026 . -196) 148540) ((-1026 . -1187) 148510) ((-1026 . -721) 148489) ((-1026 . -718) 148468) ((-1026 . -759) 148422) ((-1026 . -756) 148376) ((-1026 . -716) 148355) ((-1026 . -717) 148334) ((-1026 . -654) 148279) ((-1026 . -582) 148204) ((-1026 . -243) 148181) ((-1026 . -241) 148158) ((-1026 . -538) 148135) ((-1026 . -950) 147964) ((-1026 . -555) 147768) ((-1026 . -355) 147737) ((-1026 . -580) 147645) ((-1026 . -590) 147484) ((-1026 . -329) 147454) ((-1026 . -429) 147438) ((-1026 . -455) 147371) ((-1026 . -260) 147309) ((-1026 . -34) T) ((-1026 . -318) 147293) ((-1026 . -320) 147272) ((-1026 . -190) 147225) ((-1026 . -588) 147013) ((-1026 . -970) 146992) ((-1026 . -1025) 146971) ((-1026 . -1061) 146950) ((-1026 . -663) 146929) ((-1026 . -961) 146908) ((-1026 . -186) 146804) ((-1026 . -189) 146706) ((-1026 . -225) 146676) ((-1026 . -806) 146548) ((-1026 . -811) 146422) ((-1026 . -809) 146355) ((-1026 . -184) 146325) ((-1026 . -552) 146022) ((-1026 . -968) 145947) ((-1026 . -963) 145852) ((-1026 . -82) 145772) ((-1026 . -104) 145647) ((-1026 . -25) 145484) ((-1026 . -72) 145221) ((-1026 . -13) T) ((-1026 . -1129) T) ((-1026 . -1013) 144977) ((-1026 . -23) 144833) ((-1026 . -21) 144748) ((-1022 . -1023) 144732) ((-1022 . |MappingCategory|) 144706) ((-1022 . -1129) T) ((-1022 . -80) 144690) ((-1022 . -1013) T) ((-1022 . -552) 144672) ((-1022 . -13) T) ((-1022 . -72) T) ((-1017 . -1016) 144636) ((-1017 . -72) T) ((-1017 . -552) 144618) ((-1017 . -1013) T) ((-1017 . -241) 144574) ((-1017 . -1129) T) ((-1017 . -13) T) ((-1017 . -557) 144489) ((-1015 . -1016) 144441) ((-1015 . -72) T) ((-1015 . -552) 144423) ((-1015 . -1013) T) ((-1015 . -241) 144379) ((-1015 . -1129) T) ((-1015 . -13) T) ((-1015 . -557) 144282) ((-1014 . -320) T) ((-1014 . -72) T) ((-1014 . -13) T) ((-1014 . -1129) T) ((-1014 . -552) 144264) ((-1014 . -1013) T) ((-1009 . -369) 144248) ((-1009 . -1011) 144232) ((-1009 . -318) 144216) ((-1009 . -320) 144195) ((-1009 . -193) 144179) ((-1009 . -553) 144140) ((-1009 . -124) 144124) ((-1009 . -1035) 144108) ((-1009 . -34) T) ((-1009 . -13) T) ((-1009 . -1129) T) ((-1009 . -72) T) ((-1009 . -552) 144090) ((-1009 . -260) 144028) ((-1009 . -455) 143961) ((-1009 . -1013) T) ((-1009 . -429) 143945) ((-1009 . -76) 143929) ((-1009 . -183) 143913) ((-1008 . -995) T) ((-1008 . -430) 143894) ((-1008 . -552) 143860) ((-1008 . -555) 143841) ((-1008 . -1013) T) ((-1008 . -1129) T) ((-1008 . -13) T) ((-1008 . -72) T) ((-1008 . -64) T) ((-1004 . -1129) T) ((-1004 . -13) T) ((-1004 . -1013) 143811) ((-1004 . -552) 143770) ((-1004 . -72) 143740) ((-1003 . -995) T) ((-1003 . -430) 143721) ((-1003 . -552) 143687) ((-1003 . -555) 143668) ((-1003 . -1013) T) ((-1003 . -1129) T) ((-1003 . -13) T) ((-1003 . -72) T) ((-1003 . -64) T) ((-1001 . -1006) 143652) ((-1001 . -557) 143636) ((-1001 . -1013) 143614) ((-1001 . -552) 143581) ((-1001 . -1129) 143559) ((-1001 . -13) 143537) ((-1001 . -72) 143515) ((-1001 . -1007) 143473) ((-1000 . -228) 143457) ((-1000 . -555) 143441) ((-1000 . -950) 143425) ((-1000 . -759) T) ((-1000 . -72) T) ((-1000 . -1013) T) ((-1000 . -552) 143407) ((-1000 . -756) T) ((-1000 . -186) 143394) ((-1000 . -13) T) ((-1000 . -1129) T) ((-1000 . -189) T) ((-999 . -213) 143331) ((-999 . -555) 143074) ((-999 . -950) 142903) ((-999 . -553) NIL) ((-999 . -277) 142864) ((-999 . -355) 142848) ((-999 . -38) 142700) ((-999 . -82) 142525) ((-999 . -963) 142371) ((-999 . -968) 142217) ((-999 . -588) 142127) ((-999 . -590) 142016) ((-999 . -582) 141868) ((-999 . -654) 141720) ((-999 . -118) 141699) ((-999 . -120) 141678) ((-999 . -146) 141592) ((-999 . -495) 141526) ((-999 . -246) 141460) ((-999 . -47) 141421) ((-999 . -329) 141405) ((-999 . -580) 141353) ((-999 . -392) 141307) ((-999 . -455) 141170) ((-999 . -809) 141105) ((-999 . -806) 141003) ((-999 . -811) 140905) ((-999 . -796) NIL) ((-999 . -821) 140884) ((-999 . -1134) 140863) ((-999 . -861) 140808) ((-999 . -260) 140795) ((-999 . -190) 140774) ((-999 . -104) T) ((-999 . -25) T) ((-999 . -72) T) ((-999 . -552) 140756) ((-999 . -1013) T) ((-999 . -23) T) ((-999 . -21) T) ((-999 . -970) T) ((-999 . -1025) T) ((-999 . -1061) T) ((-999 . -663) T) ((-999 . -961) T) ((-999 . -186) 140704) ((-999 . -13) T) ((-999 . -1129) T) ((-999 . -189) 140658) ((-999 . -225) 140642) ((-999 . -184) 140626) ((-997 . -552) 140608) ((-994 . -756) T) ((-994 . -552) 140590) ((-994 . -1013) T) ((-994 . -72) T) ((-994 . -13) T) ((-994 . -1129) T) ((-994 . -759) T) ((-994 . -553) 140571) ((-991 . -661) 140550) ((-991 . -950) 140448) ((-991 . -355) 140432) ((-991 . -580) 140380) ((-991 . -590) 140257) ((-991 . -329) 140241) ((-991 . -322) 140220) ((-991 . -120) 140199) ((-991 . -555) 140024) ((-991 . -654) 139898) ((-991 . -582) 139772) ((-991 . -588) 139670) ((-991 . -968) 139583) ((-991 . -963) 139496) ((-991 . -82) 139388) ((-991 . -38) 139262) ((-991 . -353) 139241) ((-991 . -345) 139220) ((-991 . -118) 139174) ((-991 . -1066) 139153) ((-991 . -299) 139132) ((-991 . -320) 139086) ((-991 . -201) 139040) ((-991 . -246) 138994) ((-991 . -258) 138948) ((-991 . -392) 138902) ((-991 . -495) 138856) ((-991 . -832) 138810) ((-991 . -1134) 138764) ((-991 . -312) 138718) ((-991 . -190) 138646) ((-991 . -186) 138522) ((-991 . -189) 138404) ((-991 . -225) 138374) ((-991 . -806) 138246) ((-991 . -811) 138120) ((-991 . -809) 138053) ((-991 . -184) 138023) ((-991 . -553) 138007) ((-991 . -21) T) ((-991 . -23) T) ((-991 . -1013) T) ((-991 . -552) 137989) ((-991 . -1129) T) ((-991 . -13) T) ((-991 . -72) T) ((-991 . -25) T) ((-991 . -104) T) ((-991 . -961) T) ((-991 . -663) T) ((-991 . -1061) T) ((-991 . -1025) T) ((-991 . -970) T) ((-991 . -146) T) ((-989 . -1013) T) ((-989 . -552) 137971) ((-989 . -1129) T) ((-989 . -13) T) ((-989 . -72) T) ((-989 . -241) 137950) ((-988 . -1013) T) ((-988 . -552) 137932) ((-988 . -1129) T) ((-988 . -13) T) ((-988 . -72) T) ((-987 . -1013) T) ((-987 . -552) 137914) ((-987 . -1129) T) ((-987 . -13) T) ((-987 . -72) T) ((-987 . -241) 137893) ((-987 . -950) 137870) ((-987 . -555) 137847) ((-986 . -1129) T) ((-986 . -13) T) ((-985 . -995) T) ((-985 . -430) 137828) ((-985 . -552) 137794) ((-985 . -555) 137775) ((-985 . -1013) T) ((-985 . -1129) T) ((-985 . -13) T) ((-985 . -72) T) ((-985 . -64) T) ((-978 . -995) T) ((-978 . -430) 137756) ((-978 . -552) 137722) ((-978 . -555) 137703) ((-978 . -1013) T) ((-978 . -1129) T) ((-978 . -13) T) ((-978 . -72) T) ((-978 . -64) T) ((-975 . -483) T) ((-975 . -1134) T) ((-975 . -1066) T) ((-975 . -950) 137685) ((-975 . -553) 137600) ((-975 . -933) T) ((-975 . -796) 137582) ((-975 . -755) T) ((-975 . -721) T) ((-975 . -718) T) ((-975 . -759) T) ((-975 . -756) T) ((-975 . -716) T) ((-975 . -714) T) ((-975 . -740) T) ((-975 . -590) 137554) ((-975 . -580) 137536) ((-975 . -832) T) ((-975 . -495) T) ((-975 . -246) T) ((-975 . -146) T) ((-975 . -555) 137508) ((-975 . -654) 137495) ((-975 . -582) 137482) ((-975 . -968) 137469) ((-975 . -963) 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. -552) 130023) ((-884 . -1129) T) ((-884 . -13) T) ((-884 . -72) T) ((-884 . -25) T) ((-884 . -104) T) ((-883 . -995) T) ((-883 . -430) 130004) ((-883 . -552) 129970) ((-883 . -555) 129951) ((-883 . -1013) T) ((-883 . -1129) T) ((-883 . -13) T) ((-883 . -72) T) ((-883 . -64) T) ((-877 . -880) T) ((-877 . -72) T) ((-877 . -552) 129933) ((-877 . -1013) T) ((-877 . -604) T) ((-877 . -13) T) ((-877 . -1129) T) ((-877 . -84) T) ((-877 . -555) 129917) ((-876 . -552) 129899) ((-875 . -1013) T) ((-875 . -552) 129881) ((-875 . -1129) T) ((-875 . -13) T) ((-875 . -72) T) ((-875 . -320) 129834) ((-875 . -663) 129736) ((-875 . -1025) 129638) ((-875 . -23) 129452) ((-875 . -25) 129266) ((-875 . -104) 129124) ((-875 . -413) 129077) ((-875 . -21) 129032) ((-875 . -588) 128976) ((-875 . -717) 128929) ((-875 . -716) 128882) ((-875 . -756) 128784) ((-875 . -759) 128686) ((-875 . -718) 128639) ((-875 . -721) 128592) ((-869 . -19) 128576) ((-869 . -1035) 128560) ((-869 . -318) 128544) ((-869 . -34) T) 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-201) T) ((-817 . -345) T) ((-817 . -189) T) ((-817 . -1129) T) ((-817 . -13) T) ((-817 . -186) 122717) ((-817 . -961) T) ((-817 . -663) T) ((-817 . -1061) T) ((-817 . -1025) T) ((-817 . -970) T) ((-817 . -21) T) ((-817 . -23) T) ((-817 . -1013) T) ((-817 . -552) 122699) ((-817 . -72) T) ((-817 . -25) T) ((-817 . -104) T) ((-817 . -190) T) ((-817 . -280) 122686) ((-817 . -120) 122668) ((-817 . -950) 122655) ((-817 . -1187) 122642) ((-817 . -1198) 122629) ((-817 . -553) 122611) ((-816 . -1013) T) ((-816 . -552) 122593) ((-816 . -1129) T) ((-816 . -13) T) ((-816 . -72) T) ((-813 . -815) 122577) ((-813 . -759) 122531) ((-813 . -756) 122485) ((-813 . -663) T) ((-813 . -1013) T) ((-813 . -552) 122467) ((-813 . -72) T) ((-813 . -1025) T) ((-813 . -413) T) ((-813 . -1129) T) ((-813 . -13) T) ((-813 . -241) 122446) ((-812 . -92) 122430) ((-812 . -429) 122414) ((-812 . -1013) 122392) ((-812 . -455) 122325) ((-812 . -260) 122263) ((-812 . -552) 122177) ((-812 . -72) 122131) ((-812 . -1129) T) 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121586) ((-781 . -1066) 121564) ((-781 . -950) 121431) ((-781 . -555) 121330) ((-781 . -553) 121133) ((-781 . -933) 121112) ((-781 . -821) 121091) ((-781 . -794) 121075) ((-781 . -755) 121054) ((-781 . -721) 121033) ((-781 . -718) 121012) ((-781 . -759) 120966) ((-781 . -756) 120920) ((-781 . -716) 120899) ((-781 . -714) 120878) ((-781 . -740) 120857) ((-781 . -796) 120782) ((-781 . -343) 120766) ((-781 . -580) 120714) ((-781 . -590) 120630) ((-781 . -329) 120614) ((-781 . -241) 120572) ((-781 . -260) 120537) ((-781 . -455) 120449) ((-781 . -288) 120433) ((-781 . -201) T) ((-781 . -82) 120364) ((-781 . -963) 120316) ((-781 . -968) 120268) ((-781 . -246) T) ((-781 . -654) 120220) ((-781 . -582) 120172) ((-781 . -588) 120109) ((-781 . -38) 120061) ((-781 . -258) T) ((-781 . -392) T) ((-781 . -146) T) ((-781 . -495) T) ((-781 . -832) T) ((-781 . -1134) T) ((-781 . -312) T) ((-781 . -190) 120040) ((-781 . -186) 119988) ((-781 . -189) 119942) ((-781 . -225) 119926) ((-781 . -806) 119850) ((-781 . -811) 119776) ((-781 . -809) 119735) ((-781 . -184) 119719) ((-781 . -120) 119673) ((-781 . -118) 119652) ((-781 . -104) T) ((-781 . -25) T) ((-781 . -72) T) ((-781 . -13) T) ((-781 . -1129) T) ((-781 . -552) 119634) ((-781 . -1013) T) ((-781 . -23) T) ((-781 . -21) T) ((-781 . -961) T) ((-781 . -663) T) ((-781 . -1061) T) ((-781 . -1025) T) ((-781 . -970) T) ((-780 . -904) 119611) ((-780 . -1066) NIL) ((-780 . -950) 119588) ((-780 . -555) 119518) ((-780 . -553) NIL) ((-780 . -933) NIL) ((-780 . -821) NIL) ((-780 . -794) 119495) ((-780 . -755) NIL) ((-780 . -721) NIL) ((-780 . -718) NIL) ((-780 . -759) NIL) ((-780 . -756) NIL) ((-780 . -716) NIL) ((-780 . -714) NIL) ((-780 . -740) NIL) ((-780 . -796) NIL) ((-780 . -343) 119472) ((-780 . -580) 119449) ((-780 . -590) 119394) ((-780 . -329) 119371) ((-780 . -241) 119301) ((-780 . -260) 119245) ((-780 . -455) 119108) ((-780 . -288) 119085) ((-780 . -201) T) ((-780 . -82) 119002) ((-780 . -963) 118947) ((-780 . -968) 118892) ((-780 . -246) T) ((-780 . -654) 118837) ((-780 . -582) 118782) ((-780 . -588) 118712) ((-780 . -38) 118657) ((-780 . -258) T) ((-780 . -392) T) ((-780 . -146) T) ((-780 . -495) T) ((-780 . -832) T) ((-780 . -1134) T) ((-780 . -312) T) ((-780 . -190) NIL) ((-780 . -186) NIL) ((-780 . -189) NIL) ((-780 . -225) 118634) ((-780 . -806) NIL) ((-780 . -811) NIL) ((-780 . -809) NIL) ((-780 . -184) 118611) ((-780 . -120) T) ((-780 . -118) NIL) ((-780 . -104) T) ((-780 . -25) T) ((-780 . -72) T) ((-780 . -13) T) ((-780 . -1129) T) ((-780 . -552) 118593) ((-780 . -1013) T) ((-780 . -23) T) ((-780 . -21) T) ((-780 . -961) T) ((-780 . -663) T) ((-780 . -1061) T) ((-780 . -1025) T) ((-780 . -970) T) ((-778 . -779) 118577) ((-778 . -832) T) ((-778 . -495) T) ((-778 . -246) T) ((-778 . -146) T) ((-778 . -555) 118549) ((-778 . -654) 118536) ((-778 . -582) 118523) ((-778 . -968) 118510) ((-778 . -963) 118497) ((-778 . -82) 118482) ((-778 . -38) 118469) ((-778 . -392) T) ((-778 . -258) T) ((-778 . -961) T) ((-778 . -663) T) ((-778 . -1061) T) ((-778 . -1025) T) ((-778 . -970) T) ((-778 . -21) T) ((-778 . -588) 118441) ((-778 . -23) T) ((-778 . -1013) T) ((-778 . -552) 118423) ((-778 . -1129) T) ((-778 . -13) T) ((-778 . -72) T) ((-778 . -25) T) ((-778 . -104) T) ((-778 . -590) 118410) ((-778 . -120) T) ((-775 . -961) T) ((-775 . -663) T) ((-775 . -1061) T) ((-775 . -1025) T) ((-775 . -970) T) ((-775 . -21) T) ((-775 . -588) 118355) ((-775 . -23) T) ((-775 . -1013) T) ((-775 . -552) 118317) ((-775 . -1129) T) ((-775 . -13) T) ((-775 . -72) T) ((-775 . -25) T) ((-775 . -104) T) ((-775 . -590) 118277) ((-775 . -555) 118212) ((-775 . -430) 118189) ((-775 . -38) 118159) ((-775 . -82) 118124) ((-775 . -963) 118094) ((-775 . -968) 118064) ((-775 . -582) 118034) ((-775 . -654) 118004) ((-774 . -1013) T) ((-774 . -552) 117986) ((-774 . -1129) T) ((-774 . -13) T) ((-774 . -72) T) ((-773 . -752) T) ((-773 . -759) T) ((-773 . -756) T) ((-773 . -1013) T) ((-773 . -552) 117968) ((-773 . -1129) T) ((-773 . -13) T) ((-773 . -72) T) ((-773 . -320) T) ((-773 . -553) 117890) ((-772 . -1013) T) ((-772 . -552) 117872) ((-772 . -1129) T) ((-772 . -13) T) ((-772 . -72) T) ((-771 . -770) T) ((-771 . -147) T) ((-771 . -552) 117854) ((-767 . -756) T) ((-767 . -552) 117836) ((-767 . -1013) T) ((-767 . -72) T) ((-767 . -13) T) ((-767 . -1129) T) ((-767 . -759) T) ((-764 . -761) 117820) ((-764 . -950) 117718) ((-764 . -555) 117616) ((-764 . -355) 117600) ((-764 . -654) 117570) ((-764 . -582) 117540) ((-764 . -590) 117514) ((-764 . -588) 117473) ((-764 . -104) T) ((-764 . -25) T) ((-764 . -72) T) ((-764 . -13) T) ((-764 . -1129) T) ((-764 . -552) 117455) ((-764 . -1013) T) ((-764 . -23) T) ((-764 . -21) T) ((-764 . -968) 117439) ((-764 . -963) 117423) ((-764 . -82) 117402) ((-764 . -961) T) ((-764 . -663) T) ((-764 . -1061) T) ((-764 . -1025) T) ((-764 . -970) T) ((-764 . -38) 117372) ((-763 . -761) 117356) ((-763 . -950) 117254) ((-763 . -555) 117173) ((-763 . -355) 117157) ((-763 . -654) 117127) ((-763 . -582) 117097) ((-763 . -590) 117071) ((-763 . -588) 117030) ((-763 . -104) T) ((-763 . -25) T) ((-763 . -72) T) ((-763 . -13) T) ((-763 . -1129) T) ((-763 . -552) 117012) ((-763 . -1013) T) ((-763 . -23) T) ((-763 . -21) T) ((-763 . -968) 116996) ((-763 . -963) 116980) ((-763 . -82) 116959) ((-763 . -961) T) ((-763 . -663) T) ((-763 . -1061) T) ((-763 . -1025) T) ((-763 . -970) T) ((-763 . -38) 116929) ((-757 . -759) T) ((-757 . -1129) T) ((-757 . -13) T) ((-757 . -72) T) ((-757 . -430) 116913) ((-757 . -552) 116861) ((-757 . -555) 116845) ((-750 . -1013) T) ((-750 . -552) 116827) ((-750 . -1129) T) ((-750 . -13) T) ((-750 . -72) T) ((-750 . -355) 116811) ((-750 . -555) 116684) ((-750 . -950) 116582) ((-750 . -21) 116537) ((-750 . -588) 116457) ((-750 . -23) 116412) ((-750 . -25) 116367) ((-750 . -104) 116322) ((-750 . -755) 116301) ((-750 . -721) 116280) ((-750 . -718) 116259) ((-750 . -759) 116238) ((-750 . -756) 116217) ((-750 . -716) 116196) ((-750 . -714) 116175) 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((-743 . -21) 115242) ((-743 . -588) 115162) ((-743 . -23) 115117) ((-743 . -25) 115072) ((-743 . -104) 115027) ((-743 . -755) 115006) ((-743 . -721) 114985) ((-743 . -718) 114964) ((-743 . -759) 114943) ((-743 . -756) 114922) ((-743 . -716) 114901) ((-743 . -714) 114880) ((-743 . -961) 114859) ((-743 . -663) 114838) ((-743 . -1061) 114817) ((-743 . -1025) 114796) ((-743 . -970) 114775) ((-743 . -590) 114748) ((-743 . -120) 114727) ((-741 . -645) 114711) ((-741 . -555) 114666) ((-741 . -654) 114636) ((-741 . -582) 114606) ((-741 . -590) 114580) ((-741 . -588) 114539) ((-741 . -104) T) ((-741 . -25) T) ((-741 . -72) T) ((-741 . -13) T) ((-741 . -1129) T) ((-741 . -552) 114521) ((-741 . -1013) T) ((-741 . -23) T) ((-741 . -21) T) ((-741 . -968) 114505) ((-741 . -963) 114489) ((-741 . -82) 114468) ((-741 . -961) T) ((-741 . -663) T) ((-741 . -1061) T) ((-741 . -1025) T) ((-741 . -970) T) ((-741 . -38) 114438) ((-741 . -190) 114417) ((-741 . -186) 114390) ((-741 . -189) 114369) ((-739 . -336) 114353) ((-739 . -555) 114337) ((-739 . -950) 114321) ((-739 . -759) T) ((-739 . -756) T) ((-739 . -1025) T) ((-739 . -72) T) ((-739 . -13) T) ((-739 . -1129) T) ((-739 . -552) 114303) ((-739 . -1013) T) ((-739 . -663) T) ((-739 . -754) T) ((-739 . -766) T) ((-738 . -228) 114287) ((-738 . -555) 114271) ((-738 . -950) 114255) ((-738 . -759) T) ((-738 . -72) T) ((-738 . -1013) T) ((-738 . -552) 114237) ((-738 . -756) T) ((-738 . -186) 114224) ((-738 . -13) T) ((-738 . -1129) T) ((-738 . -189) T) ((-737 . -82) 114159) ((-737 . -963) 114110) ((-737 . -968) 114061) ((-737 . -21) T) ((-737 . -588) 113997) ((-737 . -23) T) ((-737 . -1013) T) ((-737 . -552) 113966) ((-737 . -1129) T) ((-737 . -13) T) ((-737 . -72) T) ((-737 . -25) T) ((-737 . -104) T) ((-737 . -590) 113917) ((-737 . -190) T) ((-737 . -555) 113826) ((-737 . -970) T) ((-737 . -1025) T) ((-737 . -1061) T) ((-737 . -663) T) ((-737 . -961) T) ((-737 . -186) 113813) ((-737 . -189) T) ((-737 . -430) 113797) ((-737 . -312) 113776) ((-737 . -1134) 113755) ((-737 . -832) 113734) ((-737 . -495) 113713) ((-737 . -146) 113692) ((-737 . -654) 113629) ((-737 . -582) 113566) ((-737 . -38) 113503) ((-737 . -392) 113482) ((-737 . -258) 113461) ((-737 . -246) 113440) ((-737 . -201) 113419) ((-736 . -213) 113358) ((-736 . -555) 113102) ((-736 . -950) 112932) ((-736 . -553) NIL) ((-736 . -277) 112894) ((-736 . -355) 112878) ((-736 . -38) 112730) ((-736 . -82) 112555) ((-736 . -963) 112401) ((-736 . -968) 112247) ((-736 . -588) 112157) ((-736 . -590) 112046) ((-736 . -582) 111898) ((-736 . -654) 111750) ((-736 . -118) 111729) ((-736 . -120) 111708) ((-736 . -146) 111622) ((-736 . -495) 111556) ((-736 . -246) 111490) ((-736 . -47) 111452) ((-736 . -329) 111436) ((-736 . -580) 111384) ((-736 . -392) 111338) ((-736 . -455) 111203) ((-736 . -809) 111139) ((-736 . -806) 111038) ((-736 . -811) 110941) ((-736 . -796) NIL) ((-736 . -821) 110920) ((-736 . -1134) 110899) ((-736 . -861) 110846) ((-736 . -260) 110833) ((-736 . -190) 110812) ((-736 . -104) T) ((-736 . -25) T) ((-736 . -72) T) ((-736 . -552) 110794) ((-736 . -1013) T) ((-736 . -23) T) ((-736 . -21) T) ((-736 . -970) T) ((-736 . -1025) T) ((-736 . -1061) T) ((-736 . -663) T) ((-736 . -961) T) ((-736 . -186) 110742) ((-736 . -13) T) ((-736 . -1129) T) ((-736 . -189) 110696) ((-736 . -225) 110680) ((-736 . -184) 110664) ((-735 . -196) 110643) ((-735 . -1187) 110613) ((-735 . -721) 110592) ((-735 . -718) 110571) ((-735 . -759) 110525) ((-735 . -756) 110479) ((-735 . -716) 110458) ((-735 . -717) 110437) ((-735 . -654) 110382) ((-735 . -582) 110307) ((-735 . -243) 110284) ((-735 . -241) 110261) ((-735 . -538) 110238) ((-735 . -950) 110067) ((-735 . -555) 109871) ((-735 . -355) 109840) ((-735 . -580) 109748) ((-735 . -590) 109587) ((-735 . -329) 109557) ((-735 . -429) 109541) ((-735 . -455) 109474) ((-735 . -260) 109412) ((-735 . -34) T) ((-735 . -318) 109396) ((-735 . -320) 109375) ((-735 . -190) 109328) ((-735 . -588) 109116) ((-735 . -970) 109095) 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103526) ((-704 . -146) 103420) ((-704 . -392) 103354) ((-704 . -258) 103333) ((-704 . -241) 103260) ((-704 . -190) T) ((-704 . -104) T) ((-704 . -25) T) ((-704 . -72) T) ((-704 . -552) 103221) ((-704 . -1013) T) ((-704 . -23) T) ((-704 . -21) T) ((-704 . -970) T) ((-704 . -1025) T) ((-704 . -1061) T) ((-704 . -663) T) ((-704 . -961) T) ((-704 . -186) 103208) ((-704 . -13) T) ((-704 . -1129) T) ((-704 . -189) T) ((-704 . -225) 103192) ((-704 . -184) 103176) ((-703 . -977) 103143) ((-703 . -553) 102778) ((-703 . -260) 102765) ((-703 . -455) 102717) ((-703 . -277) 102689) ((-703 . -950) 102548) ((-703 . -355) 102532) ((-703 . -38) 102384) ((-703 . -555) 102157) ((-703 . -590) 102046) ((-703 . -588) 101956) ((-703 . -970) T) ((-703 . -1025) T) ((-703 . -1061) T) ((-703 . -663) T) ((-703 . -961) T) ((-703 . -82) 101781) ((-703 . -963) 101627) ((-703 . -968) 101473) ((-703 . -21) T) ((-703 . -23) T) ((-703 . -1013) T) ((-703 . -552) 101387) ((-703 . -1129) T) ((-703 . -13) T) ((-703 . -72) T) ((-703 . -25) T) ((-703 . -104) T) ((-703 . -582) 101239) ((-703 . -654) 101091) ((-703 . -118) 101070) ((-703 . -120) 101049) ((-703 . -146) 100963) ((-703 . -495) 100897) ((-703 . -246) 100831) ((-703 . -47) 100803) ((-703 . -329) 100787) ((-703 . -580) 100735) ((-703 . -392) 100689) ((-703 . -809) 100673) ((-703 . -806) 100655) ((-703 . -811) 100639) ((-703 . -796) 100498) ((-703 . -821) 100477) ((-703 . -1134) 100456) ((-703 . -861) 100423) ((-696 . -1013) T) ((-696 . -552) 100405) ((-696 . -1129) T) ((-696 . -13) T) ((-696 . -72) T) ((-694 . -717) T) ((-694 . -104) T) ((-694 . -25) T) ((-694 . -72) T) ((-694 . -13) T) ((-694 . -1129) T) ((-694 . -552) 100387) ((-694 . -1013) T) ((-694 . -23) T) ((-694 . -716) T) ((-694 . -756) T) ((-694 . -759) T) ((-694 . -718) T) ((-694 . -721) T) ((-694 . -663) T) ((-694 . -1025) T) ((-675 . -676) 100371) ((-675 . -1011) 100355) ((-675 . -193) 100339) ((-675 . -553) 100300) ((-675 . -124) 100284) ((-675 . -1035) 100268) ((-675 . -34) T) 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87542) ((-572 . -21) T) ((-572 . -588) 87511) ((-572 . -23) T) ((-572 . -1013) T) ((-572 . -552) 87480) ((-572 . -1129) T) ((-572 . -13) T) ((-572 . -72) T) ((-572 . -25) T) ((-572 . -104) T) ((-572 . -590) 87464) ((-572 . -582) 87448) ((-572 . -654) 87432) ((-572 . -361) 87397) ((-572 . -316) 87332) ((-572 . -241) 87290) ((-571 . -1107) 87265) ((-571 . -183) 87209) ((-571 . -76) 87153) ((-571 . -1035) 87097) ((-571 . -124) 87041) ((-571 . -553) NIL) ((-571 . -193) 86985) ((-571 . -538) 86960) ((-571 . -260) 86805) ((-571 . -455) 86605) ((-571 . -429) 86535) ((-571 . -241) 86488) ((-571 . -243) 86463) ((-571 . -549) 86438) ((-571 . -1013) T) ((-571 . -552) 86420) ((-571 . -72) T) ((-571 . -1129) T) ((-571 . -13) T) ((-571 . -34) T) ((-571 . -318) 86364) ((-566 . -413) T) ((-566 . -1025) T) ((-566 . -72) T) ((-566 . -13) T) ((-566 . -1129) T) ((-566 . -552) 86346) ((-566 . -1013) T) ((-566 . -663) T) ((-565 . -995) T) ((-565 . -430) 86327) ((-565 . -552) 86293) ((-565 . -555) 86274) 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. -968) 53929) ((-334 . -963) 53913) ((-334 . -82) 53892) ((-333 . -82) 53871) ((-333 . -963) 53855) ((-333 . -968) 53839) ((-333 . -21) T) ((-333 . -588) 53808) ((-333 . -23) T) ((-333 . -1013) T) ((-333 . -552) 53790) ((-333 . -1129) T) ((-333 . -13) T) ((-333 . -72) T) ((-333 . -25) T) ((-333 . -104) T) ((-333 . -590) 53774) ((-333 . -449) 53753) ((-333 . -557) 53718) ((-333 . -654) 53688) ((-333 . -582) 53658) ((-330 . -347) T) ((-330 . -120) T) ((-330 . -555) 53608) ((-330 . -590) 53573) ((-330 . -588) 53523) ((-330 . -104) T) ((-330 . -25) T) ((-330 . -72) T) ((-330 . -13) T) ((-330 . -1129) T) ((-330 . -552) 53490) ((-330 . -1013) T) ((-330 . -23) T) ((-330 . -21) T) ((-330 . -970) T) ((-330 . -1025) T) ((-330 . -1061) T) ((-330 . -663) T) ((-330 . -961) T) ((-330 . -553) 53404) ((-330 . -312) T) ((-330 . -1134) T) ((-330 . -832) T) ((-330 . -495) T) ((-330 . -146) T) ((-330 . -654) 53369) ((-330 . -582) 53334) ((-330 . -38) 53299) ((-330 . -392) T) ((-330 . -258) T) ((-330 . -82) 53248) ((-330 . -963) 53213) ((-330 . -968) 53178) ((-330 . -246) T) ((-330 . -201) T) ((-330 . -755) T) ((-330 . -721) T) ((-330 . -718) T) ((-330 . -759) T) ((-330 . -756) T) ((-330 . -716) T) ((-330 . -714) T) ((-330 . -796) 53160) ((-330 . -915) T) ((-330 . -933) T) ((-330 . -950) 53120) ((-330 . -973) T) ((-330 . -190) T) ((-330 . -186) 53107) ((-330 . -189) T) ((-330 . -1115) T) ((-330 . -1118) T) ((-330 . -433) T) ((-330 . -239) T) ((-330 . -66) T) ((-330 . -35) T) ((-330 . -557) 53089) ((-313 . -314) 53066) ((-313 . -72) T) ((-313 . -13) T) ((-313 . -1129) T) ((-313 . -552) 53048) ((-313 . -1013) T) ((-310 . -413) T) ((-310 . -1025) T) ((-310 . -72) T) ((-310 . -13) T) ((-310 . -1129) T) ((-310 . -552) 53030) ((-310 . -1013) T) ((-310 . -663) T) ((-310 . -950) 53014) ((-310 . -555) 52998) ((-308 . -280) 52982) ((-308 . -190) 52961) ((-308 . -186) 52934) ((-308 . -189) 52913) ((-308 . -320) 52892) ((-308 . -1066) 52871) ((-308 . -299) 52850) ((-308 . -120) 52829) ((-308 . 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. -23) T) ((-171 . -21) T) ((-171 . -961) T) ((-171 . -663) T) ((-171 . -1061) T) ((-171 . -1025) T) ((-171 . -970) T) ((-168 . -752) T) ((-168 . -759) T) ((-168 . -756) T) ((-168 . -1013) T) ((-168 . -552) 15536) ((-168 . -1129) T) ((-168 . -13) T) ((-168 . -72) T) ((-168 . -320) T) ((-167 . -1013) T) ((-167 . -552) 15518) ((-167 . -1129) T) ((-167 . -13) T) ((-167 . -72) T) ((-167 . -555) 15495) ((-166 . -1013) T) ((-166 . -552) 15477) ((-166 . -1129) T) ((-166 . -13) T) ((-166 . -72) T) ((-161 . -1013) T) ((-161 . -552) 15459) ((-161 . -1129) T) ((-161 . -13) T) ((-161 . -72) T) ((-158 . -1013) T) ((-158 . -552) 15441) ((-158 . -1129) T) ((-158 . -13) T) ((-158 . -72) T) ((-157 . -160) T) ((-157 . -1013) T) ((-157 . -552) 15423) ((-157 . -1129) T) ((-157 . -13) T) ((-157 . -72) T) ((-157 . -747) 15405) ((-154 . -995) T) ((-154 . -430) 15386) ((-154 . -552) 15352) ((-154 . -555) 15333) ((-154 . -1013) T) ((-154 . -1129) T) ((-154 . -13) T) ((-154 . -72) T) ((-154 . -64) T) ((-149 . 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((-1 . -72) T))
\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index 811145ba..a1519e71 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3577824389) -(3999 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3577831631) +(3998 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| |AbelianMonoid&| @@ -139,7 +139,7 @@ |HomogeneousAggregate&| |HomogeneousAggregate| |HomotopicTo| |Hostname| |HyperbolicFunctionCategory&| |HyperbolicFunctionCategory| |InnerAlgFactor| |InnerAlgebraicNumber| |IndexedOneDimensionalArray| |InnerTwoDimensionalArray| - |ChineseRemainderToolsForIntegralBases| |IntegralBasisTools| |IndexedBits| + 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T) ((-23) . T) ((-25) . T) ((-38 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-38 |#1|) . T) ((-38 $) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-35) |has| |#1| (-1116)) ((-66) |has| |#1| (-1116)) ((-72) . T) ((-82 (-350 (-485)) (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-82 |#1| |#1|) . T) ((-82 $ $) . T) ((-104) . T) ((-118) OR (|has| |#1| (-299)) (|has| |#1| (-118))) ((-120) |has| |#1| (-120)) ((-556 (-350 (-485))) OR (|has| |#1| (-951 (-350 (-485)))) (|has| |#1| (-299)) (|has| |#1| (-312))) ((-556 (-485)) . T) ((-556 |#1|) . T) ((-556 $) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-553 (-773)) . T) ((-146) . T) ((-554 (-142 (-179))) |has| |#1| (-934)) ((-554 (-142 (-330))) |has| |#1| (-934)) ((-554 (-474)) |has| |#1| (-554 (-474))) ((-554 (-801 (-330))) |has| |#1| (-554 (-801 (-330)))) ((-554 (-801 (-485))) |has| |#1| (-554 (-801 (-485)))) ((-554 (-1086 |#1|)) . 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T) ((-392) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-433) |has| |#1| (-1116)) ((-456 (-1091) |#1|) |has| |#1| (-456 (-1091) |#1|)) ((-456 |#1| |#1|) |has| |#1| (-260 |#1|)) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-13) . T) ((-589 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-591 (-485)) |has| |#1| (-581 (-485))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-583 |#1|) . T) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-581 (-485)) |has| |#1| (-581 (-485))) ((-581 |#1|) . T) ((-655 (-350 (-485))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-655 |#1|) . 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T) ((-23) . T) ((-25) . T) ((-38 (-350 (-484))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-38 |#1|) . T) ((-38 $) OR (|has| |#1| (-495)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-35) |has| |#1| (-1115)) ((-66) |has| |#1| (-1115)) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-82 |#1| |#1|) . T) ((-82 $ $) . T) ((-104) . T) ((-118) OR (|has| |#1| (-299)) (|has| |#1| (-118))) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) OR (|has| |#1| (-950 (-350 (-484)))) (|has| |#1| (-299)) (|has| |#1| (-312))) ((-555 (-484)) . T) ((-555 |#1|) . T) ((-555 $) OR (|has| |#1| (-495)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-552 (-772)) . T) ((-146) . T) ((-553 (-142 (-179))) |has| |#1| (-933)) ((-553 (-142 (-330))) |has| |#1| (-933)) ((-553 (-473)) |has| |#1| (-553 (-473))) ((-553 (-800 (-330))) |has| |#1| (-553 (-800 (-330)))) ((-553 (-800 (-484))) |has| |#1| (-553 (-800 (-484)))) ((-553 (-1085 |#1|)) . T) ((-186 $) OR (|has| |#1| (-299)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-184 |#1|) . T) ((-190) OR (|has| |#1| (-299)) (|has| |#1| (-190))) ((-189) OR (|has| |#1| (-299)) (|has| |#1| (-189)) (|has| |#1| (-190))) ((-225 |#1|) . T) ((-201) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-239) |has| |#1| (-1115)) ((-241 |#1| $) |has| |#1| (-241 |#1| |#1|)) ((-246) OR (|has| |#1| (-495)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-258) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-260 |#1|) |has| |#1| (-260 |#1|)) ((-312) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-345) |has| |#1| (-299)) ((-320) OR (|has| |#1| (-299)) (|has| |#1| (-320))) ((-299) |has| |#1| (-299)) ((-322 |#1| (-1085 |#1|)) . T) ((-353 |#1| (-1085 |#1|)) . T) ((-288 |#1|) . T) ((-329 |#1|) . T) ((-343 |#1|) . T) ((-355 |#1|) . 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T) ((-654 $) OR (|has| |#1| (-495)) (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-661 |#1| (-1085 |#1|)) . T) ((-663) . T) ((-806 $ (-1090)) OR (|has| |#1| (-811 (-1090))) (|has| |#1| (-809 (-1090)))) ((-809 (-1090)) |has| |#1| (-809 (-1090))) ((-811 (-1090)) OR (|has| |#1| (-811 (-1090))) (|has| |#1| (-809 (-1090)))) ((-796 (-330)) |has| |#1| (-796 (-330))) ((-796 (-484)) |has| |#1| (-796 (-484))) ((-794 |#1|) . T) ((-821) -12 (|has| |#1| (-258)) (|has| |#1| (-821))) ((-832) OR (|has| |#1| (-299)) (|has| |#1| (-312)) (|has| |#1| (-258))) ((-915) -12 (|has| |#1| (-915)) (|has| |#1| (-1115))) ((-950 (-350 (-484))) |has| |#1| (-950 (-350 (-484)))) ((-950 (-484)) |has| |#1| (-950 (-484))) ((-950 |#1|) . T) ((-963 (-350 (-484))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-963 |#1|) . T) ((-963 $) . T) ((-968 (-350 (-484))) OR (|has| |#1| (-299)) (|has| |#1| (-312))) ((-968 |#1|) . T) ((-968 $) . T) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . 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T) ((-186 $) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) (-12 (|has| |#2| (-190)) (|has| |#2| (-962)))) ((-184 |#2|) |has| |#2| (-962)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-962))) ((-189) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-962))) (-12 (|has| |#2| (-190)) (|has| |#2| (-962)))) ((-225 |#2|) |has| |#2| (-962)) ((-241 (-485) |#2|) . T) ((-243 (-485) |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-320) |has| |#2| (-320)) ((-318 |#2|) . T) ((-329 |#2|) |has| |#2| (-962)) ((-355 |#2|) |has| |#2| (-1014)) ((-429 |#2|) . T) ((-539 (-485) |#2|) . T) ((-456 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1014))) ((-13) . T) ((-589 (-485)) OR (|has| |#2| (-962)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-589 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-664)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-589 $) |has| |#2| (-962)) ((-591 (-485)) -12 (|has| |#2| (-581 (-485))) (|has| |#2| (-962))) ((-591 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-591 $) |has| |#2| (-962)) ((-583 |#2|) OR (|has| |#2| (-664)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-581 (-485)) -12 (|has| |#2| (-581 (-485))) (|has| |#2| (-962))) ((-581 |#2|) |has| |#2| (-962)) ((-655 |#2|) OR (|has| |#2| (-312)) (|has| |#2| (-146))) ((-664) |has| |#2| (-962)) ((-717) |has| |#2| (-718)) ((-718) |has| |#2| (-718)) ((-719) |has| |#2| (-718)) ((-722) |has| |#2| (-718)) ((-757) OR (|has| |#2| (-757)) (|has| |#2| (-718))) ((-760) OR (|has| |#2| (-757)) (|has| |#2| (-718))) ((-807 $ (-1091)) OR (-12 (|has| |#2| (-812 (-1091))) (|has| |#2| (-962))) (-12 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962)))) ((-810 (-1091)) -12 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962))) ((-812 (-1091)) OR (-12 (|has| |#2| (-812 (-1091))) (|has| |#2| (-962))) (-12 (|has| |#2| (-810 (-1091))) (|has| |#2| (-962)))) ((-951 (-350 (-485))) -12 (|has| |#2| (-951 (-350 (-485)))) (|has| |#2| (-1014))) ((-951 (-485)) -12 (|has| |#2| (-951 (-485))) (|has| |#2| (-1014))) ((-951 |#2|) |has| |#2| (-1014)) ((-964 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-664)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-969 |#2|) OR (|has| |#2| (-962)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-962) |has| |#2| (-962)) ((-971) |has| |#2| (-962)) ((-1026) |has| |#2| (-962)) ((-1062) |has| |#2| (-962)) ((-1014) OR (|has| |#2| (-1014)) (|has| |#2| (-962)) (|has| |#2| (-757)) (|has| |#2| (-718)) (|has| |#2| (-664)) (|has| |#2| (-320)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1130) . T) ((-1188 |#2|) |has| |#2| (-312))) -((-2569 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-3189 (((-85) $) NIL (|has| |#2| (-23)) ELT)) (-3708 (($ (-831)) 63 (|has| |#2| (-962)) ELT)) (-2199 (((-1186) $ (-485) (-485)) NIL (|has| $ (-6 -3997)) ELT)) (-2484 (($ $ $) 69 (|has| |#2| (-718)) ELT)) (-1313 (((-3 $ #1="failed") $ $) 54 (|has| |#2| (-104)) ELT)) (-3137 (((-695)) NIL (|has| |#2| (-320)) ELT)) (-3789 ((|#2| $ (-485) |#2|) NIL (|has| $ (-6 -3997)) ELT)) (-3725 (($) NIL T CONST)) (-3158 (((-3 (-485) #1#) $) NIL (-12 (|has| |#2| (-951 (-485))) (|has| |#2| (-1014))) ELT) (((-3 (-350 (-485)) #1#) $) NIL (-12 (|has| |#2| (-951 (-350 (-485)))) (|has| |#2| (-1014))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1014)) ELT)) (-3157 (((-485) $) NIL (-12 (|has| |#2| (-951 (-485))) (|has| |#2| (-1014))) ELT) (((-350 (-485)) $) NIL (-12 (|has| |#2| (-951 (-350 (-485)))) (|has| |#2| (-1014))) ELT) ((|#2| $) 29 (|has| |#2| (-1014)) ELT)) (-2280 (((-631 (-485)) (-631 $)) NIL (-12 (|has| |#2| (-581 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T) ((-72) OR (|has| |#2| (-1013)) (|has| |#2| (-961)) (|has| |#2| (-756)) (|has| |#2| (-717)) (|has| |#2| (-663)) (|has| |#2| (-320)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-72)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-82 |#2| |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-104) OR (|has| |#2| (-961)) (|has| |#2| (-717)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-21))) ((-555 (-350 (-484))) -12 (|has| |#2| (-950 (-350 (-484)))) (|has| |#2| (-1013))) ((-555 (-484)) OR (|has| |#2| (-961)) (-12 (|has| |#2| (-950 (-484))) (|has| |#2| (-1013)))) ((-555 |#2|) |has| |#2| (-1013)) ((-552 (-772)) OR (|has| |#2| (-1013)) (|has| |#2| (-961)) (|has| |#2| (-756)) (|has| |#2| (-717)) (|has| |#2| (-663)) (|has| |#2| (-320)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-552 (-772))) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-552 (-1179 |#2|)) . T) ((-186 $) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-961))) (-12 (|has| |#2| (-190)) (|has| |#2| (-961)))) ((-184 |#2|) |has| |#2| (-961)) ((-190) -12 (|has| |#2| (-190)) (|has| |#2| (-961))) ((-189) OR (-12 (|has| |#2| (-189)) (|has| |#2| (-961))) (-12 (|has| |#2| (-190)) (|has| |#2| (-961)))) ((-225 |#2|) |has| |#2| (-961)) ((-241 (-484) |#2|) . T) ((-243 (-484) |#2|) . T) ((-260 |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-320) |has| |#2| (-320)) ((-318 |#2|) . T) ((-329 |#2|) |has| |#2| (-961)) ((-355 |#2|) |has| |#2| (-1013)) ((-429 |#2|) . T) ((-538 (-484) |#2|) . T) ((-455 |#2| |#2|) -12 (|has| |#2| (-260 |#2|)) (|has| |#2| (-1013))) ((-13) . T) ((-588 (-484)) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-21))) ((-588 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-663)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-588 $) |has| |#2| (-961)) ((-590 (-484)) -12 (|has| |#2| (-580 (-484))) (|has| |#2| (-961))) ((-590 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-590 $) |has| |#2| (-961)) ((-582 |#2|) OR (|has| |#2| (-663)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-580 (-484)) -12 (|has| |#2| (-580 (-484))) (|has| |#2| (-961))) ((-580 |#2|) |has| |#2| (-961)) ((-654 |#2|) OR (|has| |#2| (-312)) (|has| |#2| (-146))) ((-663) |has| |#2| (-961)) ((-716) |has| |#2| (-717)) ((-717) |has| |#2| (-717)) ((-718) |has| |#2| (-717)) ((-721) |has| |#2| (-717)) ((-756) OR (|has| |#2| (-756)) (|has| |#2| (-717))) ((-759) OR (|has| |#2| (-756)) (|has| |#2| (-717))) ((-806 $ (-1090)) OR (-12 (|has| |#2| (-811 (-1090))) (|has| |#2| (-961))) (-12 (|has| |#2| (-809 (-1090))) (|has| |#2| (-961)))) ((-809 (-1090)) -12 (|has| |#2| (-809 (-1090))) (|has| |#2| (-961))) ((-811 (-1090)) OR (-12 (|has| |#2| (-811 (-1090))) (|has| |#2| (-961))) (-12 (|has| |#2| (-809 (-1090))) (|has| |#2| (-961)))) ((-950 (-350 (-484))) -12 (|has| |#2| (-950 (-350 (-484)))) (|has| |#2| (-1013))) ((-950 (-484)) -12 (|has| |#2| (-950 (-484))) (|has| |#2| (-1013))) ((-950 |#2|) |has| |#2| (-1013)) ((-963 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-663)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-968 |#2|) OR (|has| |#2| (-961)) (|has| |#2| (-312)) (|has| |#2| (-146))) ((-961) |has| |#2| (-961)) ((-970) |has| |#2| (-961)) ((-1025) |has| |#2| (-961)) ((-1061) |has| |#2| (-961)) ((-1013) OR (|has| |#2| (-1013)) (|has| |#2| (-961)) (|has| |#2| (-756)) (|has| |#2| (-717)) (|has| |#2| (-663)) (|has| |#2| (-320)) (|has| |#2| (-312)) (|has| |#2| (-146)) (|has| |#2| (-104)) (|has| |#2| (-25)) (|has| |#2| (-23)) (|has| |#2| (-21))) ((-1129) . T) ((-1187 |#2|) |has| |#2| (-312))) +((-2568 (((-85) $ $) NIL (|has| |#2| (-72)) ELT)) (-3188 (((-85) $) NIL (|has| |#2| (-23)) ELT)) (-3707 (($ (-830)) 63 (|has| |#2| (-961)) ELT)) (-2198 (((-1185) $ (-484) (-484)) NIL (|has| $ (-6 -3996)) ELT)) (-2483 (($ $ $) 69 (|has| |#2| (-717)) ELT)) (-1312 (((-3 $ #1="failed") $ $) 54 (|has| |#2| (-104)) ELT)) (-3136 (((-694)) NIL (|has| |#2| (-320)) ELT)) (-3788 ((|#2| $ (-484) |#2|) NIL (|has| $ (-6 -3996)) ELT)) (-3724 (($) NIL T CONST)) (-3157 (((-3 (-484) #1#) $) NIL (-12 (|has| |#2| (-950 (-484))) (|has| |#2| (-1013))) ELT) (((-3 (-350 (-484)) #1#) $) NIL (-12 (|has| |#2| (-950 (-350 (-484)))) (|has| |#2| (-1013))) ELT) (((-3 |#2| #1#) $) 31 (|has| |#2| (-1013)) ELT)) (-3156 (((-484) $) NIL (-12 (|has| |#2| (-950 (-484))) (|has| |#2| (-1013))) ELT) (((-350 (-484)) $) NIL (-12 (|has| |#2| (-950 (-350 (-484)))) (|has| |#2| (-1013))) ELT) ((|#2| $) 29 (|has| |#2| (-1013)) ELT)) (-2279 (((-630 (-484)) (-630 $)) NIL (-12 (|has| |#2| (-580 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T) ((-589 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 $) . T) ((-591 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-591 (-485)) |has| |#1| (-581 (-485))) ((-591 |#1|) . T) ((-591 $) . T) ((-583 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-583 |#1|) |has| |#1| (-146)) ((-583 $) OR (|has| |#1| (-822)) (|has| |#1| (-496)) (|has| |#1| (-392))) ((-581 (-485)) |has| |#1| (-581 (-485))) ((-581 |#1|) . T) ((-655 (-350 (-485))) |has| |#1| (-38 (-350 (-485)))) ((-655 |#1|) |has| |#1| (-146)) ((-655 $) OR (|has| |#1| (-822)) (|has| |#1| (-496)) (|has| |#1| (-392))) ((-664) . T) ((-807 $ (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-807 $ |#3|) . T) ((-810 (-1091)) |has| |#1| (-810 (-1091))) ((-810 |#3|) . T) ((-812 (-1091)) OR (|has| |#1| (-812 (-1091))) (|has| |#1| (-810 (-1091)))) ((-812 |#3|) . 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T) ((-582 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392))) ((-580 (-484)) |has| |#1| (-580 (-484))) ((-580 |#1|) . T) ((-654 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392))) ((-663) . T) ((-806 $ |#3|) . T) ((-809 |#3|) . T) ((-811 |#3|) . T) ((-796 (-330)) -12 (|has| |#1| (-796 (-330))) (|has| |#3| (-796 (-330)))) ((-796 (-484)) -12 (|has| |#1| (-796 (-484))) (|has| |#3| (-796 (-484)))) ((-821) |has| |#1| (-821)) ((-950 (-350 (-484))) |has| |#1| (-950 (-350 (-484)))) ((-950 (-484)) |has| |#1| (-950 (-484))) ((-950 |#1|) . T) ((-950 |#3|) . T) ((-963 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-963 |#1|) . T) ((-963 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-146))) ((-968 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-968 |#1|) . T) ((-968 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . T) ((-1134) |has| |#1| (-821))) +((-3081 (((-583 |#2|) |#5|) 40 T ELT)) (-3083 (((-1085 |#5|) |#5| |#2| (-1085 |#5|)) 23 T ELT) (((-350 (-1085 |#5|)) |#5| |#2|) 16 T ELT)) (-3084 ((|#5| (-350 (-1085 |#5|)) |#2|) 30 T ELT)) (-3082 (((-3 |#2| #1="failed") |#5|) 70 T ELT)) (-2823 (((-3 (-583 |#5|) #1#) |#5|) 64 T ELT)) (-2825 (((-3 (-2 (|:| |val| |#5|) (|:| -2401 (-484))) #1#) |#5|) 53 T ELT)) (-2822 (((-3 (-583 |#5|) #1#) |#5|) 66 T ELT)) (-2824 (((-3 (-2 (|:| |var| |#2|) (|:| -2401 (-484))) #1#) |#5|) 56 T ELT))) +(((-862 |#1| |#2| |#3| |#4| |#5|) (-10 -7 (-15 -3081 ((-583 |#2|) |#5|)) (-15 -3082 ((-3 |#2| #1="failed") |#5|)) (-15 -3083 ((-350 (-1085 |#5|)) |#5| |#2|)) (-15 -3084 (|#5| (-350 (-1085 |#5|)) |#2|)) (-15 -3083 ((-1085 |#5|) |#5| |#2| (-1085 |#5|))) (-15 -2822 ((-3 (-583 |#5|) #1#) |#5|)) (-15 -2823 ((-3 (-583 |#5|) #1#) |#5|)) (-15 -2824 ((-3 (-2 (|:| |var| |#2|) (|:| -2401 (-484))) #1#) |#5|)) (-15 -2825 ((-3 (-2 (|:| |val| |#5|) (|:| -2401 (-484))) #1#) |#5|))) (-717) 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T) ((-590 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-590 (-484)) |has| |#1| (-580 (-484))) ((-590 |#1|) . T) ((-590 $) . T) ((-582 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392))) ((-580 (-484)) |has| |#1| (-580 (-484))) ((-580 |#1|) . T) ((-654 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392))) ((-663) . T) ((-806 $ |#3|) . T) ((-809 |#3|) . T) ((-811 |#3|) . T) ((-796 (-330)) -12 (|has| |#1| (-796 (-330))) (|has| |#3| (-796 (-330)))) ((-796 (-484)) -12 (|has| |#1| (-796 (-484))) (|has| |#3| (-796 (-484)))) ((-861 |#1| |#2| |#3|) . T) ((-821) |has| |#1| (-821)) ((-950 (-350 (-484))) |has| |#1| (-950 (-350 (-484)))) ((-950 (-484)) |has| |#1| (-950 (-484))) ((-950 |#1|) . T) ((-950 |#3|) . T) ((-963 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-963 |#1|) . T) ((-963 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-146))) ((-968 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-968 |#1|) . T) ((-968 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1129) . 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T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-485) (-1026)) ((-246) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-485)))) ((-456 (-1091) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-456 (-1091) |#2|))) ((-456 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-496) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-13) . T) ((-589 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-589 (-485)) . T) ((-589 |#1|) . T) ((-589 |#2|) |has| |#1| (-312)) ((-589 $) . T) ((-591 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-591 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-312)) ((-591 $) . T) ((-583 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-583 |#1|) |has| |#1| (-146)) ((-583 |#2|) |has| |#1| (-312)) ((-583 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-581 (-485)) -12 (|has| |#1| (-312)) (|has| |#2| (-581 (-485)))) ((-581 |#2|) |has| |#1| (-312)) ((-655 (-350 (-485))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-485))))) ((-655 |#1|) |has| |#1| (-146)) ((-655 |#2|) |has| |#1| (-312)) ((-655 $) OR (|has| |#1| (-496)) (|has| |#1| (-312))) ((-664) . 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(NIL T NIL NIL) -7 NIL NIL NIL) (-1207 2815530 2815683 2815872 "YSTREAM" NIL YSTREAM (NIL T) -7 NIL NIL NIL) (-1206 2814992 2815295 2815408 "YDIAGRAM" NIL YDIAGRAM (NIL) -8 NIL NIL NIL) (-1205 2812552 2814454 2814657 "XRPOLY" NIL XRPOLY (NIL T T) -8 NIL NIL NIL) (-1204 2809316 2810969 2811540 "XPR" NIL XPR (NIL T T) -8 NIL NIL NIL) (-1203 2806573 2808303 2808357 "XPOLYC" 2808642 XPOLYC (NIL T T) -9 NIL 2808755 NIL) (-1202 2804092 2806077 2806280 "XPOLY" NIL XPOLY (NIL T) -8 NIL NIL NIL) (-1201 2800340 2802951 2803339 "XPBWPOLY" NIL XPBWPOLY (NIL T T) -8 NIL NIL NIL) (-1200 2795187 2796820 2796874 "XFALG" 2799019 XFALG (NIL T T) -9 NIL 2799803 NIL) (-1199 2790343 2793076 2793118 "XF" 2793736 XF (NIL T) -9 NIL 2794132 NIL) (-1198 2790061 2790171 2790338 "XF-" NIL XF- (NIL T T) -7 NIL NIL NIL) (-1197 2789288 2789410 2789614 "XEXPPKG" NIL XEXPPKG (NIL T T T) -7 NIL NIL NIL) (-1196 2787030 2789188 2789283 "XDPOLY" NIL XDPOLY (NIL T T) -8 NIL NIL NIL) (-1195 2785611 2786406 2786448 "XALG" 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2753569 "VIEW" NIL VIEW (NIL) -7 NIL NIL NIL) (-1181 2751595 2751876 2752192 "VECTOR2" NIL VECTOR2 (NIL T T) -7 NIL NIL NIL) (-1180 2746864 2751422 2751514 "VECTOR" NIL VECTOR (NIL T) -8 NIL NIL NIL) (-1179 2740100 2744556 2744599 "VECTCAT" 2745587 VECTCAT (NIL T) -9 NIL 2746171 NIL) (-1178 2739379 2739705 2740095 "VECTCAT-" NIL VECTCAT- (NIL T T) -7 NIL NIL NIL) (-1177 2738873 2739115 2739235 "VARIABLE" NIL VARIABLE (NIL NIL) -8 NIL NIL NIL) (-1176 2738806 2738811 2738841 "UTYPE" 2738846 UTYPE (NIL) -9 NIL NIL NIL) (-1175 2737793 2737969 2738230 "UTSODETL" NIL UTSODETL (NIL T T T T) -7 NIL NIL NIL) (-1174 2735644 2736152 2736676 "UTSODE" NIL UTSODE (NIL T T) -7 NIL NIL NIL) (-1173 2725526 2731496 2731538 "UTSCAT" 2732636 UTSCAT (NIL T) -9 NIL 2733393 NIL) (-1172 2723591 2724534 2725521 "UTSCAT-" NIL UTSCAT- (NIL T T) -7 NIL NIL NIL) (-1171 2723265 2723314 2723445 "UTS2" NIL UTS2 (NIL T T T T) -7 NIL NIL NIL) (-1170 2714976 2721461 2721940 "UTS" NIL UTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1169 2708975 2711784 2711827 "URAGG" 2713897 URAGG (NIL T) -9 NIL 2714619 NIL) (-1168 2706990 2707952 2708970 "URAGG-" NIL URAGG- (NIL T T) -7 NIL NIL NIL) (-1167 2702697 2705966 2706428 "UPXSSING" NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL NIL) (-1166 2695126 2702621 2702692 "UPXSCONS" NIL UPXSCONS (NIL T T) -8 NIL NIL NIL) (-1165 2683777 2691264 2691325 "UPXSCCA" 2691893 UPXSCCA (NIL T T) -9 NIL 2692125 NIL) (-1164 2683498 2683600 2683772 "UPXSCCA-" NIL UPXSCCA- (NIL T T T) -7 NIL NIL NIL) (-1163 2672050 2679262 2679304 "UPXSCAT" 2679944 UPXSCAT (NIL T) -9 NIL 2680552 NIL) (-1162 2671563 2671648 2671825 "UPXS2" NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1161 2663249 2671154 2671416 "UPXS" NIL UPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1160 2662144 2662414 2662764 "UPSQFREE" NIL UPSQFREE (NIL T T) -7 NIL NIL NIL) (-1159 2654847 2658332 2658386 "UPSCAT" 2659455 UPSCAT (NIL T T) -9 NIL 2660219 NIL) (-1158 2654267 2654519 2654842 "UPSCAT-" NIL UPSCAT- (NIL T T T) -7 NIL NIL NIL) (-1157 2653941 2653990 2654121 "UPOLYC2" NIL UPOLYC2 (NIL T T T T) -7 NIL NIL NIL) (-1156 2638071 2647025 2647067 "UPOLYC" 2649145 UPOLYC (NIL T) -9 NIL 2650365 NIL) (-1155 2632126 2634974 2638066 "UPOLYC-" NIL UPOLYC- (NIL T T) -7 NIL NIL NIL) (-1154 2631562 2631687 2631850 "UPMP" NIL UPMP (NIL T T) -7 NIL NIL NIL) (-1153 2631196 2631283 2631422 "UPDIVP" NIL UPDIVP (NIL T T) -7 NIL NIL NIL) (-1152 2630009 2630276 2630580 "UPDECOMP" NIL UPDECOMP (NIL T T) -7 NIL NIL NIL) (-1151 2629342 2629472 2629657 "UPCDEN" NIL UPCDEN (NIL T T T) -7 NIL NIL NIL) (-1150 2628934 2629009 2629156 "UP2" NIL UP2 (NIL NIL T NIL T) -7 NIL NIL NIL) (-1149 2619698 2628700 2628828 "UP" NIL UP (NIL NIL T) -8 NIL NIL NIL) (-1148 2619060 2619197 2619402 "UNISEG2" NIL UNISEG2 (NIL T T) -7 NIL NIL NIL) (-1147 2617661 2618508 2618784 "UNISEG" NIL UNISEG (NIL T) -8 NIL NIL NIL) (-1146 2616890 2617087 2617312 "UNIFACT" NIL UNIFACT (NIL T) -7 NIL NIL NIL) (-1145 2603700 2616814 2616885 "ULSCONS" NIL ULSCONS (NIL T T) -8 NIL NIL NIL) (-1144 2583506 2596741 2596802 "ULSCCAT" 2597433 ULSCCAT (NIL T T) -9 NIL 2597720 NIL) (-1143 2582841 2583127 2583501 "ULSCCAT-" NIL ULSCCAT- (NIL T T T) -7 NIL NIL NIL) (-1142 2571213 2578347 2578389 "ULSCAT" 2579242 ULSCAT (NIL T) -9 NIL 2579972 NIL) (-1141 2570726 2570811 2570988 "ULS2" NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL NIL) (-1140 2552843 2570225 2570466 "ULS" NIL ULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1139 2551877 2552570 2552684 "UINT8" NIL UINT8 (NIL) -8 NIL NIL 2552795) (-1138 2550910 2551603 2551717 "UINT64" NIL UINT64 (NIL) -8 NIL NIL 2551828) (-1137 2549943 2550636 2550750 "UINT32" NIL UINT32 (NIL) -8 NIL NIL 2550861) (-1136 2548976 2549669 2549783 "UINT16" NIL UINT16 (NIL) -8 NIL NIL 2549894) (-1135 2546983 2548204 2548234 "UFD" 2548445 UFD (NIL) -9 NIL 2548558 NIL) (-1134 2546827 2546884 2546978 "UFD-" NIL UFD- (NIL T) -7 NIL NIL NIL) (-1133 2546079 2546286 2546502 "UDVO" NIL UDVO (NIL) -7 NIL NIL NIL) (-1132 2544299 2544752 2545217 "UDPO" NIL UDPO (NIL T) -7 NIL NIL NIL) (-1131 2544024 2544264 2544294 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1130 2543962 2543967 2543997 "TYPE" 2544002 TYPE (NIL) -9 NIL 2544009 NIL) (-1129 2543121 2543341 2543581 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1128 2542299 2542730 2542965 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1127 2540453 2541026 2541565 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1126 2539487 2539723 2539959 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1125 2527986 2532302 2532398 "TSETCAT" 2537613 TSETCAT (NIL T T T T) -9 NIL 2539114 NIL) (-1124 2524323 2526139 2527981 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1123 2518715 2523549 2523831 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1122 2514052 2515065 2515994 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1121 2513549 2513624 2513787 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1120 2511625 2511915 2512270 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1119 2511109 2511258 2511288 "TRIGCAT" 2511501 TRIGCAT (NIL) -9 NIL NIL NIL) (-1118 2510860 2510963 2511104 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1117 2508008 2509968 2510247 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1116 2507114 2507810 2507840 "TRANFUN" 2507875 TRANFUN (NIL) -9 NIL 2507941 NIL) (-1115 2506578 2506829 2507109 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1114 2506415 2506453 2506514 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1113 2505872 2506003 2506154 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1112 2504613 2505270 2505506 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1111 2504425 2504462 2504534 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1110 2502639 2503285 2503714 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1109 2501019 2501356 2501678 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1108 2489962 2498854 2498910 "TBAGG" 2499227 TBAGG (NIL T T) -9 NIL 2499437 NIL) (-1107 2485473 2487660 2489957 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1106 2484950 2485075 2485220 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1105 2484460 2484780 2484870 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1104 2483957 2484074 2484212 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1103 2475261 2483885 2483952 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1102 2471014 2472309 2473554 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1101 2470383 2470542 2470723 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1100 2467537 2468290 2469073 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1099 2467311 2467501 2467532 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1098 2466265 2466950 2467076 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2467262) (-1097 2465529 2466077 2466156 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2466216) (-1096 2462352 2463511 2464211 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1095 2460035 2460718 2461352 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1094 2456113 2457159 2458136 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1093 2453212 2455768 2455997 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1092 2452808 2452895 2453017 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1091 2449432 2450906 2451725 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1090 2442392 2448629 2448922 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1089 2434078 2441983 2442245 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2433357 2433496 2433713 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1087 2433041 2433106 2433217 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1086 2423764 2432753 2432878 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1085 2422494 2422792 2423147 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1084 2421899 2421977 2422168 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1083 2404051 2421398 2421639 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1082 2403650 2403922 2403991 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1081 2402986 2403267 2403407 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1080 2397588 2398847 2399800 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1079 2397120 2397220 2397384 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1078 2392231 2393513 2394660 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1077 2386689 2388160 2389471 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1076 2379604 2381668 2383459 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1075 2370558 2379542 2379599 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1074 2365405 2370272 2370387 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1073 2364992 2365075 2365219 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1072 2364143 2364344 2364579 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1071 2363883 2363941 2364034 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1070 2356625 2362088 2362694 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1069 2355801 2356006 2356237 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1068 2355046 2355417 2355564 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1067 2354534 2354776 2354806 "STEP" 2354900 STEP (NIL) -9 NIL 2354971 NIL) (-1066 2345828 2354452 2354529 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1065 2340047 2344626 2344669 "STAGG" 2345096 STAGG (NIL T) -9 NIL 2345270 NIL) (-1064 2338426 2339174 2340042 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1063 2336736 2338253 2338345 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1062 2336016 2336555 2336585 "SRING" 2336590 SRING (NIL) -9 NIL 2336610 NIL) (-1061 2328791 2334554 2334993 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1060 2322565 2324004 2325508 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1059 2315122 2319881 2319911 "SRAGG" 2321210 SRAGG (NIL) -9 NIL 2321814 NIL) (-1058 2314419 2314739 2315117 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1057 2308627 2313741 2314164 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1056 2302979 2305995 2306731 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1055 2299408 2300227 2300864 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1054 2298383 2298688 2298718 "SPFCAT" 2299162 SPFCAT (NIL) -9 NIL NIL NIL) (-1053 2297320 2297572 2297836 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1052 2288078 2290352 2290382 "SPADXPT" 2295019 SPADXPT (NIL) -9 NIL 2297143 NIL) (-1051 2287880 2287926 2287995 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1050 2285536 2287844 2287875 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1049 2277210 2279299 2279341 "SPACEC" 2283656 SPACEC (NIL T) -9 NIL 2285461 NIL) (-1048 2275039 2277157 2277205 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1047 2273975 2274164 2274454 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1046 2272379 2272712 2273123 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1045 2271644 2271878 2272139 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1044 2267824 2268784 2269779 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1043 2264182 2264881 2265610 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1042 2258102 2263504 2263600 "SNTSCAT" 2263605 SNTSCAT (NIL T T T T) -9 NIL 2263675 NIL) (-1041 2251923 2256743 2257133 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1040 2245695 2251842 2251918 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1039 2244127 2244458 2244856 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1038 2235867 2240693 2240795 "SMATCAT" 2242138 SMATCAT (NIL NIL T T T) -9 NIL 2242686 NIL) (-1037 2233708 2234692 2235862 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1036 2231826 2233177 2233220 "SMAGG" 2233305 SMAGG (NIL T) -9 NIL 2233369 NIL) (-1035 2229551 2231012 2231055 "SKAGG" 2231316 SKAGG (NIL T) -9 NIL 2231452 NIL) (-1034 2225597 2229371 2229482 "SINT" NIL SINT (NIL) -8 NIL NIL 2229523) (-1033 2225407 2225451 2225517 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1032 2224482 2224714 2224982 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1031 2223486 2223648 2223924 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1030 2222832 2223172 2223295 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1029 2222178 2222485 2222625 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1028 2220289 2220781 2221287 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1027 2213882 2220208 2220284 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1026 2213385 2213622 2213652 "SGROUP" 2213745 SGROUP (NIL) -9 NIL 2213807 NIL) (-1025 2213275 2213307 2213380 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1024 2212913 2212953 2212994 "SGPOPC" 2212999 SGPOPC (NIL T) -9 NIL 2213200 NIL) (-1023 2212447 2212724 2212830 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1022 2209870 2210639 2211361 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1021 2203889 2209291 2209387 "SFRTCAT" 2209392 SFRTCAT (NIL T T T T) -9 NIL 2209430 NIL) (-1020 2198281 2199394 2200521 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1019 2192457 2193618 2194782 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1018 2191429 2192331 2192452 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1017 2187037 2187932 2188027 "SEXCAT" 2190640 SEXCAT (NIL T T T T T) -9 NIL 2191191 NIL) (-1016 2186010 2186964 2187032 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1015 2184401 2184986 2185288 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1014 2183924 2184109 2184139 "SETCAT" 2184256 SETCAT (NIL) -9 NIL 2184340 NIL) (-1013 2183756 2183820 2183919 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1012 2179983 2182210 2182253 "SETAGG" 2183121 SETAGG (NIL T) -9 NIL 2183459 NIL) (-1011 2179589 2179741 2179978 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1010 2176696 2179536 2179584 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1009 2176162 2176472 2176572 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1008 2175289 2175655 2175716 "SEGXCAT" 2176002 SEGXCAT (NIL T T) -9 NIL 2176122 NIL) (-1007 2174214 2174482 2174525 "SEGCAT" 2175047 SEGCAT (NIL T) -9 NIL 2175268 NIL) (-1006 2173894 2173959 2174072 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1005 2172960 2173430 2173638 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1004 2172538 2172817 2172893 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1003 2171903 2172039 2172243 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1002 2170969 2171716 2171898 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1001 2170222 2170917 2170964 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-1000 2161707 2170089 2170217 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-999 2160567 2160857 2161174 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-998 2159873 2160085 2160273 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-997 2159223 2159380 2159556 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-996 2158796 2159027 2159055 "SASTCAT" 2159060 SASTCAT (NIL) -9 NIL 2159073 NIL) (-995 2158263 2158688 2158762 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-994 2157866 2157907 2158078 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-993 2157497 2157538 2157695 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-992 2150578 2157414 2157492 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-991 2149228 2149557 2149953 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-990 2147989 2148350 2148650 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2115121 NIL) (-977 2084824 2087647 2090720 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-976 2080991 2084572 2084710 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-975 2079319 2080058 2080314 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-974 2074962 2077774 2077802 "RNS" 2078064 RNS (NIL) -9 NIL 2078316 NIL) (-973 2073865 2074352 2074889 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-972 2072983 2073384 2073584 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-971 2072121 2072683 2072711 "RNG" 2072771 RNG (NIL) -9 NIL 2072825 NIL) (-970 2072010 2072044 2072116 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-969 2071272 2071777 2071817 "RMODULE" 2071822 RMODULE (NIL T) -9 NIL 2071848 NIL) (-968 2070211 2070317 2070647 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-967 2067210 2069801 2070094 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-966 2060005 2062344 2062456 "RMATCAT" 2065761 RMATCAT (NIL NIL NIL T T T) -9 NIL 2066727 NIL) (-965 2059522 2059701 2060000 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-964 2059090 2059301 2059342 "RLINSET" 2059403 RLINSET (NIL T) -9 NIL 2059447 NIL) (-963 2058735 2058816 2058942 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-962 2057581 2058312 2058340 "RING" 2058395 RING (NIL) -9 NIL 2058487 NIL) (-961 2057426 2057482 2057576 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-960 2056480 2056747 2057003 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-959 2047620 2056108 2056309 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-958 2046845 2047356 2047395 "RGBCSPC" 2047452 RGBCSPC (NIL T) -9 NIL 2047503 NIL) (-957 2045879 2046365 2046404 "RGBCMDL" 2046632 RGBCMDL (NIL T) -9 NIL 2046746 NIL) (-956 2045591 2045660 2045761 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-955 2045354 2045395 2045490 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-954 2043778 2044208 2044588 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-953 2041365 2042033 2042701 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-952 2040915 2041013 2041173 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-951 2040537 2040635 2040676 "RETRACT" 2040807 RETRACT (NIL T) -9 NIL 2040894 NIL) (-950 2040417 2040448 2040532 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-949 2040019 2040291 2040358 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-948 2038499 2039390 2039587 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-947 2038190 2038251 2038347 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-946 2037933 2037974 2038079 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-945 2037668 2037709 2037818 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-944 2032739 2034190 2035405 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-943 2029838 2030596 2031404 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-942 2027807 2028429 2029029 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-941 2020595 2026358 2026794 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-940 2019907 2020187 2020336 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-939 2019392 2019507 2019672 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-938 2014985 2018795 2019016 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-937 2014217 2014416 2014629 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-936 2011507 2012345 2013227 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-935 2008089 2009125 2010184 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-934 2007925 2007978 2008006 "REAL" 2008011 REAL (NIL) -9 NIL 2008046 NIL) (-933 2007415 2007719 2007810 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-932 2006895 2006973 2007178 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-931 2006128 2006320 2006531 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-930 2005016 2005313 2005680 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-929 2003283 2003753 2004286 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-928 2002205 2002482 2002869 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-927 2001032 2001341 2001760 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-926 1994380 1997892 1997920 "RCFIELD" 1999197 RCFIELD (NIL) -9 NIL 1999927 NIL) (-925 1992998 1993610 1994307 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-924 1989202 1991090 1991131 "RCAGG" 1992198 RCAGG (NIL T) -9 NIL 1992659 NIL) (-923 1988929 1989039 1989197 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-922 1988374 1988503 1988664 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-921 1987991 1988070 1988189 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-920 1987406 1987556 1987706 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-919 1987188 1987238 1987309 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-918 1979630 1986306 1986614 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-917 1969332 1979497 1979625 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-916 1968966 1969059 1969087 "RADCAT" 1969244 RADCAT (NIL) -9 NIL NIL NIL) (-915 1968804 1968864 1968961 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-914 1967057 1968635 1968724 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-913 1966738 1966787 1966914 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-912 1959025 1963109 1963149 "QUATCAT" 1963927 QUATCAT (NIL T) -9 NIL 1964691 NIL) (-911 1956275 1957555 1958931 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-910 1952115 1956225 1956270 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-909 1949635 1951149 1951190 "QUAGG" 1951565 QUAGG (NIL T) -9 NIL 1951741 NIL) (-908 1949237 1949509 1949576 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-907 1948243 1948873 1949036 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-906 1947924 1947973 1948100 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-905 1937524 1943693 1943733 "QFCAT" 1944391 QFCAT (NIL T) -9 NIL 1945384 NIL) (-904 1934408 1935847 1937430 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-903 1933954 1934088 1934218 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-902 1928150 1929311 1930473 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-901 1927569 1927749 1927981 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-900 1925391 1925919 1926342 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-899 1924290 1924532 1924849 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-898 1922651 1922849 1923202 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-897 1918407 1919623 1919664 "PTRANFN" 1921548 PTRANFN (NIL T) -9 NIL NIL NIL) (-896 1917054 1917399 1917720 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-895 1916747 1916810 1916917 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-894 1910954 1915525 1915565 "PTCAT" 1915857 PTCAT (NIL T) -9 NIL 1916010 NIL) (-893 1910647 1910688 1910812 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-892 1909526 1909842 1910176 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-891 1898405 1900966 1903275 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-890 1891445 1894188 1894282 "PSETCAT" 1897256 PSETCAT (NIL T T T T) -9 NIL 1898065 NIL) (-889 1889895 1890629 1891440 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-888 1889214 1889409 1889437 "PSCURVE" 1889705 PSCURVE (NIL) -9 NIL 1889872 NIL) (-887 1884816 1886636 1886700 "PSCAT" 1887535 PSCAT (NIL T T T) -9 NIL 1887774 NIL) (-886 1884130 1884412 1884811 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-885 1882527 1883442 1883705 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-884 1882018 1882321 1882412 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-883 1873038 1875460 1877648 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-882 1870914 1872338 1872378 "PRQAGG" 1872561 PRQAGG (NIL T) -9 NIL 1872664 NIL) (-881 1870087 1870533 1870561 "PROPLOG" 1870700 PROPLOG (NIL) -9 NIL 1870814 NIL) (-880 1869762 1869825 1869948 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-879 1869198 1869337 1869509 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-878 1867446 1868209 1868506 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-877 1866998 1867130 1867258 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-876 1861439 1865938 1866758 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-875 1861268 1861306 1861365 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-874 1860707 1860847 1860998 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-873 1859175 1859594 1860060 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-872 1858892 1858953 1858981 "PRIMCAT" 1859105 PRIMCAT (NIL) -9 NIL NIL NIL) (-871 1858063 1858259 1858487 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-870 1854097 1858013 1858058 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-869 1853796 1853858 1853969 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-868 1850932 1853445 1853678 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-867 1850383 1850540 1850568 "PPCURVE" 1850773 PPCURVE (NIL) -9 NIL 1850909 NIL) (-866 1849996 1850241 1850324 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-865 1847752 1848173 1848765 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-864 1847195 1847259 1847492 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-863 1843915 1844401 1845012 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-862 1829506 1835635 1835699 "POLYCAT" 1839184 POLYCAT (NIL T T T) -9 NIL 1841061 NIL) (-861 1825016 1827163 1829501 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-860 1824673 1824747 1824866 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-859 1824366 1824429 1824536 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-858 1817729 1824099 1824258 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-857 1816616 1816879 1817155 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-856 1815220 1815533 1815863 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-855 1810535 1815170 1815215 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-854 1809023 1809434 1809809 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-853 1807780 1808089 1808485 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-852 1807451 1807535 1807652 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-851 1807030 1807105 1807279 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-850 1806516 1806612 1806772 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-849 1805988 1806108 1806262 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-848 1804883 1805101 1805478 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-847 1804494 1804579 1804731 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-846 1804045 1804127 1804308 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-845 1803737 1803818 1803931 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-844 1803250 1803325 1803533 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-843 1802598 1802726 1802928 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-842 1801960 1802094 1802257 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-841 1801264 1801446 1801627 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-840 1800987 1801061 1801155 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-839 1797555 1798744 1799660 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-838 1796639 1796840 1797075 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-837 1792204 1793588 1794730 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-836 1772125 1777012 1781859 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-835 1771865 1771918 1772021 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-834 1771306 1771440 1771620 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-833 1769315 1770536 1770564 "PID" 1770761 PID (NIL) -9 NIL 1770888 NIL) (-832 1769103 1769146 1769221 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-831 1768290 1768950 1769037 "PI" NIL PI (NIL) -8 NIL NIL 1769077) (-830 1767742 1767893 1768069 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-829 1764070 1765028 1765933 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-828 1762434 1762723 1763089 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-827 1761876 1761991 1762152 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-826 1758417 1760745 1761098 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-825 1757023 1757303 1757628 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-824 1755788 1756042 1756390 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-823 1754498 1754725 1755077 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-822 1751508 1753068 1753096 "PFECAT" 1753689 PFECAT (NIL) -9 NIL 1754066 NIL) (-821 1751131 1751296 1751503 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-820 1749955 1750237 1750538 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-819 1748137 1748524 1748954 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-818 1744107 1748063 1748132 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-817 1740010 1741157 1742024 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-816 1737942 1739031 1739072 "PERMCAT" 1739471 PERMCAT (NIL T) -9 NIL 1739768 NIL) (-815 1737638 1737685 1737808 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-814 1734087 1735768 1736413 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-813 1731556 1733842 1733963 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-812 1730425 1730688 1730729 "PDSPC" 1731262 PDSPC (NIL T) -9 NIL 1731507 NIL) (-811 1729792 1730058 1730420 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-810 1728427 1729420 1729461 "PDRING" 1729466 PDRING (NIL T) -9 NIL 1729493 NIL) (-809 1727137 1727926 1727979 "PDMOD" 1727984 PDMOD (NIL T T) -9 NIL 1728087 NIL) (-808 1726230 1726442 1726691 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-807 1725835 1725902 1725956 "PDDOM" 1726121 PDDOM (NIL T T) -9 NIL 1726201 NIL) (-806 1725687 1725723 1725830 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-805 1725473 1725512 1725601 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-804 1723790 1724544 1724843 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-803 1723479 1723542 1723651 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-802 1721617 1722047 1722498 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-801 1715237 1717066 1718358 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-800 1714868 1714941 1715073 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-799 1712570 1713250 1713731 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-798 1710774 1711202 1711605 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-797 1710220 1710468 1710509 "PATMAB" 1710616 PATMAB (NIL T) -9 NIL 1710699 NIL) (-796 1708867 1709271 1709528 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-795 1708405 1708536 1708577 "PATAB" 1708582 PATAB (NIL T) -9 NIL 1708754 NIL) (-794 1706948 1707385 1707808 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-793 1706626 1706701 1706803 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-792 1706315 1706378 1706487 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-791 1706120 1706166 1706233 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-790 1705798 1705873 1705975 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-789 1705487 1705550 1705659 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-788 1705178 1705248 1705345 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-787 1704867 1704930 1705039 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-786 1704028 1704407 1704586 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-785 1703635 1703733 1703852 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-784 1702603 1703028 1703247 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-783 1701268 1701922 1702282 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-782 1694358 1700672 1700866 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-781 1686779 1693856 1694040 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-780 1683504 1685419 1685459 "PADICCT" 1686040 PADICCT (NIL NIL) -9 NIL 1686322 NIL) (-779 1681494 1683454 1683499 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-778 1680656 1680866 1681132 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-777 1679998 1680141 1680345 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-776 1678379 1679406 1679684 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-775 1677903 1678162 1678259 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-774 1676962 1677640 1677812 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-773 1667384 1670253 1672452 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-772 1666776 1667090 1667216 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-771 1666053 1666248 1666276 "OUTBCON" 1666594 OUTBCON (NIL) -9 NIL 1666760 NIL) (-770 1665761 1665891 1666048 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-769 1665142 1665287 1665448 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-768 1664513 1664940 1665029 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-767 1663928 1664343 1664371 "OSGROUP" 1664376 OSGROUP (NIL) -9 NIL 1664398 NIL) (-766 1662892 1663153 1663438 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-765 1660161 1662767 1662887 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-764 1657302 1659912 1660038 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-763 1655320 1655848 1656408 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-762 1648662 1651202 1651242 "OREPCAT" 1653563 OREPCAT (NIL T) -9 NIL 1654665 NIL) (-761 1646688 1647622 1648657 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-760 1645885 1646156 1646184 "ORDTYPE" 1646489 ORDTYPE (NIL) -9 NIL 1646647 NIL) (-759 1645419 1645630 1645880 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-758 1644881 1645257 1645414 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-757 1644375 1644738 1644766 "ORDSET" 1644771 ORDSET (NIL) -9 NIL 1644793 NIL) (-756 1642940 1643962 1643990 "ORDRING" 1643995 ORDRING (NIL) -9 NIL 1644023 NIL) (-755 1642188 1642745 1642773 "ORDMON" 1642778 ORDMON (NIL) -9 NIL 1642799 NIL) (-754 1641492 1641654 1641846 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-753 1640703 1641211 1641239 "ORDFIN" 1641304 ORDFIN (NIL) -9 NIL 1641378 NIL) (-752 1640097 1640236 1640422 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-751 1636772 1639065 1639471 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-750 1636179 1636534 1636639 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-749 1635987 1636032 1636098 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-748 1635288 1635564 1635605 "OPERCAT" 1635816 OPERCAT (NIL T) -9 NIL 1635912 NIL) (-747 1635100 1635167 1635283 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-746 1632466 1633902 1634398 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-745 1631887 1632014 1632188 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-744 1628788 1631026 1631392 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-743 1625554 1628200 1628240 "OMSAGG" 1628301 OMSAGG (NIL T) -9 NIL 1628365 NIL) (-742 1623966 1625225 1625393 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-741 1622162 1623403 1623431 "OINTDOM" 1623436 OINTDOM (NIL) -9 NIL 1623457 NIL) (-740 1619592 1621164 1621493 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-739 1618846 1619542 1619587 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-738 1616048 1618687 1618841 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-737 1607585 1615919 1616043 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-736 1601149 1607476 1607580 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-735 1600121 1600358 1600631 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-734 1597755 1598425 1599129 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-733 1593532 1594492 1595515 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-732 1593040 1593128 1593322 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-731 1590489 1591071 1591744 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-730 1587884 1588392 1588988 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-729 1584881 1585420 1586066 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-728 1584236 1584344 1584602 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-727 1583394 1583519 1583740 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-726 1579678 1580474 1581387 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-725 1579118 1579213 1579435 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-724 1578799 1578848 1578975 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-723 1575402 1578598 1578717 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-722 1574562 1575184 1575212 "OCAMON" 1575217 OCAMON (NIL) -9 NIL 1575238 NIL) (-721 1568774 1571588 1571628 "OC" 1572723 OC (NIL T) -9 NIL 1573579 NIL) (-720 1566774 1567700 1568680 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-719 1566190 1566608 1566636 "OASGP" 1566641 OASGP (NIL) -9 NIL 1566661 NIL) (-718 1565253 1565902 1565930 "OAMONS" 1565970 OAMONS (NIL) -9 NIL 1566013 NIL) (-717 1564398 1564979 1565007 "OAMON" 1565064 OAMON (NIL) -9 NIL 1565115 NIL) (-716 1564294 1564326 1564393 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-715 1563045 1563819 1563847 "OAGROUP" 1563993 OAGROUP (NIL) -9 NIL 1564085 NIL) (-714 1562836 1562923 1563040 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-713 1562576 1562632 1562720 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-712 1557638 1559201 1560728 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-711 1554333 1555367 1556402 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-710 1553443 1553676 1553894 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-709 1542304 1545332 1547780 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-708 1536325 1541727 1541821 "NTSCAT" 1541826 NTSCAT (NIL T T T T) -9 NIL 1541864 NIL) (-707 1535666 1535845 1536038 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-706 1535359 1535422 1535529 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-705 1523026 1532979 1533789 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-704 1512035 1522891 1523021 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-703 1510755 1511080 1511437 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-702 1509591 1509855 1510213 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-701 1508758 1508891 1509107 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-700 1507076 1507395 1507801 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-699 1506789 1506823 1506947 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-698 1506608 1506643 1506712 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-697 1506384 1506574 1506603 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-696 1505948 1506015 1506192 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-695 1504234 1505311 1505566 "NNI" NIL NNI (NIL) -8 NIL NIL 1505913) (-694 1502962 1503299 1503663 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-693 1501939 1502191 1502493 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-692 1501026 1501591 1501632 "NETCLT" 1501803 NETCLT (NIL T) -9 NIL 1501884 NIL) (-691 1499930 1500197 1500478 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-690 1499729 1499772 1499847 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-689 1498260 1498648 1499068 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-688 1496893 1497859 1497887 "NASRING" 1497997 NASRING (NIL) -9 NIL 1498077 NIL) (-687 1496738 1496794 1496888 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-686 1495667 1496345 1496373 "NARNG" 1496490 NARNG (NIL) -9 NIL 1496581 NIL) (-685 1495443 1495528 1495662 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-684 1494209 1494963 1495003 "NAALG" 1495082 NAALG (NIL T) -9 NIL 1495143 NIL) (-683 1494079 1494114 1494204 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-682 1489058 1490243 1491429 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-681 1488453 1488540 1488724 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-680 1480463 1484957 1485009 "MTSCAT" 1486069 MTSCAT (NIL T T) -9 NIL 1486583 NIL) (-679 1480229 1480289 1480381 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-678 1480055 1480094 1480154 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-677 1476921 1479606 1479647 "MSETAGG" 1479652 MSETAGG (NIL T) -9 NIL 1479686 NIL) (-676 1473191 1475966 1476285 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-675 1469465 1471288 1472028 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-674 1469102 1469175 1469304 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-673 1468755 1468796 1468940 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-672 1466620 1466957 1467388 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-671 1460018 1466519 1466615 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-670 1459543 1459584 1459792 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-669 1459102 1459151 1459334 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-668 1458376 1458469 1458688 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1456993 1457354 1457744 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-666 1456514 1456581 1456620 "MONOPC" 1456680 MONOPC (NIL T) -9 NIL 1456899 NIL) (-665 1455965 1456301 1456429 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-664 1455107 1455486 1455514 "MONOID" 1455732 MONOID (NIL) -9 NIL 1455876 NIL) (-663 1454766 1454916 1455102 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-662 1443704 1450574 1450633 "MONOGEN" 1451307 MONOGEN (NIL T T) -9 NIL 1451763 NIL) (-661 1441716 1442602 1443585 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-660 1440430 1440974 1441002 "MONADWU" 1441393 MONADWU (NIL) -9 NIL 1441628 NIL) (-659 1439978 1440178 1440425 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-658 1439255 1439556 1439584 "MONAD" 1439791 MONAD (NIL) -9 NIL 1439903 NIL) (-657 1439022 1439118 1439250 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-656 1437412 1438182 1438461 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-655 1436546 1437073 1437113 "MODULE" 1437118 MODULE (NIL T) -9 NIL 1437156 NIL) (-654 1436225 1436351 1436541 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-653 1433936 1434822 1435136 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-652 1431115 1432532 1433045 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-651 1429749 1430323 1430599 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-650 1418968 1428414 1428827 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-649 1415924 1417968 1418237 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-648 1415008 1415375 1415565 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-647 1414577 1414626 1414805 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-646 1412402 1413398 1413438 "MLO" 1413855 MLO (NIL T) -9 NIL 1414095 NIL) (-645 1410283 1410810 1411405 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-644 1409751 1409847 1410001 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-643 1409421 1409497 1409620 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-642 1408633 1408819 1409047 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-641 1408126 1408242 1408398 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-640 1407498 1407612 1407797 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-639 1406525 1406798 1407075 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-638 1405958 1406046 1406217 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-637 1403116 1403995 1404874 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-636 1401783 1402131 1402484 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-635 1398444 1400907 1400948 "MDAGG" 1401205 MDAGG (NIL T) -9 NIL 1401350 NIL) (-634 1397718 1397882 1398082 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-633 1396796 1397082 1397312 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-632 1394893 1395470 1396031 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-631 1390799 1394483 1394730 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-630 1387148 1387917 1388651 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-629 1385901 1386070 1386399 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-628 1375552 1379007 1379083 "MATCAT" 1384071 MATCAT (NIL T T T) -9 NIL 1385517 NIL) (-627 1372833 1374139 1375547 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-626 1371234 1371594 1371978 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-625 1370367 1370564 1370786 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-624 1369118 1369444 1369771 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-623 1368280 1368682 1368858 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-622 1367949 1368013 1368136 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-621 1367597 1367670 1367784 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-620 1367132 1367247 1367389 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-619 1365341 1366109 1366410 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-618 1364835 1365137 1365227 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-617 1358348 1363150 1363191 "LZSTAGG" 1363968 LZSTAGG (NIL T) -9 NIL 1364258 NIL) (-616 1355467 1356901 1358343 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-615 1352854 1353820 1354303 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-614 1352435 1352714 1352788 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-613 1344752 1352296 1352430 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-612 1344115 1344260 1344488 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-611 1341599 1342297 1343009 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-610 1339711 1340034 1340482 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-609 1333015 1338780 1338821 "LSAGG" 1338883 LSAGG (NIL T) -9 NIL 1338961 NIL) (-608 1330709 1331808 1333010 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-607 1328189 1330058 1330307 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-606 1327856 1327947 1328070 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-605 1327527 1327606 1327634 "LOGIC" 1327745 LOGIC (NIL) -9 NIL 1327827 NIL) (-604 1327422 1327451 1327522 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-603 1326741 1326899 1327092 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-602 1325526 1325775 1326126 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-601 1321348 1324147 1324187 "LODOCAT" 1324619 LODOCAT (NIL T) -9 NIL 1324830 NIL) (-600 1321141 1321217 1321343 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-599 1318141 1321018 1321136 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-598 1315239 1318091 1318136 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-597 1312326 1315169 1315234 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-596 1311379 1311554 1311856 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-595 1309511 1310641 1310894 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-594 1304610 1307670 1307711 "LNAGG" 1308573 LNAGG (NIL T) -9 NIL 1309008 NIL) (-593 1303997 1304264 1304605 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-592 1300569 1301510 1302147 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-591 1299831 1300336 1300376 "LMODULE" 1300381 LMODULE (NIL T) -9 NIL 1300407 NIL) (-590 1297162 1299567 1299690 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-589 1296730 1296941 1296982 "LLINSET" 1297043 LLINSET (NIL T) -9 NIL 1297087 NIL) (-588 1296406 1296666 1296725 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-587 1296005 1296085 1296224 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-586 1294456 1294804 1295203 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-585 1293627 1293823 1294051 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-584 1286826 1292883 1293137 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-583 1286403 1286636 1286677 "LINSET" 1286682 LINSET (NIL T) -9 NIL 1286715 NIL) (-582 1285304 1286026 1286193 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-581 1283570 1284325 1284365 "LINEXP" 1284851 LINEXP (NIL T) -9 NIL 1285124 NIL) (-580 1282192 1283179 1283360 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-579 1281019 1281291 1281593 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-578 1280232 1280821 1280931 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-577 1277782 1278504 1279254 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-576 1276412 1276709 1277100 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-575 1275205 1275807 1275847 "LIECAT" 1275987 LIECAT (NIL T) -9 NIL 1276138 NIL) (-574 1275079 1275112 1275200 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-573 1269335 1274769 1274997 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-572 1259751 1269011 1269167 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-571 1256203 1257152 1258087 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-570 1254827 1255735 1255763 "LFCAT" 1255970 LFCAT (NIL) -9 NIL 1256109 NIL) (-569 1253066 1253396 1253741 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-568 1250583 1251248 1251929 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-567 1247595 1248573 1249076 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-566 1247086 1247389 1247480 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-565 1245793 1246117 1246517 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-564 1245059 1245144 1245370 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-563 1240062 1243627 1244163 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-562 1239687 1239737 1239897 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-561 1238458 1239231 1239271 "LALG" 1239332 LALG (NIL T) -9 NIL 1239390 NIL) (-560 1238241 1238318 1238453 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-559 1236094 1237509 1237760 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-558 1235923 1235953 1235994 "KVTFROM" 1236056 KVTFROM (NIL T) -9 NIL NIL NIL) (-557 1234739 1235454 1235643 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-556 1234568 1234598 1234639 "KRCFROM" 1234701 KRCFROM (NIL T) -9 NIL NIL NIL) (-555 1233670 1233867 1234162 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-554 1233499 1233529 1233570 "KONVERT" 1233632 KONVERT (NIL T) -9 NIL NIL NIL) (-553 1233328 1233358 1233399 "KOERCE" 1233461 KOERCE (NIL T) -9 NIL NIL NIL) (-552 1232898 1232991 1233123 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-551 1230951 1231845 1232217 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-550 1222164 1228790 1228844 "KDAGG" 1229220 KDAGG (NIL T T) -9 NIL 1229446 NIL) (-549 1221629 1221861 1222159 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-548 1214608 1221421 1221567 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-547 1214258 1214540 1214603 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-546 1213228 1213727 1213976 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-545 1212354 1212803 1213008 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-544 1211218 1211710 1212010 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-543 1210500 1210899 1211060 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-542 1210210 1210446 1210495 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-541 1204465 1209900 1210128 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-540 1203883 1204216 1204336 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-539 1200049 1202060 1202114 "IXAGG" 1203041 IXAGG (NIL T T) -9 NIL 1203498 NIL) (-538 1199255 1199626 1200044 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-537 1198222 1198497 1198760 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-536 1196884 1197091 1197384 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-535 1195835 1196057 1196340 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-534 1195510 1195573 1195696 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-533 1194772 1195144 1195318 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-532 1192748 1194048 1194322 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-531 1182296 1188065 1189222 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-530 1181541 1181693 1181929 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-529 1181032 1181335 1181426 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-528 1180325 1180416 1180629 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-527 1179457 1179682 1179922 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-526 1177870 1178251 1178679 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-525 1177655 1177699 1177775 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-524 1176505 1176802 1177097 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-523 1175778 1176129 1176280 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-522 1174981 1175112 1175325 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-521 1173136 1173633 1174177 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-520 1170217 1171485 1172174 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-519 1170042 1170082 1170142 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-518 1166040 1169968 1170037 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-517 1164043 1165979 1166035 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-516 1163414 1163713 1163843 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-515 1162867 1163155 1163287 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-514 1161948 1162573 1162699 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-513 1161358 1161852 1161880 "IOBCON" 1161885 IOBCON (NIL) -9 NIL 1161906 NIL) (-512 1160929 1160993 1161175 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-511 1152973 1155344 1157669 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-510 1150084 1150867 1151731 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-509 1149761 1149858 1149975 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-508 1147203 1149697 1149756 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-507 1145315 1145844 1146411 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-506 1144817 1144931 1145071 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-505 1143201 1143607 1144069 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-504 1140980 1141574 1142185 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-503 1138353 1138963 1139683 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-502 1137757 1137915 1138123 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-501 1137276 1137362 1137550 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-500 1135481 1136002 1136459 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-499 1128563 1130216 1131945 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-498 1127929 1128091 1128264 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-497 1125802 1126266 1126810 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-496 1123928 1124878 1124906 "INTDOM" 1125205 INTDOM (NIL) -9 NIL 1125410 NIL) (-495 1123481 1123683 1123923 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-494 1119288 1121760 1121814 "INTCAT" 1122610 INTCAT (NIL T) -9 NIL 1122926 NIL) (-493 1118853 1118973 1119100 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-492 1117693 1117865 1118171 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-491 1117266 1117362 1117519 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-490 1108549 1117173 1117261 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-489 1107847 1108402 1108467 "INT8" NIL INT8 (NIL) -8 NIL NIL 1108501) (-488 1107144 1107699 1107764 "INT64" NIL INT64 (NIL) -8 NIL NIL 1107798) (-487 1106441 1106996 1107061 "INT32" NIL INT32 (NIL) -8 NIL NIL 1107095) (-486 1105738 1106293 1106358 "INT16" NIL INT16 (NIL) -8 NIL NIL 1106392) (-485 1102201 1105657 1105733 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-484 1096258 1099741 1099769 "INS" 1100699 INS (NIL) -9 NIL 1101358 NIL) (-483 1094320 1095238 1096185 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-482 1093379 1093602 1093877 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-481 1092593 1092734 1092931 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-480 1091583 1091724 1091961 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-479 1090735 1090899 1091159 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-478 1090015 1090130 1090318 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-477 1088754 1089023 1089347 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-476 1088034 1088175 1088358 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-475 1087697 1087769 1087867 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-474 1084775 1086261 1086784 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-473 1084374 1084481 1084595 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-472 1083530 1084175 1084276 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-471 1082380 1082648 1082969 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-470 1081370 1082310 1082375 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-469 1080995 1081075 1081192 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-468 1079909 1080454 1080658 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-467 1076004 1077059 1078002 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-466 1074858 1075181 1075209 "INBCON" 1075722 INBCON (NIL) -9 NIL 1075988 NIL) (-465 1074312 1074577 1074853 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-464 1073806 1074108 1074198 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-463 1073263 1073572 1073677 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-462 1072103 1072242 1072557 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-461 1070527 1070794 1071131 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-460 1065370 1070458 1070522 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-459 1064750 1065084 1065199 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-458 1059710 1064188 1064374 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-457 1058740 1059632 1059705 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-456 1058312 1058389 1058443 "IEVALAB" 1058650 IEVALAB (NIL T T) -9 NIL NIL NIL) (-455 1058067 1058147 1058307 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-454 1057452 1057679 1057836 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-453 1056445 1057372 1057447 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-452 1055508 1056365 1056440 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-451 1054590 1055237 1055374 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-450 1052953 1053524 1053575 "IDPC" 1054081 IDPC (NIL T T) -9 NIL 1054394 NIL) (-449 1052241 1052875 1052948 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-448 1051411 1052163 1052236 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-447 1051104 1051317 1051377 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-446 1050808 1050848 1050887 "IDEMOPC" 1050892 IDEMOPC (NIL T) -9 NIL 1051029 NIL) (-445 1047879 1048760 1049652 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-444 1041505 1042782 1043821 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-443 1040767 1040897 1041096 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-442 1039940 1040439 1040577 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-441 1038329 1038660 1039051 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-440 1034251 1038285 1038324 "IBITS" NIL IBITS (NIL NIL) -8 NIL NIL NIL) (-439 1031509 1032133 1032828 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1029735 1030215 1030748 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1027717 1029641 1029730 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1023731 1027655 1027712 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1017310 1022695 1023163 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1016878 1016941 1017114 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1016370 1016519 1016547 "HYPCAT" 1016754 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1016026 1016179 1016365 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1015639 1015884 1015967 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1015472 1015521 1015562 "HOMOTOP" 1015567 HOMOTOP (NIL T) -9 NIL 1015600 NIL) (-429 1012050 1013420 1013461 "HOAGG" 1014432 HOAGG (NIL T) -9 NIL 1015151 NIL) (-428 1011056 1011526 1012045 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 1004256 1010781 1010929 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 1003191 1003449 1003712 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 1002126 1003056 1003186 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 1000473 1001959 1002047 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 999788 1000140 1000273 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 993395 999721 999783 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 986534 993131 993282 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 985987 986144 986307 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 977287 985904 985982 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 976778 977081 977172 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 974328 976565 976744 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 969874 974211 974323 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 961151 969771 969869 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 953088 960520 960775 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 952112 952621 952649 "GROUP" 952852 GROUP (NIL) -9 NIL 952986 NIL) (-412 951655 951856 952107 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 950327 950666 951053 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 949149 949506 949557 "GRMOD" 950086 GRMOD (NIL T T) -9 NIL 950252 NIL) (-409 948968 949016 949144 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 945091 946302 947302 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 943813 944137 944452 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 943366 943494 943635 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 942439 942938 942989 "GRALG" 943142 GRALG (NIL T T) -9 NIL 943232 NIL) (-404 942158 942259 942434 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 939039 941851 942016 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 938452 938515 938772 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 934306 935202 935727 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 933481 933683 933921 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 928484 929411 930430 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 928232 928289 928378 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 927714 927803 927968 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 927223 927264 927477 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 926024 926307 926611 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 919299 925714 925875 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 909082 914089 915193 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 907134 908237 908265 "GCDDOM" 908520 GCDDOM (NIL) -9 NIL 908677 NIL) (-391 906757 906914 907129 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 897550 900020 902408 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 895685 896010 896428 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 894626 894815 895082 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 893497 893704 894008 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 892960 893102 893250 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 891572 891920 892233 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 890117 890438 890760 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 887743 888099 888504 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 880995 882656 884234 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 880647 880868 880936 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 880271 880492 880573 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 878368 879051 879511 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 876961 877268 877660 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 875616 875975 876299 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 874919 875043 875230 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 873893 874159 874506 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 871551 872081 872563 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 871134 871194 871363 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 869434 870348 870651 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 868582 868716 868939 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 867753 867914 868141 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 863869 866667 866708 "FSAGG" 867078 FSAGG (NIL T) -9 NIL 867339 NIL) (-368 862223 862982 863774 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 860179 860475 861019 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 859226 859408 859708 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 858907 858956 859083 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 839063 848564 848605 "FS" 852475 FS (NIL T) -9 NIL 854753 NIL) (-363 831294 834787 838766 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 830828 830955 831107 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 825351 828509 828549 "FRNAALG" 829869 FRNAALG (NIL T) -9 NIL 830467 NIL) (-360 822092 823343 824601 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 821773 821822 821949 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 820260 820817 821111 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 819546 819639 819926 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 817380 818146 818462 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 816489 816932 816973 "FRETRCT" 816978 FRETRCT (NIL T) -9 NIL 817149 NIL) (-354 815862 816140 816484 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 812606 814126 814185 "FRAMALG" 815067 FRAMALG (NIL T T) -9 NIL 815359 NIL) (-352 811202 811753 812383 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 810895 810958 811065 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 804536 810700 810890 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 804229 804292 804399 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 796537 801108 802436 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 790315 793818 793846 "FPS" 794965 FPS (NIL) -9 NIL 795521 NIL) (-346 789872 790005 790169 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 786682 788725 788753 "FPC" 788978 FPC (NIL) -9 NIL 789120 NIL) (-344 786528 786580 786677 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 785305 786014 786055 "FPATMAB" 786060 FPATMAB (NIL T) -9 NIL 786212 NIL) (-342 783735 784331 784678 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 783310 783368 783541 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 781813 782708 782882 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 780428 780933 780961 "FNCAT" 781418 FNCAT (NIL) -9 NIL 781675 NIL) (-338 779885 780395 780423 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 778472 779834 779880 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 775060 776418 776459 "FMONCAT" 777676 FMONCAT (NIL T) -9 NIL 778280 NIL) (-335 771918 772996 773049 "FMCAT" 774230 FMCAT (NIL T T) -9 NIL 774722 NIL) (-334 770618 771741 771840 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 769666 770466 770613 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 767853 768305 768799 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 765788 766324 766902 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 759174 764125 764739 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 757655 758756 758796 "FLINEXP" 758801 FLINEXP (NIL T) -9 NIL 758894 NIL) (-328 757064 757323 757650 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 756279 756438 756659 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 753162 754241 754293 "FLALG" 755520 FLALG (NIL T T) -9 NIL 755987 NIL) (-325 752333 752494 752721 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 745874 749732 749773 "FLAGG" 751028 FLAGG (NIL T) -9 NIL 751675 NIL) (-323 744982 745386 745869 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 741543 742807 742866 "FINRALG" 743994 FINRALG (NIL T T) -9 NIL 744502 NIL) (-321 740934 741199 741538 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 740232 740528 740556 "FINITE" 740752 FINITE (NIL) -9 NIL 740859 NIL) (-319 740140 740166 740227 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 737597 738818 738859 "FINAGG" 739489 FINAGG (NIL T) -9 NIL 739801 NIL) (-317 737037 737296 737592 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 728998 731589 731629 "FINAALG" 735281 FINAALG (NIL T) -9 NIL 736719 NIL) (-315 725265 726510 727633 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 723817 724236 724290 "FILECAT" 724974 FILECAT (NIL T T) -9 NIL 725190 NIL) (-313 723168 723642 723745 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 720416 722294 722322 "FIELD" 722362 FIELD (NIL) -9 NIL 722442 NIL) (-311 719441 719902 720411 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 717445 718391 718737 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 716688 716869 717088 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 711958 716626 716683 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 711620 711687 711822 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 711160 711202 711411 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 707840 708717 709494 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 703124 707772 707835 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 697803 702613 702803 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 692284 697084 697342 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 686491 691735 691946 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 685514 685724 686039 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 680954 683659 683687 "FFIELDC" 684306 FFIELDC (NIL) -9 NIL 684681 NIL) (-298 680023 680463 680949 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 679638 679696 679820 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 677782 678305 678822 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 672876 677581 677682 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 667976 672665 672772 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 662642 667767 667875 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 662096 662145 662380 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 640671 651705 651791 "FFCAT" 656941 FFCAT (NIL T T T) -9 NIL 658377 NIL) (-290 636911 638137 639443 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 631754 636842 636906 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 630646 631115 631156 "FEVALAB" 631240 FEVALAB (NIL T) -9 NIL 631501 NIL) (-287 630051 630303 630641 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 626878 627789 627904 "FDIVCAT" 629471 FDIVCAT (NIL T T T T) -9 NIL 629907 NIL) (-285 626672 626704 626873 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 625979 626072 626349 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 624465 625463 625666 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 623558 623942 624144 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 622680 623169 623309 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 614267 618910 618950 "FAXF" 620751 FAXF (NIL T) -9 NIL 621441 NIL) (-279 612183 612987 613802 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 607200 611705 611879 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 601658 604081 604133 "FAMR" 605144 FAMR (NIL T T) -9 NIL 605603 NIL) (-276 600857 601222 601653 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 599878 600799 600852 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 597472 598351 598404 "FAMONC" 599345 FAMONC (NIL T T) -9 NIL 599730 NIL) (-273 596028 597330 597467 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 594108 594469 594871 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 593385 593582 593804 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 585245 592832 593031 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 583264 583834 584420 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 580166 580808 581528 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 575323 576030 576835 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 575012 575075 575184 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 559805 574061 574487 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 550332 559125 559413 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 549826 550128 550218 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 549602 549792 549821 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 549291 549359 549472 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 548808 548950 548991 "EVALAB" 549161 EVALAB (NIL T) -9 NIL 549265 NIL) (-259 548436 548582 548803 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 545479 547074 547102 "EUCDOM" 547656 EUCDOM (NIL) -9 NIL 548005 NIL) (-257 544406 544899 545474 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 544131 544187 544287 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 543819 543883 543992 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 537590 539490 539518 "ES" 542260 ES (NIL) -9 NIL 543644 NIL) (-253 534105 535637 537429 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 533453 533606 533782 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 524759 533383 533448 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524448 524511 524620 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 518075 521200 522633 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514378 515474 516567 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 513207 513557 513862 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 512092 512823 512851 "ENTIRER" 512856 ENTIRER (NIL) -9 NIL 512900 NIL) (-245 511981 512015 512087 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508614 510411 510760 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507706 507917 507971 "ELTAGG" 508351 ELTAGG (NIL T T) -9 NIL 508562 NIL) (-242 507486 507560 507701 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 507232 507267 507321 "ELTAB" 507405 ELTAB (NIL T T) -9 NIL 507457 NIL) (-240 506483 506653 506852 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 506207 506281 506309 "ELEMFUN" 506414 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 506107 506134 506202 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500657 504148 504189 "ELAGG" 505126 ELAGG (NIL T) -9 NIL 505586 NIL) (-236 499455 499993 500652 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 498873 499040 499196 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 497786 498105 498384 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 491179 493177 494004 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 485158 487154 487964 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 482972 483378 483849 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 473972 475885 477426 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 473085 473586 473735 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 471783 472457 472497 "DVARCAT" 472780 DVARCAT (NIL T) -9 NIL 472920 NIL) (-227 471202 471466 471778 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 463269 471070 471197 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461607 462398 462439 "DSEXT" 462802 DSEXT (NIL T) -9 NIL 463096 NIL) (-224 460412 460936 461602 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 460136 460201 460299 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456287 457503 458634 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 451933 453288 454352 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450608 450969 451355 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450294 450353 450471 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 449269 449567 449857 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 448854 448929 449079 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 441267 443379 445494 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 436784 437803 438882 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433514 435430 435471 "DQAGG" 436100 DQAGG (NIL T) -9 NIL 436373 NIL) (-213 420057 427697 427779 "DPOLCAT" 429616 DPOLCAT (NIL T T T T) -9 NIL 430159 NIL) (-212 416465 418113 420052 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409623 416363 416460 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402690 409452 409618 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 402283 402543 402632 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401697 402145 402225 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400983 401308 401459 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 394122 400719 400870 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391871 393188 393228 "DMEXT" 393233 DMEXT (NIL T) -9 NIL 393408 NIL) (-204 391527 391589 391733 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 385005 391012 391202 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381675 383828 383869 "DLAGG" 384419 DLAGG (NIL T) -9 NIL 384648 NIL) (-201 380026 380897 380925 "DIVRING" 381017 DIVRING (NIL) -9 NIL 381100 NIL) (-200 379477 379721 380021 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377905 378322 378728 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376942 377163 377428 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370569 376874 376937 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 359021 365329 365382 "DIRPCAT" 365638 DIRPCAT (NIL NIL T) -9 NIL 366513 NIL) (-195 357027 357797 358684 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 356474 356640 356826 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 353024 355360 355401 "DIOPS" 355833 DIOPS (NIL T) -9 NIL 356059 NIL) (-192 352684 352828 353019 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351691 352437 352465 "DIOID" 352470 DIOID (NIL) -9 NIL 352492 NIL) (-190 350519 351348 351376 "DIFRING" 351381 DIFRING (NIL) -9 NIL 351402 NIL) (-189 350155 350253 350281 "DIFFSPC" 350400 DIFFSPC (NIL) -9 NIL 350475 NIL) (-188 349896 349998 350150 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348799 349424 349464 "DIFFMOD" 349469 DIFFMOD (NIL T) -9 NIL 349566 NIL) (-186 348483 348540 348581 "DIFFDOM" 348702 DIFFDOM (NIL T) -9 NIL 348770 NIL) (-185 348364 348394 348478 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 346037 347558 347598 "DIFEXT" 347603 DIFEXT (NIL T) -9 NIL 347755 NIL) (-183 343202 345538 345579 "DIAGG" 345584 DIAGG (NIL T) -9 NIL 345604 NIL) (-182 342758 342948 343197 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 338104 341948 342225 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 334562 335615 336625 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 329112 333716 334043 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 327678 327970 328345 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324798 326050 326446 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 322671 324629 324718 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 322054 322199 322381 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 319372 320096 320896 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 317481 317939 318501 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 316864 317197 317311 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 310064 316589 316737 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307984 308494 308998 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 307623 307672 307823 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 306882 307444 307535 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304906 305348 305708 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 304198 304487 304633 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 303649 303795 303947 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 301011 301804 302531 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 300450 300596 300767 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 298522 298833 299200 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 298079 298334 298435 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 297280 297663 297691 "CTORCAT" 297872 CTORCAT (NIL) -9 NIL 297984 NIL) (-159 296983 297117 297275 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 296476 296733 296841 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295892 296323 296396 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 295351 295468 295621 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 291745 292501 293256 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 291236 291539 291630 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 290455 290664 290892 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289959 290064 290268 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 289712 289746 289852 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL NIL) (-150 286651 287413 288131 "COORDSYS" NIL COORDSYS (NIL T) -7 NIL NIL NIL) (-149 286170 286312 286451 "CONTOUR" NIL CONTOUR (NIL) -8 NIL NIL NIL) (-148 282063 284633 285125 "CONTFRAC" NIL CONTFRAC (NIL T) -8 NIL NIL NIL) (-147 281937 281964 281992 "CONDUIT" 282029 CONDUIT (NIL) -9 NIL NIL NIL) (-146 280816 281547 281575 "COMRING" 281580 COMRING (NIL) -9 NIL 281630 NIL) (-145 279981 280348 280526 "COMPPROP" NIL COMPPROP (NIL) -8 NIL NIL NIL) (-144 279677 279718 279846 "COMPLPAT" NIL COMPLPAT (NIL T T T) -7 NIL NIL NIL) (-143 279370 279433 279540 "COMPLEX2" NIL COMPLEX2 (NIL T T) -7 NIL NIL NIL) (-142 268212 279320 279365 "COMPLEX" NIL COMPLEX (NIL T) -8 NIL NIL NIL) (-141 267673 267812 267972 "COMPILER" NIL COMPILER (NIL) -7 NIL NIL NIL) (-140 267426 267467 267565 "COMPFACT" NIL COMPFACT (NIL T T) -7 NIL NIL NIL) (-139 248857 261107 261147 "COMPCAT" 262148 COMPCAT (NIL T) -9 NIL 263490 NIL) (-138 241395 244908 248501 "COMPCAT-" NIL COMPCAT- (NIL T T) -7 NIL NIL NIL) (-137 241154 241188 241290 "COMMUPC" NIL COMMUPC (NIL T T T) -7 NIL NIL NIL) (-136 240984 241023 241081 "COMMONOP" NIL COMMONOP (NIL) -7 NIL NIL NIL) (-135 240565 240844 240918 "COMMAAST" NIL COMMAAST (NIL) -8 NIL NIL NIL) (-134 240142 240383 240470 "COMM" NIL COMM (NIL) -8 NIL NIL NIL) (-133 239337 239585 239613 "COMBOPC" 239951 COMBOPC (NIL) -9 NIL 240126 NIL) (-132 238401 238653 238895 "COMBINAT" NIL COMBINAT (NIL T) -7 NIL NIL NIL) (-131 235333 236017 236640 "COMBF" NIL COMBF (NIL T T) -7 NIL NIL NIL) (-130 234213 234664 234899 "COLOR" NIL COLOR (NIL) -8 NIL NIL NIL) (-129 233704 234007 234098 "COLONAST" NIL COLONAST (NIL) -8 NIL NIL NIL) (-128 233391 233444 233569 "CMPLXRT" NIL CMPLXRT (NIL T T) -7 NIL NIL NIL) (-127 232861 233171 233269 "CLLCTAST" NIL CLLCTAST (NIL) -8 NIL NIL NIL) (-126 229381 230451 231531 "CLIP" NIL CLIP (NIL) -7 NIL NIL NIL) (-125 227676 228661 228899 "CLIF" NIL CLIF (NIL NIL T NIL) -8 NIL NIL NIL) (-124 223792 225796 225837 "CLAGG" 226763 CLAGG (NIL T) -9 NIL 227296 NIL) (-123 222685 223212 223787 "CLAGG-" NIL CLAGG- (NIL T T) -7 NIL NIL NIL) (-122 222314 222405 222545 "CINTSLPE" NIL CINTSLPE (NIL T T) -7 NIL NIL NIL) (-121 220251 220758 221306 "CHVAR" NIL CHVAR (NIL T T T) -7 NIL NIL NIL) (-120 219212 219943 219971 "CHARZ" 219976 CHARZ (NIL) -9 NIL 219990 NIL) (-119 219006 219052 219130 "CHARPOL" NIL CHARPOL (NIL T) -7 NIL NIL NIL) (-118 217845 218608 218636 "CHARNZ" 218697 CHARNZ (NIL) -9 NIL 218745 NIL) (-117 215323 216420 216943 "CHAR" NIL CHAR (NIL) -8 NIL NIL NIL) (-116 215031 215110 215138 "CFCAT" 215249 CFCAT (NIL) -9 NIL NIL NIL) (-115 214374 214503 214685 "CDEN" NIL CDEN (NIL T T T) -7 NIL NIL NIL) (-114 210516 213787 214067 "CCLASS" NIL CCLASS (NIL) -8 NIL NIL NIL) (-113 209894 210081 210258 "CATEGORY" NIL -10 (NIL) -8 NIL NIL NIL) (-112 209422 209841 209889 "CATCTOR" NIL CATCTOR (NIL) -8 NIL NIL NIL) (-111 208895 209204 209301 "CATAST" NIL CATAST (NIL) -8 NIL NIL NIL) (-110 208386 208689 208780 "CASEAST" NIL CASEAST (NIL) -8 NIL NIL NIL) (-109 207635 207795 208016 "CARTEN2" NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL NIL) (-108 203735 204992 205700 "CARTEN" NIL CARTEN (NIL NIL NIL T) -8 NIL NIL NIL) (-107 202101 203132 203383 "CARD" NIL CARD (NIL) -8 NIL NIL NIL) (-106 201682 201961 202035 "CAPSLAST" NIL CAPSLAST (NIL) -8 NIL NIL NIL) (-105 201116 201369 201397 "CACHSET" 201529 CACHSET (NIL) -9 NIL 201607 NIL) (-104 200468 200883 200911 "CABMON" 200961 CABMON (NIL) -9 NIL 201017 NIL) (-103 199998 200262 200372 "BYTEORD" NIL BYTEORD (NIL) -8 NIL NIL NIL) (-102 195385 199666 199827 "BYTEBUF" NIL BYTEBUF (NIL) -8 NIL NIL NIL) (-101 194355 195059 195194 "BYTE" NIL BYTE (NIL) -8 NIL NIL 195357) (-100 191979 194122 194228 "BTREE" NIL BTREE (NIL T) -8 NIL NIL NIL) (-99 189563 191722 191841 "BTOURN" NIL BTOURN (NIL T) -8 NIL NIL NIL) (-98 186936 188987 189026 "BTCAT" 189093 BTCAT (NIL T) -9 NIL 189171 NIL) (-97 186687 186785 186931 "BTCAT-" NIL BTCAT- (NIL T T) -7 NIL NIL NIL) (-96 181930 185899 185925 "BTAGG" 186036 BTAGG (NIL) -9 NIL 186144 NIL) (-95 181561 181722 181925 "BTAGG-" NIL BTAGG- (NIL T) -7 NIL NIL NIL) (-94 178787 181042 181243 "BSTREE" NIL BSTREE (NIL T) -8 NIL NIL NIL) (-93 178057 178209 178387 "BRILL" NIL BRILL (NIL T) -7 NIL NIL NIL) (-92 174594 176763 176802 "BRAGG" 177443 BRAGG (NIL T) -9 NIL 177700 NIL) (-91 173549 174044 174589 "BRAGG-" NIL BRAGG- (NIL T T) -7 NIL NIL NIL) (-90 166083 173054 173235 "BPADICRT" NIL BPADICRT (NIL NIL) -8 NIL NIL NIL) (-89 164075 166035 166078 "BPADIC" NIL BPADIC (NIL NIL) -8 NIL NIL NIL) (-88 163808 163844 163955 "BOUNDZRO" NIL BOUNDZRO (NIL T T) -7 NIL NIL NIL) (-87 162047 162480 162928 "BOP1" NIL BOP1 (NIL T) -7 NIL NIL NIL) (-86 158013 159429 160319 "BOP" NIL BOP (NIL) -8 NIL NIL NIL) (-85 156889 157780 157902 "BOOLEAN" NIL BOOLEAN (NIL) -8 NIL NIL NIL) (-84 156475 156632 156658 "BOOLE" 156766 BOOLE (NIL) -9 NIL 156847 NIL) (-83 156268 156349 156470 "BOOLE-" NIL BOOLE- (NIL T) -7 NIL NIL NIL) (-82 155406 155933 155983 "BMODULE" 155988 BMODULE (NIL T T) -9 NIL 156052 NIL) (-81 151176 155263 155332 "BITS" NIL BITS (NIL) -8 NIL NIL NIL) (-80 150989 151029 151068 "BINOPC" 151073 BINOPC (NIL T) -9 NIL 151118 NIL) (-79 150531 150804 150906 "BINOP" NIL BINOP (NIL T) -8 NIL NIL NIL) (-78 150052 150196 150334 "BINDING" NIL BINDING (NIL) -8 NIL NIL NIL) (-77 143258 149782 149927 "BINARY" NIL BINARY (NIL) -8 NIL NIL NIL) (-76 140996 142487 142526 "BGAGG" 142782 BGAGG (NIL T) -9 NIL 142919 NIL) (-75 140865 140903 140991 "BGAGG-" NIL BGAGG- (NIL T T) -7 NIL NIL NIL) (-74 139716 139917 140202 "BEZOUT" NIL BEZOUT (NIL T T T T T) -7 NIL NIL NIL) (-73 136518 138885 139201 "BBTREE" NIL BBTREE (NIL T) -8 NIL NIL NIL) (-72 136103 136196 136222 "BASTYPE" 136393 BASTYPE (NIL) -9 NIL 136489 NIL) (-71 135873 135969 136098 "BASTYPE-" NIL BASTYPE- (NIL T) -7 NIL NIL NIL) (-70 135388 135476 135626 "BALFACT" NIL BALFACT (NIL T T) -7 NIL NIL NIL) (-69 134287 134962 135147 "AUTOMOR" NIL AUTOMOR (NIL T) -8 NIL NIL NIL) (-68 134013 134018 134044 "ATTREG" 134049 ATTREG (NIL) -9 NIL NIL NIL) (-67 133618 133890 133955 "ATTRAST" NIL ATTRAST (NIL) -8 NIL NIL NIL) (-66 133118 133267 133293 "ATRIG" 133494 ATRIG (NIL) -9 NIL NIL NIL) (-65 132973 133026 133113 "ATRIG-" NIL ATRIG- (NIL T) -7 NIL NIL NIL) (-64 132543 132774 132800 "ASTCAT" 132805 ASTCAT (NIL) -9 NIL 132835 NIL) (-63 132342 132419 132538 "ASTCAT-" NIL ASTCAT- (NIL T) -7 NIL NIL NIL) (-62 130654 132175 132263 "ASTACK" NIL ASTACK (NIL T) -8 NIL NIL NIL) (-61 129461 129774 130139 "ASSOCEQ" NIL ASSOCEQ (NIL T T) -7 NIL NIL NIL) (-60 127421 129391 129456 "ARRAY2" NIL ARRAY2 (NIL T) -8 NIL NIL NIL) (-59 126612 126803 127024 "ARRAY12" NIL ARRAY12 (NIL T T) -7 NIL NIL NIL) (-58 122352 126343 126457 "ARRAY1" NIL ARRAY1 (NIL T) -8 NIL NIL NIL) (-57 116792 118690 118765 "ARR2CAT" 121277 ARR2CAT (NIL T T T) -9 NIL 121995 NIL) (-56 115753 116235 116787 "ARR2CAT-" NIL ARR2CAT- (NIL T T T T) -7 NIL NIL NIL) (-55 115121 115492 115614 "ARITY" NIL ARITY (NIL) -8 NIL NIL NIL) (-54 114053 114221 114517 "APPRULE" NIL APPRULE (NIL T T T) -7 NIL NIL NIL) (-53 113754 113808 113926 "APPLYORE" NIL APPLYORE (NIL T T T) -7 NIL NIL NIL) (-52 113137 113283 113439 "ANY1" NIL ANY1 (NIL T) -7 NIL NIL NIL) (-51 112542 112832 112952 "ANY" NIL ANY (NIL) -8 NIL NIL NIL) (-50 110110 111271 111594 "ANTISYM" NIL ANTISYM (NIL T NIL) -8 NIL NIL NIL) (-49 109635 109895 109991 "ANON" NIL ANON (NIL) -8 NIL NIL NIL) (-48 103330 108697 109139 "AN" NIL AN (NIL) -8 NIL NIL NIL) (-47 98864 100527 100577 "AMR" 101315 AMR (NIL T T) -9 NIL 101912 NIL) (-46 98218 98498 98859 "AMR-" NIL AMR- (NIL T T T) -7 NIL NIL NIL) (-45 79726 98152 98213 "ALIST" NIL ALIST (NIL T T) -8 NIL NIL NIL) (-44 76129 79402 79571 "ALGSC" NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-43 73139 73799 74406 "ALGPKG" NIL ALGPKG (NIL T T) -7 NIL NIL NIL) (-42 72518 72631 72815 "ALGMFACT" NIL ALGMFACT (NIL T T T) -7 NIL NIL NIL) (-41 68930 69555 70147 "ALGMANIP" NIL ALGMANIP (NIL T T) -7 NIL NIL NIL) (-40 58419 68623 68773 "ALGFF" NIL ALGFF (NIL T T T NIL) -8 NIL NIL NIL) (-39 57736 57890 58068 "ALGFACT" NIL ALGFACT (NIL T) -7 NIL NIL NIL) (-38 56449 57244 57282 "ALGEBRA" 57287 ALGEBRA (NIL T) -9 NIL 57327 NIL) (-37 56235 56312 56444 "ALGEBRA-" NIL ALGEBRA- (NIL T T) -7 NIL NIL NIL) (-36 34180 53397 53449 "ALAGG" 53584 ALAGG (NIL T T) -9 NIL 53742 NIL) (-35 33680 33829 33855 "AHYP" 34056 AHYP (NIL) -9 NIL NIL NIL) (-34 32976 33157 33183 "AGG" 33464 AGG (NIL) -9 NIL 33651 NIL) (-33 32819 32877 32971 "AGG-" NIL AGG- (NIL T) -7 NIL NIL NIL) (-32 30958 31418 31818 "AF" NIL AF (NIL T T) -7 NIL NIL NIL) (-31 30453 30756 30845 "ADDAST" NIL ADDAST (NIL) -8 NIL NIL NIL) (-30 29823 30118 30274 "ACPLOT" NIL ACPLOT (NIL) -8 NIL NIL NIL) (-29 17381 26660 26698 "ACFS" 27305 ACFS (NIL T) -9 NIL 27544 NIL) (-28 16004 16614 17376 "ACFS-" NIL ACFS- (NIL T T) -7 NIL NIL NIL) (-27 11556 13935 13961 "ACF" 14840 ACF (NIL) -9 NIL 15252 NIL) (-26 10652 11058 11551 "ACF-" NIL ACF- (NIL 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T) ((-23) . T) ((-47 |#1| (-484)) . T) ((-25) . T) ((-38 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 |#2|) |has| |#1| (-312)) ((-38 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-350 (-484)))) ((-66) |has| |#1| (-38 (-350 (-484)))) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-82 |#1| |#1|) . T) ((-82 |#2| |#2|) |has| |#1| (-312)) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-118))) (|has| |#1| (-118))) ((-120) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-740))) (-12 (|has| |#1| (-312)) (|has| |#2| (-120))) (|has| |#1| (-120))) ((-555 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-555 (-484)) . T) ((-555 (-1090)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1090)))) ((-555 |#1|) |has| |#1| (-146)) ((-555 |#2|) . 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T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-553 (-179)) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-553 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-553 (-473)) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-473)))) ((-553 (-800 (-330))) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-800 (-330))))) ((-553 (-800 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-553 (-800 (-484))))) ((-186 $) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-184 |#2|) |has| |#1| (-312)) ((-190) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-189) OR (|has| |#1| (-15 * (|#1| (-484) |#1|))) (-12 (|has| |#1| (-312)) (|has| |#2| (-189))) (-12 (|has| |#1| (-312)) (|has| |#2| (-190)))) ((-225 |#2|) |has| |#1| (-312)) ((-201) |has| |#1| (-312)) ((-239) |has| |#1| (-38 (-350 (-484)))) ((-241 (-484) |#1|) . T) ((-241 |#2| $) -12 (|has| |#1| (-312)) (|has| |#2| (-241 |#2| |#2|))) ((-241 $ $) |has| (-484) (-1025)) ((-246) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-260 |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-312) |has| |#1| (-312)) ((-288 |#2|) |has| |#1| (-312)) ((-329 |#2|) |has| |#1| (-312)) ((-343 |#2|) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-484)))) ((-455 (-1090) |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-455 (-1090) |#2|))) ((-455 |#2| |#2|) -12 (|has| |#1| (-312)) (|has| |#2| (-260 |#2|))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-13) . T) ((-588 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 |#2|) |has| |#1| (-312)) ((-588 $) . T) ((-590 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-590 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-590 |#1|) . T) ((-590 |#2|) |has| |#1| (-312)) ((-590 $) . T) ((-582 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-582 |#1|) |has| |#1| (-146)) ((-582 |#2|) |has| |#1| (-312)) ((-582 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-580 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-580 (-484)))) ((-580 |#2|) |has| |#1| (-312)) ((-654 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-654 |#1|) |has| |#1| (-146)) ((-654 |#2|) |has| |#1| (-312)) ((-654 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-663) . T) ((-714) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-716) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-718) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-721) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-740) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-755) -12 (|has| |#1| (-312)) (|has| |#2| (-740))) ((-756) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-756))) (-12 (|has| |#1| (-312)) (|has| |#2| (-740)))) ((-759) OR (-12 (|has| |#1| (-312)) (|has| |#2| (-756))) (-12 (|has| |#1| (-312)) (|has| |#2| (-740)))) ((-806 $ (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-809 (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-811 (-1090)) OR (-12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-484) |#1|)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-811 (-1090)))) (-12 (|has| |#1| (-312)) (|has| |#2| (-809 (-1090))))) ((-796 (-330)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-330)))) ((-796 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-796 (-484)))) ((-794 |#2|) |has| |#1| (-312)) ((-821) -12 (|has| |#1| (-312)) (|has| |#2| (-821))) ((-886 |#1| (-484) (-994)) . T) ((-832) |has| |#1| (-312)) ((-904 |#2|) |has| |#1| (-312)) ((-915) |has| |#1| (-38 (-350 (-484)))) ((-933) -12 (|has| |#1| (-312)) (|has| |#2| (-933))) ((-950 (-350 (-484))) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-484)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-484)))) ((-950 (-1090)) -12 (|has| |#1| (-312)) (|has| |#2| (-950 (-1090)))) ((-950 |#2|) . T) ((-963 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-963 |#1|) . T) ((-963 |#2|) |has| |#1| (-312)) ((-963 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-968 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-968 |#1|) . T) ((-968 |#2|) |has| |#1| (-312)) ((-968 $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-961) . T) ((-970) . T) ((-1025) . T) ((-1061) . T) ((-1013) . T) ((-1066) -12 (|has| |#1| (-312)) (|has| |#2| (-1066))) ((-1115) |has| |#1| (-38 (-350 (-484)))) ((-1118) |has| |#1| (-38 (-350 (-484)))) ((-1129) . T) ((-1134) |has| |#1| (-312)) ((-1141 |#1|) . T) ((-1158 |#1| (-484)) . 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T) ((-23) . T) ((-47 |#1| (-694)) . T) ((-25) . T) ((-38 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-312))) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) OR (|has| |#1| (-950 (-350 (-484)))) (|has| |#1| (-38 (-350 (-484))))) ((-555 (-484)) . T) ((-555 (-994)) . T) ((-555 |#1|) . T) ((-555 $) OR (|has| |#1| (-821)) (|has| |#1| (-495)) (|has| |#1| (-392)) (|has| |#1| (-312))) ((-552 (-772)) . 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T) ((-23) . T) ((-47 |#1| |#2|) . T) ((-25) . T) ((-38 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) |has| |#1| (-495)) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-555 (-484)) . T) ((-555 |#1|) |has| |#1| (-146)) ((-555 $) |has| |#1| (-495)) ((-552 (-772)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-190) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-189) |has| |#1| (-15 * (|#1| |#2| |#1|))) ((-241 |#2| |#1|) . T) ((-241 $ $) |has| |#2| (-1025)) ((-246) |has| |#1| (-495)) ((-495) |has| |#1| (-495)) ((-13) . T) ((-588 (-350 (-484))) |has| |#1| (-38 (-350 (-484)))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . 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T) ((-23) . T) ((-47 |#1| (-350 (-484))) . T) ((-25) . T) ((-38 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-38 |#1|) |has| |#1| (-146)) ((-38 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-35) |has| |#1| (-38 (-350 (-484)))) ((-66) |has| |#1| (-38 (-350 (-484)))) ((-72) . T) ((-82 (-350 (-484)) (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-82 |#1| |#1|) . T) ((-82 $ $) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-104) . T) ((-118) |has| |#1| (-118)) ((-120) |has| |#1| (-120)) ((-555 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-555 (-484)) . T) ((-555 |#1|) |has| |#1| (-146)) ((-555 |#2|) . T) ((-555 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-552 (-772)) . T) ((-146) OR (|has| |#1| (-495)) (|has| |#1| (-312)) (|has| |#1| (-146))) ((-186 $) |has| |#1| (-15 * (|#1| (-350 (-484)) |#1|))) ((-190) |has| |#1| (-15 * (|#1| (-350 (-484)) |#1|))) ((-189) |has| |#1| (-15 * (|#1| (-350 (-484)) |#1|))) ((-201) |has| |#1| (-312)) ((-239) |has| |#1| (-38 (-350 (-484)))) ((-241 (-350 (-484)) |#1|) . T) ((-241 $ $) |has| (-350 (-484)) (-1025)) ((-246) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-258) |has| |#1| (-312)) ((-312) |has| |#1| (-312)) ((-392) |has| |#1| (-312)) ((-433) |has| |#1| (-38 (-350 (-484)))) ((-495) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-13) . T) ((-588 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-588 (-484)) . T) ((-588 |#1|) . T) ((-588 $) . T) ((-590 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-590 |#1|) . T) ((-590 $) . T) ((-582 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-582 |#1|) |has| |#1| (-146)) ((-582 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-654 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-654 |#1|) |has| |#1| (-146)) ((-654 $) OR (|has| |#1| (-495)) (|has| |#1| (-312))) ((-663) . T) ((-806 $ (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-350 (-484)) |#1|)))) ((-809 (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-350 (-484)) |#1|)))) ((-811 (-1090)) -12 (|has| |#1| (-809 (-1090))) (|has| |#1| (-15 * (|#1| (-350 (-484)) |#1|)))) ((-886 |#1| (-350 (-484)) (-994)) . T) ((-832) |has| |#1| (-312)) ((-915) |has| |#1| (-38 (-350 (-484)))) ((-950 |#2|) . T) ((-963 (-350 (-484))) OR (|has| |#1| (-312)) (|has| |#1| (-38 (-350 (-484))))) ((-963 |#1|) . 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UDPO (NIL T) -7 NIL NIL NIL) (-1130 2539315 2539555 2539585 "TYPEAST" NIL TYPEAST (NIL) -8 NIL NIL NIL) (-1129 2539253 2539258 2539288 "TYPE" 2539293 TYPE (NIL) -9 NIL 2539300 NIL) (-1128 2538412 2538632 2538872 "TWOFACT" NIL TWOFACT (NIL T) -7 NIL NIL NIL) (-1127 2537590 2538021 2538256 "TUPLE" NIL TUPLE (NIL T) -8 NIL NIL NIL) (-1126 2535744 2536317 2536856 "TUBETOOL" NIL TUBETOOL (NIL) -7 NIL NIL NIL) (-1125 2534778 2535014 2535250 "TUBE" NIL TUBE (NIL T) -8 NIL NIL NIL) (-1124 2523277 2527593 2527689 "TSETCAT" 2532904 TSETCAT (NIL T T T T) -9 NIL 2534405 NIL) (-1123 2519614 2521430 2523272 "TSETCAT-" NIL TSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-1122 2514006 2518840 2519122 "TS" NIL TS (NIL T) -8 NIL NIL NIL) (-1121 2509343 2510356 2511285 "TRMANIP" NIL TRMANIP (NIL T T) -7 NIL NIL NIL) (-1120 2508840 2508915 2509078 "TRIMAT" NIL TRIMAT (NIL T T T T) -7 NIL NIL NIL) (-1119 2506916 2507206 2507561 "TRIGMNIP" NIL TRIGMNIP (NIL T T) -7 NIL NIL NIL) (-1118 2506400 2506549 2506579 "TRIGCAT" 2506792 TRIGCAT (NIL) -9 NIL NIL NIL) (-1117 2506151 2506254 2506395 "TRIGCAT-" NIL TRIGCAT- (NIL T) -7 NIL NIL NIL) (-1116 2503316 2505257 2505538 "TREE" NIL TREE (NIL T) -8 NIL NIL NIL) (-1115 2502422 2503118 2503148 "TRANFUN" 2503183 TRANFUN (NIL) -9 NIL 2503249 NIL) (-1114 2501886 2502137 2502417 "TRANFUN-" NIL TRANFUN- (NIL T) -7 NIL NIL NIL) (-1113 2501723 2501761 2501822 "TOPSP" NIL TOPSP (NIL) -7 NIL NIL NIL) (-1112 2501180 2501311 2501462 "TOOLSIGN" NIL TOOLSIGN (NIL T) -7 NIL NIL NIL) (-1111 2499921 2500578 2500814 "TEXTFILE" NIL TEXTFILE (NIL) -8 NIL NIL NIL) (-1110 2499733 2499770 2499842 "TEX1" NIL TEX1 (NIL T) -7 NIL NIL NIL) (-1109 2497947 2498593 2499022 "TEX" NIL TEX (NIL) -8 NIL NIL NIL) (-1108 2496327 2496664 2496986 "TBCMPPK" NIL TBCMPPK (NIL T T) -7 NIL NIL NIL) (-1107 2485234 2494107 2494163 "TBAGG" 2494480 TBAGG (NIL T T) -9 NIL 2494690 NIL) (-1106 2480745 2482932 2485229 "TBAGG-" NIL TBAGG- (NIL T T T) -7 NIL NIL NIL) (-1105 2480222 2480347 2480492 "TANEXP" NIL TANEXP (NIL T) -7 NIL NIL NIL) (-1104 2479732 2480052 2480142 "TALGOP" NIL TALGOP (NIL T) -8 NIL NIL NIL) (-1103 2479229 2479346 2479484 "TABLEAU" NIL TABLEAU (NIL T) -8 NIL NIL NIL) (-1102 2470552 2479157 2479224 "TABLE" NIL TABLE (NIL T T) -8 NIL NIL NIL) (-1101 2466305 2467600 2468845 "TABLBUMP" NIL TABLBUMP (NIL T) -7 NIL NIL NIL) (-1100 2465674 2465833 2466014 "SYSTEM" NIL SYSTEM (NIL) -7 NIL NIL NIL) (-1099 2462828 2463581 2464364 "SYSSOLP" NIL SYSSOLP (NIL T) -7 NIL NIL NIL) (-1098 2462602 2462792 2462823 "SYSPTR" NIL SYSPTR (NIL) -8 NIL NIL NIL) (-1097 2461556 2462241 2462367 "SYSNNI" NIL SYSNNI (NIL NIL) -8 NIL NIL 2462553) (-1096 2460820 2461368 2461447 "SYSINT" NIL SYSINT (NIL NIL) -8 NIL NIL 2461507) (-1095 2457643 2458802 2459502 "SYNTAX" NIL SYNTAX (NIL) -8 NIL NIL NIL) (-1094 2455326 2456009 2456643 "SYMTAB" NIL SYMTAB (NIL) -8 NIL NIL NIL) (-1093 2451404 2452450 2453427 "SYMS" NIL SYMS (NIL) -8 NIL NIL NIL) (-1092 2448503 2451059 2451288 "SYMPOLY" NIL SYMPOLY (NIL T) -8 NIL NIL NIL) (-1091 2448099 2448186 2448308 "SYMFUNC" NIL SYMFUNC (NIL T) -7 NIL NIL NIL) (-1090 2444723 2446197 2447016 "SYMBOL" NIL SYMBOL (NIL) -8 NIL NIL NIL) (-1089 2437683 2443920 2444213 "SUTS" NIL SUTS (NIL T NIL NIL) -8 NIL NIL NIL) (-1088 2429369 2437274 2437536 "SUPXS" NIL SUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-1087 2428648 2428787 2429004 "SUPFRACF" NIL SUPFRACF (NIL T T T T) -7 NIL NIL NIL) (-1086 2428332 2428397 2428508 "SUP2" NIL SUP2 (NIL T T) -7 NIL NIL NIL) (-1085 2419055 2428044 2428169 "SUP" NIL SUP (NIL T) -8 NIL NIL NIL) (-1084 2417785 2418083 2418438 "SUMRF" NIL SUMRF (NIL T) -7 NIL NIL NIL) (-1083 2417190 2417268 2417459 "SUMFS" NIL SUMFS (NIL T T) -7 NIL NIL NIL) (-1082 2399342 2416689 2416930 "SULS" NIL SULS (NIL T NIL NIL) -8 NIL NIL NIL) (-1081 2398941 2399213 2399282 "SUCHTAST" NIL SUCHTAST (NIL) -8 NIL NIL NIL) (-1080 2398277 2398558 2398698 "SUCH" NIL SUCH (NIL T T) -8 NIL NIL NIL) (-1079 2392879 2394138 2395091 "SUBSPACE" NIL SUBSPACE (NIL NIL T) -8 NIL NIL NIL) (-1078 2392411 2392511 2392675 "SUBRESP" NIL SUBRESP (NIL T T) -7 NIL NIL NIL) (-1077 2387522 2388804 2389951 "STTFNC" NIL STTFNC (NIL T) -7 NIL NIL NIL) (-1076 2381980 2383451 2384762 "STTF" NIL STTF (NIL T) -7 NIL NIL NIL) (-1075 2374895 2376959 2378750 "STTAYLOR" NIL STTAYLOR (NIL T) -7 NIL NIL NIL) (-1074 2365868 2374833 2374890 "STRTBL" NIL STRTBL (NIL T) -8 NIL NIL NIL) (-1073 2360734 2365582 2365697 "STRING" NIL STRING (NIL) -8 NIL NIL NIL) (-1072 2360321 2360404 2360548 "STREAM3" NIL STREAM3 (NIL T T T) -7 NIL NIL NIL) (-1071 2359472 2359673 2359908 "STREAM2" NIL STREAM2 (NIL T T) -7 NIL NIL NIL) (-1070 2359212 2359270 2359363 "STREAM1" NIL STREAM1 (NIL T) -7 NIL NIL NIL) (-1069 2351954 2357417 2358023 "STREAM" NIL STREAM (NIL T) -8 NIL NIL NIL) (-1068 2351130 2351335 2351566 "STINPROD" NIL STINPROD (NIL T) -7 NIL NIL NIL) (-1067 2350375 2350746 2350893 "STEPAST" NIL STEPAST (NIL) -8 NIL NIL NIL) (-1066 2349863 2350105 2350135 "STEP" 2350229 STEP (NIL) -9 NIL 2350300 NIL) (-1065 2341176 2349781 2349858 "STBL" NIL STBL (NIL T T NIL) -8 NIL NIL NIL) (-1064 2335395 2339974 2340017 "STAGG" 2340444 STAGG (NIL T) -9 NIL 2340618 NIL) (-1063 2333774 2334522 2335390 "STAGG-" NIL STAGG- (NIL T T) -7 NIL NIL NIL) (-1062 2332103 2333601 2333693 "STACK" NIL STACK (NIL T) -8 NIL NIL NIL) (-1061 2331383 2331922 2331952 "SRING" 2331957 SRING (NIL) -9 NIL 2331977 NIL) (-1060 2324158 2329921 2330360 "SREGSET" NIL SREGSET (NIL T T T T) -8 NIL NIL NIL) (-1059 2317932 2319371 2320875 "SRDCMPK" NIL SRDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1058 2310487 2315227 2315257 "SRAGG" 2316556 SRAGG (NIL) -9 NIL 2317160 NIL) (-1057 2309784 2310104 2310482 "SRAGG-" NIL SRAGG- (NIL T) -7 NIL NIL NIL) (-1056 2303992 2309106 2309529 "SQMATRIX" NIL SQMATRIX (NIL NIL T) -8 NIL NIL NIL) (-1055 2298344 2301360 2302096 "SPLTREE" NIL SPLTREE (NIL T T) -8 NIL NIL NIL) (-1054 2294773 2295592 2296229 "SPLNODE" NIL SPLNODE (NIL T T) -8 NIL NIL NIL) (-1053 2293748 2294053 2294083 "SPFCAT" 2294527 SPFCAT (NIL) -9 NIL NIL NIL) (-1052 2292685 2292937 2293201 "SPECOUT" NIL SPECOUT (NIL) -7 NIL NIL NIL) (-1051 2283443 2285717 2285747 "SPADXPT" 2290384 SPADXPT (NIL) -9 NIL 2292508 NIL) (-1050 2283245 2283291 2283360 "SPADPRSR" NIL SPADPRSR (NIL) -7 NIL NIL NIL) (-1049 2280901 2283209 2283240 "SPADAST" NIL SPADAST (NIL) -8 NIL NIL NIL) (-1048 2272575 2274664 2274706 "SPACEC" 2279021 SPACEC (NIL T) -9 NIL 2280826 NIL) (-1047 2270404 2272522 2272570 "SPACE3" NIL SPACE3 (NIL T) -8 NIL NIL NIL) (-1046 2269340 2269529 2269819 "SORTPAK" NIL SORTPAK (NIL T T) -7 NIL NIL NIL) (-1045 2267744 2268077 2268488 "SOLVETRA" NIL SOLVETRA (NIL T) -7 NIL NIL NIL) (-1044 2267009 2267243 2267504 "SOLVESER" NIL SOLVESER (NIL T) -7 NIL NIL NIL) (-1043 2263189 2264149 2265144 "SOLVERAD" NIL SOLVERAD (NIL T) -7 NIL NIL NIL) (-1042 2259547 2260246 2260975 "SOLVEFOR" NIL SOLVEFOR (NIL T T) -7 NIL NIL NIL) (-1041 2253467 2258869 2258965 "SNTSCAT" 2258970 SNTSCAT (NIL T T T T) -9 NIL 2259040 NIL) (-1040 2247288 2252108 2252498 "SMTS" NIL SMTS (NIL T T T) -8 NIL NIL NIL) (-1039 2241060 2247207 2247283 "SMP" NIL SMP (NIL T T) -8 NIL NIL NIL) (-1038 2239492 2239823 2240221 "SMITH" NIL SMITH (NIL T T T T) -7 NIL NIL NIL) (-1037 2231232 2236058 2236160 "SMATCAT" 2237503 SMATCAT (NIL NIL T T T) -9 NIL 2238051 NIL) (-1036 2229073 2230057 2231227 "SMATCAT-" NIL SMATCAT- (NIL T NIL T T T) -7 NIL NIL NIL) (-1035 2227180 2228531 2228574 "SMAGG" 2228659 SMAGG (NIL T) -9 NIL 2228734 NIL) (-1034 2224905 2226347 2226390 "SKAGG" 2226651 SKAGG (NIL T) -9 NIL 2226787 NIL) (-1033 2220951 2224725 2224836 "SINT" NIL SINT (NIL) -8 NIL NIL 2224877) (-1032 2220761 2220805 2220871 "SIMPAN" NIL SIMPAN (NIL) -7 NIL NIL NIL) (-1031 2219836 2220068 2220336 "SIGNRF" NIL SIGNRF (NIL T) -7 NIL NIL NIL) (-1030 2218840 2219002 2219278 "SIGNEF" NIL SIGNEF (NIL T T) -7 NIL NIL NIL) (-1029 2218186 2218526 2218649 "SIGAST" NIL SIGAST (NIL) -8 NIL NIL NIL) (-1028 2217532 2217839 2217979 "SIG" NIL SIG (NIL) -8 NIL NIL NIL) (-1027 2215643 2216135 2216641 "SHP" NIL SHP (NIL T NIL) -7 NIL NIL NIL) (-1026 2209236 2215562 2215638 "SHDP" NIL SHDP (NIL NIL NIL T) -8 NIL NIL NIL) (-1025 2208739 2208976 2209006 "SGROUP" 2209099 SGROUP (NIL) -9 NIL 2209161 NIL) (-1024 2208629 2208661 2208734 "SGROUP-" NIL SGROUP- (NIL T) -7 NIL NIL NIL) (-1023 2208267 2208307 2208348 "SGPOPC" 2208353 SGPOPC (NIL T) -9 NIL 2208554 NIL) (-1022 2207801 2208078 2208184 "SGPOP" NIL SGPOP (NIL T) -8 NIL NIL NIL) (-1021 2205224 2205993 2206715 "SGCF" NIL SGCF (NIL) -7 NIL NIL NIL) (-1020 2199243 2204645 2204741 "SFRTCAT" 2204746 SFRTCAT (NIL T T T T) -9 NIL 2204784 NIL) (-1019 2193635 2194748 2195875 "SFRGCD" NIL SFRGCD (NIL T T T T T) -7 NIL NIL NIL) (-1018 2187811 2188972 2190136 "SFQCMPK" NIL SFQCMPK (NIL T T T T T) -7 NIL NIL NIL) (-1017 2186783 2187685 2187806 "SEXOF" NIL SEXOF (NIL T T T T T) -8 NIL NIL NIL) (-1016 2182391 2183286 2183381 "SEXCAT" 2185994 SEXCAT (NIL T T T T T) -9 NIL 2186545 NIL) (-1015 2181364 2182318 2182386 "SEX" NIL SEX (NIL) -8 NIL NIL NIL) (-1014 2179755 2180340 2180642 "SETMN" NIL SETMN (NIL NIL NIL) -8 NIL NIL NIL) (-1013 2179278 2179463 2179493 "SETCAT" 2179610 SETCAT (NIL) -9 NIL 2179694 NIL) (-1012 2179110 2179174 2179273 "SETCAT-" NIL SETCAT- (NIL T) -7 NIL NIL NIL) (-1011 2175337 2177564 2177607 "SETAGG" 2178475 SETAGG (NIL T) -9 NIL 2178813 NIL) (-1010 2174943 2175095 2175332 "SETAGG-" NIL SETAGG- (NIL T T) -7 NIL NIL NIL) (-1009 2172069 2174890 2174938 "SET" NIL SET (NIL T) -8 NIL NIL NIL) (-1008 2171535 2171845 2171945 "SEQAST" NIL SEQAST (NIL) -8 NIL NIL NIL) (-1007 2170662 2171028 2171089 "SEGXCAT" 2171375 SEGXCAT (NIL T T) -9 NIL 2171495 NIL) (-1006 2169587 2169855 2169898 "SEGCAT" 2170420 SEGCAT (NIL T) -9 NIL 2170641 NIL) (-1005 2169267 2169332 2169445 "SEGBIND2" NIL SEGBIND2 (NIL T T) -7 NIL NIL NIL) (-1004 2168333 2168803 2169011 "SEGBIND" NIL SEGBIND (NIL T) -8 NIL NIL NIL) (-1003 2167911 2168190 2168266 "SEGAST" NIL SEGAST (NIL) -8 NIL NIL NIL) (-1002 2167276 2167412 2167616 "SEG2" NIL SEG2 (NIL T T) -7 NIL NIL NIL) (-1001 2166342 2167089 2167271 "SEG" NIL SEG (NIL T) -8 NIL NIL NIL) (-1000 2165595 2166290 2166337 "SDVAR" NIL SDVAR (NIL T) -8 NIL NIL NIL) (-999 2157082 2165464 2165590 "SDPOL" NIL SDPOL (NIL T) -8 NIL NIL NIL) (-998 2155942 2156232 2156549 "SCPKG" NIL SCPKG (NIL T) -7 NIL NIL NIL) (-997 2155248 2155460 2155648 "SCOPE" NIL SCOPE (NIL) -8 NIL NIL NIL) (-996 2154598 2154755 2154931 "SCACHE" NIL SCACHE (NIL T) -7 NIL NIL NIL) (-995 2154171 2154402 2154430 "SASTCAT" 2154435 SASTCAT (NIL) -9 NIL 2154448 NIL) (-994 2153638 2154063 2154137 "SAOS" NIL SAOS (NIL) -8 NIL NIL NIL) (-993 2153241 2153282 2153453 "SAERFFC" NIL SAERFFC (NIL T T T) -7 NIL NIL NIL) (-992 2152872 2152913 2153070 "SAEFACT" NIL SAEFACT (NIL T T T) -7 NIL NIL NIL) (-991 2145953 2152789 2152867 "SAE" NIL SAE (NIL T T NIL) -8 NIL NIL NIL) (-990 2144603 2144932 2145328 "RURPK" NIL RURPK (NIL T NIL) -7 NIL NIL NIL) (-989 2143364 2143725 2144025 "RULESET" NIL RULESET (NIL T T T) -8 NIL NIL NIL) (-988 2142988 2143209 2143290 "RULECOLD" NIL RULECOLD (NIL NIL) -8 NIL NIL NIL) (-987 2140448 2141082 2141535 "RULE" NIL RULE (NIL T T T) -8 NIL NIL NIL) (-986 2140287 2140320 2140388 "RTVALUE" NIL RTVALUE (NIL) -8 NIL NIL NIL) (-985 2139778 2140081 2140172 "RSTRCAST" NIL RSTRCAST (NIL) -8 NIL NIL NIL) (-984 2135406 2136274 2137185 "RSETGCD" NIL RSETGCD (NIL T T T T T) -7 NIL NIL NIL) (-983 2124359 2129761 2129855 "RSETCAT" 2133911 RSETCAT (NIL T T T T) -9 NIL 2134999 NIL) (-982 2122897 2123539 2124354 "RSETCAT-" NIL RSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-981 2116671 2118116 2119623 "RSDCMPK" NIL RSDCMPK (NIL T T T T T) -7 NIL NIL NIL) (-980 2114553 2115110 2115182 "RRCC" 2116255 RRCC (NIL T T) -9 NIL 2116596 NIL) (-979 2114078 2114277 2114548 "RRCC-" NIL RRCC- (NIL T T T) -7 NIL NIL NIL) (-978 2113548 2113858 2113956 "RPTAST" NIL RPTAST (NIL) -8 NIL NIL NIL) (-977 2086100 2096813 2096877 "RPOLCAT" 2107351 RPOLCAT (NIL T T T) -9 NIL 2110496 NIL) (-976 2080199 2083022 2086095 "RPOLCAT-" NIL RPOLCAT- (NIL T T T T) -7 NIL NIL NIL) (-975 2076366 2079947 2080085 "ROMAN" NIL ROMAN (NIL) -8 NIL NIL NIL) (-974 2074694 2075433 2075689 "ROIRC" NIL ROIRC (NIL T T) -8 NIL NIL NIL) (-973 2070337 2073149 2073177 "RNS" 2073439 RNS (NIL) -9 NIL 2073691 NIL) (-972 2069240 2069727 2070264 "RNS-" NIL RNS- (NIL T) -7 NIL NIL NIL) (-971 2068358 2068759 2068959 "RNGBIND" NIL RNGBIND (NIL T T) -8 NIL NIL NIL) (-970 2067496 2068058 2068086 "RNG" 2068146 RNG (NIL) -9 NIL 2068200 NIL) (-969 2067385 2067419 2067491 "RNG-" NIL RNG- (NIL T) -7 NIL NIL NIL) (-968 2066647 2067152 2067192 "RMODULE" 2067197 RMODULE (NIL T) -9 NIL 2067223 NIL) (-967 2065586 2065692 2066022 "RMCAT2" NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL NIL) (-966 2062585 2065176 2065469 "RMATRIX" NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL NIL) (-965 2055380 2057719 2057831 "RMATCAT" 2061136 RMATCAT (NIL NIL NIL T T T) -9 NIL 2062102 NIL) (-964 2054897 2055076 2055375 "RMATCAT-" NIL RMATCAT- (NIL T NIL NIL T T T) -7 NIL NIL NIL) (-963 2054465 2054676 2054717 "RLINSET" 2054778 RLINSET (NIL T) -9 NIL 2054822 NIL) (-962 2054110 2054191 2054317 "RINTERP" NIL RINTERP (NIL NIL T) -7 NIL NIL NIL) (-961 2052956 2053687 2053715 "RING" 2053770 RING (NIL) -9 NIL 2053862 NIL) (-960 2052801 2052857 2052951 "RING-" NIL RING- (NIL T) -7 NIL NIL NIL) (-959 2051855 2052122 2052378 "RIDIST" NIL RIDIST (NIL) -7 NIL NIL NIL) (-958 2042995 2051483 2051684 "RGCHAIN" NIL RGCHAIN (NIL T NIL) -8 NIL NIL NIL) (-957 2042220 2042731 2042770 "RGBCSPC" 2042827 RGBCSPC (NIL T) -9 NIL 2042878 NIL) (-956 2041254 2041740 2041779 "RGBCMDL" 2042007 RGBCMDL (NIL T) -9 NIL 2042121 NIL) (-955 2040966 2041035 2041136 "RFFACTOR" NIL RFFACTOR (NIL T) -7 NIL NIL NIL) (-954 2040729 2040770 2040865 "RFFACT" NIL RFFACT (NIL T) -7 NIL NIL NIL) (-953 2039153 2039583 2039963 "RFDIST" NIL RFDIST (NIL) -7 NIL NIL NIL) (-952 2036740 2037408 2038076 "RF" NIL RF (NIL T) -7 NIL NIL NIL) (-951 2036290 2036388 2036548 "RETSOL" NIL RETSOL (NIL T T) -7 NIL NIL NIL) (-950 2035912 2036010 2036051 "RETRACT" 2036182 RETRACT (NIL T) -9 NIL 2036269 NIL) (-949 2035792 2035823 2035907 "RETRACT-" NIL RETRACT- (NIL T T) -7 NIL NIL NIL) (-948 2035394 2035666 2035733 "RETAST" NIL RETAST (NIL) -8 NIL NIL NIL) (-947 2033874 2034765 2034962 "RESRING" NIL RESRING (NIL T T T T NIL) -8 NIL NIL NIL) (-946 2033565 2033626 2033722 "RESLATC" NIL RESLATC (NIL T) -7 NIL NIL NIL) (-945 2033308 2033349 2033454 "REPSQ" NIL REPSQ (NIL T) -7 NIL NIL NIL) (-944 2033043 2033084 2033193 "REPDB" NIL REPDB (NIL T) -7 NIL NIL NIL) (-943 2028114 2029565 2030780 "REP2" NIL REP2 (NIL T) -7 NIL NIL NIL) (-942 2025213 2025971 2026779 "REP1" NIL REP1 (NIL T) -7 NIL NIL NIL) (-941 2023182 2023804 2024404 "REP" NIL REP (NIL) -7 NIL NIL NIL) (-940 2015970 2021733 2022169 "REGSET" NIL REGSET (NIL T T T T) -8 NIL NIL NIL) (-939 2015282 2015562 2015711 "REF" NIL REF (NIL T) -8 NIL NIL NIL) (-938 2014767 2014882 2015047 "REDORDER" NIL REDORDER (NIL T T) -7 NIL NIL NIL) (-937 2010360 2014170 2014391 "RECLOS" NIL RECLOS (NIL T) -8 NIL NIL NIL) (-936 2009592 2009791 2010004 "REALSOLV" NIL REALSOLV (NIL) -7 NIL NIL NIL) (-935 2006882 2007720 2008602 "REAL0Q" NIL REAL0Q (NIL T) -7 NIL NIL NIL) (-934 2003464 2004500 2005559 "REAL0" NIL REAL0 (NIL T) -7 NIL NIL NIL) (-933 2003300 2003353 2003381 "REAL" 2003386 REAL (NIL) -9 NIL 2003421 NIL) (-932 2002790 2003094 2003185 "RDUCEAST" NIL RDUCEAST (NIL) -8 NIL NIL NIL) (-931 2002270 2002348 2002553 "RDIV" NIL RDIV (NIL T T T T T) -7 NIL NIL NIL) (-930 2001503 2001695 2001906 "RDIST" NIL RDIST (NIL T) -7 NIL NIL NIL) (-929 2000391 2000688 2001055 "RDETRS" NIL RDETRS (NIL T T) -7 NIL NIL NIL) (-928 1998658 1999128 1999661 "RDETR" NIL RDETR (NIL T T) -7 NIL NIL NIL) (-927 1997580 1997857 1998244 "RDEEFS" NIL RDEEFS (NIL T T) -7 NIL NIL NIL) (-926 1996407 1996716 1997135 "RDEEF" NIL RDEEF (NIL T T) -7 NIL NIL NIL) (-925 1989755 1993267 1993295 "RCFIELD" 1994572 RCFIELD (NIL) -9 NIL 1995302 NIL) (-924 1988373 1988985 1989682 "RCFIELD-" NIL RCFIELD- (NIL T) -7 NIL NIL NIL) (-923 1984577 1986465 1986506 "RCAGG" 1987573 RCAGG (NIL T) -9 NIL 1988034 NIL) (-922 1984304 1984414 1984572 "RCAGG-" NIL RCAGG- (NIL T T) -7 NIL NIL NIL) (-921 1983749 1983878 1984039 "RATRET" NIL RATRET (NIL T) -7 NIL NIL NIL) (-920 1983366 1983445 1983564 "RATFACT" NIL RATFACT (NIL T) -7 NIL NIL NIL) (-919 1982781 1982931 1983081 "RANDSRC" NIL RANDSRC (NIL) -7 NIL NIL NIL) (-918 1982563 1982613 1982684 "RADUTIL" NIL RADUTIL (NIL) -7 NIL NIL NIL) (-917 1975005 1981681 1981989 "RADIX" NIL RADIX (NIL NIL) -8 NIL NIL NIL) (-916 1964707 1974872 1975000 "RADFF" NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL NIL) (-915 1964341 1964434 1964462 "RADCAT" 1964619 RADCAT (NIL) -9 NIL NIL NIL) (-914 1964179 1964239 1964336 "RADCAT-" NIL RADCAT- (NIL T) -7 NIL NIL NIL) (-913 1962451 1964010 1964099 "QUEUE" NIL QUEUE (NIL T) -8 NIL NIL NIL) (-912 1962132 1962181 1962308 "QUATCT2" NIL QUATCT2 (NIL T T T T) -7 NIL NIL NIL) (-911 1954419 1958503 1958543 "QUATCAT" 1959321 QUATCAT (NIL T) -9 NIL 1960085 NIL) (-910 1951669 1952949 1954325 "QUATCAT-" NIL QUATCAT- (NIL T T) -7 NIL NIL NIL) (-909 1947509 1951619 1951664 "QUAT" NIL QUAT (NIL T) -8 NIL NIL NIL) (-908 1945029 1946524 1946565 "QUAGG" 1946940 QUAGG (NIL T) -9 NIL 1947116 NIL) (-907 1944631 1944903 1944970 "QQUTAST" NIL QQUTAST (NIL) -8 NIL NIL NIL) (-906 1943637 1944267 1944430 "QFORM" NIL QFORM (NIL NIL T) -8 NIL NIL NIL) (-905 1943318 1943367 1943494 "QFCAT2" NIL QFCAT2 (NIL T T T T) -7 NIL NIL NIL) (-904 1932918 1939087 1939127 "QFCAT" 1939785 QFCAT (NIL T) -9 NIL 1940778 NIL) (-903 1929802 1931241 1932824 "QFCAT-" NIL QFCAT- (NIL T T) -7 NIL NIL NIL) (-902 1929348 1929482 1929612 "QEQUAT" NIL QEQUAT (NIL) -8 NIL NIL NIL) (-901 1923544 1924705 1925867 "QCMPACK" NIL QCMPACK (NIL T T T T T) -7 NIL NIL NIL) (-900 1922963 1923143 1923375 "QALGSET2" NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL NIL) (-899 1920785 1921313 1921736 "QALGSET" NIL QALGSET (NIL T T T T) -8 NIL NIL NIL) (-898 1919684 1919926 1920243 "PWFFINTB" NIL PWFFINTB (NIL T T T T) -7 NIL NIL NIL) (-897 1918045 1918243 1918596 "PUSHVAR" NIL PUSHVAR (NIL T T T T) -7 NIL NIL NIL) (-896 1913801 1915017 1915058 "PTRANFN" 1916942 PTRANFN (NIL T) -9 NIL NIL NIL) (-895 1912448 1912793 1913114 "PTPACK" NIL PTPACK (NIL T) -7 NIL NIL NIL) (-894 1912141 1912204 1912311 "PTFUNC2" NIL PTFUNC2 (NIL T T) -7 NIL NIL NIL) (-893 1906348 1910900 1910940 "PTCAT" 1911232 PTCAT (NIL T) -9 NIL 1911385 NIL) (-892 1906041 1906082 1906206 "PSQFR" NIL PSQFR (NIL T T T T) -7 NIL NIL NIL) (-891 1904920 1905236 1905570 "PSEUDLIN" NIL PSEUDLIN (NIL T) -7 NIL NIL NIL) (-890 1893799 1896360 1898669 "PSETPK" NIL PSETPK (NIL T T T T) -7 NIL NIL NIL) (-889 1886839 1889582 1889676 "PSETCAT" 1892650 PSETCAT (NIL T T T T) -9 NIL 1893459 NIL) (-888 1885289 1886023 1886834 "PSETCAT-" NIL PSETCAT- (NIL T T T T T) -7 NIL NIL NIL) (-887 1884608 1884803 1884831 "PSCURVE" 1885099 PSCURVE (NIL) -9 NIL 1885266 NIL) (-886 1880210 1882030 1882094 "PSCAT" 1882929 PSCAT (NIL T T T) -9 NIL 1883168 NIL) (-885 1879524 1879806 1880205 "PSCAT-" NIL PSCAT- (NIL T T T T) -7 NIL NIL NIL) (-884 1877921 1878836 1879099 "PRTITION" NIL PRTITION (NIL) -8 NIL NIL NIL) (-883 1877412 1877715 1877806 "PRTDAST" NIL PRTDAST (NIL) -8 NIL NIL NIL) (-882 1868432 1870854 1873042 "PRS" NIL PRS (NIL T T) -7 NIL NIL NIL) (-881 1866308 1867713 1867753 "PRQAGG" 1867936 PRQAGG (NIL T) -9 NIL 1868039 NIL) (-880 1865481 1865927 1865955 "PROPLOG" 1866094 PROPLOG (NIL) -9 NIL 1866208 NIL) (-879 1865156 1865219 1865342 "PROPFUN2" NIL PROPFUN2 (NIL T T) -7 NIL NIL NIL) (-878 1864592 1864731 1864903 "PROPFUN1" NIL PROPFUN1 (NIL T) -7 NIL NIL NIL) (-877 1862840 1863603 1863900 "PROPFRML" NIL PROPFRML (NIL T) -8 NIL NIL NIL) (-876 1862392 1862524 1862652 "PROPERTY" NIL PROPERTY (NIL) -8 NIL NIL NIL) (-875 1856833 1861332 1862152 "PRODUCT" NIL PRODUCT (NIL T T) -8 NIL NIL NIL) (-874 1856662 1856700 1856759 "PRINT" NIL PRINT (NIL) -7 NIL NIL NIL) (-873 1856101 1856241 1856392 "PRIMES" NIL PRIMES (NIL T) -7 NIL NIL NIL) (-872 1854569 1854988 1855454 "PRIMELT" NIL PRIMELT (NIL T) -7 NIL NIL NIL) (-871 1854286 1854347 1854375 "PRIMCAT" 1854499 PRIMCAT (NIL) -9 NIL NIL NIL) (-870 1853457 1853653 1853881 "PRIMARR2" NIL PRIMARR2 (NIL T T) -7 NIL NIL NIL) (-869 1849510 1853407 1853452 "PRIMARR" NIL PRIMARR (NIL T) -8 NIL NIL NIL) (-868 1849209 1849271 1849382 "PREASSOC" NIL PREASSOC (NIL T T) -7 NIL NIL NIL) (-867 1846345 1848858 1849091 "PR" NIL PR (NIL T T) -8 NIL NIL NIL) (-866 1845796 1845953 1845981 "PPCURVE" 1846186 PPCURVE (NIL) -9 NIL 1846322 NIL) (-865 1845409 1845654 1845737 "PORTNUM" NIL PORTNUM (NIL) -8 NIL NIL NIL) (-864 1843165 1843586 1844178 "POLYROOT" NIL POLYROOT (NIL T T T T T) -7 NIL NIL NIL) (-863 1842608 1842672 1842905 "POLYLIFT" NIL POLYLIFT (NIL T T T T T) -7 NIL NIL NIL) (-862 1839328 1839814 1840425 "POLYCATQ" NIL POLYCATQ (NIL T T T T T) -7 NIL NIL NIL) (-861 1824919 1831048 1831112 "POLYCAT" 1834597 POLYCAT (NIL T T T) -9 NIL 1836474 NIL) (-860 1820429 1822576 1824914 "POLYCAT-" NIL POLYCAT- (NIL T T T T) -7 NIL NIL NIL) (-859 1820086 1820160 1820279 "POLY2UP" NIL POLY2UP (NIL NIL T) -7 NIL NIL NIL) (-858 1819779 1819842 1819949 "POLY2" NIL POLY2 (NIL T T) -7 NIL NIL NIL) (-857 1813142 1819512 1819671 "POLY" NIL POLY (NIL T) -8 NIL NIL NIL) (-856 1812029 1812292 1812568 "POLUTIL" NIL POLUTIL (NIL T T) -7 NIL NIL NIL) (-855 1810633 1810946 1811276 "POLTOPOL" NIL POLTOPOL (NIL NIL T) -7 NIL NIL NIL) (-854 1805967 1810583 1810628 "POINT" NIL POINT (NIL T) -8 NIL NIL NIL) (-853 1804455 1804866 1805241 "PNTHEORY" NIL PNTHEORY (NIL) -7 NIL NIL NIL) (-852 1803212 1803521 1803917 "PMTOOLS" NIL PMTOOLS (NIL T T T) -7 NIL NIL NIL) (-851 1802883 1802967 1803084 "PMSYM" NIL PMSYM (NIL T) -7 NIL NIL NIL) (-850 1802462 1802537 1802711 "PMQFCAT" NIL PMQFCAT (NIL T T T) -7 NIL NIL NIL) (-849 1801948 1802044 1802204 "PMPREDFS" NIL PMPREDFS (NIL T T T) -7 NIL NIL NIL) (-848 1801420 1801540 1801694 "PMPRED" NIL PMPRED (NIL T) -7 NIL NIL NIL) (-847 1800315 1800533 1800910 "PMPLCAT" NIL PMPLCAT (NIL T T T T T) -7 NIL NIL NIL) (-846 1799926 1800011 1800163 "PMLSAGG" NIL PMLSAGG (NIL T T T) -7 NIL NIL NIL) (-845 1799477 1799559 1799740 "PMKERNEL" NIL PMKERNEL (NIL T T) -7 NIL NIL NIL) (-844 1799169 1799250 1799363 "PMINS" NIL PMINS (NIL T) -7 NIL NIL NIL) (-843 1798682 1798757 1798965 "PMFS" NIL PMFS (NIL T T T) -7 NIL NIL NIL) (-842 1798030 1798158 1798360 "PMDOWN" NIL PMDOWN (NIL T T T) -7 NIL NIL NIL) (-841 1797392 1797526 1797689 "PMASSFS" NIL PMASSFS (NIL T T) -7 NIL NIL NIL) (-840 1796696 1796878 1797059 "PMASS" NIL PMASS (NIL) -7 NIL NIL NIL) (-839 1796419 1796493 1796587 "PLOTTOOL" NIL PLOTTOOL (NIL) -7 NIL NIL NIL) (-838 1792987 1794176 1795092 "PLOT3D" NIL PLOT3D (NIL) -8 NIL NIL NIL) (-837 1792071 1792272 1792507 "PLOT1" NIL PLOT1 (NIL T) -7 NIL NIL NIL) (-836 1787636 1789020 1790162 "PLOT" NIL PLOT (NIL) -8 NIL NIL NIL) (-835 1767557 1772444 1777291 "PLEQN" NIL PLEQN (NIL T T T T) -7 NIL NIL NIL) (-834 1767297 1767350 1767453 "PINTERPA" NIL PINTERPA (NIL T T) -7 NIL NIL NIL) (-833 1766738 1766872 1767052 "PINTERP" NIL PINTERP (NIL NIL T) -7 NIL NIL NIL) (-832 1764747 1765968 1765996 "PID" 1766193 PID (NIL) -9 NIL 1766320 NIL) (-831 1764535 1764578 1764653 "PICOERCE" NIL PICOERCE (NIL T) -7 NIL NIL NIL) (-830 1763722 1764382 1764469 "PI" NIL PI (NIL) -8 NIL NIL 1764509) (-829 1763174 1763325 1763501 "PGROEB" NIL PGROEB (NIL T) -7 NIL NIL NIL) (-828 1759502 1760460 1761365 "PGE" NIL PGE (NIL) -7 NIL NIL NIL) (-827 1757866 1758155 1758521 "PGCD" NIL PGCD (NIL T T T T) -7 NIL NIL NIL) (-826 1757308 1757423 1757584 "PFRPAC" NIL PFRPAC (NIL T) -7 NIL NIL NIL) (-825 1753849 1756177 1756530 "PFR" NIL PFR (NIL T) -8 NIL NIL NIL) (-824 1752455 1752735 1753060 "PFOTOOLS" NIL PFOTOOLS (NIL T T) -7 NIL NIL NIL) (-823 1751220 1751474 1751822 "PFOQ" NIL PFOQ (NIL T T T) -7 NIL NIL NIL) (-822 1749930 1750157 1750509 "PFO" NIL PFO (NIL T T T T T) -7 NIL NIL NIL) (-821 1746940 1748500 1748528 "PFECAT" 1749121 PFECAT (NIL) -9 NIL 1749498 NIL) (-820 1746563 1746728 1746935 "PFECAT-" NIL PFECAT- (NIL T) -7 NIL NIL NIL) (-819 1745387 1745669 1745970 "PFBRU" NIL PFBRU (NIL T T) -7 NIL NIL NIL) (-818 1743569 1743956 1744386 "PFBR" NIL PFBR (NIL T T T T) -7 NIL NIL NIL) (-817 1739539 1743495 1743564 "PF" NIL PF (NIL NIL) -8 NIL NIL NIL) (-816 1735442 1736589 1737456 "PERMGRP" NIL PERMGRP (NIL T) -8 NIL NIL NIL) (-815 1733374 1734463 1734504 "PERMCAT" 1734903 PERMCAT (NIL T) -9 NIL 1735200 NIL) (-814 1733070 1733117 1733240 "PERMAN" NIL PERMAN (NIL NIL T) -7 NIL NIL NIL) (-813 1729519 1731200 1731845 "PERM" NIL PERM (NIL T) -8 NIL NIL NIL) (-812 1726988 1729274 1729395 "PENDTREE" NIL PENDTREE (NIL T) -8 NIL NIL NIL) (-811 1725857 1726120 1726161 "PDSPC" 1726694 PDSPC (NIL T) -9 NIL 1726939 NIL) (-810 1725224 1725490 1725852 "PDSPC-" NIL PDSPC- (NIL T T) -7 NIL NIL NIL) (-809 1723859 1724852 1724893 "PDRING" 1724898 PDRING (NIL T) -9 NIL 1724925 NIL) (-808 1722569 1723358 1723411 "PDMOD" 1723416 PDMOD (NIL T T) -9 NIL 1723519 NIL) (-807 1721662 1721874 1722123 "PDECOMP" NIL PDECOMP (NIL T T) -7 NIL NIL NIL) (-806 1721267 1721334 1721388 "PDDOM" 1721553 PDDOM (NIL T T) -9 NIL 1721633 NIL) (-805 1721119 1721155 1721262 "PDDOM-" NIL PDDOM- (NIL T T T) -7 NIL NIL NIL) (-804 1720905 1720944 1721033 "PCOMP" NIL PCOMP (NIL T T) -7 NIL NIL NIL) (-803 1719222 1719976 1720275 "PBWLB" NIL PBWLB (NIL T) -8 NIL NIL NIL) (-802 1718911 1718974 1719083 "PATTERN2" NIL PATTERN2 (NIL T T) -7 NIL NIL NIL) (-801 1717049 1717479 1717930 "PATTERN1" NIL PATTERN1 (NIL T T) -7 NIL NIL NIL) (-800 1710669 1712498 1713790 "PATTERN" NIL PATTERN (NIL T) -8 NIL NIL NIL) (-799 1710300 1710373 1710505 "PATRES2" NIL PATRES2 (NIL T T T) -7 NIL NIL NIL) (-798 1708002 1708682 1709163 "PATRES" NIL PATRES (NIL T T) -8 NIL NIL NIL) (-797 1706206 1706634 1707037 "PATMATCH" NIL PATMATCH (NIL T T T) -7 NIL NIL NIL) (-796 1705652 1705900 1705941 "PATMAB" 1706048 PATMAB (NIL T) -9 NIL 1706131 NIL) (-795 1704299 1704703 1704960 "PATLRES" NIL PATLRES (NIL T T T) -8 NIL NIL NIL) (-794 1703837 1703968 1704009 "PATAB" 1704014 PATAB (NIL T) -9 NIL 1704186 NIL) (-793 1702380 1702817 1703240 "PARTPERM" NIL PARTPERM (NIL) -7 NIL NIL NIL) (-792 1702058 1702133 1702235 "PARSURF" NIL PARSURF (NIL T) -8 NIL NIL NIL) (-791 1701747 1701810 1701919 "PARSU2" NIL PARSU2 (NIL T T) -7 NIL NIL NIL) (-790 1701552 1701598 1701665 "PARSER" NIL PARSER (NIL) -7 NIL NIL NIL) (-789 1701230 1701305 1701407 "PARSCURV" NIL PARSCURV (NIL T) -8 NIL NIL NIL) (-788 1700919 1700982 1701091 "PARSC2" NIL PARSC2 (NIL T T) -7 NIL NIL NIL) (-787 1700610 1700680 1700777 "PARPCURV" NIL PARPCURV (NIL T) -8 NIL NIL NIL) (-786 1700299 1700362 1700471 "PARPC2" NIL PARPC2 (NIL T T) -7 NIL NIL NIL) (-785 1699460 1699839 1700018 "PARAMAST" NIL PARAMAST (NIL) -8 NIL NIL NIL) (-784 1699067 1699165 1699284 "PAN2EXPR" NIL PAN2EXPR (NIL) -7 NIL NIL NIL) (-783 1698035 1698460 1698679 "PALETTE" NIL PALETTE (NIL) -8 NIL NIL NIL) (-782 1696700 1697354 1697714 "PAIR" NIL PAIR (NIL T T) -8 NIL NIL NIL) (-781 1689790 1696104 1696298 "PADICRC" NIL PADICRC (NIL NIL T) -8 NIL NIL NIL) (-780 1682211 1689288 1689472 "PADICRAT" NIL PADICRAT (NIL NIL) -8 NIL NIL NIL) (-779 1678936 1680851 1680891 "PADICCT" 1681472 PADICCT (NIL NIL) -9 NIL 1681754 NIL) (-778 1676926 1678886 1678931 "PADIC" NIL PADIC (NIL NIL) -8 NIL NIL NIL) (-777 1676088 1676298 1676564 "PADEPAC" NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL NIL) (-776 1675430 1675573 1675777 "PADE" NIL PADE (NIL T T T) -7 NIL NIL NIL) (-775 1673811 1674838 1675116 "OWP" NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-774 1673335 1673594 1673691 "OVERSET" NIL OVERSET (NIL) -8 NIL NIL NIL) (-773 1672394 1673072 1673244 "OVAR" NIL OVAR (NIL NIL) -8 NIL NIL NIL) (-772 1662816 1665685 1667884 "OUTFORM" NIL OUTFORM (NIL) -8 NIL NIL NIL) (-771 1662208 1662522 1662648 "OUTBFILE" NIL OUTBFILE (NIL) -8 NIL NIL NIL) (-770 1661485 1661680 1661708 "OUTBCON" 1662026 OUTBCON (NIL) -9 NIL 1662192 NIL) (-769 1661193 1661323 1661480 "OUTBCON-" NIL OUTBCON- (NIL T) -7 NIL NIL NIL) (-768 1660574 1660719 1660880 "OUT" NIL OUT (NIL) -7 NIL NIL NIL) (-767 1659945 1660372 1660461 "OSI" NIL OSI (NIL) -8 NIL NIL NIL) (-766 1659360 1659775 1659803 "OSGROUP" 1659808 OSGROUP (NIL) -9 NIL 1659830 NIL) (-765 1658324 1658585 1658870 "ORTHPOL" NIL ORTHPOL (NIL T) -7 NIL NIL NIL) (-764 1655593 1658199 1658319 "OREUP" NIL OREUP (NIL NIL T NIL NIL) -8 NIL NIL NIL) (-763 1652734 1655344 1655470 "ORESUP" NIL ORESUP (NIL T NIL NIL) -8 NIL NIL NIL) (-762 1650752 1651280 1651840 "OREPCTO" NIL OREPCTO (NIL T T) -7 NIL NIL NIL) (-761 1644094 1646634 1646674 "OREPCAT" 1648995 OREPCAT (NIL T) -9 NIL 1650097 NIL) (-760 1642120 1643054 1644089 "OREPCAT-" NIL OREPCAT- (NIL T T) -7 NIL NIL NIL) (-759 1641317 1641588 1641616 "ORDTYPE" 1641921 ORDTYPE (NIL) -9 NIL 1642079 NIL) (-758 1640851 1641062 1641312 "ORDTYPE-" NIL ORDTYPE- (NIL T) -7 NIL NIL NIL) (-757 1640313 1640689 1640846 "ORDSTRCT" NIL ORDSTRCT (NIL T NIL) -8 NIL NIL NIL) (-756 1639807 1640170 1640198 "ORDSET" 1640203 ORDSET (NIL) -9 NIL 1640225 NIL) (-755 1638372 1639394 1639422 "ORDRING" 1639427 ORDRING (NIL) -9 NIL 1639455 NIL) (-754 1637620 1638177 1638205 "ORDMON" 1638210 ORDMON (NIL) -9 NIL 1638231 NIL) (-753 1636924 1637086 1637278 "ORDFUNS" NIL ORDFUNS (NIL NIL T) -7 NIL NIL NIL) (-752 1636135 1636643 1636671 "ORDFIN" 1636736 ORDFIN (NIL) -9 NIL 1636810 NIL) (-751 1635529 1635668 1635854 "ORDCOMP2" NIL ORDCOMP2 (NIL T T) -7 NIL NIL NIL) (-750 1632204 1634497 1634903 "ORDCOMP" NIL ORDCOMP (NIL T) -8 NIL NIL NIL) (-749 1631611 1631966 1632071 "OPSIG" NIL OPSIG (NIL) -8 NIL NIL NIL) (-748 1631419 1631464 1631530 "OPQUERY" NIL OPQUERY (NIL) -7 NIL NIL NIL) (-747 1630720 1630996 1631037 "OPERCAT" 1631248 OPERCAT (NIL T) -9 NIL 1631344 NIL) (-746 1630532 1630599 1630715 "OPERCAT-" NIL OPERCAT- (NIL T T) -7 NIL NIL NIL) (-745 1627898 1629334 1629830 "OP" NIL OP (NIL T) -8 NIL NIL NIL) (-744 1627319 1627446 1627620 "ONECOMP2" NIL ONECOMP2 (NIL T T) -7 NIL NIL NIL) (-743 1624220 1626458 1626824 "ONECOMP" NIL ONECOMP (NIL T) -8 NIL NIL NIL) (-742 1620986 1623613 1623653 "OMSAGG" 1623714 OMSAGG (NIL T) -9 NIL 1623778 NIL) (-741 1619398 1620657 1620825 "OMLO" NIL OMLO (NIL T T) -8 NIL NIL NIL) (-740 1617594 1618835 1618863 "OINTDOM" 1618868 OINTDOM (NIL) -9 NIL 1618889 NIL) (-739 1615024 1616596 1616925 "OFMONOID" NIL OFMONOID (NIL T) -8 NIL NIL NIL) (-738 1614278 1614974 1615019 "ODVAR" NIL ODVAR (NIL T) -8 NIL NIL NIL) (-737 1611480 1614119 1614273 "ODR" NIL ODR (NIL T T NIL) -8 NIL NIL NIL) (-736 1603017 1611351 1611475 "ODPOL" NIL ODPOL (NIL T) -8 NIL NIL NIL) (-735 1596581 1602908 1603012 "ODP" NIL ODP (NIL NIL T NIL) -8 NIL NIL NIL) (-734 1595553 1595790 1596063 "ODETOOLS" NIL ODETOOLS (NIL T T) -7 NIL NIL NIL) (-733 1593187 1593857 1594561 "ODESYS" NIL ODESYS (NIL T T) -7 NIL NIL NIL) (-732 1588964 1589924 1590947 "ODERTRIC" NIL ODERTRIC (NIL T T) -7 NIL NIL NIL) (-731 1588472 1588560 1588754 "ODERED" NIL ODERED (NIL T T T T T) -7 NIL NIL NIL) (-730 1585921 1586503 1587176 "ODERAT" NIL ODERAT (NIL T T) -7 NIL NIL NIL) (-729 1583316 1583824 1584420 "ODEPRRIC" NIL ODEPRRIC (NIL T T T T) -7 NIL NIL NIL) (-728 1580313 1580852 1581498 "ODEPRIM" NIL ODEPRIM (NIL T T T T) -7 NIL NIL NIL) (-727 1579668 1579776 1580034 "ODEPAL" NIL ODEPAL (NIL T T T T) -7 NIL NIL NIL) (-726 1578826 1578951 1579172 "ODEINT" NIL ODEINT (NIL T T) -7 NIL NIL NIL) (-725 1575110 1575906 1576819 "ODEEF" NIL ODEEF (NIL T T) -7 NIL NIL NIL) (-724 1574550 1574645 1574867 "ODECONST" NIL ODECONST (NIL T T T) -7 NIL NIL NIL) (-723 1574231 1574280 1574407 "OCTCT2" NIL OCTCT2 (NIL T T T T) -7 NIL NIL NIL) (-722 1570834 1574030 1574149 "OCT" NIL OCT (NIL T) -8 NIL NIL NIL) (-721 1569994 1570616 1570644 "OCAMON" 1570649 OCAMON (NIL) -9 NIL 1570670 NIL) (-720 1564206 1567020 1567060 "OC" 1568155 OC (NIL T) -9 NIL 1569011 NIL) (-719 1562206 1563132 1564112 "OC-" NIL OC- (NIL T T) -7 NIL NIL NIL) (-718 1561622 1562040 1562068 "OASGP" 1562073 OASGP (NIL) -9 NIL 1562093 NIL) (-717 1560685 1561334 1561362 "OAMONS" 1561402 OAMONS (NIL) -9 NIL 1561445 NIL) (-716 1559830 1560411 1560439 "OAMON" 1560496 OAMON (NIL) -9 NIL 1560547 NIL) (-715 1559726 1559758 1559825 "OAMON-" NIL OAMON- (NIL T) -7 NIL NIL NIL) (-714 1558477 1559251 1559279 "OAGROUP" 1559425 OAGROUP (NIL) -9 NIL 1559517 NIL) (-713 1558268 1558355 1558472 "OAGROUP-" NIL OAGROUP- (NIL T) -7 NIL NIL NIL) (-712 1558008 1558064 1558152 "NUMTUBE" NIL NUMTUBE (NIL T) -7 NIL NIL NIL) (-711 1553070 1554633 1556160 "NUMQUAD" NIL NUMQUAD (NIL) -7 NIL NIL NIL) (-710 1549765 1550799 1551834 "NUMODE" NIL NUMODE (NIL) -7 NIL NIL NIL) (-709 1548875 1549108 1549326 "NUMFMT" NIL NUMFMT (NIL) -7 NIL NIL NIL) (-708 1537736 1540764 1543212 "NUMERIC" NIL NUMERIC (NIL T) -7 NIL NIL NIL) (-707 1531757 1537159 1537253 "NTSCAT" 1537258 NTSCAT (NIL T T T T) -9 NIL 1537296 NIL) (-706 1531098 1531277 1531470 "NTPOLFN" NIL NTPOLFN (NIL T) -7 NIL NIL NIL) (-705 1530791 1530854 1530961 "NSUP2" NIL NSUP2 (NIL T T) -7 NIL NIL NIL) (-704 1518458 1528411 1529221 "NSUP" NIL NSUP (NIL T) -8 NIL NIL NIL) (-703 1507467 1518323 1518453 "NSMP" NIL NSMP (NIL T T) -8 NIL NIL NIL) (-702 1506187 1506512 1506869 "NREP" NIL NREP (NIL T) -7 NIL NIL NIL) (-701 1505023 1505287 1505645 "NPCOEF" NIL NPCOEF (NIL T T T T T) -7 NIL NIL NIL) (-700 1504190 1504323 1504539 "NORMRETR" NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL NIL) (-699 1502508 1502827 1503233 "NORMPK" NIL NORMPK (NIL T T T T T) -7 NIL NIL NIL) (-698 1502221 1502255 1502379 "NORMMA" NIL NORMMA (NIL T T T T) -7 NIL NIL NIL) (-697 1502040 1502075 1502144 "NONE1" NIL NONE1 (NIL T) -7 NIL NIL NIL) (-696 1501816 1502006 1502035 "NONE" NIL NONE (NIL) -8 NIL NIL NIL) (-695 1501380 1501447 1501624 "NODE1" NIL NODE1 (NIL T T) -7 NIL NIL NIL) (-694 1499666 1500743 1500998 "NNI" NIL NNI (NIL) -8 NIL NIL 1501345) (-693 1498394 1498731 1499095 "NLINSOL" NIL NLINSOL (NIL T) -7 NIL NIL NIL) (-692 1497371 1497623 1497925 "NFINTBAS" NIL NFINTBAS (NIL T T) -7 NIL NIL NIL) (-691 1496458 1497023 1497064 "NETCLT" 1497235 NETCLT (NIL T) -9 NIL 1497316 NIL) (-690 1495362 1495629 1495910 "NCODIV" NIL NCODIV (NIL T T) -7 NIL NIL NIL) (-689 1495161 1495204 1495279 "NCNTFRAC" NIL NCNTFRAC (NIL T) -7 NIL NIL NIL) (-688 1493692 1494080 1494500 "NCEP" NIL NCEP (NIL T) -7 NIL NIL NIL) (-687 1492325 1493291 1493319 "NASRING" 1493429 NASRING (NIL) -9 NIL 1493509 NIL) (-686 1492170 1492226 1492320 "NASRING-" NIL NASRING- (NIL T) -7 NIL NIL NIL) (-685 1491099 1491777 1491805 "NARNG" 1491922 NARNG (NIL) -9 NIL 1492013 NIL) (-684 1490875 1490960 1491094 "NARNG-" NIL NARNG- (NIL T) -7 NIL NIL NIL) (-683 1489641 1490395 1490435 "NAALG" 1490514 NAALG (NIL T) -9 NIL 1490575 NIL) (-682 1489511 1489546 1489636 "NAALG-" NIL NAALG- (NIL T T) -7 NIL NIL NIL) (-681 1484490 1485675 1486861 "MULTSQFR" NIL MULTSQFR (NIL T T T T) -7 NIL NIL NIL) (-680 1483885 1483972 1484156 "MULTFACT" NIL MULTFACT (NIL T T T T) -7 NIL NIL NIL) (-679 1475895 1480389 1480441 "MTSCAT" 1481501 MTSCAT (NIL T T) -9 NIL 1482015 NIL) (-678 1475661 1475721 1475813 "MTHING" NIL MTHING (NIL T) -7 NIL NIL NIL) (-677 1475487 1475526 1475586 "MSYSCMD" NIL MSYSCMD (NIL) -7 NIL NIL NIL) (-676 1472353 1475019 1475060 "MSETAGG" 1475065 MSETAGG (NIL T) -9 NIL 1475099 NIL) (-675 1468640 1471396 1471717 "MSET" NIL MSET (NIL T) -8 NIL NIL NIL) (-674 1464914 1466737 1467477 "MRING" NIL MRING (NIL T T) -8 NIL NIL NIL) (-673 1464551 1464624 1464753 "MRF2" NIL MRF2 (NIL T T T) -7 NIL NIL NIL) (-672 1464204 1464245 1464389 "MRATFAC" NIL MRATFAC (NIL T T T T) -7 NIL NIL NIL) (-671 1462069 1462406 1462837 "MPRFF" NIL MPRFF (NIL T T T T) -7 NIL NIL NIL) (-670 1455467 1461968 1462064 "MPOLY" NIL MPOLY (NIL NIL T) -8 NIL NIL NIL) (-669 1454992 1455033 1455241 "MPCPF" NIL MPCPF (NIL T T T T) -7 NIL NIL NIL) (-668 1454551 1454600 1454783 "MPC3" NIL MPC3 (NIL T T T T T T T) -7 NIL NIL NIL) (-667 1453825 1453918 1454137 "MPC2" NIL MPC2 (NIL T T T T T T T) -7 NIL NIL NIL) (-666 1452442 1452803 1453193 "MONOTOOL" NIL MONOTOOL (NIL T T) -7 NIL NIL NIL) (-665 1451963 1452030 1452069 "MONOPC" 1452129 MONOPC (NIL T) -9 NIL 1452348 NIL) (-664 1451414 1451750 1451878 "MONOP" NIL MONOP (NIL T) -8 NIL NIL NIL) (-663 1450556 1450935 1450963 "MONOID" 1451181 MONOID (NIL) -9 NIL 1451325 NIL) (-662 1450215 1450365 1450551 "MONOID-" NIL MONOID- (NIL T) -7 NIL NIL NIL) (-661 1439153 1446023 1446082 "MONOGEN" 1446756 MONOGEN (NIL T T) -9 NIL 1447212 NIL) (-660 1437165 1438051 1439034 "MONOGEN-" NIL MONOGEN- (NIL T T T) -7 NIL NIL NIL) (-659 1435879 1436423 1436451 "MONADWU" 1436842 MONADWU (NIL) -9 NIL 1437077 NIL) (-658 1435427 1435627 1435874 "MONADWU-" NIL MONADWU- (NIL T) -7 NIL NIL NIL) (-657 1434704 1435005 1435033 "MONAD" 1435240 MONAD (NIL) -9 NIL 1435352 NIL) (-656 1434471 1434567 1434699 "MONAD-" NIL MONAD- (NIL T) -7 NIL NIL NIL) (-655 1432861 1433631 1433910 "MOEBIUS" NIL MOEBIUS (NIL T) -8 NIL NIL NIL) (-654 1431995 1432522 1432562 "MODULE" 1432567 MODULE (NIL T) -9 NIL 1432605 NIL) (-653 1431674 1431800 1431990 "MODULE-" NIL MODULE- (NIL T T) -7 NIL NIL NIL) (-652 1429385 1430271 1430585 "MODRING" NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-651 1426564 1427981 1428494 "MODOP" NIL MODOP (NIL T T) -8 NIL NIL NIL) (-650 1425198 1425772 1426048 "MODMONOM" NIL MODMONOM (NIL T T NIL) -8 NIL NIL NIL) (-649 1414417 1423863 1424276 "MODMON" NIL MODMON (NIL T T) -8 NIL NIL NIL) (-648 1411373 1413417 1413686 "MODFIELD" NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL NIL) (-647 1410457 1410824 1411014 "MMLFORM" NIL MMLFORM (NIL) -8 NIL NIL NIL) (-646 1410026 1410075 1410254 "MMAP" NIL MMAP (NIL T T T T T T) -7 NIL NIL NIL) (-645 1407851 1408847 1408887 "MLO" 1409304 MLO (NIL T) -9 NIL 1409544 NIL) (-644 1405732 1406259 1406854 "MLIFT" NIL MLIFT (NIL T T T T) -7 NIL NIL NIL) (-643 1405200 1405296 1405450 "MKUCFUNC" NIL MKUCFUNC (NIL T T T) -7 NIL NIL NIL) (-642 1404870 1404946 1405069 "MKRECORD" NIL MKRECORD (NIL T T) -7 NIL NIL NIL) (-641 1404082 1404268 1404496 "MKFUNC" NIL MKFUNC (NIL T) -7 NIL NIL NIL) (-640 1403575 1403691 1403847 "MKFLCFN" NIL MKFLCFN (NIL T) -7 NIL NIL NIL) (-639 1402947 1403061 1403246 "MKBCFUNC" NIL MKBCFUNC (NIL T T T T) -7 NIL NIL NIL) (-638 1401974 1402247 1402524 "MHROWRED" NIL MHROWRED (NIL T) -7 NIL NIL NIL) (-637 1401407 1401495 1401666 "MFINFACT" NIL MFINFACT (NIL T T T T) -7 NIL NIL NIL) (-636 1398565 1399444 1400323 "MESH" NIL MESH (NIL) -7 NIL NIL NIL) (-635 1397232 1397580 1397933 "MDDFACT" NIL MDDFACT (NIL T) -7 NIL NIL NIL) (-634 1393893 1396337 1396378 "MDAGG" 1396635 MDAGG (NIL T) -9 NIL 1396780 NIL) (-633 1393167 1393331 1393531 "MCDEN" NIL MCDEN (NIL T T) -7 NIL NIL NIL) (-632 1392245 1392531 1392761 "MAYBE" NIL MAYBE (NIL T) -8 NIL NIL NIL) (-631 1390342 1390919 1391480 "MATSTOR" NIL MATSTOR (NIL T) -7 NIL NIL NIL) (-630 1386248 1389932 1390179 "MATRIX" NIL MATRIX (NIL T) -8 NIL NIL NIL) (-629 1382597 1383366 1384100 "MATLIN" NIL MATLIN (NIL T T T T) -7 NIL NIL NIL) (-628 1381350 1381519 1381848 "MATCAT2" NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-627 1371001 1374456 1374532 "MATCAT" 1379520 MATCAT (NIL T T T) -9 NIL 1380966 NIL) (-626 1368282 1369588 1370996 "MATCAT-" NIL MATCAT- (NIL T T T T) -7 NIL NIL NIL) (-625 1366683 1367043 1367427 "MAPPKG3" NIL MAPPKG3 (NIL T T T) -7 NIL NIL NIL) (-624 1365816 1366013 1366235 "MAPPKG2" NIL MAPPKG2 (NIL T T) -7 NIL NIL NIL) (-623 1364567 1364893 1365220 "MAPPKG1" NIL MAPPKG1 (NIL T) -7 NIL NIL NIL) (-622 1363729 1364131 1364307 "MAPPAST" NIL MAPPAST (NIL) -8 NIL NIL NIL) (-621 1363398 1363462 1363585 "MAPHACK3" NIL MAPHACK3 (NIL T T T) -7 NIL NIL NIL) (-620 1363046 1363119 1363233 "MAPHACK2" NIL MAPHACK2 (NIL T T) -7 NIL NIL NIL) (-619 1362581 1362696 1362838 "MAPHACK1" NIL MAPHACK1 (NIL T) -7 NIL NIL NIL) (-618 1360790 1361558 1361859 "MAGMA" NIL MAGMA (NIL T) -8 NIL NIL NIL) (-617 1360284 1360586 1360676 "MACROAST" NIL MACROAST (NIL) -8 NIL NIL NIL) (-616 1353797 1358599 1358640 "LZSTAGG" 1359417 LZSTAGG (NIL T) -9 NIL 1359707 NIL) (-615 1350916 1352350 1353792 "LZSTAGG-" NIL LZSTAGG- (NIL T T) -7 NIL NIL NIL) (-614 1348303 1349269 1349752 "LWORD" NIL LWORD (NIL T) -8 NIL NIL NIL) (-613 1347884 1348163 1348237 "LSTAST" NIL LSTAST (NIL) -8 NIL NIL NIL) (-612 1340201 1347745 1347879 "LSQM" NIL LSQM (NIL NIL T) -8 NIL NIL NIL) (-611 1339564 1339709 1339937 "LSPP" NIL LSPP (NIL T T T T) -7 NIL NIL NIL) (-610 1337048 1337746 1338458 "LSMP1" NIL LSMP1 (NIL T) -7 NIL NIL NIL) (-609 1335160 1335483 1335931 "LSMP" NIL LSMP (NIL T T T T) -7 NIL NIL NIL) (-608 1328464 1334210 1334251 "LSAGG" 1334313 LSAGG (NIL T) -9 NIL 1334391 NIL) (-607 1326158 1327257 1328459 "LSAGG-" NIL LSAGG- (NIL T T) -7 NIL NIL NIL) (-606 1323638 1325507 1325756 "LPOLY" NIL LPOLY (NIL T T) -8 NIL NIL NIL) (-605 1323305 1323396 1323519 "LPEFRAC" NIL LPEFRAC (NIL T) -7 NIL NIL NIL) (-604 1322976 1323055 1323083 "LOGIC" 1323194 LOGIC (NIL) -9 NIL 1323276 NIL) (-603 1322871 1322900 1322971 "LOGIC-" NIL LOGIC- (NIL T) -7 NIL NIL NIL) (-602 1322190 1322348 1322541 "LODOOPS" NIL LODOOPS (NIL T T) -7 NIL NIL NIL) (-601 1320975 1321224 1321575 "LODOF" NIL LODOF (NIL T T) -7 NIL NIL NIL) (-600 1316797 1319596 1319636 "LODOCAT" 1320068 LODOCAT (NIL T) -9 NIL 1320279 NIL) (-599 1316590 1316666 1316792 "LODOCAT-" NIL LODOCAT- (NIL T T) -7 NIL NIL NIL) (-598 1313590 1316467 1316585 "LODO2" NIL LODO2 (NIL T T) -8 NIL NIL NIL) (-597 1310688 1313540 1313585 "LODO1" NIL LODO1 (NIL T) -8 NIL NIL NIL) (-596 1307775 1310618 1310683 "LODO" NIL LODO (NIL T NIL) -8 NIL NIL NIL) (-595 1306828 1307003 1307305 "LODEEF" NIL LODEEF (NIL T T T) -7 NIL NIL NIL) (-594 1304960 1306090 1306343 "LO" NIL LO (NIL T T T) -8 NIL NIL NIL) (-593 1300059 1303119 1303160 "LNAGG" 1304022 LNAGG (NIL T) -9 NIL 1304457 NIL) (-592 1299446 1299713 1300054 "LNAGG-" NIL LNAGG- (NIL T T) -7 NIL NIL NIL) (-591 1296018 1296959 1297596 "LMOPS" NIL LMOPS (NIL T T NIL) -8 NIL NIL NIL) (-590 1295280 1295785 1295825 "LMODULE" 1295830 LMODULE (NIL T) -9 NIL 1295856 NIL) (-589 1292630 1295016 1295139 "LMDICT" NIL LMDICT (NIL T) -8 NIL NIL NIL) (-588 1292198 1292409 1292450 "LLINSET" 1292511 LLINSET (NIL T) -9 NIL 1292555 NIL) (-587 1291874 1292134 1292193 "LITERAL" NIL LITERAL (NIL T) -8 NIL NIL NIL) (-586 1291473 1291553 1291692 "LIST3" NIL LIST3 (NIL T T T) -7 NIL NIL NIL) (-585 1289924 1290272 1290671 "LIST2MAP" NIL LIST2MAP (NIL T T) -7 NIL NIL NIL) (-584 1289095 1289291 1289519 "LIST2" NIL LIST2 (NIL T T) -7 NIL NIL NIL) (-583 1282313 1288351 1288605 "LIST" NIL LIST (NIL T) -8 NIL NIL NIL) (-582 1281890 1282123 1282164 "LINSET" 1282169 LINSET (NIL T) -9 NIL 1282202 NIL) (-581 1280791 1281513 1281680 "LINFORM" NIL LINFORM (NIL T NIL) -8 NIL NIL NIL) (-580 1279057 1279812 1279852 "LINEXP" 1280338 LINEXP (NIL T) -9 NIL 1280611 NIL) (-579 1277679 1278666 1278847 "LINELT" NIL LINELT (NIL T NIL) -8 NIL NIL NIL) (-578 1276506 1276778 1277080 "LINDEP" NIL LINDEP (NIL T T) -7 NIL NIL NIL) (-577 1275719 1276308 1276418 "LINBASIS" NIL LINBASIS (NIL NIL) -8 NIL NIL NIL) (-576 1273269 1273991 1274741 "LIMITRF" NIL LIMITRF (NIL T) -7 NIL NIL NIL) (-575 1271899 1272196 1272587 "LIMITPS" NIL LIMITPS (NIL T T) -7 NIL NIL NIL) (-574 1270692 1271294 1271334 "LIECAT" 1271474 LIECAT (NIL T) -9 NIL 1271625 NIL) (-573 1270566 1270599 1270687 "LIECAT-" NIL LIECAT- (NIL T T) -7 NIL NIL NIL) (-572 1264822 1270256 1270484 "LIE" NIL LIE (NIL T T) -8 NIL NIL NIL) (-571 1255257 1264498 1264654 "LIB" NIL LIB (NIL) -8 NIL NIL NIL) (-570 1251709 1252658 1253593 "LGROBP" NIL LGROBP (NIL NIL T) -7 NIL NIL NIL) (-569 1250333 1251241 1251269 "LFCAT" 1251476 LFCAT (NIL) -9 NIL 1251615 NIL) (-568 1248572 1248902 1249247 "LF" NIL LF (NIL T T) -7 NIL NIL NIL) (-567 1246089 1246754 1247435 "LEXTRIPK" NIL LEXTRIPK (NIL T NIL) -7 NIL NIL NIL) (-566 1243101 1244079 1244582 "LEXP" NIL LEXP (NIL T T NIL) -8 NIL NIL NIL) (-565 1242592 1242895 1242986 "LETAST" NIL LETAST (NIL) -8 NIL NIL NIL) (-564 1241299 1241623 1242023 "LEADCDET" NIL LEADCDET (NIL T T T T) -7 NIL NIL NIL) (-563 1240565 1240650 1240876 "LAZM3PK" NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL NIL) (-562 1235568 1239133 1239669 "LAUPOL" NIL LAUPOL (NIL T T) -8 NIL NIL NIL) (-561 1235193 1235243 1235403 "LAPLACE" NIL LAPLACE (NIL T T) -7 NIL NIL NIL) (-560 1233964 1234737 1234777 "LALG" 1234838 LALG (NIL T) -9 NIL 1234896 NIL) (-559 1233747 1233824 1233959 "LALG-" NIL LALG- (NIL T T) -7 NIL NIL NIL) (-558 1231600 1233015 1233266 "LA" NIL LA (NIL T T T) -8 NIL NIL NIL) (-557 1231429 1231459 1231500 "KVTFROM" 1231562 KVTFROM (NIL T) -9 NIL NIL NIL) (-556 1230245 1230960 1231149 "KTVLOGIC" NIL KTVLOGIC (NIL) -8 NIL NIL NIL) (-555 1230074 1230104 1230145 "KRCFROM" 1230207 KRCFROM (NIL T) -9 NIL NIL NIL) (-554 1229176 1229373 1229668 "KOVACIC" NIL KOVACIC (NIL T T) -7 NIL NIL NIL) (-553 1229005 1229035 1229076 "KONVERT" 1229138 KONVERT (NIL T) -9 NIL NIL NIL) (-552 1228834 1228864 1228905 "KOERCE" 1228967 KOERCE (NIL T) -9 NIL NIL NIL) (-551 1228404 1228497 1228629 "KERNEL2" NIL KERNEL2 (NIL T T) -7 NIL NIL NIL) (-550 1226457 1227351 1227723 "KERNEL" NIL KERNEL (NIL T) -8 NIL NIL NIL) (-549 1217634 1224241 1224295 "KDAGG" 1224671 KDAGG (NIL T T) -9 NIL 1224897 NIL) (-548 1217099 1217331 1217629 "KDAGG-" NIL KDAGG- (NIL T T T) -7 NIL NIL NIL) (-547 1210097 1216891 1217037 "KAFILE" NIL KAFILE (NIL T) -8 NIL NIL NIL) (-546 1209747 1210029 1210092 "JVMOP" NIL JVMOP (NIL) -8 NIL NIL NIL) (-545 1208717 1209216 1209465 "JVMMDACC" NIL JVMMDACC (NIL) -8 NIL NIL NIL) (-544 1207843 1208292 1208497 "JVMFDACC" NIL JVMFDACC (NIL) -8 NIL NIL NIL) (-543 1206707 1207199 1207499 "JVMCSTTG" NIL JVMCSTTG (NIL) -8 NIL NIL NIL) (-542 1205989 1206388 1206549 "JVMCFACC" NIL JVMCFACC (NIL) -8 NIL NIL NIL) (-541 1205699 1205935 1205984 "JVMBCODE" NIL JVMBCODE (NIL) -8 NIL NIL NIL) (-540 1199954 1205389 1205617 "JORDAN" NIL JORDAN (NIL T T) -8 NIL NIL NIL) (-539 1199372 1199705 1199825 "JOINAST" NIL JOINAST (NIL) -8 NIL NIL NIL) (-538 1195538 1197549 1197603 "IXAGG" 1198530 IXAGG (NIL T T) -9 NIL 1198987 NIL) (-537 1194744 1195115 1195533 "IXAGG-" NIL IXAGG- (NIL T T T) -7 NIL NIL NIL) (-536 1193711 1193986 1194249 "ITUPLE" NIL ITUPLE (NIL T) -8 NIL NIL NIL) (-535 1192373 1192580 1192873 "ITRIGMNP" NIL ITRIGMNP (NIL T T T) -7 NIL NIL NIL) (-534 1191324 1191546 1191829 "ITFUN3" NIL ITFUN3 (NIL T T T) -7 NIL NIL NIL) (-533 1190999 1191062 1191185 "ITFUN2" NIL ITFUN2 (NIL T T) -7 NIL NIL NIL) (-532 1190261 1190633 1190807 "ITFORM" NIL ITFORM (NIL) -8 NIL NIL NIL) (-531 1188237 1189537 1189811 "ITAYLOR" NIL ITAYLOR (NIL T) -8 NIL NIL NIL) (-530 1177785 1183554 1184711 "ISUPS" NIL ISUPS (NIL T) -8 NIL NIL NIL) (-529 1177030 1177182 1177418 "ISUMP" NIL ISUMP (NIL T T T T) -7 NIL NIL NIL) (-528 1176521 1176824 1176915 "ISAST" NIL ISAST (NIL) -8 NIL NIL NIL) (-527 1175814 1175905 1176118 "IRURPK" NIL IRURPK (NIL T T T T T) -7 NIL NIL NIL) (-526 1174946 1175171 1175411 "IRSN" NIL IRSN (NIL) -7 NIL NIL NIL) (-525 1173359 1173740 1174168 "IRRF2F" NIL IRRF2F (NIL T) -7 NIL NIL NIL) (-524 1173144 1173188 1173264 "IRREDFFX" NIL IRREDFFX (NIL T) -7 NIL NIL NIL) (-523 1171994 1172291 1172586 "IROOT" NIL IROOT (NIL T) -7 NIL NIL NIL) (-522 1171267 1171618 1171769 "IRFORM" NIL IRFORM (NIL) -8 NIL NIL NIL) (-521 1170470 1170601 1170814 "IR2F" NIL IR2F (NIL T T) -7 NIL NIL NIL) (-520 1168625 1169122 1169666 "IR2" NIL IR2 (NIL T T) -7 NIL NIL NIL) (-519 1165706 1166974 1167663 "IR" NIL IR (NIL T) -8 NIL NIL NIL) (-518 1165531 1165571 1165631 "IPRNTPK" NIL IPRNTPK (NIL) -7 NIL NIL NIL) (-517 1161529 1165457 1165526 "IPF" NIL IPF (NIL NIL) -8 NIL NIL NIL) (-516 1159532 1161468 1161524 "IPADIC" NIL IPADIC (NIL NIL NIL) -8 NIL NIL NIL) (-515 1158903 1159202 1159332 "IP4ADDR" NIL IP4ADDR (NIL) -8 NIL NIL NIL) (-514 1158356 1158644 1158776 "IOMODE" NIL IOMODE (NIL) -8 NIL NIL NIL) (-513 1157437 1158062 1158188 "IOBFILE" NIL IOBFILE (NIL) -8 NIL NIL NIL) (-512 1156847 1157341 1157369 "IOBCON" 1157374 IOBCON (NIL) -9 NIL 1157395 NIL) (-511 1156418 1156482 1156664 "INVLAPLA" NIL INVLAPLA (NIL T T) -7 NIL NIL NIL) (-510 1148462 1150833 1153158 "INTTR" NIL INTTR (NIL T T) -7 NIL NIL NIL) (-509 1145573 1146356 1147220 "INTTOOLS" NIL INTTOOLS (NIL T T) -7 NIL NIL NIL) (-508 1145250 1145347 1145464 "INTSLPE" NIL INTSLPE (NIL) -7 NIL NIL NIL) (-507 1142692 1145186 1145245 "INTRVL" NIL INTRVL (NIL T) -8 NIL NIL NIL) (-506 1140804 1141333 1141900 "INTRF" NIL INTRF (NIL T) -7 NIL NIL NIL) (-505 1140306 1140420 1140560 "INTRET" NIL INTRET (NIL T) -7 NIL NIL NIL) (-504 1138690 1139096 1139558 "INTRAT" NIL INTRAT (NIL T T) -7 NIL NIL NIL) (-503 1136469 1137063 1137674 "INTPM" NIL INTPM (NIL T T) -7 NIL NIL NIL) (-502 1133842 1134452 1135172 "INTPAF" NIL INTPAF (NIL T T T) -7 NIL NIL NIL) (-501 1133246 1133404 1133612 "INTHERTR" NIL INTHERTR (NIL T T) -7 NIL NIL NIL) (-500 1132765 1132851 1133039 "INTHERAL" NIL INTHERAL (NIL T T T T) -7 NIL NIL NIL) (-499 1130970 1131491 1131948 "INTHEORY" NIL INTHEORY (NIL) -7 NIL NIL NIL) (-498 1124052 1125705 1127434 "INTG0" NIL INTG0 (NIL T T T) -7 NIL NIL NIL) (-497 1123418 1123580 1123753 "INTFACT" NIL INTFACT (NIL T) -7 NIL NIL NIL) (-496 1121291 1121755 1122299 "INTEF" NIL INTEF (NIL T T) -7 NIL NIL NIL) (-495 1119417 1120367 1120395 "INTDOM" 1120694 INTDOM (NIL) -9 NIL 1120899 NIL) (-494 1118970 1119172 1119412 "INTDOM-" NIL INTDOM- (NIL T) -7 NIL NIL NIL) (-493 1114777 1117249 1117303 "INTCAT" 1118099 INTCAT (NIL T) -9 NIL 1118415 NIL) (-492 1114342 1114462 1114589 "INTBIT" NIL INTBIT (NIL) -7 NIL NIL NIL) (-491 1113182 1113354 1113660 "INTALG" NIL INTALG (NIL T T T T T) -7 NIL NIL NIL) (-490 1112755 1112851 1113008 "INTAF" NIL INTAF (NIL T T) -7 NIL NIL NIL) (-489 1104057 1112662 1112750 "INTABL" NIL INTABL (NIL T T T) -8 NIL NIL NIL) (-488 1103355 1103910 1103975 "INT8" NIL INT8 (NIL) -8 NIL NIL 1104009) (-487 1102652 1103207 1103272 "INT64" NIL INT64 (NIL) -8 NIL NIL 1103306) (-486 1101949 1102504 1102569 "INT32" NIL INT32 (NIL) -8 NIL NIL 1102603) (-485 1101246 1101801 1101866 "INT16" NIL INT16 (NIL) -8 NIL NIL 1101900) (-484 1097709 1101165 1101241 "INT" NIL INT (NIL) -8 NIL NIL NIL) (-483 1091766 1095249 1095277 "INS" 1096207 INS (NIL) -9 NIL 1096866 NIL) (-482 1089828 1090746 1091693 "INS-" NIL INS- (NIL T) -7 NIL NIL NIL) (-481 1088887 1089110 1089385 "INPSIGN" NIL INPSIGN (NIL T T) -7 NIL NIL NIL) (-480 1088101 1088242 1088439 "INPRODPF" NIL INPRODPF (NIL T T) -7 NIL NIL NIL) (-479 1087091 1087232 1087469 "INPRODFF" NIL INPRODFF (NIL T T T T) -7 NIL NIL NIL) (-478 1086243 1086407 1086667 "INNMFACT" NIL INNMFACT (NIL T T T T) -7 NIL NIL NIL) (-477 1085523 1085638 1085826 "INMODGCD" NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL NIL) (-476 1084262 1084531 1084855 "INFSP" NIL INFSP (NIL T T T) -7 NIL NIL NIL) (-475 1083542 1083683 1083866 "INFPROD0" NIL INFPROD0 (NIL T T) -7 NIL NIL NIL) (-474 1083205 1083277 1083375 "INFORM1" NIL INFORM1 (NIL T) -7 NIL NIL NIL) (-473 1080283 1081769 1082292 "INFORM" NIL INFORM (NIL) -8 NIL NIL NIL) (-472 1079882 1079989 1080103 "INFINITY" NIL INFINITY (NIL) -7 NIL NIL NIL) (-471 1079038 1079683 1079784 "INETCLTS" NIL INETCLTS (NIL) -8 NIL NIL NIL) (-470 1077888 1078156 1078477 "INEP" NIL INEP (NIL T T T) -7 NIL NIL NIL) (-469 1076878 1077818 1077883 "INDE" NIL INDE (NIL T) -8 NIL NIL NIL) (-468 1076503 1076583 1076700 "INCRMAPS" NIL INCRMAPS (NIL T) -7 NIL NIL NIL) (-467 1075417 1075962 1076166 "INBFILE" NIL INBFILE (NIL) -8 NIL NIL NIL) (-466 1071512 1072567 1073510 "INBFF" NIL INBFF (NIL T) -7 NIL NIL NIL) (-465 1070366 1070689 1070717 "INBCON" 1071230 INBCON (NIL) -9 NIL 1071496 NIL) (-464 1069820 1070085 1070361 "INBCON-" NIL INBCON- (NIL T) -7 NIL NIL NIL) (-463 1069314 1069616 1069706 "INAST" NIL INAST (NIL) -8 NIL NIL NIL) (-462 1068771 1069080 1069185 "IMPTAST" NIL IMPTAST (NIL) -8 NIL NIL NIL) (-461 1067611 1067750 1068065 "IMATQF" NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL NIL) (-460 1066035 1066302 1066639 "IMATLIN" NIL IMATLIN (NIL T T T T) -7 NIL NIL NIL) (-459 1060878 1065966 1066030 "IFF" NIL IFF (NIL NIL NIL) -8 NIL NIL NIL) (-458 1060258 1060592 1060707 "IFAST" NIL IFAST (NIL) -8 NIL NIL NIL) (-457 1055237 1059696 1059882 "IFARRAY" NIL IFARRAY (NIL T NIL) -8 NIL NIL NIL) (-456 1054267 1055159 1055232 "IFAMON" NIL IFAMON (NIL T T NIL) -8 NIL NIL NIL) (-455 1053839 1053916 1053970 "IEVALAB" 1054177 IEVALAB (NIL T T) -9 NIL NIL NIL) (-454 1053594 1053674 1053834 "IEVALAB-" NIL IEVALAB- (NIL T T T) -7 NIL NIL NIL) (-453 1052979 1053206 1053363 "IDPT" NIL IDPT (NIL T T) -8 NIL NIL NIL) (-452 1051972 1052899 1052974 "IDPOAMS" NIL IDPOAMS (NIL T T) -8 NIL NIL NIL) (-451 1051035 1051892 1051967 "IDPOAM" NIL IDPOAM (NIL T T) -8 NIL NIL NIL) (-450 1050117 1050764 1050901 "IDPO" NIL IDPO (NIL T T) -8 NIL NIL NIL) (-449 1048480 1049051 1049102 "IDPC" 1049608 IDPC (NIL T T) -9 NIL 1049921 NIL) (-448 1047768 1048402 1048475 "IDPAM" NIL IDPAM (NIL T T) -8 NIL NIL NIL) (-447 1046938 1047690 1047763 "IDPAG" NIL IDPAG (NIL T T) -8 NIL NIL NIL) (-446 1046631 1046844 1046904 "IDENT" NIL IDENT (NIL) -8 NIL NIL NIL) (-445 1046335 1046375 1046414 "IDEMOPC" 1046419 IDEMOPC (NIL T) -9 NIL 1046556 NIL) (-444 1043406 1044287 1045179 "IDECOMP" NIL IDECOMP (NIL NIL NIL) -7 NIL NIL NIL) (-443 1037032 1038309 1039348 "IDEAL" NIL IDEAL (NIL T T T T) -8 NIL NIL NIL) (-442 1036294 1036424 1036623 "ICDEN" NIL ICDEN (NIL T T T T) -7 NIL NIL NIL) (-441 1035467 1035966 1036104 "ICARD" NIL ICARD (NIL) -8 NIL NIL NIL) (-440 1033856 1034187 1034578 "IBPTOOLS" NIL IBPTOOLS (NIL T T T T) -7 NIL NIL NIL) (-439 1031114 1031738 1032433 "IBATOOL" NIL IBATOOL (NIL T T T) -7 NIL NIL NIL) (-438 1029340 1029820 1030353 "IBACHIN" NIL IBACHIN (NIL T T T) -7 NIL NIL NIL) (-437 1027322 1029246 1029335 "IARRAY2" NIL IARRAY2 (NIL T T T) -8 NIL NIL NIL) (-436 1023355 1027260 1027317 "IARRAY1" NIL IARRAY1 (NIL T NIL) -8 NIL NIL NIL) (-435 1016934 1022319 1022787 "IAN" NIL IAN (NIL) -8 NIL NIL NIL) (-434 1016502 1016565 1016738 "IALGFACT" NIL IALGFACT (NIL T T T T) -7 NIL NIL NIL) (-433 1015994 1016143 1016171 "HYPCAT" 1016378 HYPCAT (NIL) -9 NIL NIL NIL) (-432 1015650 1015803 1015989 "HYPCAT-" NIL HYPCAT- (NIL T) -7 NIL NIL NIL) (-431 1015263 1015508 1015591 "HOSTNAME" NIL HOSTNAME (NIL) -8 NIL NIL NIL) (-430 1015096 1015145 1015186 "HOMOTOP" 1015191 HOMOTOP (NIL T) -9 NIL 1015224 NIL) (-429 1011674 1013044 1013085 "HOAGG" 1014056 HOAGG (NIL T) -9 NIL 1014775 NIL) (-428 1010680 1011150 1011669 "HOAGG-" NIL HOAGG- (NIL T T) -7 NIL NIL NIL) (-427 1003880 1010405 1010553 "HEXADEC" NIL HEXADEC (NIL) -8 NIL NIL NIL) (-426 1002815 1003073 1003336 "HEUGCD" NIL HEUGCD (NIL T) -7 NIL NIL NIL) (-425 1001750 1002680 1002810 "HELLFDIV" NIL HELLFDIV (NIL T T T T) -8 NIL NIL NIL) (-424 1000116 1001583 1001671 "HEAP" NIL HEAP (NIL T) -8 NIL NIL NIL) (-423 999431 999783 999916 "HEADAST" NIL HEADAST (NIL) -8 NIL NIL NIL) (-422 993038 999364 999426 "HDP" NIL HDP (NIL NIL T) -8 NIL NIL NIL) (-421 986177 992774 992925 "HDMP" NIL HDMP (NIL NIL T) -8 NIL NIL NIL) (-420 985630 985787 985950 "HB" NIL HB (NIL) -7 NIL NIL NIL) (-419 976949 985547 985625 "HASHTBL" NIL HASHTBL (NIL T T NIL) -8 NIL NIL NIL) (-418 976440 976743 976834 "HASAST" NIL HASAST (NIL) -8 NIL NIL NIL) (-417 973990 976227 976406 "HACKPI" NIL HACKPI (NIL) -8 NIL NIL NIL) (-416 969536 973873 973985 "GTSET" NIL GTSET (NIL T T T T) -8 NIL NIL NIL) (-415 960832 969433 969531 "GSTBL" NIL GSTBL (NIL T T T NIL) -8 NIL NIL NIL) (-414 952769 960201 960456 "GSERIES" NIL GSERIES (NIL T NIL NIL) -8 NIL NIL NIL) (-413 951793 952302 952330 "GROUP" 952533 GROUP (NIL) -9 NIL 952667 NIL) (-412 951336 951537 951788 "GROUP-" NIL GROUP- (NIL T) -7 NIL NIL NIL) (-411 950008 950347 950734 "GROEBSOL" NIL GROEBSOL (NIL NIL T T) -7 NIL NIL NIL) (-410 948830 949187 949238 "GRMOD" 949767 GRMOD (NIL T T) -9 NIL 949933 NIL) (-409 948649 948697 948825 "GRMOD-" NIL GRMOD- (NIL T T T) -7 NIL NIL NIL) (-408 944772 945983 946983 "GRIMAGE" NIL GRIMAGE (NIL) -8 NIL NIL NIL) (-407 943494 943818 944133 "GRDEF" NIL GRDEF (NIL) -7 NIL NIL NIL) (-406 943047 943175 943316 "GRAY" NIL GRAY (NIL) -7 NIL NIL NIL) (-405 942120 942619 942670 "GRALG" 942823 GRALG (NIL T T) -9 NIL 942913 NIL) (-404 941839 941940 942115 "GRALG-" NIL GRALG- (NIL T T T) -7 NIL NIL NIL) (-403 938720 941532 941697 "GPOLSET" NIL GPOLSET (NIL T T T T) -8 NIL NIL NIL) (-402 938133 938196 938453 "GOSPER" NIL GOSPER (NIL T T T T T) -7 NIL NIL NIL) (-401 933987 934883 935408 "GMODPOL" NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL NIL) (-400 933162 933364 933602 "GHENSEL" NIL GHENSEL (NIL T T) -7 NIL NIL NIL) (-399 928165 929092 930111 "GENUPS" NIL GENUPS (NIL T T) -7 NIL NIL NIL) (-398 927913 927970 928059 "GENUFACT" NIL GENUFACT (NIL T) -7 NIL NIL NIL) (-397 927395 927484 927649 "GENPGCD" NIL GENPGCD (NIL T T T T) -7 NIL NIL NIL) (-396 926904 926945 927158 "GENMFACT" NIL GENMFACT (NIL T T T T T) -7 NIL NIL NIL) (-395 925705 925988 926292 "GENEEZ" NIL GENEEZ (NIL T T) -7 NIL NIL NIL) (-394 918980 925395 925556 "GDMP" NIL GDMP (NIL NIL T T) -8 NIL NIL NIL) (-393 908763 913770 914874 "GCNAALG" NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL NIL) (-392 906815 907918 907946 "GCDDOM" 908201 GCDDOM (NIL) -9 NIL 908358 NIL) (-391 906438 906595 906810 "GCDDOM-" NIL GCDDOM- (NIL T) -7 NIL NIL NIL) (-390 897231 899701 902089 "GBINTERN" NIL GBINTERN (NIL T T T T) -7 NIL NIL NIL) (-389 895366 895691 896109 "GBF" NIL GBF (NIL T T T T) -7 NIL NIL NIL) (-388 894307 894496 894763 "GBEUCLID" NIL GBEUCLID (NIL T T T T) -7 NIL NIL NIL) (-387 893178 893385 893689 "GB" NIL GB (NIL T T T T) -7 NIL NIL NIL) (-386 892641 892783 892931 "GAUSSFAC" NIL GAUSSFAC (NIL) -7 NIL NIL NIL) (-385 891253 891601 891914 "GALUTIL" NIL GALUTIL (NIL T) -7 NIL NIL NIL) (-384 889798 890119 890441 "GALPOLYU" NIL GALPOLYU (NIL T T) -7 NIL NIL NIL) (-383 887424 887780 888185 "GALFACTU" NIL GALFACTU (NIL T T T) -7 NIL NIL NIL) (-382 880676 882337 883915 "GALFACT" NIL GALFACT (NIL T) -7 NIL NIL NIL) (-381 880328 880549 880617 "FUNDESC" NIL FUNDESC (NIL) -8 NIL NIL NIL) (-380 879952 880173 880254 "FUNCTION" NIL FUNCTION (NIL NIL) -8 NIL NIL NIL) (-379 878049 878732 879192 "FT" NIL FT (NIL) -8 NIL NIL NIL) (-378 876642 876949 877341 "FSUPFACT" NIL FSUPFACT (NIL T T T) -7 NIL NIL NIL) (-377 875297 875656 875980 "FST" NIL FST (NIL) -8 NIL NIL NIL) (-376 874600 874724 874911 "FSRED" NIL FSRED (NIL T T) -7 NIL NIL NIL) (-375 873574 873840 874187 "FSPRMELT" NIL FSPRMELT (NIL T T) -7 NIL NIL NIL) (-374 871232 871762 872244 "FSPECF" NIL FSPECF (NIL T T) -7 NIL NIL NIL) (-373 870815 870875 871044 "FSINT" NIL FSINT (NIL T T) -7 NIL NIL NIL) (-372 869115 870029 870332 "FSERIES" NIL FSERIES (NIL T T) -8 NIL NIL NIL) (-371 868263 868397 868620 "FSCINT" NIL FSCINT (NIL T T) -7 NIL NIL NIL) (-370 867434 867595 867822 "FSAGG2" NIL FSAGG2 (NIL T T T T) -7 NIL NIL NIL) (-369 863550 866329 866370 "FSAGG" 866740 FSAGG (NIL T) -9 NIL 867001 NIL) (-368 861904 862663 863455 "FSAGG-" NIL FSAGG- (NIL T T) -7 NIL NIL NIL) (-367 859860 860156 860700 "FS2UPS" NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL NIL) (-366 858907 859089 859389 "FS2EXPXP" NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL NIL) (-365 858588 858637 858764 "FS2" NIL FS2 (NIL T T T T) -7 NIL NIL NIL) (-364 838744 848245 848286 "FS" 852156 FS (NIL T) -9 NIL 854434 NIL) (-363 830975 834468 838447 "FS-" NIL FS- (NIL T T) -7 NIL NIL NIL) (-362 830509 830636 830788 "FRUTIL" NIL FRUTIL (NIL T) -7 NIL NIL NIL) (-361 825032 828190 828230 "FRNAALG" 829550 FRNAALG (NIL T) -9 NIL 830148 NIL) (-360 821773 823024 824282 "FRNAALG-" NIL FRNAALG- (NIL T T) -7 NIL NIL NIL) (-359 821454 821503 821630 "FRNAAF2" NIL FRNAAF2 (NIL T T T T) -7 NIL NIL NIL) (-358 819941 820498 820792 "FRMOD" NIL FRMOD (NIL T T T T NIL) -8 NIL NIL NIL) (-357 819227 819320 819607 "FRIDEAL2" NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-356 817061 817827 818143 "FRIDEAL" NIL FRIDEAL (NIL T T T T) -8 NIL NIL NIL) (-355 816170 816613 816654 "FRETRCT" 816659 FRETRCT (NIL T) -9 NIL 816830 NIL) (-354 815543 815821 816165 "FRETRCT-" NIL FRETRCT- (NIL T T) -7 NIL NIL NIL) (-353 812287 813807 813866 "FRAMALG" 814748 FRAMALG (NIL T T) -9 NIL 815040 NIL) (-352 810883 811434 812064 "FRAMALG-" NIL FRAMALG- (NIL T T T) -7 NIL NIL NIL) (-351 810576 810639 810746 "FRAC2" NIL FRAC2 (NIL T T) -7 NIL NIL NIL) (-350 804217 810381 810571 "FRAC" NIL FRAC (NIL T) -8 NIL NIL NIL) (-349 803910 803973 804080 "FR2" NIL FR2 (NIL T T) -7 NIL NIL NIL) (-348 796218 800789 802117 "FR" NIL FR (NIL T) -8 NIL NIL NIL) (-347 789996 793499 793527 "FPS" 794646 FPS (NIL) -9 NIL 795202 NIL) (-346 789553 789686 789850 "FPS-" NIL FPS- (NIL T) -7 NIL NIL NIL) (-345 786363 788406 788434 "FPC" 788659 FPC (NIL) -9 NIL 788801 NIL) (-344 786209 786261 786358 "FPC-" NIL FPC- (NIL T) -7 NIL NIL NIL) (-343 784986 785695 785736 "FPATMAB" 785741 FPATMAB (NIL T) -9 NIL 785893 NIL) (-342 783416 784012 784359 "FPARFRAC" NIL FPARFRAC (NIL T T) -8 NIL NIL NIL) (-341 782991 783049 783222 "FORDER" NIL FORDER (NIL T T T T) -7 NIL NIL NIL) (-340 781494 782389 782563 "FNLA" NIL FNLA (NIL NIL NIL T) -8 NIL NIL NIL) (-339 780109 780614 780642 "FNCAT" 781099 FNCAT (NIL) -9 NIL 781356 NIL) (-338 779566 780076 780104 "FNAME" NIL FNAME (NIL) -8 NIL NIL NIL) (-337 778153 779515 779561 "FMONOID" NIL FMONOID (NIL T) -8 NIL NIL NIL) (-336 774741 776099 776140 "FMONCAT" 777357 FMONCAT (NIL T) -9 NIL 777961 NIL) (-335 771599 772677 772730 "FMCAT" 773911 FMCAT (NIL T T) -9 NIL 774403 NIL) (-334 770299 771422 771521 "FM1" NIL FM1 (NIL T T) -8 NIL NIL NIL) (-333 769347 770147 770294 "FM" NIL FM (NIL T T) -8 NIL NIL NIL) (-332 767534 767986 768480 "FLOATRP" NIL FLOATRP (NIL T) -7 NIL NIL NIL) (-331 765469 766005 766583 "FLOATCP" NIL FLOATCP (NIL T) -7 NIL NIL NIL) (-330 758855 763806 764420 "FLOAT" NIL FLOAT (NIL) -8 NIL NIL NIL) (-329 757336 758437 758477 "FLINEXP" 758482 FLINEXP (NIL T) -9 NIL 758575 NIL) (-328 756745 757004 757331 "FLINEXP-" NIL FLINEXP- (NIL T T) -7 NIL NIL NIL) (-327 755960 756119 756340 "FLASORT" NIL FLASORT (NIL T T) -7 NIL NIL NIL) (-326 752843 753922 753974 "FLALG" 755201 FLALG (NIL T T) -9 NIL 755668 NIL) (-325 752014 752175 752402 "FLAGG2" NIL FLAGG2 (NIL T T T T) -7 NIL NIL NIL) (-324 745555 749413 749454 "FLAGG" 750709 FLAGG (NIL T) -9 NIL 751356 NIL) (-323 744663 745067 745550 "FLAGG-" NIL FLAGG- (NIL T T) -7 NIL NIL NIL) (-322 741224 742488 742547 "FINRALG" 743675 FINRALG (NIL T T) -9 NIL 744183 NIL) (-321 740615 740880 741219 "FINRALG-" NIL FINRALG- (NIL T T T) -7 NIL NIL NIL) (-320 739913 740209 740237 "FINITE" 740433 FINITE (NIL) -9 NIL 740540 NIL) (-319 739821 739847 739908 "FINITE-" NIL FINITE- (NIL T) -7 NIL NIL NIL) (-318 737278 738499 738540 "FINAGG" 739170 FINAGG (NIL T) -9 NIL 739482 NIL) (-317 736718 736977 737273 "FINAGG-" NIL FINAGG- (NIL T T) -7 NIL NIL NIL) (-316 728679 731270 731310 "FINAALG" 734962 FINAALG (NIL T) -9 NIL 736400 NIL) (-315 724946 726191 727314 "FINAALG-" NIL FINAALG- (NIL T T) -7 NIL NIL NIL) (-314 723498 723917 723971 "FILECAT" 724655 FILECAT (NIL T T) -9 NIL 724871 NIL) (-313 722849 723323 723426 "FILE" NIL FILE (NIL T) -8 NIL NIL NIL) (-312 720097 721975 722003 "FIELD" 722043 FIELD (NIL) -9 NIL 722123 NIL) (-311 719122 719583 720092 "FIELD-" NIL FIELD- (NIL T) -7 NIL NIL NIL) (-310 717126 718072 718418 "FGROUP" NIL FGROUP (NIL T) -8 NIL NIL NIL) (-309 716369 716550 716769 "FGLMICPK" NIL FGLMICPK (NIL T NIL) -7 NIL NIL NIL) (-308 711639 716307 716364 "FFX" NIL FFX (NIL T NIL) -8 NIL NIL NIL) (-307 711301 711368 711503 "FFSLPE" NIL FFSLPE (NIL T T T) -7 NIL NIL NIL) (-306 710841 710883 711092 "FFPOLY2" NIL FFPOLY2 (NIL T T) -7 NIL NIL NIL) (-305 707521 708398 709175 "FFPOLY" NIL FFPOLY (NIL T) -7 NIL NIL NIL) (-304 702805 707453 707516 "FFP" NIL FFP (NIL T NIL) -8 NIL NIL NIL) (-303 697484 702294 702484 "FFNBX" NIL FFNBX (NIL T NIL) -8 NIL NIL NIL) (-302 691965 696765 697023 "FFNBP" NIL FFNBP (NIL T NIL) -8 NIL NIL NIL) (-301 686172 691416 691627 "FFNB" NIL FFNB (NIL NIL NIL) -8 NIL NIL NIL) (-300 685195 685405 685720 "FFINTBAS" NIL FFINTBAS (NIL T T T) -7 NIL NIL NIL) (-299 680635 683340 683368 "FFIELDC" 683987 FFIELDC (NIL) -9 NIL 684362 NIL) (-298 679704 680144 680630 "FFIELDC-" NIL FFIELDC- (NIL T) -7 NIL NIL NIL) (-297 679319 679377 679501 "FFHOM" NIL FFHOM (NIL T T T) -7 NIL NIL NIL) (-296 677463 677986 678503 "FFF" NIL FFF (NIL T) -7 NIL NIL NIL) (-295 672557 677262 677363 "FFCGX" NIL FFCGX (NIL T NIL) -8 NIL NIL NIL) (-294 667657 672346 672453 "FFCGP" NIL FFCGP (NIL T NIL) -8 NIL NIL NIL) (-293 662323 667448 667556 "FFCG" NIL FFCG (NIL NIL NIL) -8 NIL NIL NIL) (-292 661777 661826 662061 "FFCAT2" NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-291 640352 651386 651472 "FFCAT" 656622 FFCAT (NIL T T T) -9 NIL 658058 NIL) (-290 636592 637818 639124 "FFCAT-" NIL FFCAT- (NIL T T T T) -7 NIL NIL NIL) (-289 631435 636523 636587 "FF" NIL FF (NIL NIL NIL) -8 NIL NIL NIL) (-288 630327 630796 630837 "FEVALAB" 630921 FEVALAB (NIL T) -9 NIL 631182 NIL) (-287 629732 629984 630322 "FEVALAB-" NIL FEVALAB- (NIL T T) -7 NIL NIL NIL) (-286 626559 627470 627585 "FDIVCAT" 629152 FDIVCAT (NIL T T T T) -9 NIL 629588 NIL) (-285 626353 626385 626554 "FDIVCAT-" NIL FDIVCAT- (NIL T T T T T) -7 NIL NIL NIL) (-284 625660 625753 626030 "FDIV2" NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL NIL) (-283 624146 625144 625347 "FDIV" NIL FDIV (NIL T T T T) -8 NIL NIL NIL) (-282 623239 623623 623825 "FCTRDATA" NIL FCTRDATA (NIL) -8 NIL NIL NIL) (-281 622361 622850 622990 "FCOMP" NIL FCOMP (NIL T) -8 NIL NIL NIL) (-280 613948 618591 618631 "FAXF" 620432 FAXF (NIL T) -9 NIL 621122 NIL) (-279 611864 612668 613483 "FAXF-" NIL FAXF- (NIL T T) -7 NIL NIL NIL) (-278 606900 611386 611560 "FARRAY" NIL FARRAY (NIL T) -8 NIL NIL NIL) (-277 601358 603781 603833 "FAMR" 604844 FAMR (NIL T T) -9 NIL 605303 NIL) (-276 600557 600922 601353 "FAMR-" NIL FAMR- (NIL T T T) -7 NIL NIL NIL) (-275 599578 600499 600552 "FAMONOID" NIL FAMONOID (NIL T) -8 NIL NIL NIL) (-274 597172 598051 598104 "FAMONC" 599045 FAMONC (NIL T T) -9 NIL 599430 NIL) (-273 595728 597030 597167 "FAGROUP" NIL FAGROUP (NIL T) -8 NIL NIL NIL) (-272 593808 594169 594571 "FACUTIL" NIL FACUTIL (NIL T T T T) -7 NIL NIL NIL) (-271 593085 593282 593504 "FACTFUNC" NIL FACTFUNC (NIL T) -7 NIL NIL NIL) (-270 584945 592532 592731 "EXPUPXS" NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL NIL) (-269 582964 583534 584120 "EXPRTUBE" NIL EXPRTUBE (NIL) -7 NIL NIL NIL) (-268 579866 580508 581228 "EXPRODE" NIL EXPRODE (NIL T T) -7 NIL NIL NIL) (-267 575023 575730 576535 "EXPR2UPS" NIL EXPR2UPS (NIL T T) -7 NIL NIL NIL) (-266 574712 574775 574884 "EXPR2" NIL EXPR2 (NIL T T) -7 NIL NIL NIL) (-265 559505 573761 574187 "EXPR" NIL EXPR (NIL T) -8 NIL NIL NIL) (-264 550032 558825 559113 "EXPEXPAN" NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL NIL) (-263 549526 549828 549918 "EXITAST" NIL EXITAST (NIL) -8 NIL NIL NIL) (-262 549302 549492 549521 "EXIT" NIL EXIT (NIL) -8 NIL NIL NIL) (-261 548991 549059 549172 "EVALCYC" NIL EVALCYC (NIL T) -7 NIL NIL NIL) (-260 548508 548650 548691 "EVALAB" 548861 EVALAB (NIL T) -9 NIL 548965 NIL) (-259 548136 548282 548503 "EVALAB-" NIL EVALAB- (NIL T T) -7 NIL NIL NIL) (-258 545179 546774 546802 "EUCDOM" 547356 EUCDOM (NIL) -9 NIL 547705 NIL) (-257 544106 544599 545174 "EUCDOM-" NIL EUCDOM- (NIL T) -7 NIL NIL NIL) (-256 543831 543887 543987 "ES2" NIL ES2 (NIL T T) -7 NIL NIL NIL) (-255 543519 543583 543692 "ES1" NIL ES1 (NIL T T) -7 NIL NIL NIL) (-254 537290 539190 539218 "ES" 541960 ES (NIL) -9 NIL 543344 NIL) (-253 533805 535337 537129 "ES-" NIL ES- (NIL T) -7 NIL NIL NIL) (-252 533153 533306 533482 "ERROR" NIL ERROR (NIL) -7 NIL NIL NIL) (-251 524478 533083 533148 "EQTBL" NIL EQTBL (NIL T T) -8 NIL NIL NIL) (-250 524167 524230 524339 "EQ2" NIL EQ2 (NIL T T) -7 NIL NIL NIL) (-249 517794 520919 522352 "EQ" NIL EQ (NIL T) -8 NIL NIL NIL) (-248 514097 515193 516286 "EP" NIL EP (NIL T) -7 NIL NIL NIL) (-247 512926 513276 513581 "ENV" NIL ENV (NIL) -8 NIL NIL NIL) (-246 511811 512542 512570 "ENTIRER" 512575 ENTIRER (NIL) -9 NIL 512619 NIL) (-245 511700 511734 511806 "ENTIRER-" NIL ENTIRER- (NIL T) -7 NIL NIL NIL) (-244 508333 510130 510479 "EMR" NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL NIL) (-243 507425 507636 507690 "ELTAGG" 508070 ELTAGG (NIL T T) -9 NIL 508281 NIL) (-242 507205 507279 507420 "ELTAGG-" NIL ELTAGG- (NIL T T T) -7 NIL NIL NIL) (-241 506951 506986 507040 "ELTAB" 507124 ELTAB (NIL T T) -9 NIL 507176 NIL) (-240 506202 506372 506571 "ELFUTS" NIL ELFUTS (NIL T T) -7 NIL NIL NIL) (-239 505926 506000 506028 "ELEMFUN" 506133 ELEMFUN (NIL) -9 NIL NIL NIL) (-238 505826 505853 505921 "ELEMFUN-" NIL ELEMFUN- (NIL T) -7 NIL NIL NIL) (-237 500372 503845 503886 "ELAGG" 504823 ELAGG (NIL T) -9 NIL 505286 NIL) (-236 499170 499708 500367 "ELAGG-" NIL ELAGG- (NIL T T) -7 NIL NIL NIL) (-235 498588 498755 498911 "ELABOR" NIL ELABOR (NIL) -8 NIL NIL NIL) (-234 497501 497820 498099 "ELABEXPR" NIL ELABEXPR (NIL) -8 NIL NIL NIL) (-233 490894 492892 493719 "EFUPXS" NIL EFUPXS (NIL T T T T) -7 NIL NIL NIL) (-232 484873 486869 487679 "EFULS" NIL EFULS (NIL T T T) -7 NIL NIL NIL) (-231 482687 483093 483564 "EFSTRUC" NIL EFSTRUC (NIL T T) -7 NIL NIL NIL) (-230 473687 475600 477141 "EF" NIL EF (NIL T T) -7 NIL NIL NIL) (-229 472800 473301 473450 "EAB" NIL EAB (NIL) -8 NIL NIL NIL) (-228 471498 472172 472212 "DVARCAT" 472495 DVARCAT (NIL T) -9 NIL 472635 NIL) (-227 470917 471181 471493 "DVARCAT-" NIL DVARCAT- (NIL T T) -7 NIL NIL NIL) (-226 462984 470785 470912 "DSMP" NIL DSMP (NIL T T T) -8 NIL NIL NIL) (-225 461322 462113 462154 "DSEXT" 462517 DSEXT (NIL T) -9 NIL 462811 NIL) (-224 460127 460651 461317 "DSEXT-" NIL DSEXT- (NIL T T) -7 NIL NIL NIL) (-223 459851 459916 460014 "DROPT1" NIL DROPT1 (NIL T) -7 NIL NIL NIL) (-222 456002 457218 458349 "DROPT0" NIL DROPT0 (NIL) -7 NIL NIL NIL) (-221 451648 453003 454067 "DROPT" NIL DROPT (NIL) -8 NIL NIL NIL) (-220 450323 450684 451070 "DRAWPT" NIL DRAWPT (NIL) -7 NIL NIL NIL) (-219 450009 450068 450186 "DRAWHACK" NIL DRAWHACK (NIL T) -7 NIL NIL NIL) (-218 448984 449282 449572 "DRAWCX" NIL DRAWCX (NIL) -7 NIL NIL NIL) (-217 448569 448644 448794 "DRAWCURV" NIL DRAWCURV (NIL T T) -7 NIL NIL NIL) (-216 440982 443094 445209 "DRAWCFUN" NIL DRAWCFUN (NIL) -7 NIL NIL NIL) (-215 436499 437518 438597 "DRAW" NIL DRAW (NIL T) -7 NIL NIL NIL) (-214 433229 435126 435167 "DQAGG" 435796 DQAGG (NIL T) -9 NIL 436069 NIL) (-213 419772 427412 427494 "DPOLCAT" 429331 DPOLCAT (NIL T T T T) -9 NIL 429874 NIL) (-212 416180 417828 419767 "DPOLCAT-" NIL DPOLCAT- (NIL T T T T T) -7 NIL NIL NIL) (-211 409338 416078 416175 "DPMO" NIL DPMO (NIL NIL T T) -8 NIL NIL NIL) (-210 402405 409167 409333 "DPMM" NIL DPMM (NIL NIL T T T) -8 NIL NIL NIL) (-209 401998 402258 402347 "DOMTMPLT" NIL DOMTMPLT (NIL) -8 NIL NIL NIL) (-208 401412 401860 401940 "DOMCTOR" NIL DOMCTOR (NIL) -8 NIL NIL NIL) (-207 400698 401023 401174 "DOMAIN" NIL DOMAIN (NIL) -8 NIL NIL NIL) (-206 393837 400434 400585 "DMP" NIL DMP (NIL NIL T) -8 NIL NIL NIL) (-205 391586 392903 392943 "DMEXT" 392948 DMEXT (NIL T) -9 NIL 393123 NIL) (-204 391242 391304 391448 "DLP" NIL DLP (NIL T) -7 NIL NIL NIL) (-203 384739 390727 390917 "DLIST" NIL DLIST (NIL T) -8 NIL NIL NIL) (-202 381409 383562 383603 "DLAGG" 384153 DLAGG (NIL T) -9 NIL 384382 NIL) (-201 379760 380631 380659 "DIVRING" 380751 DIVRING (NIL) -9 NIL 380834 NIL) (-200 379211 379455 379755 "DIVRING-" NIL DIVRING- (NIL T) -7 NIL NIL NIL) (-199 377639 378056 378462 "DISPLAY" NIL DISPLAY (NIL) -7 NIL NIL NIL) (-198 376676 376897 377162 "DIRPROD2" NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL NIL) (-197 370303 376608 376671 "DIRPROD" NIL DIRPROD (NIL NIL T) -8 NIL NIL NIL) (-196 358755 365063 365116 "DIRPCAT" 365372 DIRPCAT (NIL NIL T) -9 NIL 366247 NIL) (-195 356761 357531 358418 "DIRPCAT-" NIL DIRPCAT- (NIL T NIL T) -7 NIL NIL NIL) (-194 356208 356374 356560 "DIOSP" NIL DIOSP (NIL) -7 NIL NIL NIL) (-193 352758 355075 355116 "DIOPS" 355548 DIOPS (NIL T) -9 NIL 355774 NIL) (-192 352418 352562 352753 "DIOPS-" NIL DIOPS- (NIL T T) -7 NIL NIL NIL) (-191 351425 352171 352199 "DIOID" 352204 DIOID (NIL) -9 NIL 352226 NIL) (-190 350253 351082 351110 "DIFRING" 351115 DIFRING (NIL) -9 NIL 351136 NIL) (-189 349889 349987 350015 "DIFFSPC" 350134 DIFFSPC (NIL) -9 NIL 350209 NIL) (-188 349630 349732 349884 "DIFFSPC-" NIL DIFFSPC- (NIL T) -7 NIL NIL NIL) (-187 348533 349158 349198 "DIFFMOD" 349203 DIFFMOD (NIL T) -9 NIL 349300 NIL) (-186 348217 348274 348315 "DIFFDOM" 348436 DIFFDOM (NIL T) -9 NIL 348504 NIL) (-185 348098 348128 348212 "DIFFDOM-" NIL DIFFDOM- (NIL T T) -7 NIL NIL NIL) (-184 345771 347292 347332 "DIFEXT" 347337 DIFEXT (NIL T) -9 NIL 347489 NIL) (-183 342936 345253 345294 "DIAGG" 345299 DIAGG (NIL T) -9 NIL 345319 NIL) (-182 342492 342682 342931 "DIAGG-" NIL DIAGG- (NIL T T) -7 NIL NIL NIL) (-181 337838 341682 341959 "DHMATRIX" NIL DHMATRIX (NIL T) -8 NIL NIL NIL) (-180 334296 335349 336359 "DFSFUN" NIL DFSFUN (NIL) -7 NIL NIL NIL) (-179 328846 333450 333777 "DFLOAT" NIL DFLOAT (NIL) -8 NIL NIL NIL) (-178 327412 327704 328079 "DFINTTLS" NIL DFINTTLS (NIL T T) -7 NIL NIL NIL) (-177 324532 325784 326180 "DERHAM" NIL DERHAM (NIL T NIL) -8 NIL NIL NIL) (-176 322424 324363 324452 "DEQUEUE" NIL DEQUEUE (NIL T) -8 NIL NIL NIL) (-175 321807 321952 322134 "DEGRED" NIL DEGRED (NIL T T) -7 NIL NIL NIL) (-174 319125 319849 320649 "DEFINTRF" NIL DEFINTRF (NIL T) -7 NIL NIL NIL) (-173 317234 317692 318254 "DEFINTEF" NIL DEFINTEF (NIL T T) -7 NIL NIL NIL) (-172 316617 316950 317064 "DEFAST" NIL DEFAST (NIL) -8 NIL NIL NIL) (-171 309817 316342 316490 "DECIMAL" NIL DECIMAL (NIL) -8 NIL NIL NIL) (-170 307737 308247 308751 "DDFACT" NIL DDFACT (NIL T T) -7 NIL NIL NIL) (-169 307376 307425 307576 "DBLRESP" NIL DBLRESP (NIL T T T T) -7 NIL NIL NIL) (-168 306635 307197 307288 "DBASIS" NIL DBASIS (NIL NIL) -8 NIL NIL NIL) (-167 304659 305101 305461 "DBASE" NIL DBASE (NIL T) -8 NIL NIL NIL) (-166 303951 304240 304386 "DATAARY" NIL DATAARY (NIL NIL T) -8 NIL NIL NIL) (-165 303402 303548 303700 "CYCLOTOM" NIL CYCLOTOM (NIL) -7 NIL NIL NIL) (-164 300764 301557 302284 "CYCLES" NIL CYCLES (NIL) -7 NIL NIL NIL) (-163 300203 300349 300520 "CVMP" NIL CVMP (NIL T) -7 NIL NIL NIL) (-162 298275 298586 298953 "CTRIGMNP" NIL CTRIGMNP (NIL T T) -7 NIL NIL NIL) (-161 297832 298087 298188 "CTORKIND" NIL CTORKIND (NIL) -8 NIL NIL NIL) (-160 297033 297416 297444 "CTORCAT" 297625 CTORCAT (NIL) -9 NIL 297737 NIL) (-159 296736 296870 297028 "CTORCAT-" NIL CTORCAT- (NIL T) -7 NIL NIL NIL) (-158 296229 296486 296594 "CTORCALL" NIL CTORCALL (NIL T) -8 NIL NIL NIL) (-157 295645 296076 296149 "CTOR" NIL CTOR (NIL) -8 NIL NIL NIL) (-156 295104 295221 295374 "CSTTOOLS" NIL CSTTOOLS (NIL T T) -7 NIL NIL NIL) (-155 291498 292254 293009 "CRFP" NIL CRFP (NIL T T) -7 NIL NIL NIL) (-154 290989 291292 291383 "CRCEAST" NIL CRCEAST (NIL) -8 NIL NIL NIL) (-153 290208 290417 290645 "CRAPACK" NIL CRAPACK (NIL T) -7 NIL NIL NIL) (-152 289712 289817 290021 "CPMATCH" NIL CPMATCH (NIL T T T) -7 NIL NIL NIL) (-151 289465 289499 289605 "CPIMA" NIL CPIMA (NIL T T T) -7 NIL NIL 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\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index af48990c..e3238bd7 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,794 +1,794 @@ -(631528 . 3577824391) +(631528 . 3577831633) (((*1 *2 *3 *4) - (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) - (-5 *2 (-1180 (-350 (-485)))) (-5 *1 (-1209 *4))))) + (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) + (-5 *2 (-1179 (-350 (-484)))) (-5 *1 (-1208 *4))))) (((*1 *2 *3) - (|partial| -12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) - (-5 *2 (-1180 (-485))) (-5 *1 (-1209 *4))))) + (|partial| -12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) + (-5 *2 (-1179 (-484))) (-5 *1 (-1208 *4))))) (((*1 *2 *3) - (-12 (-5 *3 (-1180 *4)) (-4 *4 (-13 (-962) (-581 (-485)))) (-5 *2 (-85)) - (-5 *1 (-1209 *4))))) + (-12 (-5 *3 (-1179 *4)) (-4 *4 (-13 (-961) (-580 (-484)))) (-5 *2 (-85)) + (-5 *1 (-1208 *4))))) (((*1 *2 *3) - 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\ No newline at end of file |