diff options
Diffstat (limited to 'src/share')
| -rw-r--r-- | src/share/algebra/browse.daase | 1536 | ||||
| -rw-r--r-- | src/share/algebra/category.daase | 1246 | ||||
| -rw-r--r-- | src/share/algebra/compress.daase | 1299 | ||||
| -rw-r--r-- | src/share/algebra/interp.daase | 8628 | ||||
| -rw-r--r-- | src/share/algebra/operation.daase | 31393 |
5 files changed, 22057 insertions, 22045 deletions
diff --git a/src/share/algebra/browse.daase b/src/share/algebra/browse.daase index 70334282..967cece3 100644 --- a/src/share/algebra/browse.daase +++ b/src/share/algebra/browse.daase @@ -1,12 +1,12 @@ -(2235836 . 3415311729) +(2236562 . 3416411997) (-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."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-20 S) ((|constructor| (NIL "The class of abelian groups,{} \\spadignore{i.e.} additive monoids where each element has an additive inverse. \\blankline")) (* (($ (|Integer|) $) "\\spad{n*x} is the product of \\spad{x} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x-y} is the difference of \\spad{x} and \\spad{y} \\spadignore{i.e.} \\spad{x + (-y)}.") (($ $) "\\spad{-x} is the additive inverse of \\spad{x}."))) @@ -38,7 +38,7 @@ NIL NIL (-27) ((|constructor| (NIL "Model for algebraically closed fields.")) (|zerosOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. Otherwise they are implicit algebraic quantities. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|zeroOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity which displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}; if possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity.") (($ (|Polynomial| $)) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. If possible,{} \\spad{y} is expressed in terms of radicals. Otherwise it is an implicit algebraic quantity. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootsOf| (((|List| $) (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) (|Polynomial| $)) "\\spad{rootsOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ (|SparseUnivariatePolynomial| $) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ (|SparseUnivariatePolynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}.") (($ (|Polynomial| $)) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-28 S R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) @@ -46,23 +46,23 @@ NIL NIL (-29 R) ((|constructor| (NIL "Model for algebraically closed function spaces.")) (|zerosOf| (((|List| $) $ (|Symbol|)) "\\spad{zerosOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible,{} and otherwise as implicit algebraic quantities which display as \\spad{'yi}. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{zerosOf(p)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}. The \\spad{yi}\\spad{'s} are expressed in radicals if possible. The returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable.")) (|zeroOf| (($ $ (|Symbol|)) "\\spad{zeroOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity which displays as \\spad{'y}.") (($ $) "\\spad{zeroOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. The value \\spad{y} is expressed in terms of radicals if possible,{}and otherwise as an implicit algebraic quantity. Error: if \\spad{p} has more than one variable.")) (|rootsOf| (((|List| $) $ (|Symbol|)) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; The returned roots display as \\spad{'y1},{}...,{}\\spad{'yn}. Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values.") (((|List| $) $) "\\spad{rootsOf(p,{} y)} returns \\spad{[y1,{}...,{}yn]} such that \\spad{p(\\spad{yi}) = 0}; Note: the returned symbols \\spad{y1},{}...,{}\\spad{yn} are bound in the interpreter to respective root values. Error: if \\spad{p} has more than one variable \\spad{y}.")) (|rootOf| (($ $ (|Symbol|)) "\\spad{rootOf(p,{}y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}.") (($ $) "\\spad{rootOf(p)} returns \\spad{y} such that \\spad{p(y) = 0}. Error: if \\spad{p} has more than one variable \\spad{y}."))) -((-4241 . T) (-4239 . T) (-4238 . T) ((-4246 "*") . T) (-4237 . T) (-4242 . T) (-4236 . T) (-3656 . T)) +((-4245 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4241 . T) (-4246 . T) (-4240 . T) (-4069 . T)) NIL (-30) ((|constructor| (NIL "\\indented{1}{Plot a NON-SINGULAR plane algebraic curve \\spad{p}(\\spad{x},{}\\spad{y}) = 0.} Author: Clifton \\spad{J}. Williamson Date Created: Fall 1988 Date Last Updated: 27 April 1990 Keywords: algebraic curve,{} non-singular,{} plot Examples: References:")) (|refine| (($ $ (|DoubleFloat|)) "\\spad{refine(p,{}x)} \\undocumented{}")) (|makeSketch| (($ (|Polynomial| (|Integer|)) (|Symbol|) (|Symbol|) (|Segment| (|Fraction| (|Integer|))) (|Segment| (|Fraction| (|Integer|)))) "\\spad{makeSketch(p,{}x,{}y,{}a..b,{}c..d)} creates an ACPLOT of the curve \\spad{p = 0} in the region {\\em a <= x <= b,{} c <= y <= d}. More specifically,{} 'makeSketch' plots a non-singular algebraic curve \\spad{p = 0} in an rectangular region {\\em xMin <= x <= xMax},{} {\\em yMin <= y <= yMax}. The user inputs \\spad{makeSketch(p,{}x,{}y,{}xMin..xMax,{}yMin..yMax)}. Here \\spad{p} is a polynomial in the variables \\spad{x} and \\spad{y} with integer coefficients (\\spad{p} belongs to the domain \\spad{Polynomial Integer}). The case where \\spad{p} is a polynomial in only one of the variables is allowed. The variables \\spad{x} and \\spad{y} are input to specify the the coordinate axes. The horizontal axis is the \\spad{x}-axis and the vertical axis is the \\spad{y}-axis. The rational numbers xMin,{}...,{}yMax specify the boundaries of the region in which the curve is to be plotted."))) NIL NIL -(-31 R -2315) +(-31 R -3539) ((|constructor| (NIL "This package provides algebraic functions over an integral domain.")) (|iroot| ((|#2| |#1| (|Integer|)) "\\spad{iroot(p,{} n)} should be a non-exported function.")) (|definingPolynomial| ((|#2| |#2|) "\\spad{definingPolynomial(f)} returns the defining polynomial of \\spad{f} as an element of \\spad{F}. Error: if \\spad{f} is not a kernel.")) (|minPoly| (((|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{minPoly(k)} returns the defining polynomial of \\spad{k}.")) (** ((|#2| |#2| (|Fraction| (|Integer|))) "\\spad{x ** q} is \\spad{x} raised to the rational power \\spad{q}.")) (|droot| (((|OutputForm|) (|List| |#2|)) "\\spad{droot(l)} should be a non-exported function.")) (|inrootof| ((|#2| (|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{inrootof(p,{} x)} should be a non-exported function.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}. Error: if \\spad{op} is not an algebraic operator,{} that is,{} an \\spad{n}th root or implicit algebraic operator.")) (|rootOf| ((|#2| (|SparseUnivariatePolynomial| |#2|) (|Symbol|)) "\\spad{rootOf(p,{} y)} returns \\spad{y} such that \\spad{p(y) = 0}. The object returned displays as \\spad{'y}."))) NIL ((|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (-32 S) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) NIL -((|HasAttribute| |#1| (QUOTE -4244))) +((|HasAttribute| |#1| (QUOTE -4248))) (-33) ((|constructor| (NIL "The notion of aggregate serves to model any data structure aggregate,{} designating any collection of objects,{} with heterogenous or homogeneous members,{} with a finite or infinite number of members,{} explicitly or implicitly represented. An aggregate can in principle represent everything from a string of characters to abstract sets such as \"the set of \\spad{x} satisfying relation {\\em r(x)}\" An attribute \\spadatt{finiteAggregate} is used to assert that a domain has a finite number of elements.")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# u} returns the number of items in \\spad{u}.")) (|sample| (($) "\\spad{sample yields} a value of type \\%")) (|size?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{size?(u,{}n)} tests if \\spad{u} has exactly \\spad{n} elements.")) (|more?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{more?(u,{}n)} tests if \\spad{u} has greater than \\spad{n} elements.")) (|less?| (((|Boolean|) $ (|NonNegativeInteger|)) "\\spad{less?(u,{}n)} tests if \\spad{u} has less than \\spad{n} elements.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(u)} tests if \\spad{u} has 0 elements.")) (|empty| (($) "\\spad{empty()}\\$\\spad{D} creates an aggregate of type \\spad{D} with 0 elements. Note: The {\\em \\$D} can be dropped if understood by context,{} \\spadignore{e.g.} \\axiom{u: \\spad{D} \\spad{:=} empty()}.")) (|copy| (($ $) "\\spad{copy(u)} returns a top-level (non-recursive) copy of \\spad{u}. Note: for collections,{} \\axiom{copy(\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u}]}.")) (|eq?| (((|Boolean|) $ $) "\\spad{eq?(u,{}v)} tests if \\spad{u} and \\spad{v} are same objects."))) -((-3656 . T)) +((-4069 . T)) NIL (-34) ((|constructor| (NIL "Category for the inverse hyperbolic trigonometric functions.")) (|atanh| (($ $) "\\spad{atanh(x)} returns the hyperbolic arc-tangent of \\spad{x}.")) (|asinh| (($ $) "\\spad{asinh(x)} returns the hyperbolic arc-sine of \\spad{x}.")) (|asech| (($ $) "\\spad{asech(x)} returns the hyperbolic arc-secant of \\spad{x}.")) (|acsch| (($ $) "\\spad{acsch(x)} returns the hyperbolic arc-cosecant of \\spad{x}.")) (|acoth| (($ $) "\\spad{acoth(x)} returns the hyperbolic arc-cotangent of \\spad{x}.")) (|acosh| (($ $) "\\spad{acosh(x)} returns the hyperbolic arc-cosine of \\spad{x}."))) @@ -70,7 +70,7 @@ NIL NIL (-35 |Key| |Entry|) ((|constructor| (NIL "An association list is a list of key entry pairs which may be viewed as a table. It is a poor mans version of a table: searching for a key is a linear operation.")) (|assoc| (((|Union| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)) "failed") |#1| $) "\\spad{assoc(k,{}u)} returns the element \\spad{x} in association list \\spad{u} stored with key \\spad{k},{} or \"failed\" if \\spad{u} has no key \\spad{k}."))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-36 S R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#2|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) @@ -78,17 +78,17 @@ NIL NIL (-37 R) ((|constructor| (NIL "The category of associative algebras (modules which are themselves rings). \\blankline")) (|coerce| (($ |#1|) "\\spad{coerce(r)} maps the ring element \\spad{r} to a member of the algebra."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL (-38 UP) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in \\spadtype{AlgebraicNumber}.")) (|doublyTransitive?| (((|Boolean|) |#1|) "\\spad{doublyTransitive?(p)} is \\spad{true} if \\spad{p} is irreducible over over the field \\spad{K} generated by its coefficients,{} and if \\spad{p(X) / (X - a)} is irreducible over \\spad{K(a)} where \\spad{p(a) = 0}.")) (|split| (((|Factored| |#1|) |#1|) "\\spad{split(p)} returns a prime factorisation of \\spad{p} over its splitting field.")) (|factor| (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns a prime factorisation of \\spad{p} over the field generated by its coefficients.") (((|Factored| |#1|) |#1| (|List| (|AlgebraicNumber|))) "\\spad{factor(p,{} [a1,{}...,{}an])} returns a prime factorisation of \\spad{p} over the field generated by its coefficients and a1,{}...,{}an."))) NIL NIL -(-39 -2315 UP UPUP -3507) +(-39 -3539 UP UPUP -2547) ((|constructor| (NIL "Function field defined by \\spad{f}(\\spad{x},{} \\spad{y}) = 0.")) (|knownInfBasis| (((|Void|) (|NonNegativeInteger|)) "\\spad{knownInfBasis(n)} \\undocumented{}"))) -((-4237 |has| (-383 |#2|) (-339)) (-4242 |has| (-383 |#2|) (-339)) (-4236 |has| (-383 |#2|) (-339)) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3262 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3262 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3262 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3262 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) -(-40 R -2315) +((-4241 |has| (-383 |#2|) (-339)) (-4246 |has| (-383 |#2|) (-339)) (-4240 |has| (-383 |#2|) (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3172 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3172 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3172 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) +(-40 R -3539) ((|constructor| (NIL "AlgebraicManipulations provides functions to simplify and expand expressions involving algebraic operators.")) (|rootKerSimp| ((|#2| (|BasicOperator|) |#2| (|NonNegativeInteger|)) "\\spad{rootKerSimp(op,{}f,{}n)} should be local but conditional.")) (|rootSimp| ((|#2| |#2|) "\\spad{rootSimp(f)} transforms every radical of the form \\spad{(a * b**(q*n+r))**(1/n)} appearing in \\spad{f} into \\spad{b**q * (a * b**r)**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{b}.")) (|rootProduct| ((|#2| |#2|) "\\spad{rootProduct(f)} combines every product of the form \\spad{(a**(1/n))**m * (a**(1/s))**t} into a single power of a root of \\spad{a},{} and transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form.")) (|rootPower| ((|#2| |#2|) "\\spad{rootPower(f)} transforms every radical power of the form \\spad{(a**(1/n))**m} into a simpler form if \\spad{m} and \\spad{n} have a common factor.")) (|ratPoly| (((|SparseUnivariatePolynomial| |#2|) |#2|) "\\spad{ratPoly(f)} returns a polynomial \\spad{p} such that \\spad{p} has no algebraic coefficients,{} and \\spad{p(f) = 0}.")) (|ratDenom| ((|#2| |#2| (|List| (|Kernel| |#2|))) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic from the denominators in \\spad{f}.") ((|#2| |#2| (|List| |#2|)) "\\spad{ratDenom(f,{} [a1,{}...,{}an])} removes the \\spad{ai}\\spad{'s} which are algebraic kernels from the denominators in \\spad{f}.") ((|#2| |#2| |#2|) "\\spad{ratDenom(f,{} a)} removes \\spad{a} from the denominators in \\spad{f} if \\spad{a} is an algebraic kernel.") ((|#2| |#2|) "\\spad{ratDenom(f)} rationalizes the denominators appearing in \\spad{f} by moving all the algebraic quantities into the numerators.")) (|rootSplit| ((|#2| |#2|) "\\spad{rootSplit(f)} transforms every radical of the form \\spad{(a/b)**(1/n)} appearing in \\spad{f} into \\spad{a**(1/n) / b**(1/n)}. This transformation is not in general valid for all complex numbers \\spad{a} and \\spad{b}.")) (|coerce| (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(x)} \\undocumented")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(x)} \\undocumented")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(x)} \\undocumented"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -406) (|devaluate| |#1|))))) @@ -102,23 +102,23 @@ NIL ((|HasCategory| |#1| (QUOTE (-284)))) (-43 R |n| |ls| |gamma|) ((|constructor| (NIL "AlgebraGivenByStructuralConstants implements finite rank algebras over a commutative ring,{} given by the structural constants \\spad{gamma} with respect to a fixed basis \\spad{[a1,{}..,{}an]},{} where \\spad{gamma} is an \\spad{n}-vector of \\spad{n} by \\spad{n} matrices \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{ai} * aj = gammaij1 * a1 + ... + gammaijn * an}. The symbols for the fixed basis have to be given as a list of symbols.")) (|coerce| (($ (|Vector| |#1|)) "\\spad{coerce(v)} converts a vector to a member of the algebra by forming a linear combination with the basis element. Note: the vector is assumed to have length equal to the dimension of the algebra."))) -((-4241 |has| |#1| (-515)) (-4239 . T) (-4238 . T)) +((-4245 |has| |#1| (-515)) (-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-44 |Key| |Entry|) ((|constructor| (NIL "\\spadtype{AssociationList} implements association lists. These may be viewed as lists of pairs where the first part is a key and the second is the stored value. For example,{} the key might be a string with a persons employee identification number and the value might be a record with personnel data."))) -((-4244 . T) (-4245 . T)) -((-3262 (-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|))))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-3172 (-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|))))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-45 S R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#2|) "\\spad{p/c} divides \\spad{p} by the coefficient \\spad{c}.")) (|coefficient| ((|#2| $ |#3|) "\\spad{coefficient(p,{}e)} extracts the coefficient of the monomial with exponent \\spad{e} from polynomial \\spad{p},{} or returns zero if exponent is not present.")) (|reductum| (($ $) "\\spad{reductum(u)} returns \\spad{u} minus its leading monomial returns zero if handed the zero element.")) (|monomial| (($ |#2| |#3|) "\\spad{monomial(r,{}e)} makes a term from a coefficient \\spad{r} and an exponent \\spad{e}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(p)} tests if \\spad{p} is a single monomial.")) (|map| (($ (|Mapping| |#2| |#2|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients of the non-zero monomials of \\spad{u}.")) (|degree| ((|#3| $) "\\spad{degree(p)} returns the maximum of the exponents of the terms of \\spad{p}.")) (|leadingMonomial| (($ $) "\\spad{leadingMonomial(p)} returns the monomial of \\spad{p} with the highest degree.")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-339)))) (-46 R E) ((|constructor| (NIL "Abelian monoid ring elements (not necessarily of finite support) of this ring are of the form formal SUM (r_i * e_i) where the r_i are coefficents and the e_i,{} elements of the ordered abelian monoid,{} are thought of as exponents or monomials. The monomials commute with each other,{} and with the coefficients (which themselves may or may not be commutative). See \\spadtype{FiniteAbelianMonoidRing} for the case of finite support a useful common model for polynomials and power series. Conceptually at least,{} only the non-zero terms are ever operated on.")) (/ (($ $ |#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| $) "\\spad{leadingCoefficient(p)} returns the coefficient highest degree term of \\spad{p}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-47) ((|constructor| (NIL "Algebraic closure of the rational numbers,{} with mathematical =")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| $ (QUOTE (-973))) (|HasCategory| $ (LIST (QUOTE -964) (QUOTE (-523))))) (-48) ((|constructor| (NIL "This domain implements anonymous functions")) (|body| (((|Syntax|) $) "\\spad{body(f)} returns the body of the unnamed function \\spad{`f'}.")) (|parameters| (((|List| (|Symbol|)) $) "\\spad{parameters(f)} returns the list of parameters bound by \\spad{`f'}."))) @@ -126,7 +126,7 @@ NIL NIL (-49 R |lVar|) ((|constructor| (NIL "The domain of antisymmetric polynomials.")) (|map| (($ (|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}."))) -((-4241 . T)) +((-4245 . T)) NIL (-50 S) ((|constructor| (NIL "\\spadtype{AnyFunctions1} implements several utility functions for working with \\spadtype{Any}. These functions are used to go back and forth between objects of \\spadtype{Any} and objects of other types.")) (|retract| ((|#1| (|Any|)) "\\spad{retract(a)} tries to convert \\spad{a} into an object of type \\spad{S}. If possible,{} it returns the object. Error: if no such retraction is possible.")) (|retractable?| (((|Boolean|) (|Any|)) "\\spad{retractable?(a)} tests if \\spad{a} can be converted into an object of type \\spad{S}.")) (|retractIfCan| (((|Union| |#1| "failed") (|Any|)) "\\spad{retractIfCan(a)} tries change \\spad{a} into an object of type \\spad{S}. If it can,{} then such an object is returned. Otherwise,{} \"failed\" is returned.")) (|coerce| (((|Any|) |#1|) "\\spad{coerce(s)} creates an object of \\spadtype{Any} from the object \\spad{s} of type \\spad{S}."))) @@ -140,7 +140,7 @@ 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 -(-53 |Base| R -2315) +(-53 |Base| R -3539) ((|constructor| (NIL "This package apply rewrite rules to expressions,{} calling the pattern matcher.")) (|localUnquote| ((|#3| |#3| (|List| (|Symbol|))) "\\spad{localUnquote(f,{}ls)} is a local function.")) (|applyRules| ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3| (|PositiveInteger|)) "\\spad{applyRules([r1,{}...,{}rn],{} expr,{} n)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} a most \\spad{n} times.") ((|#3| (|List| (|RewriteRule| |#1| |#2| |#3|)) |#3|) "\\spad{applyRules([r1,{}...,{}rn],{} expr)} applies the rules \\spad{r1},{}...,{}\\spad{rn} to \\spad{f} an unlimited number of times,{} \\spadignore{i.e.} until none of \\spad{r1},{}...,{}\\spad{rn} is applicable to the expression."))) NIL NIL @@ -150,7 +150,7 @@ NIL NIL (-55 R |Row| |Col|) ((|constructor| (NIL "\\indented{1}{TwoDimensionalArrayCategory is a general array category which} allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and columns returned as objects of type Col. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa.")) (|map!| (($ (|Mapping| |#1| |#1|) $) "\\spad{map!(f,{}a)} assign \\spad{a(i,{}j)} to \\spad{f(a(i,{}j))} for all \\spad{i,{} j}")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $ |#1|) "\\spad{map(f,{}a,{}b,{}r)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} when both \\spad{a(i,{}j)} and \\spad{b(i,{}j)} exist; else \\spad{c(i,{}j) = f(r,{} b(i,{}j))} when \\spad{a(i,{}j)} does not exist; else \\spad{c(i,{}j) = f(a(i,{}j),{}r)} when \\spad{b(i,{}j)} does not exist; otherwise \\spad{c(i,{}j) = f(r,{}r)}.") (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i,{} j}") (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = f(a(i,{}j))} for all \\spad{i,{} j}")) (|setColumn!| (($ $ (|Integer|) |#3|) "\\spad{setColumn!(m,{}j,{}v)} sets to \\spad{j}th column of \\spad{m} to \\spad{v}")) (|setRow!| (($ $ (|Integer|) |#2|) "\\spad{setRow!(m,{}i,{}v)} sets to \\spad{i}th row of \\spad{m} to \\spad{v}")) (|qsetelt!| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{qsetelt!(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} NO error check to determine if indices are in proper ranges")) (|setelt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{setelt(m,{}i,{}j,{}r)} sets the element in the \\spad{i}th row and \\spad{j}th column of \\spad{m} to \\spad{r} error check to determine if indices are in proper ranges")) (|parts| (((|List| |#1|) $) "\\spad{parts(m)} returns a list of the elements of \\spad{m} in row major order")) (|column| ((|#3| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of \\spad{m} error check to determine if index is in proper ranges")) (|row| ((|#2| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of \\spad{m} error check to determine if index is in proper ranges")) (|qelt| ((|#1| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} NO error check to determine if indices are in proper ranges")) (|elt| ((|#1| $ (|Integer|) (|Integer|) |#1|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise") ((|#1| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the array \\spad{m} error check to determine if indices are in proper ranges")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the array \\spad{m}")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the array \\spad{m}")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the array \\spad{m}")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the array \\spad{m}")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the array \\spad{m}")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the array \\spad{m}")) (|fill!| (($ $ |#1|) "\\spad{fill!(m,{}r)} fills \\spad{m} with \\spad{r}\\spad{'s}")) (|new| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{new(m,{}n,{}r)} is an \\spad{m}-by-\\spad{n} array all of whose entries are \\spad{r}")) (|finiteAggregate| ((|attribute|) "two-dimensional arrays are finite")) (|shallowlyMutable| ((|attribute|) "one may destructively alter arrays"))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-56 A B) ((|constructor| (NIL "\\indented{1}{This package provides tools for operating on one-dimensional arrays} with unary and binary functions involving different underlying types")) (|map| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1|) (|OneDimensionalArray| |#1|)) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of one-dimensional array \\spad{a} resulting in a new one-dimensional array over a possibly different underlying domain.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the one-dimensional array \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|scan| (((|OneDimensionalArray| |#2|) (|Mapping| |#2| |#1| |#2|) (|OneDimensionalArray| |#1|) |#2|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-arrays \\spad{x} of one-dimensional array \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}."))) @@ -158,65 +158,65 @@ NIL NIL (-57 S) ((|constructor| (NIL "This is the domain of 1-based one dimensional arrays")) (|oneDimensionalArray| (($ (|NonNegativeInteger|) |#1|) "\\spad{oneDimensionalArray(n,{}s)} creates an array from \\spad{n} copies of element \\spad{s}") (($ (|List| |#1|)) "\\spad{oneDimensionalArray(l)} creates an array from a list of elements \\spad{l}"))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-58 R) ((|constructor| (NIL "\\indented{1}{A TwoDimensionalArray is a two dimensional array with} 1-based indexing for both rows and columns.")) (|shallowlyMutable| ((|attribute|) "One may destructively alter TwoDimensionalArray\\spad{'s}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-59 -4038) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-59 -4198) ((|constructor| (NIL "\\spadtype{ASP10} produces Fortran for Type 10 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. This ASP computes the values of a set of functions,{} for example:\\begin{verbatim} SUBROUTINE COEFFN(P,Q,DQDL,X,ELAM,JINT) DOUBLE PRECISION ELAM,P,Q,X,DQDL INTEGER JINT P=1.0D0 Q=((-1.0D0*X**3)+ELAM*X*X-2.0D0)/(X*X) DQDL=1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE JINT) (QUOTE X) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-60 -4038) +(-60 -4198) ((|constructor| (NIL "\\spadtype{Asp12} produces Fortran for Type 12 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package} etc.,{} for example:\\begin{verbatim} SUBROUTINE MONIT (MAXIT,IFLAG,ELAM,FINFO) DOUBLE PRECISION ELAM,FINFO(15) INTEGER MAXIT,IFLAG IF(MAXIT.EQ.-1)THEN PRINT*,\"Output from Monit\" ENDIF PRINT*,MAXIT,IFLAG,ELAM,(FINFO(I),I=1,4) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP12}."))) NIL NIL -(-61 -4038) +(-61 -4198) ((|constructor| (NIL "\\spadtype{Asp19} produces Fortran for Type 19 ASPs,{} evaluating a set of functions and their jacobian at a given point,{} for example:\\begin{verbatim} SUBROUTINE LSFUN2(M,N,XC,FVECC,FJACC,LJC) DOUBLE PRECISION FVECC(M),FJACC(LJC,N),XC(N) INTEGER M,N,LJC INTEGER I,J DO 25003 I=1,LJC DO 25004 J=1,N FJACC(I,J)=0.0D025004 CONTINUE25003 CONTINUE FVECC(1)=((XC(1)-0.14D0)*XC(3)+(15.0D0*XC(1)-2.1D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-0.18D0)*XC(3)+(7.0D0*XC(1)-1.26D0)*XC(2)+1.0D0)/( &XC(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-0.22D0)*XC(3)+(4.333333333333333D0*XC(1)-0.953333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-0.25D0)*XC(3)+(3.0D0*XC(1)-0.75D0)*XC(2)+1.0D0)/( &XC(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-0.29D0)*XC(3)+(2.2D0*XC(1)-0.6379999999999999D0)* &XC(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-0.32D0)*XC(3)+(1.666666666666667D0*XC(1)-0.533333 &3333333333D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-0.35D0)*XC(3)+(1.285714285714286D0*XC(1)-0.45D0)* &XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-0.39D0)*XC(3)+(XC(1)-0.39D0)*XC(2)+1.0D0)/(XC(3)+ &XC(2)) FVECC(9)=((XC(1)-0.37D0)*XC(3)+(XC(1)-0.37D0)*XC(2)+1.285714285714 &286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-0.58D0)*XC(3)+(XC(1)-0.58D0)*XC(2)+1.66666666666 &6667D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-0.73D0)*XC(3)+(XC(1)-0.73D0)*XC(2)+2.2D0)/(XC(3) &+XC(2)) FVECC(12)=((XC(1)-0.96D0)*XC(3)+(XC(1)-0.96D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) FJACC(1,1)=1.0D0 FJACC(1,2)=-15.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(1,3)=-1.0D0/(XC(3)**2+30.0D0*XC(2)*XC(3)+225.0D0*XC(2)**2) FJACC(2,1)=1.0D0 FJACC(2,2)=-7.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(2,3)=-1.0D0/(XC(3)**2+14.0D0*XC(2)*XC(3)+49.0D0*XC(2)**2) FJACC(3,1)=1.0D0 FJACC(3,2)=((-0.1110223024625157D-15*XC(3))-4.333333333333333D0)/( &XC(3)**2+8.666666666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2) &**2) FJACC(3,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+8.666666 &666666666D0*XC(2)*XC(3)+18.77777777777778D0*XC(2)**2) FJACC(4,1)=1.0D0 FJACC(4,2)=-3.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(4,3)=-1.0D0/(XC(3)**2+6.0D0*XC(2)*XC(3)+9.0D0*XC(2)**2) FJACC(5,1)=1.0D0 FJACC(5,2)=((-0.1110223024625157D-15*XC(3))-2.2D0)/(XC(3)**2+4.399 &999999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(5,3)=(0.1110223024625157D-15*XC(2)-1.0D0)/(XC(3)**2+4.399999 &999999999D0*XC(2)*XC(3)+4.839999999999998D0*XC(2)**2) FJACC(6,1)=1.0D0 FJACC(6,2)=((-0.2220446049250313D-15*XC(3))-1.666666666666667D0)/( &XC(3)**2+3.333333333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2) &**2) FJACC(6,3)=(0.2220446049250313D-15*XC(2)-1.0D0)/(XC(3)**2+3.333333 &333333333D0*XC(2)*XC(3)+2.777777777777777D0*XC(2)**2) FJACC(7,1)=1.0D0 FJACC(7,2)=((-0.5551115123125783D-16*XC(3))-1.285714285714286D0)/( &XC(3)**2+2.571428571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2) &**2) FJACC(7,3)=(0.5551115123125783D-16*XC(2)-1.0D0)/(XC(3)**2+2.571428 &571428571D0*XC(2)*XC(3)+1.653061224489796D0*XC(2)**2) FJACC(8,1)=1.0D0 FJACC(8,2)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(8,3)=-1.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(9,1)=1.0D0 FJACC(9,2)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(9,3)=-1.285714285714286D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)* &*2) FJACC(10,1)=1.0D0 FJACC(10,2)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(10,3)=-1.666666666666667D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(11,1)=1.0D0 FJACC(11,2)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(11,3)=-2.2D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,1)=1.0D0 FJACC(12,2)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(12,3)=-3.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(13,1)=1.0D0 FJACC(13,2)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(13,3)=-4.333333333333333D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2) &**2) FJACC(14,1)=1.0D0 FJACC(14,2)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(14,3)=-7.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,1)=1.0D0 FJACC(15,2)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) FJACC(15,3)=-15.0D0/(XC(3)**2+2.0D0*XC(2)*XC(3)+XC(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-62 -4038) +(-62 -4198) ((|constructor| (NIL "\\spadtype{Asp1} produces Fortran for Type 1 ASPs,{} needed for various NAG routines. Type 1 ASPs take a univariate expression (in the symbol \\spad{X}) and turn it into a Fortran Function like the following:\\begin{verbatim} DOUBLE PRECISION FUNCTION F(X) DOUBLE PRECISION X F=DSIN(X) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-63 -4038) +(-63 -4198) ((|constructor| (NIL "\\spadtype{Asp20} produces Fortran for Type 20 ASPs,{} for example:\\begin{verbatim} SUBROUTINE QPHESS(N,NROWH,NCOLH,JTHCOL,HESS,X,HX) DOUBLE PRECISION HX(N),X(N),HESS(NROWH,NCOLH) INTEGER JTHCOL,N,NROWH,NCOLH HX(1)=2.0D0*X(1) HX(2)=2.0D0*X(2) HX(3)=2.0D0*X(4)+2.0D0*X(3) HX(4)=2.0D0*X(4)+2.0D0*X(3) HX(5)=2.0D0*X(5) HX(6)=(-2.0D0*X(7))+(-2.0D0*X(6)) HX(7)=(-2.0D0*X(7))+(-2.0D0*X(6)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct|) (|construct| (QUOTE X) (QUOTE HESS)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-64 -4038) +(-64 -4198) ((|constructor| (NIL "\\spadtype{Asp24} produces Fortran for Type 24 ASPs which evaluate a multivariate function at a point (needed for NAG routine \\axiomOpFrom{e04jaf}{e04Package}),{} for example:\\begin{verbatim} SUBROUTINE FUNCT1(N,XC,FC) DOUBLE PRECISION FC,XC(N) INTEGER N FC=10.0D0*XC(4)**4+(-40.0D0*XC(1)*XC(4)**3)+(60.0D0*XC(1)**2+5 &.0D0)*XC(4)**2+((-10.0D0*XC(3))+(-40.0D0*XC(1)**3))*XC(4)+16.0D0*X &C(3)**4+(-32.0D0*XC(2)*XC(3)**3)+(24.0D0*XC(2)**2+5.0D0)*XC(3)**2+ &(-8.0D0*XC(2)**3*XC(3))+XC(2)**4+100.0D0*XC(2)**2+20.0D0*XC(1)*XC( &2)+10.0D0*XC(1)**4+XC(1)**2 RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-65 -4038) +(-65 -4198) ((|constructor| (NIL "\\spadtype{Asp27} produces Fortran for Type 27 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package} ,{}for example:\\begin{verbatim} FUNCTION DOT(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION W(N),Z(N),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOT=(W(16)+(-0.5D0*W(15)))*Z(16)+((-0.5D0*W(16))+W(15)+(-0.5D0*W(1 &4)))*Z(15)+((-0.5D0*W(15))+W(14)+(-0.5D0*W(13)))*Z(14)+((-0.5D0*W( &14))+W(13)+(-0.5D0*W(12)))*Z(13)+((-0.5D0*W(13))+W(12)+(-0.5D0*W(1 &1)))*Z(12)+((-0.5D0*W(12))+W(11)+(-0.5D0*W(10)))*Z(11)+((-0.5D0*W( &11))+W(10)+(-0.5D0*W(9)))*Z(10)+((-0.5D0*W(10))+W(9)+(-0.5D0*W(8)) &)*Z(9)+((-0.5D0*W(9))+W(8)+(-0.5D0*W(7)))*Z(8)+((-0.5D0*W(8))+W(7) &+(-0.5D0*W(6)))*Z(7)+((-0.5D0*W(7))+W(6)+(-0.5D0*W(5)))*Z(6)+((-0. &5D0*W(6))+W(5)+(-0.5D0*W(4)))*Z(5)+((-0.5D0*W(5))+W(4)+(-0.5D0*W(3 &)))*Z(4)+((-0.5D0*W(4))+W(3)+(-0.5D0*W(2)))*Z(3)+((-0.5D0*W(3))+W( &2)+(-0.5D0*W(1)))*Z(2)+((-0.5D0*W(2))+W(1))*Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-66 -4038) +(-66 -4198) ((|constructor| (NIL "\\spadtype{Asp28} produces Fortran for Type 28 ASPs,{} used in NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE IMAGE(IFLAG,N,Z,W,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION Z(N),W(N),IWORK(LRWORK),RWORK(LRWORK) INTEGER N,LIWORK,IFLAG,LRWORK W(1)=0.01707454969713436D0*Z(16)+0.001747395874954051D0*Z(15)+0.00 &2106973900813502D0*Z(14)+0.002957434991769087D0*Z(13)+(-0.00700554 &0882865317D0*Z(12))+(-0.01219194009813166D0*Z(11))+0.0037230647365 &3087D0*Z(10)+0.04932374658377151D0*Z(9)+(-0.03586220812223305D0*Z( &8))+(-0.04723268012114625D0*Z(7))+(-0.02434652144032987D0*Z(6))+0. &2264766947290192D0*Z(5)+(-0.1385343580686922D0*Z(4))+(-0.116530050 &8238904D0*Z(3))+(-0.2803531651057233D0*Z(2))+1.019463911841327D0*Z &(1) W(2)=0.0227345011107737D0*Z(16)+0.008812321197398072D0*Z(15)+0.010 &94012210519586D0*Z(14)+(-0.01764072463999744D0*Z(13))+(-0.01357136 &72105995D0*Z(12))+0.00157466157362272D0*Z(11)+0.05258889186338282D &0*Z(10)+(-0.01981532388243379D0*Z(9))+(-0.06095390688679697D0*Z(8) &)+(-0.04153119955569051D0*Z(7))+0.2176561076571465D0*Z(6)+(-0.0532 &5555586632358D0*Z(5))+(-0.1688977368984641D0*Z(4))+(-0.32440166056 &67343D0*Z(3))+0.9128222941872173D0*Z(2)+(-0.2419652703415429D0*Z(1 &)) W(3)=0.03371198197190302D0*Z(16)+0.02021603150122265D0*Z(15)+(-0.0 &06607305534689702D0*Z(14))+(-0.03032392238968179D0*Z(13))+0.002033 &305231024948D0*Z(12)+0.05375944956767728D0*Z(11)+(-0.0163213312502 &9967D0*Z(10))+(-0.05483186562035512D0*Z(9))+(-0.04901428822579872D &0*Z(8))+0.2091097927887612D0*Z(7)+(-0.05760560341383113D0*Z(6))+(- &0.1236679206156403D0*Z(5))+(-0.3523683853026259D0*Z(4))+0.88929961 &32269974D0*Z(3)+(-0.2995429545781457D0*Z(2))+(-0.02986582812574917 &D0*Z(1)) W(4)=0.05141563713660119D0*Z(16)+0.005239165960779299D0*Z(15)+(-0. &01623427735779699D0*Z(14))+(-0.01965809746040371D0*Z(13))+0.054688 &97337339577D0*Z(12)+(-0.014224695935687D0*Z(11))+(-0.0505181779315 &6355D0*Z(10))+(-0.04353074206076491D0*Z(9))+0.2012230497530726D0*Z &(8)+(-0.06630874514535952D0*Z(7))+(-0.1280829963720053D0*Z(6))+(-0 &.305169742604165D0*Z(5))+0.8600427128450191D0*Z(4)+(-0.32415033802 &68184D0*Z(3))+(-0.09033531980693314D0*Z(2))+0.09089205517109111D0* &Z(1) W(5)=0.04556369767776375D0*Z(16)+(-0.001822737697581869D0*Z(15))+( &-0.002512226501941856D0*Z(14))+0.02947046460707379D0*Z(13)+(-0.014 &45079632086177D0*Z(12))+(-0.05034242196614937D0*Z(11))+(-0.0376966 &3291725935D0*Z(10))+0.2171103102175198D0*Z(9)+(-0.0824949256021352 &4D0*Z(8))+(-0.1473995209288945D0*Z(7))+(-0.315042193418466D0*Z(6)) &+0.9591623347824002D0*Z(5)+(-0.3852396953763045D0*Z(4))+(-0.141718 &5427288274D0*Z(3))+(-0.03423495461011043D0*Z(2))+0.319820917706851 &6D0*Z(1) W(6)=0.04015147277405744D0*Z(16)+0.01328585741341559D0*Z(15)+0.048 &26082005465965D0*Z(14)+(-0.04319641116207706D0*Z(13))+(-0.04931323 &319055762D0*Z(12))+(-0.03526886317505474D0*Z(11))+0.22295383396730 &01D0*Z(10)+(-0.07375317649315155D0*Z(9))+(-0.1589391311991561D0*Z( &8))+(-0.328001910890377D0*Z(7))+0.952576555482747D0*Z(6)+(-0.31583 &09975786731D0*Z(5))+(-0.1846882042225383D0*Z(4))+(-0.0703762046700 &4427D0*Z(3))+0.2311852964327382D0*Z(2)+0.04254083491825025D0*Z(1) W(7)=0.06069778964023718D0*Z(16)+0.06681263884671322D0*Z(15)+(-0.0 &2113506688615768D0*Z(14))+(-0.083996867458326D0*Z(13))+(-0.0329843 &8523869648D0*Z(12))+0.2276878326327734D0*Z(11)+(-0.067356038933017 &95D0*Z(10))+(-0.1559813965382218D0*Z(9))+(-0.3363262957694705D0*Z( &8))+0.9442791158560948D0*Z(7)+(-0.3199955249404657D0*Z(6))+(-0.136 &2463839920727D0*Z(5))+(-0.1006185171570586D0*Z(4))+0.2057504515015 &423D0*Z(3)+(-0.02065879269286707D0*Z(2))+0.03160990266745513D0*Z(1 &) W(8)=0.126386868896738D0*Z(16)+0.002563370039476418D0*Z(15)+(-0.05 &581757739455641D0*Z(14))+(-0.07777893205900685D0*Z(13))+0.23117338 &45834199D0*Z(12)+(-0.06031581134427592D0*Z(11))+(-0.14805474755869 &52D0*Z(10))+(-0.3364014128402243D0*Z(9))+0.9364014128402244D0*Z(8) &+(-0.3269452524413048D0*Z(7))+(-0.1396841886557241D0*Z(6))+(-0.056 &1733845834199D0*Z(5))+0.1777789320590069D0*Z(4)+(-0.04418242260544 &359D0*Z(3))+(-0.02756337003947642D0*Z(2))+0.07361313110326199D0*Z( &1) W(9)=0.07361313110326199D0*Z(16)+(-0.02756337003947642D0*Z(15))+(- &0.04418242260544359D0*Z(14))+0.1777789320590069D0*Z(13)+(-0.056173 &3845834199D0*Z(12))+(-0.1396841886557241D0*Z(11))+(-0.326945252441 &3048D0*Z(10))+0.9364014128402244D0*Z(9)+(-0.3364014128402243D0*Z(8 &))+(-0.1480547475586952D0*Z(7))+(-0.06031581134427592D0*Z(6))+0.23 &11733845834199D0*Z(5)+(-0.07777893205900685D0*Z(4))+(-0.0558175773 &9455641D0*Z(3))+0.002563370039476418D0*Z(2)+0.126386868896738D0*Z( &1) W(10)=0.03160990266745513D0*Z(16)+(-0.02065879269286707D0*Z(15))+0 &.2057504515015423D0*Z(14)+(-0.1006185171570586D0*Z(13))+(-0.136246 &3839920727D0*Z(12))+(-0.3199955249404657D0*Z(11))+0.94427911585609 &48D0*Z(10)+(-0.3363262957694705D0*Z(9))+(-0.1559813965382218D0*Z(8 &))+(-0.06735603893301795D0*Z(7))+0.2276878326327734D0*Z(6)+(-0.032 &98438523869648D0*Z(5))+(-0.083996867458326D0*Z(4))+(-0.02113506688 &615768D0*Z(3))+0.06681263884671322D0*Z(2)+0.06069778964023718D0*Z( &1) W(11)=0.04254083491825025D0*Z(16)+0.2311852964327382D0*Z(15)+(-0.0 &7037620467004427D0*Z(14))+(-0.1846882042225383D0*Z(13))+(-0.315830 &9975786731D0*Z(12))+0.952576555482747D0*Z(11)+(-0.328001910890377D &0*Z(10))+(-0.1589391311991561D0*Z(9))+(-0.07375317649315155D0*Z(8) &)+0.2229538339673001D0*Z(7)+(-0.03526886317505474D0*Z(6))+(-0.0493 &1323319055762D0*Z(5))+(-0.04319641116207706D0*Z(4))+0.048260820054 &65965D0*Z(3)+0.01328585741341559D0*Z(2)+0.04015147277405744D0*Z(1) W(12)=0.3198209177068516D0*Z(16)+(-0.03423495461011043D0*Z(15))+(- &0.1417185427288274D0*Z(14))+(-0.3852396953763045D0*Z(13))+0.959162 &3347824002D0*Z(12)+(-0.315042193418466D0*Z(11))+(-0.14739952092889 &45D0*Z(10))+(-0.08249492560213524D0*Z(9))+0.2171103102175198D0*Z(8 &)+(-0.03769663291725935D0*Z(7))+(-0.05034242196614937D0*Z(6))+(-0. &01445079632086177D0*Z(5))+0.02947046460707379D0*Z(4)+(-0.002512226 &501941856D0*Z(3))+(-0.001822737697581869D0*Z(2))+0.045563697677763 &75D0*Z(1) W(13)=0.09089205517109111D0*Z(16)+(-0.09033531980693314D0*Z(15))+( &-0.3241503380268184D0*Z(14))+0.8600427128450191D0*Z(13)+(-0.305169 &742604165D0*Z(12))+(-0.1280829963720053D0*Z(11))+(-0.0663087451453 &5952D0*Z(10))+0.2012230497530726D0*Z(9)+(-0.04353074206076491D0*Z( &8))+(-0.05051817793156355D0*Z(7))+(-0.014224695935687D0*Z(6))+0.05 &468897337339577D0*Z(5)+(-0.01965809746040371D0*Z(4))+(-0.016234277 &35779699D0*Z(3))+0.005239165960779299D0*Z(2)+0.05141563713660119D0 &*Z(1) W(14)=(-0.02986582812574917D0*Z(16))+(-0.2995429545781457D0*Z(15)) &+0.8892996132269974D0*Z(14)+(-0.3523683853026259D0*Z(13))+(-0.1236 &679206156403D0*Z(12))+(-0.05760560341383113D0*Z(11))+0.20910979278 &87612D0*Z(10)+(-0.04901428822579872D0*Z(9))+(-0.05483186562035512D &0*Z(8))+(-0.01632133125029967D0*Z(7))+0.05375944956767728D0*Z(6)+0 &.002033305231024948D0*Z(5)+(-0.03032392238968179D0*Z(4))+(-0.00660 &7305534689702D0*Z(3))+0.02021603150122265D0*Z(2)+0.033711981971903 &02D0*Z(1) W(15)=(-0.2419652703415429D0*Z(16))+0.9128222941872173D0*Z(15)+(-0 &.3244016605667343D0*Z(14))+(-0.1688977368984641D0*Z(13))+(-0.05325 &555586632358D0*Z(12))+0.2176561076571465D0*Z(11)+(-0.0415311995556 &9051D0*Z(10))+(-0.06095390688679697D0*Z(9))+(-0.01981532388243379D &0*Z(8))+0.05258889186338282D0*Z(7)+0.00157466157362272D0*Z(6)+(-0. &0135713672105995D0*Z(5))+(-0.01764072463999744D0*Z(4))+0.010940122 &10519586D0*Z(3)+0.008812321197398072D0*Z(2)+0.0227345011107737D0*Z &(1) W(16)=1.019463911841327D0*Z(16)+(-0.2803531651057233D0*Z(15))+(-0. &1165300508238904D0*Z(14))+(-0.1385343580686922D0*Z(13))+0.22647669 &47290192D0*Z(12)+(-0.02434652144032987D0*Z(11))+(-0.04723268012114 &625D0*Z(10))+(-0.03586220812223305D0*Z(9))+0.04932374658377151D0*Z &(8)+0.00372306473653087D0*Z(7)+(-0.01219194009813166D0*Z(6))+(-0.0 &07005540882865317D0*Z(5))+0.002957434991769087D0*Z(4)+0.0021069739 &00813502D0*Z(3)+0.001747395874954051D0*Z(2)+0.01707454969713436D0* &Z(1) RETURN END\\end{verbatim}"))) NIL NIL -(-67 -4038) +(-67 -4198) ((|constructor| (NIL "\\spadtype{Asp29} produces Fortran for Type 29 ASPs,{} needed for NAG routine \\axiomOpFrom{f02fjf}{f02Package},{} for example:\\begin{verbatim} SUBROUTINE MONIT(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) DOUBLE PRECISION D(K),F(K) INTEGER K,NEXTIT,NEVALS,NVECS,ISTATE CALL F02FJZ(ISTATE,NEXTIT,NEVALS,NEVECS,K,F,D) RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP29}."))) NIL NIL -(-68 -4038) +(-68 -4198) ((|constructor| (NIL "\\spadtype{Asp30} produces Fortran for Type 30 ASPs,{} needed for NAG routine \\axiomOpFrom{f04qaf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE APROD(MODE,M,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION X(N),Y(M),RWORK(LRWORK) INTEGER M,N,LIWORK,IFAIL,LRWORK,IWORK(LIWORK),MODE DOUBLE PRECISION A(5,5) EXTERNAL F06PAF A(1,1)=1.0D0 A(1,2)=0.0D0 A(1,3)=0.0D0 A(1,4)=-1.0D0 A(1,5)=0.0D0 A(2,1)=0.0D0 A(2,2)=1.0D0 A(2,3)=0.0D0 A(2,4)=0.0D0 A(2,5)=-1.0D0 A(3,1)=0.0D0 A(3,2)=0.0D0 A(3,3)=1.0D0 A(3,4)=-1.0D0 A(3,5)=0.0D0 A(4,1)=-1.0D0 A(4,2)=0.0D0 A(4,3)=-1.0D0 A(4,4)=4.0D0 A(4,5)=-1.0D0 A(5,1)=0.0D0 A(5,2)=-1.0D0 A(5,3)=0.0D0 A(5,4)=-1.0D0 A(5,5)=4.0D0 IF(MODE.EQ.1)THEN CALL F06PAF('N',M,N,1.0D0,A,M,X,1,1.0D0,Y,1) ELSEIF(MODE.EQ.2)THEN CALL F06PAF('T',M,N,1.0D0,A,M,Y,1,1.0D0,X,1) ENDIF RETURN END\\end{verbatim}"))) NIL NIL -(-69 -4038) +(-69 -4198) ((|constructor| (NIL "\\spadtype{Asp31} produces Fortran for Type 31 ASPs,{} needed for NAG routine \\axiomOpFrom{d02ejf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE PEDERV(X,Y,PW) DOUBLE PRECISION X,Y(*) DOUBLE PRECISION PW(3,3) PW(1,1)=-0.03999999999999999D0 PW(1,2)=10000.0D0*Y(3) PW(1,3)=10000.0D0*Y(2) PW(2,1)=0.03999999999999999D0 PW(2,2)=(-10000.0D0*Y(3))+(-60000000.0D0*Y(2)) PW(2,3)=-10000.0D0*Y(2) PW(3,1)=0.0D0 PW(3,2)=60000000.0D0*Y(2) PW(3,3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-70 -4038) +(-70 -4198) ((|constructor| (NIL "\\spadtype{Asp33} produces Fortran for Type 33 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package}. The code is a dummy ASP:\\begin{verbatim} SUBROUTINE REPORT(X,V,JINT) DOUBLE PRECISION V(3),X INTEGER JINT RETURN END\\end{verbatim}")) (|outputAsFortran| (((|Void|)) "\\spad{outputAsFortran()} generates the default code for \\spadtype{ASP33}."))) NIL NIL -(-71 -4038) +(-71 -4198) ((|constructor| (NIL "\\spadtype{Asp34} produces Fortran for Type 34 ASPs,{} needed for NAG routine \\axiomOpFrom{f04mbf}{f04Package},{} for example:\\begin{verbatim} SUBROUTINE MSOLVE(IFLAG,N,X,Y,RWORK,LRWORK,IWORK,LIWORK) DOUBLE PRECISION RWORK(LRWORK),X(N),Y(N) INTEGER I,J,N,LIWORK,IFLAG,LRWORK,IWORK(LIWORK) DOUBLE PRECISION W1(3),W2(3),MS(3,3) IFLAG=-1 MS(1,1)=2.0D0 MS(1,2)=1.0D0 MS(1,3)=0.0D0 MS(2,1)=1.0D0 MS(2,2)=2.0D0 MS(2,3)=1.0D0 MS(3,1)=0.0D0 MS(3,2)=1.0D0 MS(3,3)=2.0D0 CALL F04ASF(MS,N,X,N,Y,W1,W2,IFLAG) IFLAG=-IFLAG RETURN END\\end{verbatim}"))) NIL NIL -(-72 -4038) +(-72 -4198) ((|constructor| (NIL "\\spadtype{Asp35} produces Fortran for Type 35 ASPs,{} needed for NAG routines \\axiomOpFrom{c05pbf}{c05Package},{} \\axiomOpFrom{c05pcf}{c05Package},{} for example:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,FJAC,LDFJAC,IFLAG) DOUBLE PRECISION X(N),FVEC(N),FJAC(LDFJAC,N) INTEGER LDFJAC,N,IFLAG IF(IFLAG.EQ.1)THEN FVEC(1)=(-1.0D0*X(2))+X(1) FVEC(2)=(-1.0D0*X(3))+2.0D0*X(2) FVEC(3)=3.0D0*X(3) ELSEIF(IFLAG.EQ.2)THEN FJAC(1,1)=1.0D0 FJAC(1,2)=-1.0D0 FJAC(1,3)=0.0D0 FJAC(2,1)=0.0D0 FJAC(2,2)=2.0D0 FJAC(2,3)=-1.0D0 FJAC(3,1)=0.0D0 FJAC(3,2)=0.0D0 FJAC(3,3)=3.0D0 ENDIF END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL @@ -228,55 +228,55 @@ NIL ((|constructor| (NIL "\\spadtype{Asp42} produces Fortran for Type 42 ASPs,{} needed for NAG routines \\axiomOpFrom{d02raf}{d02Package} and \\axiomOpFrom{d02saf}{d02Package} in particular. These ASPs are in fact three Fortran routines which return a vector of functions,{} and their derivatives \\spad{wrt} \\spad{Y}(\\spad{i}) and also a continuation parameter EPS,{} for example:\\begin{verbatim} SUBROUTINE G(EPS,YA,YB,BC,N) DOUBLE PRECISION EPS,YA(N),YB(N),BC(N) INTEGER N BC(1)=YA(1) BC(2)=YA(2) BC(3)=YB(2)-1.0D0 RETURN END SUBROUTINE JACOBG(EPS,YA,YB,AJ,BJ,N) DOUBLE PRECISION EPS,YA(N),AJ(N,N),BJ(N,N),YB(N) INTEGER N AJ(1,1)=1.0D0 AJ(1,2)=0.0D0 AJ(1,3)=0.0D0 AJ(2,1)=0.0D0 AJ(2,2)=1.0D0 AJ(2,3)=0.0D0 AJ(3,1)=0.0D0 AJ(3,2)=0.0D0 AJ(3,3)=0.0D0 BJ(1,1)=0.0D0 BJ(1,2)=0.0D0 BJ(1,3)=0.0D0 BJ(2,1)=0.0D0 BJ(2,2)=0.0D0 BJ(2,3)=0.0D0 BJ(3,1)=0.0D0 BJ(3,2)=1.0D0 BJ(3,3)=0.0D0 RETURN END SUBROUTINE JACGEP(EPS,YA,YB,BCEP,N) DOUBLE PRECISION EPS,YA(N),YB(N),BCEP(N) INTEGER N BCEP(1)=0.0D0 BCEP(2)=0.0D0 BCEP(3)=0.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE EPS)) (|construct| (QUOTE YA) (QUOTE YB)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-75 -4038) +(-75 -4198) ((|constructor| (NIL "\\spadtype{Asp49} produces Fortran for Type 49 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package},{} \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE OBJFUN(MODE,N,X,OBJF,OBJGRD,NSTATE,IUSER,USER) DOUBLE PRECISION X(N),OBJF,OBJGRD(N),USER(*) INTEGER N,IUSER(*),MODE,NSTATE OBJF=X(4)*X(9)+((-1.0D0*X(5))+X(3))*X(8)+((-1.0D0*X(3))+X(1))*X(7) &+(-1.0D0*X(2)*X(6)) OBJGRD(1)=X(7) OBJGRD(2)=-1.0D0*X(6) OBJGRD(3)=X(8)+(-1.0D0*X(7)) OBJGRD(4)=X(9) OBJGRD(5)=-1.0D0*X(8) OBJGRD(6)=-1.0D0*X(2) OBJGRD(7)=(-1.0D0*X(3))+X(1) OBJGRD(8)=(-1.0D0*X(5))+X(3) OBJGRD(9)=X(4) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-76 -4038) +(-76 -4198) ((|constructor| (NIL "\\spadtype{Asp4} produces Fortran for Type 4 ASPs,{} which take an expression in \\spad{X}(1) .. \\spad{X}(NDIM) and produce a real function of the form:\\begin{verbatim} DOUBLE PRECISION FUNCTION FUNCTN(NDIM,X) DOUBLE PRECISION X(NDIM) INTEGER NDIM FUNCTN=(4.0D0*X(1)*X(3)**2*DEXP(2.0D0*X(1)*X(3)))/(X(4)**2+(2.0D0* &X(2)+2.0D0)*X(4)+X(2)**2+2.0D0*X(2)+1.0D0) RETURN END\\end{verbatim}")) (|coerce| (($ (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL -(-77 -4038) +(-77 -4198) ((|constructor| (NIL "\\spadtype{Asp50} produces Fortran for Type 50 ASPs,{} needed for NAG routine \\axiomOpFrom{e04fdf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE LSFUN1(M,N,XC,FVECC) DOUBLE PRECISION FVECC(M),XC(N) INTEGER I,M,N FVECC(1)=((XC(1)-2.4D0)*XC(3)+(15.0D0*XC(1)-36.0D0)*XC(2)+1.0D0)/( &XC(3)+15.0D0*XC(2)) FVECC(2)=((XC(1)-2.8D0)*XC(3)+(7.0D0*XC(1)-19.6D0)*XC(2)+1.0D0)/(X &C(3)+7.0D0*XC(2)) FVECC(3)=((XC(1)-3.2D0)*XC(3)+(4.333333333333333D0*XC(1)-13.866666 &66666667D0)*XC(2)+1.0D0)/(XC(3)+4.333333333333333D0*XC(2)) FVECC(4)=((XC(1)-3.5D0)*XC(3)+(3.0D0*XC(1)-10.5D0)*XC(2)+1.0D0)/(X &C(3)+3.0D0*XC(2)) FVECC(5)=((XC(1)-3.9D0)*XC(3)+(2.2D0*XC(1)-8.579999999999998D0)*XC &(2)+1.0D0)/(XC(3)+2.2D0*XC(2)) FVECC(6)=((XC(1)-4.199999999999999D0)*XC(3)+(1.666666666666667D0*X &C(1)-7.0D0)*XC(2)+1.0D0)/(XC(3)+1.666666666666667D0*XC(2)) FVECC(7)=((XC(1)-4.5D0)*XC(3)+(1.285714285714286D0*XC(1)-5.7857142 &85714286D0)*XC(2)+1.0D0)/(XC(3)+1.285714285714286D0*XC(2)) FVECC(8)=((XC(1)-4.899999999999999D0)*XC(3)+(XC(1)-4.8999999999999 &99D0)*XC(2)+1.0D0)/(XC(3)+XC(2)) FVECC(9)=((XC(1)-4.699999999999999D0)*XC(3)+(XC(1)-4.6999999999999 &99D0)*XC(2)+1.285714285714286D0)/(XC(3)+XC(2)) FVECC(10)=((XC(1)-6.8D0)*XC(3)+(XC(1)-6.8D0)*XC(2)+1.6666666666666 &67D0)/(XC(3)+XC(2)) FVECC(11)=((XC(1)-8.299999999999999D0)*XC(3)+(XC(1)-8.299999999999 &999D0)*XC(2)+2.2D0)/(XC(3)+XC(2)) FVECC(12)=((XC(1)-10.6D0)*XC(3)+(XC(1)-10.6D0)*XC(2)+3.0D0)/(XC(3) &+XC(2)) FVECC(13)=((XC(1)-1.34D0)*XC(3)+(XC(1)-1.34D0)*XC(2)+4.33333333333 &3333D0)/(XC(3)+XC(2)) FVECC(14)=((XC(1)-2.1D0)*XC(3)+(XC(1)-2.1D0)*XC(2)+7.0D0)/(XC(3)+X &C(2)) FVECC(15)=((XC(1)-4.39D0)*XC(3)+(XC(1)-4.39D0)*XC(2)+15.0D0)/(XC(3 &)+XC(2)) END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE XC)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-78 -4038) +(-78 -4198) ((|constructor| (NIL "\\spadtype{Asp55} produces Fortran for Type 55 ASPs,{} needed for NAG routines \\axiomOpFrom{e04dgf}{e04Package} and \\axiomOpFrom{e04ucf}{e04Package},{} for example:\\begin{verbatim} SUBROUTINE CONFUN(MODE,NCNLN,N,NROWJ,NEEDC,X,C,CJAC,NSTATE,IUSER &,USER) DOUBLE PRECISION C(NCNLN),X(N),CJAC(NROWJ,N),USER(*) INTEGER N,IUSER(*),NEEDC(NCNLN),NROWJ,MODE,NCNLN,NSTATE IF(NEEDC(1).GT.0)THEN C(1)=X(6)**2+X(1)**2 CJAC(1,1)=2.0D0*X(1) CJAC(1,2)=0.0D0 CJAC(1,3)=0.0D0 CJAC(1,4)=0.0D0 CJAC(1,5)=0.0D0 CJAC(1,6)=2.0D0*X(6) ENDIF IF(NEEDC(2).GT.0)THEN C(2)=X(2)**2+(-2.0D0*X(1)*X(2))+X(1)**2 CJAC(2,1)=(-2.0D0*X(2))+2.0D0*X(1) CJAC(2,2)=2.0D0*X(2)+(-2.0D0*X(1)) CJAC(2,3)=0.0D0 CJAC(2,4)=0.0D0 CJAC(2,5)=0.0D0 CJAC(2,6)=0.0D0 ENDIF IF(NEEDC(3).GT.0)THEN C(3)=X(3)**2+(-2.0D0*X(1)*X(3))+X(2)**2+X(1)**2 CJAC(3,1)=(-2.0D0*X(3))+2.0D0*X(1) CJAC(3,2)=2.0D0*X(2) CJAC(3,3)=2.0D0*X(3)+(-2.0D0*X(1)) CJAC(3,4)=0.0D0 CJAC(3,5)=0.0D0 CJAC(3,6)=0.0D0 ENDIF RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-79 -4038) +(-79 -4198) ((|constructor| (NIL "\\spadtype{Asp6} produces Fortran for Type 6 ASPs,{} needed for NAG routines \\axiomOpFrom{c05nbf}{c05Package},{} \\axiomOpFrom{c05ncf}{c05Package}. These represent vectors of functions of \\spad{X}(\\spad{i}) and look like:\\begin{verbatim} SUBROUTINE FCN(N,X,FVEC,IFLAG) DOUBLE PRECISION X(N),FVEC(N) INTEGER N,IFLAG FVEC(1)=(-2.0D0*X(2))+(-2.0D0*X(1)**2)+3.0D0*X(1)+1.0D0 FVEC(2)=(-2.0D0*X(3))+(-2.0D0*X(2)**2)+3.0D0*X(2)+(-1.0D0*X(1))+1. &0D0 FVEC(3)=(-2.0D0*X(4))+(-2.0D0*X(3)**2)+3.0D0*X(3)+(-1.0D0*X(2))+1. &0D0 FVEC(4)=(-2.0D0*X(5))+(-2.0D0*X(4)**2)+3.0D0*X(4)+(-1.0D0*X(3))+1. &0D0 FVEC(5)=(-2.0D0*X(6))+(-2.0D0*X(5)**2)+3.0D0*X(5)+(-1.0D0*X(4))+1. &0D0 FVEC(6)=(-2.0D0*X(7))+(-2.0D0*X(6)**2)+3.0D0*X(6)+(-1.0D0*X(5))+1. &0D0 FVEC(7)=(-2.0D0*X(8))+(-2.0D0*X(7)**2)+3.0D0*X(7)+(-1.0D0*X(6))+1. &0D0 FVEC(8)=(-2.0D0*X(9))+(-2.0D0*X(8)**2)+3.0D0*X(8)+(-1.0D0*X(7))+1. &0D0 FVEC(9)=(-2.0D0*X(9)**2)+3.0D0*X(9)+(-1.0D0*X(8))+1.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct|) (|construct| (QUOTE X)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-80 -4038) +(-80 -4198) ((|constructor| (NIL "\\spadtype{Asp73} produces Fortran for Type 73 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE PDEF(X,Y,ALPHA,BETA,GAMMA,DELTA,EPSOLN,PHI,PSI) DOUBLE PRECISION ALPHA,EPSOLN,PHI,X,Y,BETA,DELTA,GAMMA,PSI ALPHA=DSIN(X) BETA=Y GAMMA=X*Y DELTA=DCOS(X)*DSIN(Y) EPSOLN=Y+X PHI=X PSI=Y RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-81 -4038) +(-81 -4198) ((|constructor| (NIL "\\spadtype{Asp74} produces Fortran for Type 74 ASPs,{} needed for NAG routine \\axiomOpFrom{d03eef}{d03Package},{} for example:\\begin{verbatim} SUBROUTINE BNDY(X,Y,A,B,C,IBND) DOUBLE PRECISION A,B,C,X,Y INTEGER IBND IF(IBND.EQ.0)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(X) ELSEIF(IBND.EQ.1)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.2)THEN A=1.0D0 B=0.0D0 C=DSIN(X)*DSIN(Y) ELSEIF(IBND.EQ.3)THEN A=0.0D0 B=1.0D0 C=-1.0D0*DSIN(Y) ENDIF END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X) (QUOTE Y)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-82 -4038) +(-82 -4198) ((|constructor| (NIL "\\spadtype{Asp77} produces Fortran for Type 77 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNF(X,F) DOUBLE PRECISION X DOUBLE PRECISION F(2,2) F(1,1)=0.0D0 F(1,2)=1.0D0 F(2,1)=0.0D0 F(2,2)=-10.0D0 RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-83 -4038) +(-83 -4198) ((|constructor| (NIL "\\spadtype{Asp78} produces Fortran for Type 78 ASPs,{} needed for NAG routine \\axiomOpFrom{d02gbf}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE FCNG(X,G) DOUBLE PRECISION G(*),X G(1)=0.0D0 G(2)=0.0D0 END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-84 -4038) +(-84 -4198) ((|constructor| (NIL "\\spadtype{Asp7} produces Fortran for Type 7 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bbf}{d02Package},{} \\axiomOpFrom{d02gaf}{d02Package}. These represent a vector of functions of the scalar \\spad{X} and the array \\spad{Z},{} and look like:\\begin{verbatim} SUBROUTINE FCN(X,Z,F) DOUBLE PRECISION F(*),X,Z(*) F(1)=DTAN(Z(3)) F(2)=((-0.03199999999999999D0*DCOS(Z(3))*DTAN(Z(3)))+(-0.02D0*Z(2) &**2))/(Z(2)*DCOS(Z(3))) F(3)=-0.03199999999999999D0/(X*Z(2)**2) RETURN END\\end{verbatim}")) (|coerce| (($ (|Vector| (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-85 -4038) +(-85 -4198) ((|constructor| (NIL "\\spadtype{Asp80} produces Fortran for Type 80 ASPs,{} needed for NAG routine \\axiomOpFrom{d02kef}{d02Package},{} for example:\\begin{verbatim} SUBROUTINE BDYVAL(XL,XR,ELAM,YL,YR) DOUBLE PRECISION ELAM,XL,YL(3),XR,YR(3) YL(1)=XL YL(2)=2.0D0 YR(1)=1.0D0 YR(2)=-1.0D0*DSQRT(XR+(-1.0D0*ELAM)) RETURN END\\end{verbatim}")) (|coerce| (($ (|Matrix| (|FortranExpression| (|construct| (QUOTE XL) (QUOTE XR) (QUOTE ELAM)) (|construct|) (|MachineFloat|)))) "\\spad{coerce(f)} takes objects from the appropriate instantiation of \\spadtype{FortranExpression} and turns them into an ASP."))) NIL NIL -(-86 -4038) +(-86 -4198) ((|constructor| (NIL "\\spadtype{Asp8} produces Fortran for Type 8 ASPs,{} needed for NAG routine \\axiomOpFrom{d02bbf}{d02Package}. This ASP prints intermediate values of the computed solution of an ODE and might look like:\\begin{verbatim} SUBROUTINE OUTPUT(XSOL,Y,COUNT,M,N,RESULT,FORWRD) DOUBLE PRECISION Y(N),RESULT(M,N),XSOL INTEGER M,N,COUNT LOGICAL FORWRD DOUBLE PRECISION X02ALF,POINTS(8) EXTERNAL X02ALF INTEGER I POINTS(1)=1.0D0 POINTS(2)=2.0D0 POINTS(3)=3.0D0 POINTS(4)=4.0D0 POINTS(5)=5.0D0 POINTS(6)=6.0D0 POINTS(7)=7.0D0 POINTS(8)=8.0D0 COUNT=COUNT+1 DO 25001 I=1,N RESULT(COUNT,I)=Y(I)25001 CONTINUE IF(COUNT.EQ.M)THEN IF(FORWRD)THEN XSOL=X02ALF() ELSE XSOL=-X02ALF() ENDIF ELSE XSOL=POINTS(COUNT) ENDIF END\\end{verbatim}"))) NIL NIL -(-87 -4038) +(-87 -4198) ((|constructor| (NIL "\\spadtype{Asp9} produces Fortran for Type 9 ASPs,{} needed for NAG routines \\axiomOpFrom{d02bhf}{d02Package},{} \\axiomOpFrom{d02cjf}{d02Package},{} \\axiomOpFrom{d02ejf}{d02Package}. These ASPs represent a function of a scalar \\spad{X} and a vector \\spad{Y},{} for example:\\begin{verbatim} DOUBLE PRECISION FUNCTION G(X,Y) DOUBLE PRECISION X,Y(*) G=X+Y(1) RETURN END\\end{verbatim} If the user provides a constant value for \\spad{G},{} then extra information is added via COMMON blocks used by certain routines. This specifies that the value returned by \\spad{G} in this case is to be ignored.")) (|coerce| (($ (|FortranExpression| (|construct| (QUOTE X)) (|construct| (QUOTE Y)) (|MachineFloat|))) "\\spad{coerce(f)} takes an object from the appropriate instantiation of \\spadtype{FortranExpression} and turns it into an ASP."))) NIL NIL @@ -286,8 +286,8 @@ NIL ((|HasCategory| |#1| (QUOTE (-339)))) (-89 S) ((|constructor| (NIL "A stack represented as a flexible array.")) (|arrayStack| (($ (|List| |#1|)) "\\spad{arrayStack([x,{}y,{}...,{}z])} creates an array stack with first (top) element \\spad{x},{} second element \\spad{y},{}...,{}and last element \\spad{z}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-90 S) ((|constructor| (NIL "Category for the inverse trigonometric functions.")) (|atan| (($ $) "\\spad{atan(x)} returns the arc-tangent of \\spad{x}.")) (|asin| (($ $) "\\spad{asin(x)} returns the arc-sine of \\spad{x}.")) (|asec| (($ $) "\\spad{asec(x)} returns the arc-secant of \\spad{x}.")) (|acsc| (($ $) "\\spad{acsc(x)} returns the arc-cosecant of \\spad{x}.")) (|acot| (($ $) "\\spad{acot(x)} returns the arc-cotangent of \\spad{x}.")) (|acos| (($ $) "\\spad{acos(x)} returns the arc-cosine of \\spad{x}."))) NIL @@ -298,15 +298,15 @@ NIL NIL (-92) ((|constructor| (NIL "\\axiomType{AttributeButtons} implements a database and associated adjustment mechanisms for a set of attributes. \\blankline For ODEs these attributes are \"stiffness\",{} \"stability\" (\\spadignore{i.e.} how much affect the cosine or sine component of the solution has on the stability of the result),{} \"accuracy\" and \"expense\" (\\spadignore{i.e.} how expensive is the evaluation of the ODE). All these have bearing on the cost of calculating the solution given that reducing the step-length to achieve greater accuracy requires considerable number of evaluations and calculations. \\blankline The effect of each of these attributes can be altered by increasing or decreasing the button value. \\blankline For Integration there is a button for increasing and decreasing the preset number of function evaluations for each method. This is automatically used by ANNA when a method fails due to insufficient workspace or where the limit of function evaluations has been reached before the required accuracy is achieved. \\blankline")) (|setButtonValue| (((|Float|) (|String|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}routineName,{}\\spad{n})} sets the value of the button of attribute \\spad{attributeName} to routine \\spad{routineName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|Float|)) "\\axiom{setButtonValue(attributeName,{}\\spad{n})} sets the value of all buttons of attribute \\spad{attributeName} to \\spad{n}. \\spad{n} must be in the range [0..1]. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|setAttributeButtonStep| (((|Float|) (|Float|)) "\\axiom{setAttributeButtonStep(\\spad{n})} sets the value of the steps for increasing and decreasing the button values. \\axiom{\\spad{n}} must be greater than 0 and less than 1. The preset value is 0.5.")) (|resetAttributeButtons| (((|Void|)) "\\axiom{resetAttributeButtons()} resets the Attribute buttons to a neutral level.")) (|getButtonValue| (((|Float|) (|String|) (|String|)) "\\axiom{getButtonValue(routineName,{}attributeName)} returns the current value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|decrease| (((|Float|) (|String|)) "\\axiom{decrease(attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{decrease(routineName,{}attributeName)} decreases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".")) (|increase| (((|Float|) (|String|)) "\\axiom{increase(attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with all routines. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\".") (((|Float|) (|String|) (|String|)) "\\axiom{increase(routineName,{}attributeName)} increases the value for the effect of the attribute \\axiom{attributeName} with routine \\axiom{routineName}. \\blankline \\axiom{attributeName} should be one of the values \"stiffness\",{} \"stability\",{} \"accuracy\",{} \"expense\" or \"functionEvaluations\"."))) -((-4244 . T)) +((-4248 . T)) NIL (-93) ((|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."))) -((-4244 . T) ((-4246 "*") . T) (-4245 . T) (-4241 . T) (-4239 . T) (-4238 . T) (-4237 . T) (-4242 . T) (-4236 . T) (-4235 . T) (-4234 . T) (-4233 . T) (-4232 . T) (-4240 . T) (-4243 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4231 . T)) +((-4248 . T) ((-4250 "*") . T) (-4249 . T) (-4245 . T) (-4243 . T) (-4242 . T) (-4241 . T) (-4246 . T) (-4240 . T) (-4239 . T) (-4238 . T) (-4237 . T) (-4236 . T) (-4244 . T) (-4247 . T) (|NullSquare| . T) (|JacobiIdentity| . T) (-4235 . T)) NIL (-94 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}."))) -((-4241 . T)) +((-4245 . T)) NIL (-95 R UP) ((|constructor| (NIL "This package provides balanced factorisations of polynomials.")) (|balancedFactorisation| (((|Factored| |#2|) |#2| (|List| |#2|)) "\\spad{balancedFactorisation(a,{} [b1,{}...,{}bn])} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{pi} is balanced with respect to \\spad{[b1,{}...,{}bm]}.") (((|Factored| |#2|) |#2| |#2|) "\\spad{balancedFactorisation(a,{} b)} returns a factorisation \\spad{a = p1^e1 ... pm^em} such that each \\spad{\\spad{pi}} is balanced with respect to \\spad{b}."))) @@ -322,15 +322,15 @@ NIL NIL (-98 S) ((|constructor| (NIL "\\spadtype{BalancedBinaryTree(S)} is the domain of balanced binary trees (bbtree). A balanced binary tree of \\spad{2**k} leaves,{} for some \\spad{k > 0},{} is symmetric,{} that is,{} the left and right subtree of each interior node have identical shape. In general,{} the left and right subtree of a given node can differ by at most leaf node.")) (|mapDown!| (($ $ |#1| (|Mapping| (|List| |#1|) |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. Let \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t}. The root value \\spad{x} of \\spad{t} is replaced by \\spad{p}. Then \\spad{f}(value \\spad{l},{} value \\spad{r},{} \\spad{p}),{} where \\spad{l} and \\spad{r} denote the left and right subtrees of \\spad{t},{} is evaluated producing two values \\spad{pl} and \\spad{pr}. Then \\spad{mapDown!(l,{}pl,{}f)} and \\spad{mapDown!(l,{}pr,{}f)} are evaluated.") (($ $ |#1| (|Mapping| |#1| |#1| |#1|)) "\\spad{mapDown!(t,{}p,{}f)} returns \\spad{t} after traversing \\spad{t} in \"preorder\" (node then left then right) fashion replacing the successive interior nodes as follows. The root value \\spad{x} is replaced by \\spad{q} \\spad{:=} \\spad{f}(\\spad{p},{}\\spad{x}). The mapDown!(\\spad{l},{}\\spad{q},{}\\spad{f}) and mapDown!(\\spad{r},{}\\spad{q},{}\\spad{f}) are evaluated for the left and right subtrees \\spad{l} and \\spad{r} of \\spad{t}.")) (|mapUp!| (($ $ $ (|Mapping| |#1| |#1| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}t1,{}f)} traverses \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r},{}\\spad{l1},{}\\spad{r1}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes. Values \\spad{l1} and \\spad{r1} are values at the corresponding nodes of a balanced binary tree \\spad{t1},{} of identical shape at \\spad{t}.") ((|#1| $ (|Mapping| |#1| |#1| |#1|)) "\\spad{mapUp!(t,{}f)} traverses balanced binary tree \\spad{t} in an \"endorder\" (left then right then node) fashion returning \\spad{t} with the value at each successive interior node of \\spad{t} replaced by \\spad{f}(\\spad{l},{}\\spad{r}) where \\spad{l} and \\spad{r} are the values at the immediate left and right nodes.")) (|setleaves!| (($ $ (|List| |#1|)) "\\spad{setleaves!(t,{} ls)} sets the leaves of \\spad{t} in left-to-right order to the elements of \\spad{ls}.")) (|balancedBinaryTree| (($ (|NonNegativeInteger|) |#1|) "\\spad{balancedBinaryTree(n,{} s)} creates a balanced binary tree with \\spad{n} nodes each with value \\spad{s}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-99 R UP M |Row| |Col|) ((|constructor| (NIL "\\spadtype{BezoutMatrix} contains functions for computing resultants and discriminants using Bezout matrices.")) (|bezoutDiscriminant| ((|#1| |#2|) "\\spad{bezoutDiscriminant(p)} computes the discriminant of a polynomial \\spad{p} by computing the determinant of a Bezout matrix.")) (|bezoutResultant| ((|#1| |#2| |#2|) "\\spad{bezoutResultant(p,{}q)} computes the resultant of the two polynomials \\spad{p} and \\spad{q} by computing the determinant of a Bezout matrix.")) (|bezoutMatrix| ((|#3| |#2| |#2|) "\\spad{bezoutMatrix(p,{}q)} returns the Bezout matrix for the two polynomials \\spad{p} and \\spad{q}.")) (|sylvesterMatrix| ((|#3| |#2| |#2|) "\\spad{sylvesterMatrix(p,{}q)} returns the Sylvester matrix for the two polynomials \\spad{p} and \\spad{q}."))) NIL -((|HasAttribute| |#1| (QUOTE (-4246 "*")))) +((|HasAttribute| |#1| (QUOTE (-4250 "*")))) (-100) ((|bfEntry| (((|Record| (|:| |zeros| (|Stream| (|DoubleFloat|))) (|:| |ones| (|Stream| (|DoubleFloat|))) (|:| |singularities| (|Stream| (|DoubleFloat|)))) (|Symbol|)) "\\spad{bfEntry(k)} returns the entry in the \\axiomType{BasicFunctions} table corresponding to \\spad{k}")) (|bfKeys| (((|List| (|Symbol|))) "\\spad{bfKeys()} returns the names of each function in the \\axiomType{BasicFunctions} table"))) -((-4244 . T)) +((-4248 . T)) NIL (-101 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."))) @@ -338,12 +338,12 @@ NIL NIL (-102 S) ((|constructor| (NIL "A bag aggregate is an aggregate for which one can insert and extract objects,{} and where the order in which objects are inserted determines the order of extraction. Examples of bags are stacks,{} queues,{} and dequeues.")) (|inspect| ((|#1| $) "\\spad{inspect(u)} returns an (random) element from a bag.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}u)} inserts item \\spad{x} into bag \\spad{u}.")) (|extract!| ((|#1| $) "\\spad{extract!(u)} destructively removes a (random) item from bag \\spad{u}.")) (|bag| (($ (|List| |#1|)) "\\spad{bag([x,{}y,{}...,{}z])} creates a bag with elements \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.")) (|shallowlyMutable| ((|attribute|) "shallowlyMutable means that elements of bags may be destructively changed."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL (-103) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating binary expansions.")) (|binary| (($ (|Fraction| (|Integer|))) "\\spad{binary(r)} converts a rational number to a binary expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(b)} returns the fractional part of a binary expansion.")) (|coerce| (((|RadixExpansion| 2) $) "\\spad{coerce(b)} converts a binary expansion to a radix expansion with base 2.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(b)} converts a binary expansion to a rational number."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3262 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) (-104) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Binding' is a name asosciated with a collection of properties.")) (|binding| (($ (|Symbol|) (|List| (|Property|))) "\\spad{binding(n,{}props)} constructs a binding with name \\spad{`n'} and property list `props'.")) (|properties| (((|List| (|Property|)) $) "\\spad{properties(b)} returns the properties associated with binding \\spad{b}.")) (|name| (((|Symbol|) $) "\\spad{name(b)} returns the name of binding \\spad{b}"))) NIL @@ -354,11 +354,11 @@ NIL NIL (-106) ((|constructor| (NIL "\\spadtype{Bits} provides logical functions for Indexed Bits.")) (|bits| (($ (|NonNegativeInteger|) (|Boolean|)) "\\spad{bits(n,{}b)} creates bits with \\spad{n} values of \\spad{b}"))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| (-108) (QUOTE (-1016))) (|HasCategory| (-108) (LIST (QUOTE -286) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-108) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-108) (QUOTE (-1016))) (|HasCategory| (-108) (LIST (QUOTE -563) (QUOTE (-794))))) (-107 R S) ((|constructor| (NIL "A \\spadtype{BiModule} is both a left and right module with respect to potentially different rings. \\blankline")) (|rightUnitary| ((|attribute|) "\\spad{x * 1 = x}")) (|leftUnitary| ((|attribute|) "\\spad{1 * x = x}"))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL (-108) ((|constructor| (NIL "\\indented{1}{\\spadtype{Boolean} is the elementary logic with 2 values:} \\spad{true} and \\spad{false}")) (|test| (((|Boolean|) $) "\\spad{test(b)} returns \\spad{b} and is provided for compatibility with the new compiler.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical negation of \\spad{a} or \\spad{b}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical negation of \\spad{a} and \\spad{b}.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical exclusive {\\em or} of Boolean \\spad{a} and \\spad{b}.")) (^ (($ $) "\\spad{^ n} returns the negation of \\spad{n}.")) (|false| (($) "\\spad{false} is a logical constant.")) (|true| (($) "\\spad{true} is a logical constant."))) @@ -372,25 +372,25 @@ NIL ((|constructor| (NIL "A basic operator is an object that can be applied to a list of arguments from a set,{} the result being a kernel over that set.")) (|setProperties| (($ $ (|AssociationList| (|String|) (|None|))) "\\spad{setProperties(op,{} l)} sets the property list of \\spad{op} to \\spad{l}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|setProperty| (($ $ (|String|) (|None|)) "\\spad{setProperty(op,{} s,{} v)} attaches property \\spad{s} to \\spad{op},{} and sets its value to \\spad{v}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|property| (((|Union| (|None|) "failed") $ (|String|)) "\\spad{property(op,{} s)} returns the value of property \\spad{s} if it is attached to \\spad{op},{} and \"failed\" otherwise.")) (|deleteProperty!| (($ $ (|String|)) "\\spad{deleteProperty!(op,{} s)} unattaches property \\spad{s} from \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|assert| (($ $ (|String|)) "\\spad{assert(op,{} s)} attaches property \\spad{s} to \\spad{op}. Argument \\spad{op} is modified \"in place\",{} \\spadignore{i.e.} no copy is made.")) (|has?| (((|Boolean|) $ (|String|)) "\\spad{has?(op,{} s)} tests if property \\spad{s} is attached to \\spad{op}.")) (|is?| (((|Boolean|) $ (|Symbol|)) "\\spad{is?(op,{} s)} tests if the name of \\spad{op} is \\spad{s}.")) (|input| (((|Union| (|Mapping| (|InputForm|) (|List| (|InputForm|))) "failed") $) "\\spad{input(op)} returns the \"\\%input\" property of \\spad{op} if it has one attached,{} \"failed\" otherwise.") (($ $ (|Mapping| (|InputForm|) (|List| (|InputForm|)))) "\\spad{input(op,{} foo)} attaches foo as the \"\\%input\" property of \\spad{op}. If \\spad{op} has a \"\\%input\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to InputForm as \\spad{f(a1,{}...,{}an)}.")) (|display| (($ $ (|Mapping| (|OutputForm|) (|OutputForm|))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a)} gets converted to OutputForm as \\spad{f(a)}. Argument \\spad{op} must be unary.") (($ $ (|Mapping| (|OutputForm|) (|List| (|OutputForm|)))) "\\spad{display(op,{} foo)} attaches foo as the \"\\%display\" property of \\spad{op}. If \\spad{op} has a \"\\%display\" property \\spad{f},{} then \\spad{op(a1,{}...,{}an)} gets converted to OutputForm as \\spad{f(a1,{}...,{}an)}.") (((|Union| (|Mapping| (|OutputForm|) (|List| (|OutputForm|))) "failed") $) "\\spad{display(op)} returns the \"\\%display\" property of \\spad{op} if it has one attached,{} and \"failed\" otherwise.")) (|comparison| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{comparison(op,{} foo?)} attaches foo? as the \"\\%less?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has a \"\\%less?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether \\spad{op1 < op2}.")) (|equality| (($ $ (|Mapping| (|Boolean|) $ $)) "\\spad{equality(op,{} foo?)} attaches foo? as the \"\\%equal?\" property to \\spad{op}. If op1 and op2 have the same name,{} and one of them has an \"\\%equal?\" property \\spad{f},{} then \\spad{f(op1,{} op2)} is called to decide whether op1 and op2 should be considered equal.")) (|weight| (($ $ (|NonNegativeInteger|)) "\\spad{weight(op,{} n)} attaches the weight \\spad{n} to \\spad{op}.") (((|NonNegativeInteger|) $) "\\spad{weight(op)} returns the weight attached to \\spad{op}.")) (|nary?| (((|Boolean|) $) "\\spad{nary?(op)} tests if \\spad{op} has arbitrary arity.")) (|unary?| (((|Boolean|) $) "\\spad{unary?(op)} tests if \\spad{op} is unary.")) (|nullary?| (((|Boolean|) $) "\\spad{nullary?(op)} tests if \\spad{op} is nullary.")) (|arity| (((|Union| (|NonNegativeInteger|) "failed") $) "\\spad{arity(op)} returns \\spad{n} if \\spad{op} is \\spad{n}-ary,{} and \"failed\" if \\spad{op} has arbitrary arity.")) (|operator| (($ (|Symbol|) (|NonNegativeInteger|)) "\\spad{operator(f,{} n)} makes \\spad{f} into an \\spad{n}-ary operator.") (($ (|Symbol|)) "\\spad{operator(f)} makes \\spad{f} into an operator with arbitrary arity.")) (|copy| (($ $) "\\spad{copy(op)} returns a copy of \\spad{op}.")) (|properties| (((|AssociationList| (|String|) (|None|)) $) "\\spad{properties(op)} returns the list of all the properties currently attached to \\spad{op}.")) (|name| (((|Symbol|) $) "\\spad{name(op)} returns the name of \\spad{op}."))) NIL NIL -(-111 -2315 UP) +(-111 -3539 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 (-112 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-113 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in -(\\spad{p} - 1)\\spad{/2},{}...,{}(\\spad{p} - 1)\\spad{/2}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-112 |#1|) (QUOTE (-840))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-112 |#1|) (QUOTE (-949))) (|HasCategory| (-112 |#1|) (QUOTE (-759))) (-3262 (|HasCategory| (-112 |#1|) (QUOTE (-759))) (|HasCategory| (-112 |#1|) (QUOTE (-786)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-1063))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-211))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-284))) (|HasCategory| (-112 |#1|) (QUOTE (-508))) (|HasCategory| (-112 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-112 |#1|) (QUOTE (-840))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-136))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-112 |#1|) (QUOTE (-949))) (|HasCategory| (-112 |#1|) (QUOTE (-759))) (-3172 (|HasCategory| (-112 |#1|) (QUOTE (-759))) (|HasCategory| (-112 |#1|) (QUOTE (-786)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-1063))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-112 |#1|) (QUOTE (-211))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -112) (|devaluate| |#1|)) (LIST (QUOTE -112) (|devaluate| |#1|)))) (|HasCategory| (-112 |#1|) (QUOTE (-284))) (|HasCategory| (-112 |#1|) (QUOTE (-508))) (|HasCategory| (-112 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-112 |#1|) (QUOTE (-840)))) (|HasCategory| (-112 |#1|) (QUOTE (-134))))) (-114 A S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) NIL -((|HasAttribute| |#1| (QUOTE -4245))) +((|HasAttribute| |#1| (QUOTE -4249))) (-115 S) ((|constructor| (NIL "A binary-recursive aggregate has 0,{} 1 or 2 children and serves as a model for a binary tree or a doubly-linked aggregate structure")) (|setright!| (($ $ $) "\\spad{setright!(a,{}x)} sets the right child of \\spad{t} to be \\spad{x}.")) (|setleft!| (($ $ $) "\\spad{setleft!(a,{}b)} sets the left child of \\axiom{a} to be \\spad{b}.")) (|setelt| (($ $ "right" $) "\\spad{setelt(a,{}\"right\",{}b)} (also written \\axiom{\\spad{b} . right \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setright!(a,{}\\spad{b})}.") (($ $ "left" $) "\\spad{setelt(a,{}\"left\",{}b)} (also written \\axiom{a . left \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setleft!(a,{}\\spad{b})}.")) (|right| (($ $) "\\spad{right(a)} returns the right child.")) (|elt| (($ $ "right") "\\spad{elt(a,{}\"right\")} (also written: \\axiom{a . right}) is equivalent to \\axiom{right(a)}.") (($ $ "left") "\\spad{elt(u,{}\"left\")} (also written: \\axiom{a . left}) is equivalent to \\axiom{left(a)}.")) (|left| (($ $) "\\spad{left(u)} returns the left child."))) -((-3656 . T)) +((-4069 . T)) NIL (-116 UP) ((|constructor| (NIL "\\indented{1}{Author: Frederic Lehobey,{} James \\spad{H}. Davenport} Date Created: 28 June 1994 Date Last Updated: 11 July 1997 Basic Operations: brillhartIrreducible? Related Domains: Also See: AMS Classifications: Keywords: factorization Examples: References: [1] John Brillhart,{} Note on Irreducibility Testing,{} Mathematics of Computation,{} vol. 35,{} num. 35,{} Oct. 1980,{} 1379-1381 [2] James Davenport,{} On Brillhart Irreducibility. To appear. [3] John Brillhart,{} On the Euler and Bernoulli polynomials,{} \\spad{J}. Reine Angew. Math.,{} \\spad{v}. 234,{} (1969),{} \\spad{pp}. 45-64")) (|noLinearFactor?| (((|Boolean|) |#1|) "\\spad{noLinearFactor?(p)} returns \\spad{true} if \\spad{p} can be shown to have no linear factor by a theorem of Lehmer,{} \\spad{false} else. \\spad{I} insist on the fact that \\spad{false} does not mean that \\spad{p} has a linear factor.")) (|brillhartTrials| (((|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{brillhartTrials(n)} sets to \\spad{n} the number of tests in \\spadfun{brillhartIrreducible?} and returns the previous value.") (((|NonNegativeInteger|)) "\\spad{brillhartTrials()} returns the number of tests in \\spadfun{brillhartIrreducible?}.")) (|brillhartIrreducible?| (((|Boolean|) |#1| (|Boolean|)) "\\spad{brillhartIrreducible?(p,{}noLinears)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} else. If \\spad{noLinears} is \\spad{true},{} we are being told \\spad{p} has no linear factors \\spad{false} does not mean that \\spad{p} is reducible.") (((|Boolean|) |#1|) "\\spad{brillhartIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by a remark of Brillhart,{} \\spad{false} is inconclusive."))) @@ -398,15 +398,15 @@ NIL NIL (-117 S) ((|constructor| (NIL "BinarySearchTree(\\spad{S}) is the domain of a binary trees where elements are ordered across the tree. A binary search tree is either empty or has a value which is an \\spad{S},{} and a right and left which are both BinaryTree(\\spad{S}) Elements are ordered across the tree.")) (|split| (((|Record| (|:| |less| $) (|:| |greater| $)) |#1| $) "\\spad{split(x,{}b)} splits binary tree \\spad{b} into two trees,{} one with elements greater than \\spad{x},{} the other with elements less than \\spad{x}.")) (|insertRoot!| (($ |#1| $) "\\spad{insertRoot!(x,{}b)} inserts element \\spad{x} as a root of binary search tree \\spad{b}.")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary search tree \\spad{b}.")) (|binarySearchTree| (($ (|List| |#1|)) "\\spad{binarySearchTree(l)} \\undocumented"))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-118 S) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) NIL NIL (-119) ((|constructor| (NIL "The bit aggregate category models aggregates representing large quantities of Boolean data.")) (|xor| (($ $ $) "\\spad{xor(a,{}b)} returns the logical {\\em exclusive-or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|or| (($ $ $) "\\spad{a or b} returns the logical {\\em or} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|and| (($ $ $) "\\spad{a and b} returns the logical {\\em and} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nor| (($ $ $) "\\spad{nor(a,{}b)} returns the logical {\\em nor} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (|nand| (($ $ $) "\\spad{nand(a,{}b)} returns the logical {\\em nand} of bit aggregates \\axiom{a} and \\axiom{\\spad{b}}.")) (^ (($ $) "\\spad{^ b} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}.")) (|not| (($ $) "\\spad{not(b)} returns the logical {\\em not} of bit aggregate \\axiom{\\spad{b}}."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-120 A S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#2| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) @@ -414,16 +414,16 @@ NIL NIL (-121 S) ((|constructor| (NIL "\\spadtype{BinaryTreeCategory(S)} is the category of binary trees: a tree which is either empty or else is a \\spadfun{node} consisting of a value and a \\spadfun{left} and \\spadfun{right},{} both binary trees.")) (|node| (($ $ |#1| $) "\\spad{node(left,{}v,{}right)} creates a binary tree with value \\spad{v},{} a binary tree \\spad{left},{} and a binary tree \\spad{right}.")) (|finiteAggregate| ((|attribute|) "Binary trees have a finite number of components")) (|shallowlyMutable| ((|attribute|) "Binary trees have updateable components"))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-122 S) ((|constructor| (NIL "\\spadtype{BinaryTournament(S)} is the domain of binary trees where elements are ordered down the tree. A binary search tree is either empty or is a node containing a \\spadfun{value} of type \\spad{S},{} and a \\spadfun{right} and a \\spadfun{left} which are both \\spadtype{BinaryTree(S)}")) (|insert!| (($ |#1| $) "\\spad{insert!(x,{}b)} inserts element \\spad{x} as leaves into binary tournament \\spad{b}.")) (|binaryTournament| (($ (|List| |#1|)) "\\spad{binaryTournament(ls)} creates a binary tournament with the elements of \\spad{ls} as values at the nodes."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-123 S) ((|constructor| (NIL "\\spadtype{BinaryTree(S)} is the domain of all binary trees. A binary tree over \\spad{S} is either empty or has a \\spadfun{value} which is an \\spad{S} and a \\spadfun{right} and \\spadfun{left} which are both binary trees.")) (|binaryTree| (($ $ |#1| $) "\\spad{binaryTree(l,{}v,{}r)} creates a binary tree with value \\spad{v} with left subtree \\spad{l} and right subtree \\spad{r}.") (($ |#1|) "\\spad{binaryTree(v)} is an non-empty binary tree with value \\spad{v},{} and left and right empty."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-124) ((|constructor| (NIL "This is an \\spadtype{AbelianMonoid} with the cancellation property,{} \\spadignore{i.e.} \\spad{ a+b = a+c => b=c }. This is formalised by the partial subtraction operator,{} which satisfies the axioms listed below: \\blankline")) (|subtractIfCan| (((|Union| $ "failed") $ $) "\\spad{subtractIfCan(x,{} y)} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists."))) NIL @@ -434,14 +434,14 @@ NIL NIL (-126) ((|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") $ $) "\\spad{x - y} returns an element \\spad{z} such that \\spad{z+y=x} or \"failed\" if no such element exists.")) (|commutative| ((|attribute| "*") "a domain \\spad{D} has \\spad{commutative(\"*\")} if it has an operation \\spad{\"*\": (D,{}D) -> D} which is commutative."))) -(((-4246 "*") . T)) +(((-4250 "*") . T)) NIL -(-127 |minix| -1346 S T$) +(-127 |minix| -1996 S T$) ((|constructor| (NIL "This package provides functions to enable conversion of tensors given conversion of the components.")) (|map| (((|CartesianTensor| |#1| |#2| |#4|) (|Mapping| |#4| |#3|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{map(f,{}ts)} does a componentwise conversion of the tensor \\spad{ts} to a tensor with components of type \\spad{T}.")) (|reshape| (((|CartesianTensor| |#1| |#2| |#4|) (|List| |#4|) (|CartesianTensor| |#1| |#2| |#3|)) "\\spad{reshape(lt,{}ts)} organizes the list of components \\spad{lt} into a tensor with the same shape as \\spad{ts}."))) NIL NIL -(-128 |minix| -1346 R) -((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\^= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) +(-128 |minix| -1996 R) +((|constructor| (NIL "CartesianTensor(minix,{}dim,{}\\spad{R}) provides Cartesian tensors with components belonging to a commutative ring \\spad{R}. These tensors can have any number of indices. Each index takes values from \\spad{minix} to \\spad{minix + dim - 1}.")) (|sample| (($) "\\spad{sample()} returns an object of type \\%.")) (|unravel| (($ (|List| |#3|)) "\\spad{unravel(t)} produces a tensor from a list of components such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|ravel| (((|List| |#3|) $) "\\spad{ravel(t)} produces a list of components from a tensor such that \\indented{2}{\\spad{unravel(ravel(t)) = t}.}")) (|leviCivitaSymbol| (($) "\\spad{leviCivitaSymbol()} is the rank \\spad{dim} tensor defined by \\spad{leviCivitaSymbol()(i1,{}...idim) = +1/0/-1} if \\spad{i1,{}...,{}idim} is an even/is nota /is an odd permutation of \\spad{minix,{}...,{}minix+dim-1}.")) (|kroneckerDelta| (($) "\\spad{kroneckerDelta()} is the rank 2 tensor defined by \\indented{3}{\\spad{kroneckerDelta()(i,{}j)}} \\indented{6}{\\spad{= 1\\space{2}if i = j}} \\indented{6}{\\spad{= 0 if\\space{2}i \\~= j}}")) (|reindex| (($ $ (|List| (|Integer|))) "\\spad{reindex(t,{}[i1,{}...,{}idim])} permutes the indices of \\spad{t}. For example,{} if \\spad{r = reindex(t,{} [4,{}1,{}2,{}3])} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank for tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}i,{}j,{}k)}.}")) (|transpose| (($ $ (|Integer|) (|Integer|)) "\\spad{transpose(t,{}i,{}j)} exchanges the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices of \\spad{t}. For example,{} if \\spad{r = transpose(t,{}2,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(i,{}k,{}j,{}l)}.}") (($ $) "\\spad{transpose(t)} exchanges the first and last indices of \\spad{t}. For example,{} if \\spad{r = transpose(t)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = t(l,{}j,{}k,{}i)}.}")) (|contract| (($ $ (|Integer|) (|Integer|)) "\\spad{contract(t,{}i,{}j)} is the contraction of tensor \\spad{t} which sums along the \\spad{i}\\spad{-}th and \\spad{j}\\spad{-}th indices. For example,{} if \\spad{r = contract(t,{}1,{}3)} for a rank 4 tensor \\spad{t},{} then \\spad{r} is the rank 2 \\spad{(= 4 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j) = sum(h=1..dim,{}t(h,{}i,{}h,{}j))}.}") (($ $ (|Integer|) $ (|Integer|)) "\\spad{contract(t,{}i,{}s,{}j)} is the inner product of tenors \\spad{s} and \\spad{t} which sums along the \\spad{k1}\\spad{-}th index of \\spad{t} and the \\spad{k2}\\spad{-}th index of \\spad{s}. For example,{} if \\spad{r = contract(s,{}2,{}t,{}1)} for rank 3 tensors rank 3 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is the rank 4 \\spad{(= 3 + 3 - 2)} tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = sum(h=1..dim,{}s(i,{}h,{}j)*t(h,{}k,{}l))}.}")) (* (($ $ $) "\\spad{s*t} is the inner product of the tensors \\spad{s} and \\spad{t} which contracts the last index of \\spad{s} with the first index of \\spad{t},{} \\spadignore{i.e.} \\indented{4}{\\spad{t*s = contract(t,{}rank t,{} s,{} 1)}} \\indented{4}{\\spad{t*s = sum(k=1..N,{} t[i1,{}..,{}iN,{}k]*s[k,{}j1,{}..,{}jM])}} This is compatible with the use of \\spad{M*v} to denote the matrix-vector inner product.")) (|product| (($ $ $) "\\spad{product(s,{}t)} is the outer product of the tensors \\spad{s} and \\spad{t}. For example,{} if \\spad{r = product(s,{}t)} for rank 2 tensors \\spad{s} and \\spad{t},{} then \\spad{r} is a rank 4 tensor given by \\indented{4}{\\spad{r(i,{}j,{}k,{}l) = s(i,{}j)*t(k,{}l)}.}")) (|elt| ((|#3| $ (|List| (|Integer|))) "\\spad{elt(t,{}[i1,{}...,{}iN])} gives a component of a rank \\spad{N} tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k,{}l)} gives a component of a rank 4 tensor.") ((|#3| $ (|Integer|) (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j,{}k)} gives a component of a rank 3 tensor.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(t,{}i,{}j)} gives a component of a rank 2 tensor.") ((|#3| $ (|Integer|)) "\\spad{elt(t,{}i)} gives a component of a rank 1 tensor.") ((|#3| $) "\\spad{elt(t)} gives the component of a rank 0 tensor.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(t)} returns the tensorial rank of \\spad{t} (that is,{} the number of indices). This is the same as the graded module degree.")) (|coerce| (($ (|List| $)) "\\spad{coerce([t_1,{}...,{}t_dim])} allows tensors to be constructed using lists.") (($ (|List| |#3|)) "\\spad{coerce([r_1,{}...,{}r_dim])} allows tensors to be constructed using lists.") (($ (|SquareMatrix| |#2| |#3|)) "\\spad{coerce(m)} views a matrix as a rank 2 tensor.") (($ (|DirectProduct| |#2| |#3|)) "\\spad{coerce(v)} views a vector as a rank 1 tensor."))) NIL NIL (-129) @@ -450,8 +450,8 @@ NIL NIL (-130) ((|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}."))) -((-4244 . T) (-4234 . T) (-4245 . T)) -((-3262 (-12 (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4238 . T) (-4249 . T)) +((-3172 (-12 (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-344))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) (-131 R Q A) ((|constructor| (NIL "CommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL @@ -466,7 +466,7 @@ NIL NIL (-134) ((|constructor| (NIL "Rings of Characteristic Non Zero")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(x)} returns the \\spad{p}th root of \\spad{x} where \\spad{p} is the characteristic of the ring."))) -((-4241 . T)) +((-4245 . T)) NIL (-135 R) ((|constructor| (NIL "This package provides a characteristicPolynomial function for any matrix over a commutative ring.")) (|characteristicPolynomial| ((|#1| (|Matrix| |#1|) |#1|) "\\spad{characteristicPolynomial(m,{}r)} computes the characteristic polynomial of the matrix \\spad{m} evaluated at the point \\spad{r}. In particular,{} if \\spad{r} is the polynomial \\spad{'x},{} then it returns the characteristic polynomial expressed as a polynomial in \\spad{'x}."))) @@ -474,9 +474,9 @@ NIL NIL (-136) ((|constructor| (NIL "Rings of Characteristic Zero."))) -((-4241 . T)) +((-4245 . T)) NIL -(-137 -2315 UP UPUP) +(-137 -3539 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 @@ -485,16 +485,16 @@ NIL NIL NIL (-139 A S) -((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) +((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#2| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#2|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2| |#2|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#2| (|Mapping| |#2| |#2| |#2|) $ |#2|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#2| (|Mapping| |#2| |#2| |#2|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#2| "failed") (|Mapping| (|Boolean|) |#2|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#2|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasAttribute| |#1| (QUOTE -4244))) +((|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasAttribute| |#1| (QUOTE -4248))) (-140 S) -((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{^=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) -((-3656 . T)) +((|constructor| (NIL "A collection is a homogeneous aggregate which can built from list of members. The operation used to build the aggregate is generically named \\spadfun{construct}. However,{} each collection provides its own special function with the same name as the data type,{} except with an initial lower case letter,{} \\spadignore{e.g.} \\spadfun{list} for \\spadtype{List},{} \\spadfun{flexibleArray} for \\spadtype{FlexibleArray},{} and so on.")) (|removeDuplicates| (($ $) "\\spad{removeDuplicates(u)} returns a copy of \\spad{u} with all duplicates removed.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(p,{}u)} returns a copy of \\spad{u} containing only those elements such \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{select(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | \\spad{p}(\\spad{x})]}.")) (|remove| (($ |#1| $) "\\spad{remove(x,{}u)} returns a copy of \\spad{u} with all elements \\axiom{\\spad{y} = \\spad{x}} removed. Note: \\axiom{remove(\\spad{y},{}\\spad{c}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{c} | \\spad{x} \\spad{~=} \\spad{y}]}.") (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(p,{}u)} returns a copy of \\spad{u} removing all elements \\spad{x} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true}. Note: \\axiom{remove(\\spad{p},{}\\spad{u}) \\spad{==} [\\spad{x} for \\spad{x} in \\spad{u} | not \\spad{p}(\\spad{x})]}.")) (|reduce| ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1| |#1|) "\\spad{reduce(f,{}u,{}x,{}z)} reduces the binary operation \\spad{f} across \\spad{u},{} stopping when an \"absorbing element\" \\spad{z} is encountered. As for \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})},{} \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u},{}\\spad{x})} when \\spad{u} contains no element \\spad{z}. Thus the third argument \\spad{x} is returned when \\spad{u} is empty.") ((|#1| (|Mapping| |#1| |#1| |#1|) $ |#1|) "\\spad{reduce(f,{}u,{}x)} reduces the binary operation \\spad{f} across \\spad{u},{} where \\spad{x} is the identity operation of \\spad{f}. Same as \\axiom{reduce(\\spad{f},{}\\spad{u})} if \\spad{u} has 2 or more elements. Returns \\axiom{\\spad{f}(\\spad{x},{}\\spad{y})} if \\spad{u} has one element \\spad{y},{} \\spad{x} if \\spad{u} is empty. For example,{} \\axiom{reduce(+,{}\\spad{u},{}0)} returns the sum of the elements of \\spad{u}.") ((|#1| (|Mapping| |#1| |#1| |#1|) $) "\\spad{reduce(f,{}u)} reduces the binary operation \\spad{f} across \\spad{u}. For example,{} if \\spad{u} is \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]} then \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\axiom{\\spad{f}(..\\spad{f}(\\spad{f}(\\spad{x},{}\\spad{y}),{}...),{}\\spad{z})}. Note: if \\spad{u} has one element \\spad{x},{} \\axiom{reduce(\\spad{f},{}\\spad{u})} returns \\spad{x}. Error: if \\spad{u} is empty.")) (|find| (((|Union| |#1| "failed") (|Mapping| (|Boolean|) |#1|) $) "\\spad{find(p,{}u)} returns the first \\spad{x} in \\spad{u} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \"failed\" otherwise.")) (|construct| (($ (|List| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y},{}...,{}\\spad{z})} returns the collection of elements \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}} ordered as given. Equivalently written as \\axiom{[\\spad{x},{}\\spad{y},{}...,{}\\spad{z}]\\$\\spad{D}},{} where \\spad{D} is the domain. \\spad{D} may be omitted for those of type List."))) +((-4069 . T)) NIL (-141 |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."))) -((-4239 . T) (-4238 . T) (-4241 . T)) +((-4243 . T) (-4242 . T) (-4245 . T)) NIL (-142) ((|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."))) @@ -508,7 +508,7 @@ 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 -(-145 R -2315) +(-145 R -3539) ((|constructor| (NIL "Provides combinatorial functions over an integral domain.")) (|ipow| ((|#2| (|List| |#2|)) "\\spad{ipow(l)} should be local but conditional.")) (|iidprod| ((|#2| (|List| |#2|)) "\\spad{iidprod(l)} should be local but conditional.")) (|iidsum| ((|#2| (|List| |#2|)) "\\spad{iidsum(l)} should be local but conditional.")) (|iipow| ((|#2| (|List| |#2|)) "\\spad{iipow(l)} should be local but conditional.")) (|iiperm| ((|#2| (|List| |#2|)) "\\spad{iiperm(l)} should be local but conditional.")) (|iibinom| ((|#2| (|List| |#2|)) "\\spad{iibinom(l)} should be local but conditional.")) (|iifact| ((|#2| |#2|) "\\spad{iifact(x)} should be local but conditional.")) (|product| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{product(f(n),{} n = a..b)} returns \\spad{f}(a) * ... * \\spad{f}(\\spad{b}) as a formal product.") ((|#2| |#2| (|Symbol|)) "\\spad{product(f(n),{} n)} returns the formal product \\spad{P}(\\spad{n}) which verifies \\spad{P}(\\spad{n+1})\\spad{/P}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|summation| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{summation(f(n),{} n = a..b)} returns \\spad{f}(a) + ... + \\spad{f}(\\spad{b}) as a formal sum.") ((|#2| |#2| (|Symbol|)) "\\spad{summation(f(n),{} n)} returns the formal sum \\spad{S}(\\spad{n}) which verifies \\spad{S}(\\spad{n+1}) - \\spad{S}(\\spad{n}) = \\spad{f}(\\spad{n}).")) (|factorials| ((|#2| |#2| (|Symbol|)) "\\spad{factorials(f,{} x)} rewrites the permutations and binomials in \\spad{f} involving \\spad{x} in terms of factorials.") ((|#2| |#2|) "\\spad{factorials(f)} rewrites the permutations and binomials in \\spad{f} in terms of factorials.")) (|factorial| ((|#2| |#2|) "\\spad{factorial(n)} returns the factorial of \\spad{n},{} \\spadignore{i.e.} \\spad{n!}.")) (|permutation| ((|#2| |#2| |#2|) "\\spad{permutation(n,{} r)} returns the number of permutations of \\spad{n} objects taken \\spad{r} at a time,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{n}-\\spad{r})!.")) (|binomial| ((|#2| |#2| |#2|) "\\spad{binomial(n,{} r)} returns the number of subsets of \\spad{r} objects taken among \\spad{n} objects,{} \\spadignore{i.e.} \\spad{n!/}(\\spad{r!} * (\\spad{n}-\\spad{r})!).")) (** ((|#2| |#2| |#2|) "\\spad{a ** b} is the formal exponential a**b.")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns a copy of \\spad{op} with the domain-dependent properties appropriate for \\spad{F}; error if \\spad{op} is not a combinatorial operator.")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} is \\spad{true} if \\spad{op} is a combinatorial operator."))) NIL NIL @@ -535,10 +535,10 @@ NIL (-151 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 (-840))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-339))) (|HasAttribute| |#2| (QUOTE -4240)) (|HasAttribute| |#2| (QUOTE -4243)) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-786)))) +((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-339))) (|HasAttribute| |#2| (QUOTE -4244)) (|HasAttribute| |#2| (QUOTE -4247)) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-786)))) (-152 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})"))) -((-4237 -3262 (|has| |#1| (-515)) (-12 (|has| |#1| (-284)) (|has| |#1| (-840)))) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4240 |has| |#1| (-6 -4240)) (-4243 |has| |#1| (-6 -4243)) (-2571 . T) (-3656 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 -3172 (|has| |#1| (-515)) (-12 (|has| |#1| (-284)) (|has| |#1| (-840)))) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4244 |has| |#1| (-6 -4244)) (-4247 |has| |#1| (-6 -4247)) (-4115 . T) (-4069 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-153 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."))) @@ -550,8 +550,8 @@ NIL NIL (-155 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}."))) -((-4237 -3262 (|has| |#1| (-515)) (-12 (|has| |#1| (-284)) (|has| |#1| (-840)))) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4240 |has| |#1| (-6 -4240)) (-4243 |has| |#1| (-6 -4243)) (-2571 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3262 (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-211))) (-12 (|HasCategory| |#1| 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(QUOTE (-499))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (QUOTE (-840))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| 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T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-325)))) (-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-211))) (-12 (|HasCategory| |#1| 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|#1| (QUOTE (-840)))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (QUOTE (-840))))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| |#1| (QUOTE (-982))) (-12 (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-1109)))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-211))) (-12 (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasAttribute| |#1| (QUOTE -4244)) (|HasAttribute| |#1| (QUOTE -4247)) (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-325))))) (-156 R S CS) ((|constructor| (NIL "This package supports converting complex expressions to patterns")) (|convert| (((|Pattern| |#1|) |#3|) "\\spad{convert(cs)} converts the complex expression \\spad{cs} to a pattern"))) NIL @@ -562,11 +562,11 @@ NIL NIL (-158) ((|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."))) -(((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-159 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}."))) -(((-4246 "*") . T) (-4237 . T) (-4242 . T) (-4236 . T) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") . T) (-4241 . T) (-4246 . T) (-4240 . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-160) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. A `Contour' a list of bindings making up a `virtual scope'.")) (|findBinding| (((|Union| (|Binding|) "failed") (|Symbol|) $) "\\spad{findBinding(c,{}n)} returns the first binding associated with \\spad{`n'}. Otherwise `failed'.")) (|push| (($ (|Binding|) $) "\\spad{push(c,{}b)} augments the contour with binding \\spad{`b'}.")) (|bindings| (((|List| (|Binding|)) $) "\\spad{bindings(c)} returns the list of bindings in countour \\spad{c}."))) @@ -600,7 +600,7 @@ NIL ((|constructor| (NIL "This domains represents a syntax object that designates a category,{} domain,{} or a package. See Also: Syntax,{} Domain")) (|arguments| (((|List| (|Syntax|)) $) "\\spad{arguments returns} the list of syntax objects for the arguments used to invoke the constructor.")) (|constructorName| (((|Symbol|) $) "\\spad{constructorName c} returns the name of the constructor"))) NIL NIL -(-168 R -2315) +(-168 R -3539) ((|constructor| (NIL "\\spadtype{ComplexTrigonometricManipulations} provides function that compute the real and imaginary parts of complex functions.")) (|complexForm| (((|Complex| (|Expression| |#1|)) |#2|) "\\spad{complexForm(f)} returns \\spad{[real f,{} imag f]}.")) (|trigs| ((|#2| |#2|) "\\spad{trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (|real?| (((|Boolean|) |#2|) "\\spad{real?(f)} returns \\spad{true} if \\spad{f = real f}.")) (|imag| (((|Expression| |#1|) |#2|) "\\spad{imag(f)} returns the imaginary part of \\spad{f} where \\spad{f} is a complex function.")) (|real| (((|Expression| |#1|) |#2|) "\\spad{real(f)} returns the real part of \\spad{f} where \\spad{f} is a complex function.")) (|complexElementary| ((|#2| |#2| (|Symbol|)) "\\spad{complexElementary(f,{} x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.") ((|#2| |#2|) "\\spad{complexElementary(f)} rewrites \\spad{f} in terms of the 2 fundamental complex transcendental elementary functions: \\spad{log,{} exp}.")) (|complexNormalize| ((|#2| |#2| (|Symbol|)) "\\spad{complexNormalize(f,{} x)} rewrites \\spad{f} using the least possible number of complex independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{complexNormalize(f)} rewrites \\spad{f} using the least possible number of complex independent kernels."))) NIL NIL @@ -704,19 +704,19 @@ NIL ((|constructor| (NIL "\\indented{1}{This domain implements a simple view of a database whose fields are} indexed by symbols")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} makes a database out of a list")) (- (($ $ $) "\\spad{db1-db2} returns the difference of databases \\spad{db1} and \\spad{db2} \\spadignore{i.e.} consisting of elements in \\spad{db1} but not in \\spad{db2}")) (+ (($ $ $) "\\spad{db1+db2} returns the merge of databases \\spad{db1} and \\spad{db2}")) (|fullDisplay| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{fullDisplay(db,{}start,{}end )} prints full details of entries in the range \\axiom{\\spad{start}..end} in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(db)} prints full details of each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{fullDisplay(x)} displays \\spad{x} in detail")) (|display| (((|Void|) $) "\\spad{display(db)} prints a summary line for each entry in \\axiom{\\spad{db}}.") (((|Void|) $) "\\spad{display(x)} displays \\spad{x} in some form")) (|elt| (((|DataList| (|String|)) $ (|Symbol|)) "\\spad{elt(db,{}s)} returns the \\axiom{\\spad{s}} field of each element of \\axiom{\\spad{db}}.") (($ $ (|QueryEquation|)) "\\spad{elt(db,{}q)} returns all elements of \\axiom{\\spad{db}} which satisfy \\axiom{\\spad{q}}.") (((|String|) $ (|Symbol|)) "\\spad{elt(x,{}s)} returns an element of \\spad{x} indexed by \\spad{s}"))) NIL NIL -(-194 -2315 UP UPUP R) +(-194 -3539 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 -(-195 -2315 FP) +(-195 -3539 FP) ((|constructor| (NIL "Package for the factorization of a univariate polynomial with coefficients in a finite field. The algorithm used is the \"distinct degree\" algorithm of Cantor-Zassenhaus,{} modified to use trace instead of the norm and a table for computing Frobenius as suggested by Naudin and Quitte .")) (|irreducible?| (((|Boolean|) |#2|) "\\spad{irreducible?(p)} tests whether the polynomial \\spad{p} is irreducible.")) (|tracePowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{tracePowMod(u,{}k,{}v)} produces the sum of \\spad{u**(q**i)} for \\spad{i} running and \\spad{q=} size \\spad{F}")) (|trace2PowMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{trace2PowMod(u,{}k,{}v)} produces the sum of \\spad{u**(2**i)} for \\spad{i} running from 1 to \\spad{k} all computed modulo the polynomial \\spad{v}.")) (|exptMod| ((|#2| |#2| (|NonNegativeInteger|) |#2|) "\\spad{exptMod(u,{}k,{}v)} raises the polynomial \\spad{u} to the \\spad{k}th power modulo the polynomial \\spad{v}.")) (|separateFactors| (((|List| |#2|) (|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|)))) "\\spad{separateFactors(lfact)} takes the list produced by \\spadfunFrom{separateDegrees}{DistinctDegreeFactorization} and produces the complete list of factors.")) (|separateDegrees| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |prod| |#2|))) |#2|) "\\spad{separateDegrees(p)} splits the square free polynomial \\spad{p} into factors each of which is a product of irreducibles of the same degree.")) (|distdfact| (((|Record| (|:| |cont| |#1|) (|:| |factors| (|List| (|Record| (|:| |irr| |#2|) (|:| |pow| (|Integer|)))))) |#2| (|Boolean|)) "\\spad{distdfact(p,{}sqfrflag)} produces the complete factorization of the polynomial \\spad{p} returning an internal data structure. If argument \\spad{sqfrflag} is \\spad{true},{} the polynomial is assumed square free.")) (|factorSquareFree| (((|Factored| |#2|) |#2|) "\\spad{factorSquareFree(p)} produces the complete factorization of the square free polynomial \\spad{p}.")) (|factor| (((|Factored| |#2|) |#2|) "\\spad{factor(p)} produces the complete factorization of the polynomial \\spad{p}."))) NIL NIL (-196) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions.")) (|decimal| (($ (|Fraction| (|Integer|))) "\\spad{decimal(r)} converts a rational number to a decimal expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(d)} returns the fractional part of a decimal expansion.")) (|coerce| (((|RadixExpansion| 10) $) "\\spad{coerce(d)} converts a decimal expansion to a radix expansion with base 10.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(d)} converts a decimal expansion to a rational number."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3262 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) -(-197 R -2315) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +(-197 R -3539) ((|constructor| (NIL "\\spadtype{ElementaryFunctionDefiniteIntegration} provides functions to compute definite integrals of elementary functions.")) (|innerint| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|) (|Boolean|)) "\\spad{innerint(f,{} x,{} a,{} b,{} ignore?)} should be local but conditional")) (|integrate| (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|)) (|String|)) "\\spad{integrate(f,{} x = a..b,{} \"noPole\")} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. If it is not possible to check whether \\spad{f} has a pole for \\spad{x} between a and \\spad{b} (because of parameters),{} then this function will assume that \\spad{f} has no such pole. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b} or if the last argument is not \"noPole\".") (((|Union| (|:| |f1| (|OrderedCompletion| |#2|)) (|:| |f2| (|List| (|OrderedCompletion| |#2|))) (|:| |fail| "failed") (|:| |pole| "potentialPole")) |#2| (|SegmentBinding| (|OrderedCompletion| |#2|))) "\\spad{integrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b}. Error: if \\spad{f} has a pole for \\spad{x} between a and \\spad{b}."))) NIL NIL @@ -730,19 +730,19 @@ NIL NIL (-200 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}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-201 |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}."))) -((-4241 . T)) +((-4245 . T)) NIL -(-202 R -2315) +(-202 R -3539) ((|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 (-203) ((|constructor| (NIL "\\indented{1}{\\spadtype{DoubleFloat} is intended to make accessible} hardware floating point arithmetic in \\Language{},{} either native double precision,{} or IEEE. On most machines,{} there will be hardware support for the arithmetic operations: \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and possibly also the \\spadfunFrom{sqrt}{DoubleFloat} operation. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat},{} \\spadfunFrom{atan}{DoubleFloat} are normally coded in software based on minimax polynomial/rational approximations. Note that under Lisp/VM,{} \\spadfunFrom{atan}{DoubleFloat} is not available at this time. Some general comments about the accuracy of the operations: the operations \\spadfunFrom{+}{DoubleFloat},{} \\spadfunFrom{*}{DoubleFloat},{} \\spadfunFrom{/}{DoubleFloat} and \\spadfunFrom{sqrt}{DoubleFloat} are expected to be fully accurate. The operations \\spadfunFrom{exp}{DoubleFloat},{} \\spadfunFrom{log}{DoubleFloat},{} \\spadfunFrom{sin}{DoubleFloat},{} \\spadfunFrom{cos}{DoubleFloat} and \\spadfunFrom{atan}{DoubleFloat} are not expected to be fully accurate. In particular,{} \\spadfunFrom{sin}{DoubleFloat} and \\spadfunFrom{cos}{DoubleFloat} will lose all precision for large arguments. \\blankline The \\spadtype{Float} domain provides an alternative to the \\spad{DoubleFloat} domain. It provides an arbitrary precision model of floating point arithmetic. This means that accuracy problems like those above are eliminated by increasing the working precision where necessary. \\spadtype{Float} provides some special functions such as \\spadfunFrom{erf}{DoubleFloat},{} the error function in addition to the elementary functions. The disadvantage of \\spadtype{Float} is that it is much more expensive than small floats when the latter can be used.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)} (that is,{} \\spad{|(r-f)/f| < b**(-n)}).") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|doubleFloatFormat| (((|String|) (|String|)) "change the output format for doublefloats using lisp format strings")) (|Beta| (($ $ $) "\\spad{Beta(x,{}y)} is \\spad{Gamma(x) * Gamma(y)/Gamma(x+y)}.")) (|Gamma| (($ $) "\\spad{Gamma(x)} is the Euler Gamma function.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm with base 10 for \\spad{x}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm with base 2 for \\spad{x}.")) (|hash| (((|Integer|) $) "\\spad{hash(x)} returns the hash key for \\spad{x}")) (|exp1| (($) "\\spad{exp1()} returns the natural log base \\spad{2.718281828...}.")) (** (($ $ $) "\\spad{x ** y} returns the \\spad{y}th power of \\spad{x} (equal to \\spad{exp(y log x)}).")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-2562 . T) (-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-204) ((|constructor| (NIL "This package provides special functions for double precision real and complex floating point.")) (|hypergeometric0F1| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{hypergeometric0F1(c,{}z)} is the hypergeometric function \\spad{0F1(; c; z)}.")) (|airyBi| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyBi(x)} is the Airy function \\spad{\\spad{Bi}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Bi}''(x) - x * \\spad{Bi}(x) = 0}.}")) (|airyAi| (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}") (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{airyAi(x)} is the Airy function \\spad{\\spad{Ai}(x)}. This function satisfies the differential equation: \\indented{2}{\\spad{\\spad{Ai}''(x) - x * \\spad{Ai}(x) = 0}.}")) (|besselK| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselK(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{K(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{K(v,{}x) = \\%pi/2*(I(-v,{}x) - I(v,{}x))/sin(v*\\%\\spad{pi})}.} so is not valid for integer values of \\spad{v}.")) (|besselI| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselI(v,{}x)} is the modified Bessel function of the first kind,{} \\spad{I(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) - (x^2+v^2)w(x) = 0}.}")) (|besselY| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselY(v,{}x)} is the Bessel function of the second kind,{} \\spad{Y(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.} Note: The default implmentation uses the relation \\indented{2}{\\spad{Y(v,{}x) = (J(v,{}x) cos(v*\\%\\spad{pi}) - J(-v,{}x))/sin(v*\\%\\spad{pi})}} so is not valid for integer values of \\spad{v}.")) (|besselJ| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{besselJ(v,{}x)} is the Bessel function of the first kind,{} \\spad{J(v,{}x)}. This function satisfies the differential equation: \\indented{2}{\\spad{x^2 w''(x) + x w'(x) + (x^2-v^2)w(x) = 0}.}")) (|polygamma| (((|Complex| (|DoubleFloat|)) (|NonNegativeInteger|) (|Complex| (|DoubleFloat|))) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.") (((|DoubleFloat|) (|NonNegativeInteger|) (|DoubleFloat|)) "\\spad{polygamma(n,{} x)} is the \\spad{n}-th derivative of \\spad{digamma(x)}.")) (|digamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{digamma(x)} is the function,{} \\spad{psi(x)},{} defined by \\indented{2}{\\spad{psi(x) = Gamma'(x)/Gamma(x)}.}")) (|logGamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{logGamma(x)} is the natural log of \\spad{Gamma(x)}. This can often be computed even if \\spad{Gamma(x)} cannot.")) (|Beta| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}") (((|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "\\spad{Beta(x,{} y)} is the Euler beta function,{} \\spad{B(x,{}y)},{} defined by \\indented{2}{\\spad{Beta(x,{}y) = integrate(t^(x-1)*(1-t)^(y-1),{} t=0..1)}.} This is related to \\spad{Gamma(x)} by \\indented{2}{\\spad{Beta(x,{}y) = Gamma(x)*Gamma(y) / Gamma(x + y)}.}")) (|Gamma| (((|Complex| (|DoubleFloat|)) (|Complex| (|DoubleFloat|))) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}") (((|DoubleFloat|) (|DoubleFloat|)) "\\spad{Gamma(x)} is the Euler gamma function,{} \\spad{Gamma(x)},{} defined by \\indented{2}{\\spad{Gamma(x) = integrate(t^(x-1)*exp(-t),{} t=0..\\%infinity)}.}"))) @@ -750,15 +750,15 @@ NIL NIL (-205 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}"))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4246 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-206 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 (-207 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."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL (-208 S R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) @@ -766,7 +766,7 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-209 R) ((|constructor| (NIL "Differential extensions of a ring \\spad{R}. Given a differentiation on \\spad{R},{} extend it to a differentiation on \\%.")) (D (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{D(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{D(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) (|NonNegativeInteger|)) "\\spad{differentiate(x,{} deriv,{} n)} differentiate \\spad{x} \\spad{n} times using a derivation which extends \\spad{deriv} on \\spad{R}.") (($ $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(x,{} deriv)} differentiates \\spad{x} extending the derivation deriv on \\spad{R}."))) -((-4241 . T)) +((-4245 . T)) NIL (-210 S) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) @@ -774,36 +774,36 @@ NIL NIL (-211) ((|constructor| (NIL "An ordinary differential ring,{} that is,{} a ring with an operation \\spadfun{differentiate}. \\blankline")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{D(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(x,{} n)} returns the \\spad{n}-th derivative of \\spad{x}.") (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}. This function is a simple differential operator where no variable needs to be specified."))) -((-4241 . T)) +((-4245 . T)) NIL (-212 A S) ((|constructor| (NIL "This category is a collection of operations common to both categories \\spadtype{Dictionary} and \\spadtype{MultiDictionary}")) (|select!| (($ (|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 -4244))) +((|HasAttribute| |#1| (QUOTE -4248))) (-213 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}."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL (-214) ((|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 -(-215 S -1346 R) +(-215 S -1996 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#3|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#3| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#3| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#3|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) NIL -((|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-784))) (|HasAttribute| |#3| (QUOTE -4241)) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-666))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (QUOTE (-1016)))) -(-216 -1346 R) +((|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (QUOTE (-784))) (|HasAttribute| |#3| (QUOTE -4245)) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (QUOTE (-666))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (QUOTE (-1016)))) +(-216 -1996 R) ((|constructor| (NIL "\\indented{2}{This category represents a finite cartesian product of a given type.} Many categorical properties are preserved under this construction.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the vectors \\spad{x} and \\spad{y}.")) (|unitVector| (($ (|PositiveInteger|)) "\\spad{unitVector(n)} produces a vector with 1 in position \\spad{n} and zero elsewhere.")) (|directProduct| (($ (|Vector| |#2|)) "\\spad{directProduct(v)} converts the vector \\spad{v} to become a direct product. Error: if the length of \\spad{v} is different from dim.")) (|finiteAggregate| ((|attribute|) "attribute to indicate an aggregate of finite size"))) -((-4238 |has| |#2| (-973)) (-4239 |has| |#2| (-973)) (-4241 |has| |#2| (-6 -4241)) ((-4246 "*") |has| |#2| (-158)) (-4244 . T) (-3656 . T)) +((-4242 |has| |#2| (-973)) (-4243 |has| |#2| (-973)) (-4245 |has| |#2| (-6 -4245)) ((-4250 "*") |has| |#2| (-158)) (-4248 . T) (-4069 . T)) NIL -(-217 -1346 A B) +(-217 -1996 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} direct products of elements of some type \\spad{A} and functions from \\spad{A} to another type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a direct product over \\spad{B}.")) (|map| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2|) (|DirectProduct| |#1| |#2|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#3| (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if the vector is empty.")) (|scan| (((|DirectProduct| |#1| |#3|) (|Mapping| |#3| |#2| |#3|) (|DirectProduct| |#1| |#2|) |#3|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-218 -1346 R) +(-218 -1996 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."))) -((-4238 |has| |#2| (-973)) (-4239 |has| |#2| (-973)) (-4241 |has| |#2| (-6 -4241)) ((-4246 "*") |has| |#2| (-158)) (-4244 . 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((|constructor| (NIL "DisplayPackage allows one to print strings in a nice manner,{} including highlighting substrings.")) (|sayLength| (((|Integer|) (|List| (|String|))) "\\spad{sayLength(l)} returns the length of a list of strings \\spad{l} as an integer.") (((|Integer|) (|String|)) "\\spad{sayLength(s)} returns the length of a string \\spad{s} as an integer.")) (|say| (((|Void|) (|List| (|String|))) "\\spad{say(l)} sends a list of strings \\spad{l} to output.") (((|Void|) (|String|)) "\\spad{say(s)} sends a string \\spad{s} to output.")) (|center| (((|List| (|String|)) (|List| (|String|)) (|Integer|) (|String|)) "\\spad{center(l,{}i,{}s)} takes a list of strings \\spad{l},{} and centers them within a list of strings which is \\spad{i} characters long,{} in which the remaining spaces are filled with strings composed of as many repetitions as possible of the last string parameter \\spad{s}.") (((|String|) (|String|) (|Integer|) (|String|)) "\\spad{center(s,{}i,{}s)} takes the first string \\spad{s},{} and centers it within a string of length \\spad{i},{} in which the other elements of the string are composed of as many replications as possible of the second indicated string,{} \\spad{s} which must have a length greater than that of an empty string.")) (|copies| (((|String|) (|Integer|) (|String|)) "\\spad{copies(i,{}s)} will take a string \\spad{s} and create a new string composed of \\spad{i} copies of \\spad{s}.")) (|newLine| (((|String|)) "\\spad{newLine()} sends a new line command to output.")) (|bright| (((|List| (|String|)) (|List| (|String|))) "\\spad{bright(l)} sets the font property of a list of strings,{} \\spad{l},{} to bold-face type.") (((|List| (|String|)) (|String|)) "\\spad{bright(s)} sets the font property of the string \\spad{s} to bold-face type."))) NIL @@ -814,47 +814,47 @@ NIL NIL (-221) ((|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}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}."))) -((-4237 . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-222 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."))) -((-3656 . T)) +((-4069 . T)) NIL (-223 S) ((|constructor| (NIL "This domain provides some nice functions on lists")) (|elt| (((|NonNegativeInteger|) $ "count") "\\axiom{\\spad{l}.\"count\"} returns the number of elements in \\axiom{\\spad{l}}.") (($ $ "sort") "\\axiom{\\spad{l}.sort} returns \\axiom{\\spad{l}} with elements sorted. Note: \\axiom{\\spad{l}.sort = sort(\\spad{l})}") (($ $ "unique") "\\axiom{\\spad{l}.unique} returns \\axiom{\\spad{l}} with duplicates removed. Note: \\axiom{\\spad{l}.unique = removeDuplicates(\\spad{l})}.")) (|datalist| (($ (|List| |#1|)) "\\spad{datalist(l)} creates a datalist from \\spad{l}")) (|coerce| (((|List| |#1|) $) "\\spad{coerce(x)} returns the list of elements in \\spad{x}") (($ (|List| |#1|)) "\\spad{coerce(l)} creates a datalist from \\spad{l}"))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-224 M) ((|constructor| (NIL "DiscreteLogarithmPackage implements help functions for discrete logarithms in monoids using small cyclic groups.")) (|shanksDiscLogAlgorithm| (((|Union| (|NonNegativeInteger|) "failed") |#1| |#1| (|NonNegativeInteger|)) "\\spad{shanksDiscLogAlgorithm(b,{}a,{}p)} computes \\spad{s} with \\spad{b**s = a} for assuming that \\spad{a} and \\spad{b} are elements in a 'small' cyclic group of order \\spad{p} by Shank\\spad{'s} algorithm. Note: this is a subroutine of the function \\spadfun{discreteLog}.")) (** ((|#1| |#1| (|Integer|)) "\\spad{x ** n} returns \\spad{x} raised to the integer power \\spad{n}"))) NIL NIL (-225 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is lexicographic specified by the variable list parameter with the most significant variable first in the list.")) (|reorder| (($ $ (|List| (|Integer|))) "\\spad{reorder(p,{} perm)} applies the permutation perm to the variables in a polynomial and returns the new correctly ordered polynomial"))) -(((-4246 "*") |has| |#2| (-158)) (-4237 |has| |#2| (-515)) (-4242 |has| |#2| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . 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(QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#3| (QUOTE (-784)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#3| (QUOTE (-973)))) (-12 (|HasCategory| |#3| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#3| (QUOTE (-1016))))) (-3172 (-12 (|HasCategory| |#3| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-211))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-732))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-784))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523)))))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#3| (QUOTE (-666))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -831) (QUOTE (-1087))))) (-12 (|HasCategory| |#3| (QUOTE (-211))) (|HasCategory| |#3| (QUOTE (-973)))) (-3172 (|HasCategory| |#3| (QUOTE (-973))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523)))))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#3| (QUOTE (-1016)))) (-3172 (|HasAttribute| |#3| (QUOTE -4245)) (-12 (|HasCategory| |#3| (QUOTE (-211))) (|HasCategory| |#3| (QUOTE (-973)))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-794))))) (-229 A R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#4| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#3|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#3|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#3|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#3|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) NIL ((|HasCategory| |#2| (QUOTE (-211)))) (-230 R S V E) ((|constructor| (NIL "\\spadtype{DifferentialPolynomialCategory} is a category constructor specifying basic functions in an ordinary differential polynomial ring with a given ordered set of differential indeterminates. In addition,{} it implements defaults for the basic functions. The functions \\spadfun{order} and \\spadfun{weight} are extended from the set of derivatives of differential indeterminates to the set of differential polynomials. Other operations provided on differential polynomials are \\spadfun{leader},{} \\spadfun{initial},{} \\spadfun{separant},{} \\spadfun{differentialVariables},{} and \\spadfun{isobaric?}. Furthermore,{} if the ground ring is a differential ring,{} then evaluation (substitution of differential indeterminates by elements of the ground ring or by differential polynomials) is provided by \\spadfun{eval}. A convenient way of referencing derivatives is provided by the functions \\spadfun{makeVariable}. \\blankline To construct a domain using this constructor,{} one needs to provide a ground ring \\spad{R},{} an ordered set \\spad{S} of differential indeterminates,{} a ranking \\spad{V} on the set of derivatives of the differential indeterminates,{} and a set \\spad{E} of exponents in bijection with the set of differential monomials in the given differential indeterminates. \\blankline")) (|separant| (($ $) "\\spad{separant(p)} returns the partial derivative of the differential polynomial \\spad{p} with respect to its leader.")) (|initial| (($ $) "\\spad{initial(p)} returns the leading coefficient when the differential polynomial \\spad{p} is written as a univariate polynomial in its leader.")) (|leader| ((|#3| $) "\\spad{leader(p)} returns the derivative of the highest rank appearing in the differential polynomial \\spad{p} Note: an error occurs if \\spad{p} is in the ground ring.")) (|isobaric?| (((|Boolean|) $) "\\spad{isobaric?(p)} returns \\spad{true} if every differential monomial appearing in the differential polynomial \\spad{p} has same weight,{} and returns \\spad{false} otherwise.")) (|weight| (((|NonNegativeInteger|) $ |#2|) "\\spad{weight(p,{} s)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|NonNegativeInteger|) $) "\\spad{weight(p)} returns the maximum weight of all differential monomials appearing in the differential polynomial \\spad{p}.")) (|weights| (((|List| (|NonNegativeInteger|)) $ |#2|) "\\spad{weights(p,{} s)} returns a list of weights of differential monomials appearing in the differential polynomial \\spad{p} when \\spad{p} is viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.") (((|List| (|NonNegativeInteger|)) $) "\\spad{weights(p)} returns a list of weights of differential monomials appearing in differential polynomial \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $ |#2|) "\\spad{degree(p,{} s)} returns the maximum degree of the differential polynomial \\spad{p} viewed as a differential polynomial in the differential indeterminate \\spad{s} alone.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of the differential polynomial \\spad{p},{} which is the maximum number of differentiations of a differential indeterminate,{} among all those appearing in \\spad{p}.") (((|NonNegativeInteger|) $ |#2|) "\\spad{order(p,{}s)} returns the order of the differential polynomial \\spad{p} in differential indeterminate \\spad{s}.")) (|differentialVariables| (((|List| |#2|) $) "\\spad{differentialVariables(p)} returns a list of differential indeterminates occurring in a differential polynomial \\spad{p}.")) (|makeVariable| (((|Mapping| $ (|NonNegativeInteger|)) $) "\\spad{makeVariable(p)} views \\spad{p} as an element of a differential ring,{} in such a way that the \\spad{n}-th derivative of \\spad{p} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} \\spad{:=} makeVariable(\\spad{p}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored.") (((|Mapping| $ (|NonNegativeInteger|)) |#2|) "\\spad{makeVariable(s)} views \\spad{s} as a differential indeterminate,{} in such a way that the \\spad{n}-th derivative of \\spad{s} may be simply referenced as \\spad{z}.\\spad{n} where \\spad{z} :=makeVariable(\\spad{s}). Note: In the interpreter,{} \\spad{z} is given as an internal map,{} which may be ignored."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL (-231 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}."))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-232) ((|constructor| (NIL "TopLevelDrawFunctionsForCompiledFunctions provides top level functions for drawing graphics of expressions.")) (|recolor| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{recolor()},{} uninteresting to top level user; exported in order to compile package.")) (|makeObject| (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(surface(f,{}g,{}h),{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{makeObject(f,{}a..b,{}c..d)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(f,{}a..b,{}c..d,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)},{} and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{makeObject(sp,{}curve(f,{}g,{}h),{}a..b)} returns the space \\spad{sp} of the domain \\spadtype{ThreeSpace} with the addition of the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeSpace| (|DoubleFloat|)) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{makeObject(curve(f,{}g,{}h),{}a..b,{}l)} returns a space of the domain \\spadtype{ThreeSpace} which contains the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.")) (|draw| (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|ParametricSurface| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(surface(f,{}g,{}h),{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{x = f(u,{}v)},{} \\spad{y = g(u,{}v)},{} \\spad{z = h(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}; The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)} The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of the parametric surface \\spad{f(u,{}v)} as \\spad{u} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{v} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}c..d)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}c..d,{}l)} draws the graph of \\spad{z = f(x,{}y)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)} and \\spad{y} ranges from \\spad{min(c,{}d)} to \\spad{max(c,{}d)}. and the options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of the parametric curve \\spad{f} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|ThreeDimensionalViewport|) (|ParametricSpaceCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g,{}h),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t),{} z = h(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|))) "\\spad{draw(curve(f,{}g),{}a..b)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|ParametricPlaneCurve| (|Mapping| (|DoubleFloat|) (|DoubleFloat|))) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(curve(f,{}g),{}a..b,{}l)} draws the graph of the parametric curve \\spad{x = f(t),{} y = g(t)} as \\spad{t} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|))) "\\spad{draw(f,{}a..b)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}.") (((|TwoDimensionalViewport|) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|Float|)) (|List| (|DrawOption|))) "\\spad{draw(f,{}a..b,{}l)} draws the graph of \\spad{y = f(x)} as \\spad{x} ranges from \\spad{min(a,{}b)} to \\spad{max(a,{}b)}. The options contained in the list \\spad{l} of the domain \\spad{DrawOption} are applied."))) @@ -894,8 +894,8 @@ NIL NIL (-241 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"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#3| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-242 A S) ((|constructor| (NIL "\\spadtype{DifferentialVariableCategory} constructs the set of derivatives of a given set of (ordinary) differential indeterminates. If \\spad{x},{}...,{}\\spad{y} is an ordered set of differential indeterminates,{} and the prime notation is used for differentiation,{} then the set of derivatives (including zero-th order) of the differential indeterminates is \\spad{x},{}\\spad{x'},{}\\spad{x''},{}...,{} \\spad{y},{}\\spad{y'},{}\\spad{y''},{}... (Note: in the interpreter,{} the \\spad{n}-th derivative of \\spad{y} is displayed as \\spad{y} with a subscript \\spad{n}.) This set is viewed as a set of algebraic indeterminates,{} totally ordered in a way compatible with differentiation and the given order on the differential indeterminates. Such a total order is called a ranking of the differential indeterminates. \\blankline A domain in this category is needed to construct a differential polynomial domain. Differential polynomials are ordered by a ranking on the derivatives,{} and by an order (extending the ranking) on on the set of differential monomials. One may thus associate a domain in this category with a ranking of the differential indeterminates,{} just as one associates a domain in the category \\spadtype{OrderedAbelianMonoidSup} with an ordering of the set of monomials in a set of algebraic indeterminates. The ranking is specified through the binary relation \\spadfun{<}. For example,{} one may define one derivative to be less than another by lexicographically comparing first the \\spadfun{order},{} then the given order of the differential indeterminates appearing in the derivatives. This is the default implementation. \\blankline The notion of weight generalizes that of degree. A polynomial domain may be made into a graded ring if a weight function is given on the set of indeterminates,{} Very often,{} a grading is the first step in ordering the set of monomials. For differential polynomial domains,{} this constructor provides a function \\spadfun{weight},{} which allows the assignment of a non-negative number to each derivative of a differential indeterminate. For example,{} one may define the weight of a derivative to be simply its \\spadfun{order} (this is the default assignment). This weight function can then be extended to the set of all differential polynomials,{} providing a graded ring structure.")) (|coerce| (($ |#2|) "\\spad{coerce(s)} returns \\spad{s},{} viewed as the zero-th order derivative of \\spad{s}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(v,{} n)} returns the \\spad{n}-th derivative of \\spad{v}.") (($ $) "\\spad{differentiate(v)} returns the derivative of \\spad{v}.")) (|weight| (((|NonNegativeInteger|) $) "\\spad{weight(v)} returns the weight of the derivative \\spad{v}.")) (|variable| ((|#2| $) "\\spad{variable(v)} returns \\spad{s} if \\spad{v} is any derivative of the differential indeterminate \\spad{s}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(v)} returns \\spad{n} if \\spad{v} is the \\spad{n}-th derivative of any differential indeterminate.")) (|makeVariable| (($ |#2| (|NonNegativeInteger|)) "\\spad{makeVariable(s,{} n)} returns the \\spad{n}-th derivative of a differential indeterminate \\spad{s} as an algebraic indeterminate."))) NIL @@ -940,11 +940,11 @@ NIL ((|constructor| (NIL "A domain used in the construction of the exterior algebra on a set \\spad{X} over a ring \\spad{R}. This domain represents the set of all ordered subsets of the set \\spad{X},{} assumed to be in correspondance with {1,{}2,{}3,{} ...}. The ordered subsets are themselves ordered lexicographically and are in bijective correspondance with an ordered basis of the exterior algebra. In this domain we are dealing strictly with the exponents of basis elements which can only be 0 or 1. \\blankline The multiplicative identity element of the exterior algebra corresponds to the empty subset of \\spad{X}. A coerce from List Integer to an ordered basis element is provided to allow the convenient input of expressions. Another exported function forgets the ordered structure and simply returns the list corresponding to an ordered subset.")) (|Nul| (($ (|NonNegativeInteger|)) "\\spad{Nul()} gives the basis element 1 for the algebra generated by \\spad{n} generators.")) (|exponents| (((|List| (|Integer|)) $) "\\spad{exponents(x)} converts a domain element into a list of zeros and ones corresponding to the exponents in the basis element that \\spad{x} represents.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(x)} gives the numbers of 1\\spad{'s} in \\spad{x},{} \\spadignore{i.e.} the number of non-zero exponents in the basis element that \\spad{x} represents.")) (|coerce| (($ (|List| (|Integer|))) "\\spad{coerce(l)} converts a list of 0\\spad{'s} and 1\\spad{'s} into a basis element,{} where 1 (respectively 0) designates that the variable of the corresponding index of \\spad{l} is (respectively,{} is not) present. Error: if an element of \\spad{l} is not 0 or 1."))) NIL NIL -(-253 R -2315) +(-253 R -3539) ((|constructor| (NIL "Provides elementary functions over an integral domain.")) (|localReal?| (((|Boolean|) |#2|) "\\spad{localReal?(x)} should be local but conditional")) (|specialTrigs| (((|Union| |#2| "failed") |#2| (|List| (|Record| (|:| |func| |#2|) (|:| |pole| (|Boolean|))))) "\\spad{specialTrigs(x,{}l)} should be local but conditional")) (|iiacsch| ((|#2| |#2|) "\\spad{iiacsch(x)} should be local but conditional")) (|iiasech| ((|#2| |#2|) "\\spad{iiasech(x)} should be local but conditional")) (|iiacoth| ((|#2| |#2|) "\\spad{iiacoth(x)} should be local but conditional")) (|iiatanh| ((|#2| |#2|) "\\spad{iiatanh(x)} should be local but conditional")) (|iiacosh| ((|#2| |#2|) "\\spad{iiacosh(x)} should be local but conditional")) (|iiasinh| ((|#2| |#2|) "\\spad{iiasinh(x)} should be local but conditional")) (|iicsch| ((|#2| |#2|) "\\spad{iicsch(x)} should be local but conditional")) (|iisech| ((|#2| |#2|) "\\spad{iisech(x)} should be local but conditional")) (|iicoth| ((|#2| |#2|) "\\spad{iicoth(x)} should be local but conditional")) (|iitanh| ((|#2| |#2|) "\\spad{iitanh(x)} should be local but conditional")) (|iicosh| ((|#2| |#2|) "\\spad{iicosh(x)} should be local but conditional")) (|iisinh| ((|#2| |#2|) "\\spad{iisinh(x)} should be local but conditional")) (|iiacsc| ((|#2| |#2|) "\\spad{iiacsc(x)} should be local but conditional")) (|iiasec| ((|#2| |#2|) "\\spad{iiasec(x)} should be local but conditional")) (|iiacot| ((|#2| |#2|) "\\spad{iiacot(x)} should be local but conditional")) (|iiatan| ((|#2| |#2|) "\\spad{iiatan(x)} should be local but conditional")) (|iiacos| ((|#2| |#2|) "\\spad{iiacos(x)} should be local but conditional")) (|iiasin| ((|#2| |#2|) "\\spad{iiasin(x)} should be local but conditional")) (|iicsc| ((|#2| |#2|) "\\spad{iicsc(x)} should be local but conditional")) (|iisec| ((|#2| |#2|) "\\spad{iisec(x)} should be local but conditional")) (|iicot| ((|#2| |#2|) "\\spad{iicot(x)} should be local but conditional")) (|iitan| ((|#2| |#2|) "\\spad{iitan(x)} should be local but conditional")) (|iicos| ((|#2| |#2|) "\\spad{iicos(x)} should be local but conditional")) (|iisin| ((|#2| |#2|) "\\spad{iisin(x)} should be local but conditional")) (|iilog| ((|#2| |#2|) "\\spad{iilog(x)} should be local but conditional")) (|iiexp| ((|#2| |#2|) "\\spad{iiexp(x)} should be local but conditional")) (|iisqrt3| ((|#2|) "\\spad{iisqrt3()} should be local but conditional")) (|iisqrt2| ((|#2|) "\\spad{iisqrt2()} should be local but conditional")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(p)} returns an elementary operator with the same symbol as \\spad{p}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(p)} returns \\spad{true} if operator \\spad{p} is elementary")) (|pi| ((|#2|) "\\spad{\\spad{pi}()} returns the \\spad{pi} operator")) (|acsch| ((|#2| |#2|) "\\spad{acsch(x)} applies the inverse hyperbolic cosecant operator to \\spad{x}")) (|asech| ((|#2| |#2|) "\\spad{asech(x)} applies the inverse hyperbolic secant operator to \\spad{x}")) (|acoth| ((|#2| |#2|) "\\spad{acoth(x)} applies the inverse hyperbolic cotangent operator to \\spad{x}")) (|atanh| ((|#2| |#2|) "\\spad{atanh(x)} applies the inverse hyperbolic tangent operator to \\spad{x}")) (|acosh| ((|#2| |#2|) "\\spad{acosh(x)} applies the inverse hyperbolic cosine operator to \\spad{x}")) (|asinh| ((|#2| |#2|) "\\spad{asinh(x)} applies the inverse hyperbolic sine operator to \\spad{x}")) (|csch| ((|#2| |#2|) "\\spad{csch(x)} applies the hyperbolic cosecant operator to \\spad{x}")) (|sech| ((|#2| |#2|) "\\spad{sech(x)} applies the hyperbolic secant operator to \\spad{x}")) (|coth| ((|#2| |#2|) "\\spad{coth(x)} applies the hyperbolic cotangent operator to \\spad{x}")) (|tanh| ((|#2| |#2|) "\\spad{tanh(x)} applies the hyperbolic tangent operator to \\spad{x}")) (|cosh| ((|#2| |#2|) "\\spad{cosh(x)} applies the hyperbolic cosine operator to \\spad{x}")) (|sinh| ((|#2| |#2|) "\\spad{sinh(x)} applies the hyperbolic sine operator to \\spad{x}")) (|acsc| ((|#2| |#2|) "\\spad{acsc(x)} applies the inverse cosecant operator to \\spad{x}")) (|asec| ((|#2| |#2|) "\\spad{asec(x)} applies the inverse secant operator to \\spad{x}")) (|acot| ((|#2| |#2|) "\\spad{acot(x)} applies the inverse cotangent operator to \\spad{x}")) (|atan| ((|#2| |#2|) "\\spad{atan(x)} applies the inverse tangent operator to \\spad{x}")) (|acos| ((|#2| |#2|) "\\spad{acos(x)} applies the inverse cosine operator to \\spad{x}")) (|asin| ((|#2| |#2|) "\\spad{asin(x)} applies the inverse sine operator to \\spad{x}")) (|csc| ((|#2| |#2|) "\\spad{csc(x)} applies the cosecant operator to \\spad{x}")) (|sec| ((|#2| |#2|) "\\spad{sec(x)} applies the secant operator to \\spad{x}")) (|cot| ((|#2| |#2|) "\\spad{cot(x)} applies the cotangent operator to \\spad{x}")) (|tan| ((|#2| |#2|) "\\spad{tan(x)} applies the tangent operator to \\spad{x}")) (|cos| ((|#2| |#2|) "\\spad{cos(x)} applies the cosine operator to \\spad{x}")) (|sin| ((|#2| |#2|) "\\spad{sin(x)} applies the sine operator to \\spad{x}")) (|log| ((|#2| |#2|) "\\spad{log(x)} applies the logarithm operator to \\spad{x}")) (|exp| ((|#2| |#2|) "\\spad{exp(x)} applies the exponential operator to \\spad{x}"))) NIL NIL -(-254 R -2315) +(-254 R -3539) ((|constructor| (NIL "ElementaryFunctionStructurePackage provides functions to test the algebraic independence of various elementary functions,{} using the Risch structure theorem (real and complex versions). It also provides transformations on elementary functions which are not considered simplifications.")) (|tanQ| ((|#2| (|Fraction| (|Integer|)) |#2|) "\\spad{tanQ(q,{}a)} is a local function with a conditional implementation.")) (|rootNormalize| ((|#2| |#2| (|Kernel| |#2|)) "\\spad{rootNormalize(f,{} k)} returns \\spad{f} rewriting either \\spad{k} which must be an \\spad{n}th-root in terms of radicals already in \\spad{f},{} or some radicals in \\spad{f} in terms of \\spad{k}.")) (|validExponential| (((|Union| |#2| "failed") (|List| (|Kernel| |#2|)) |#2| (|Symbol|)) "\\spad{validExponential([k1,{}...,{}kn],{}f,{}x)} returns \\spad{g} if \\spad{exp(f)=g} and \\spad{g} involves only \\spad{k1...kn},{} and \"failed\" otherwise.")) (|realElementary| ((|#2| |#2| (|Symbol|)) "\\spad{realElementary(f,{}x)} rewrites the kernels of \\spad{f} involving \\spad{x} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.") ((|#2| |#2|) "\\spad{realElementary(f)} rewrites \\spad{f} in terms of the 4 fundamental real transcendental elementary functions: \\spad{log,{} exp,{} tan,{} atan}.")) (|rischNormalize| (((|Record| (|:| |func| |#2|) (|:| |kers| (|List| (|Kernel| |#2|))) (|:| |vals| (|List| |#2|))) |#2| (|Symbol|)) "\\spad{rischNormalize(f,{} x)} returns \\spad{[g,{} [k1,{}...,{}kn],{} [h1,{}...,{}hn]]} such that \\spad{g = normalize(f,{} x)} and each \\spad{\\spad{ki}} was rewritten as \\spad{\\spad{hi}} during the normalization.")) (|normalize| ((|#2| |#2| (|Symbol|)) "\\spad{normalize(f,{} x)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels involving \\spad{x}.") ((|#2| |#2|) "\\spad{normalize(f)} rewrites \\spad{f} using the least possible number of real algebraically independent kernels."))) NIL NIL @@ -966,7 +966,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016)))) (-259 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}."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL (-260 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}."))) @@ -987,18 +987,18 @@ NIL (-264 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 -4245))) +((|HasAttribute| |#1| (QUOTE -4249))) (-265 |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 -(-266 S R |Mod| -2227 -2178 |exactQuo|) +(-266 S R |Mod| -1327 -3780 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{ModularRing},{} \\spadtype{ModularField}")) (|elt| ((|#2| $ |#2|) "\\spad{elt(x,{}r)} or \\spad{x}.\\spad{r} \\undocumented")) (|inv| (($ $) "\\spad{inv(x)} \\undocumented")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} \\undocumented")) (|exQuo| (((|Union| $ "failed") $ $) "\\spad{exQuo(x,{}y)} \\undocumented")) (|reduce| (($ |#2| |#3|) "\\spad{reduce(r,{}m)} \\undocumented")) (|coerce| ((|#2| $) "\\spad{coerce(x)} \\undocumented")) (|modulus| ((|#3| $) "\\spad{modulus(x)} \\undocumented"))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-267) ((|constructor| (NIL "Entire Rings (non-commutative Integral Domains),{} \\spadignore{i.e.} a ring not necessarily commutative which has no zero divisors. \\blankline")) (|noZeroDivisors| ((|attribute|) "if a product is zero then one of the factors must be zero."))) -((-4237 . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-268) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 19,{} 2008. An `Environment' is a stack of scope.")) (|categoryFrame| (($) "the current category environment in the interpreter.")) (|currentEnv| (($) "the current normal environment in effect.")) (|setProperties!| (($ (|Symbol|) (|List| (|Property|)) $) "setBinding!(\\spad{n},{}props,{}\\spad{e}) set the list of properties of \\spad{`n'} to `props' in `e'.")) (|getProperties| (((|Union| (|List| (|Property|)) "failed") (|Symbol|) $) "getBinding(\\spad{n},{}\\spad{e}) returns the list of properties of \\spad{`n'} in \\spad{e}; otherwise `failed'.")) (|setProperty!| (($ (|Symbol|) (|Symbol|) (|SExpression|) $) "\\spad{setProperty!(n,{}p,{}v,{}e)} binds the property `(\\spad{p},{}\\spad{v})' to \\spad{`n'} in the topmost scope of `e'.")) (|getProperty| (((|Union| (|SExpression|) "failed") (|Symbol|) (|Symbol|) $) "\\spad{getProperty(n,{}p,{}e)} returns the value of property with name \\spad{`p'} for the symbol \\spad{`n'} in environment `e'. Otherwise,{} `failed'.")) (|scopes| (((|List| (|Scope|)) $) "\\spad{scopes(e)} returns the stack of scopes in environment \\spad{e}.")) (|empty| (($) "\\spad{empty()} constructs an empty environment"))) @@ -1014,21 +1014,21 @@ NIL NIL (-271 S) ((|constructor| (NIL "Equations as mathematical objects. All properties of the basis domain,{} \\spadignore{e.g.} being an abelian group are carried over the equation domain,{} by performing the structural operations on the left and on the right hand side.")) (|subst| (($ $ $) "\\spad{subst(eq1,{}eq2)} substitutes \\spad{eq2} into both sides of \\spad{eq1} the \\spad{lhs} of \\spad{eq2} should be a kernel")) (|inv| (($ $) "\\spad{inv(x)} returns the multiplicative inverse of \\spad{x}.")) (/ (($ $ $) "\\spad{e1/e2} produces a new equation by dividing the left and right hand sides of equations e1 and e2.")) (|factorAndSplit| (((|List| $) $) "\\spad{factorAndSplit(eq)} make the right hand side 0 and factors the new left hand side. Each factor is equated to 0 and put into the resulting list without repetitions.")) (|rightOne| (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side.") (((|Union| $ "failed") $) "\\spad{rightOne(eq)} divides by the right hand side,{} if possible.")) (|leftOne| (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side.") (((|Union| $ "failed") $) "\\spad{leftOne(eq)} divides by the left hand side,{} if possible.")) (* (($ $ |#1|) "\\spad{eqn*x} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.") (($ |#1| $) "\\spad{x*eqn} produces a new equation by multiplying both sides of equation eqn by \\spad{x}.")) (- (($ $ |#1|) "\\spad{eqn-x} produces a new equation by subtracting \\spad{x} from both sides of equation eqn.") (($ |#1| $) "\\spad{x-eqn} produces a new equation by subtracting both sides of equation eqn from \\spad{x}.")) (|rightZero| (($ $) "\\spad{rightZero(eq)} subtracts the right hand side.")) (|leftZero| (($ $) "\\spad{leftZero(eq)} subtracts the left hand side.")) (+ (($ $ |#1|) "\\spad{eqn+x} produces a new equation by adding \\spad{x} to both sides of equation eqn.") (($ |#1| $) "\\spad{x+eqn} produces a new equation by adding \\spad{x} to both sides of equation eqn.")) (|eval| (($ $ (|List| $)) "\\spad{eval(eqn,{} [x1=v1,{} ... xn=vn])} replaces \\spad{xi} by \\spad{vi} in equation \\spad{eqn}.") (($ $ $) "\\spad{eval(eqn,{} x=f)} replaces \\spad{x} by \\spad{f} in equation \\spad{eqn}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(f,{}eqn)} constructs a new equation by applying \\spad{f} to both sides of \\spad{eqn}.")) (|rhs| ((|#1| $) "\\spad{rhs(eqn)} returns the right hand side of equation \\spad{eqn}.")) (|lhs| ((|#1| $) "\\spad{lhs(eqn)} returns the left hand side of equation \\spad{eqn}.")) (|swap| (($ $) "\\spad{swap(eq)} interchanges left and right hand side of equation \\spad{eq}.")) (|equation| (($ |#1| |#1|) "\\spad{equation(a,{}b)} creates an equation.")) 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Thus keys are considered equal only if they are the same instance of a structure."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-273) ((|constructor| (NIL "ErrorFunctions implements error functions callable from the system interpreter. Typically,{} these functions would be called in user functions. The simple forms of the functions take one argument which is either a string (an error message) or a list of strings which all together make up a message. The list can contain formatting codes (see below). The more sophisticated versions takes two arguments where the first argument is the name of the function from which the error was invoked and the second argument is either a string or a list of strings,{} as above. When you use the one argument version in an interpreter function,{} the system will automatically insert the name of the function as the new first argument. Thus in the user interpreter function \\indented{2}{\\spad{f x == if x < 0 then error \"negative argument\" else x}} the call to error will actually be of the form \\indented{2}{\\spad{error(\"f\",{}\"negative argument\")}} because the interpreter will have created a new first argument. \\blankline Formatting codes: error messages may contain the following formatting codes (they should either start or end a string or else have blanks around them): \\indented{3}{\\spad{\\%l}\\space{6}start a new line} \\indented{3}{\\spad{\\%b}\\space{6}start printing in a bold font (where available)} \\indented{3}{\\spad{\\%d}\\space{6}stop\\space{2}printing in a bold font (where available)} \\indented{3}{\\spad{ \\%ceon}\\space{2}start centering message lines} \\indented{3}{\\spad{\\%ceoff}\\space{2}stop\\space{2}centering message lines} \\indented{3}{\\spad{\\%rjon}\\space{3}start displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%rjoff}\\space{2}stop\\space{2}displaying lines \"ragged left\"} \\indented{3}{\\spad{\\%i}\\space{6}indent\\space{3}following lines 3 additional spaces} \\indented{3}{\\spad{\\%u}\\space{6}unindent following lines 3 additional spaces} \\indented{3}{\\spad{\\%xN}\\space{5}insert \\spad{N} blanks (eg,{} \\spad{\\%x10} inserts 10 blanks)} \\blankline")) (|error| (((|Exit|) (|String|) (|List| (|String|))) "\\spad{error(nam,{}lmsg)} displays error messages \\spad{lmsg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|String|) (|String|)) "\\spad{error(nam,{}msg)} displays error message \\spad{msg} preceded by a message containing the name \\spad{nam} of the function in which the error is contained.") (((|Exit|) (|List| (|String|))) "\\spad{error(lmsg)} displays error message \\spad{lmsg} and terminates.") (((|Exit|) (|String|)) "\\spad{error(msg)} displays error message \\spad{msg} and terminates."))) NIL NIL -(-274 -2315 S) +(-274 -3539 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 -(-275 E -2315) +(-275 E -3539) ((|constructor| (NIL "This package allows a mapping \\spad{E} \\spad{->} \\spad{F} to be lifted to a kernel over \\spad{E}; This lifting can fail if the operator of the kernel cannot be applied in \\spad{F}; Do not use this package with \\spad{E} = \\spad{F},{} since this may drop some properties of the operators.")) (|map| ((|#2| (|Mapping| |#2| |#1|) (|Kernel| |#1|)) "\\spad{map(f,{} k)} returns \\spad{g = op(f(a1),{}...,{}f(an))} where \\spad{k = op(a1,{}...,{}an)}."))) NIL NIL @@ -1066,7 +1066,7 @@ NIL NIL (-284) ((|constructor| (NIL "A constructive euclidean domain,{} \\spadignore{i.e.} one can divide producing a quotient and a remainder where the remainder is either zero or is smaller (\\spadfun{euclideanSize}) than the divisor. \\blankline Conditional attributes: \\indented{2}{multiplicativeValuation\\tab{25}\\spad{Size(a*b)=Size(a)*Size(b)}} \\indented{2}{additiveValuation\\tab{25}\\spad{Size(a*b)=Size(a)+Size(b)}}")) (|multiEuclidean| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{multiEuclidean([f1,{}...,{}fn],{}z)} returns a list of coefficients \\spad{[a1,{} ...,{} an]} such that \\spad{ z / prod \\spad{fi} = sum aj/fj}. If no such list of coefficients exists,{} \"failed\" is returned.")) (|extendedEuclidean| (((|Union| (|Record| (|:| |coef1| $) (|:| |coef2| $)) "failed") $ $ $) "\\spad{extendedEuclidean(x,{}y,{}z)} either returns a record rec where \\spad{rec.coef1*x+rec.coef2*y=z} or returns \"failed\" if \\spad{z} cannot be expressed as a linear combination of \\spad{x} and \\spad{y}.") (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{extendedEuclidean(x,{}y)} returns a record rec where \\spad{rec.coef1*x+rec.coef2*y = rec.generator} and rec.generator is a \\spad{gcd} of \\spad{x} and \\spad{y}. The \\spad{gcd} is unique only up to associates if \\spadatt{canonicalUnitNormal} is not asserted. \\spadfun{principalIdeal} provides a version of this operation which accepts an arbitrary length list of arguments.")) (|rem| (($ $ $) "\\spad{x rem y} is the same as \\spad{divide(x,{}y).remainder}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|quo| (($ $ $) "\\spad{x quo y} is the same as \\spad{divide(x,{}y).quotient}. See \\spadfunFrom{divide}{EuclideanDomain}.")) (|divide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{divide(x,{}y)} divides \\spad{x} by \\spad{y} producing a record containing a \\spad{quotient} and \\spad{remainder},{} where the remainder is smaller (see \\spadfunFrom{sizeLess?}{EuclideanDomain}) than the divisor \\spad{y}.")) (|euclideanSize| (((|NonNegativeInteger|) $) "\\spad{euclideanSize(x)} returns the euclidean size of the element \\spad{x}. Error: if \\spad{x} is zero.")) (|sizeLess?| (((|Boolean|) $ $) "\\spad{sizeLess?(x,{}y)} tests whether \\spad{x} is strictly smaller than \\spad{y} with respect to the \\spadfunFrom{euclideanSize}{EuclideanDomain}."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-285 S R) ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#2|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#2|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) @@ -1076,7 +1076,7 @@ NIL ((|constructor| (NIL "This category provides \\spadfun{eval} operations. A domain may belong to this category if it is possible to make ``evaluation\\spad{''} substitutions.")) (|eval| (($ $ (|List| (|Equation| |#1|))) "\\spad{eval(f,{} [x1 = v1,{}...,{}xn = vn])} replaces \\spad{xi} by \\spad{vi} in \\spad{f}.") (($ $ (|Equation| |#1|)) "\\spad{eval(f,{}x = v)} replaces \\spad{x} by \\spad{v} in \\spad{f}."))) NIL NIL -(-287 -2315) +(-287 -3539) ((|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 @@ -1086,8 +1086,8 @@ NIL NIL (-289 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}.")) 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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 @@ -1098,9 +1098,9 @@ NIL NIL (-292 R) ((|constructor| (NIL "Expressions involving symbolic functions.")) 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(|seriesSolve| (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} [b0,{}...,{}bn])} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} [b0,{}...,{}b(n-1)])}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{} y,{} x = a,{} y a = b)} is equivalent to \\spad{seriesSolve(eq=0,{} y,{} x=a,{} y a = b)}.") (((|Any|) |#2| (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{} y,{} x = a,{} b)} is equivalent to \\spad{seriesSolve(eq = 0,{} y,{} x = a,{} y a = b)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) |#2|) "\\spad{seriesSolve(eq,{}y,{} x=a,{} b)} is equivalent to \\spad{seriesSolve(eq,{} y,{} x=a,{} y a = b)}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{}[y1 a = b1,{}...,{} yn a = bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| |#2|) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1=0,{}...,{}eqn=0],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x=a,{} [b1,{}...,{}bn])} is equivalent to \\spad{seriesSolve([eq1,{}...,{}eqn],{} [y1,{}...,{}yn],{} x = a,{} [y1 a = b1,{}...,{} yn a = bn])}.") (((|Any|) (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Equation| |#2|) (|List| (|Equation| |#2|))) "\\spad{seriesSolve([eq1,{}...,{}eqn],{}[y1,{}...,{}yn],{}x = a,{}[y1 a = b1,{}...,{}yn a = bn])} returns a taylor series solution of \\spad{[eq1,{}...,{}eqn]} around \\spad{x = a} with initial conditions \\spad{\\spad{yi}(a) = \\spad{bi}}. Note: eqi must be of the form \\spad{\\spad{fi}(x,{} y1 x,{} y2 x,{}...,{} yn x) y1'(x) + \\spad{gi}(x,{} y1 x,{} y2 x,{}...,{} yn x) = h(x,{} y1 x,{} y2 x,{}...,{} yn x)}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{}[b0,{}...,{}b(n-1)])} returns a Taylor series solution of \\spad{eq} around \\spad{x = a} with initial conditions \\spad{y(a) = b0},{} \\spad{y'(a) = b1},{} \\spad{y''(a) = b2},{} ...,{}\\spad{y(n-1)(a) = b(n-1)} \\spad{eq} must be of the form \\spad{f(x,{} y x,{} y'(x),{}...,{} y(n-1)(x)) y(n)(x) + g(x,{}y x,{}y'(x),{}...,{}y(n-1)(x)) = h(x,{}y x,{} y'(x),{}...,{} y(n-1)(x))}.") (((|Any|) (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|Equation| |#2|)) "\\spad{seriesSolve(eq,{}y,{}x=a,{} y a = b)} returns a Taylor series solution of \\spad{eq} around \\spad{x} = a with initial condition \\spad{y(a) = b}. Note: \\spad{eq} must be of the form \\spad{f(x,{} y x) y'(x) + g(x,{} y x) = h(x,{} y x)}."))) NIL NIL @@ -1110,8 +1110,8 @@ NIL NIL (-295 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."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1458) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3262 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1957) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-296 M) ((|constructor| (NIL "computes various functions on factored arguments.")) (|log| (((|List| (|Record| (|:| |coef| (|NonNegativeInteger|)) (|:| |logand| |#1|))) (|Factored| |#1|)) "\\spad{log(f)} returns \\spad{[(a1,{}b1),{}...,{}(am,{}bm)]} such that the logarithm of \\spad{f} is equal to \\spad{a1*log(b1) + ... + am*log(bm)}.")) (|nthRoot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#1|) (|:| |radicand| (|List| |#1|))) (|Factored| |#1|) (|NonNegativeInteger|)) "\\spad{nthRoot(f,{} n)} returns \\spad{(p,{} r,{} [r1,{}...,{}rm])} such that the \\spad{n}th-root of \\spad{f} is equal to \\spad{r * \\spad{p}th-root(r1 * ... * rm)},{} where \\spad{r1},{}...,{}\\spad{rm} are distinct factors of \\spad{f},{} each of which has an exponent smaller than \\spad{p} in \\spad{f}."))) NIL @@ -1122,7 +1122,7 @@ NIL NIL (-298 S) ((|constructor| (NIL "The free abelian group on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The operation is commutative."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-731)))) (-299 S E) ((|constructor| (NIL "A free abelian monoid on a set \\spad{S} is the monoid of finite sums of the form \\spad{reduce(+,{}[\\spad{ni} * \\spad{si}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are in a given abelian monoid. The operation is commutative.")) (|highCommonTerms| (($ $ $) "\\spad{highCommonTerms(e1 a1 + ... + en an,{} f1 b1 + ... + fm bm)} returns \\indented{2}{\\spad{reduce(+,{}[max(\\spad{ei},{} \\spad{fi}) \\spad{ci}])}} where \\spad{ci} ranges in the intersection of \\spad{{a1,{}...,{}an}} and \\spad{{b1,{}...,{}bm}}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} e1 a1 +...+ en an)} returns \\spad{e1 f(a1) +...+ en f(an)}.")) (|mapCoef| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapCoef(f,{} e1 a1 +...+ en an)} returns \\spad{f(e1) a1 +...+ f(en) an}.")) (|coefficient| ((|#2| |#1| $) "\\spad{coefficient(s,{} e1 a1 + ... + en an)} returns \\spad{ei} such that \\spad{ai} = \\spad{s},{} or 0 if \\spad{s} is not one of the \\spad{ai}\\spad{'s}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th term of \\spad{x}.")) (|nthCoef| ((|#2| $ (|Integer|)) "\\spad{nthCoef(x,{} n)} returns the coefficient of the n^th term of \\spad{x}.")) (|terms| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| |#2|))) $) "\\spad{terms(e1 a1 + ... + en an)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of terms in \\spad{x}. mapGen(\\spad{f},{} a1\\spad{\\^}e1 ... an\\spad{\\^}en) returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (* (($ |#2| |#1|) "\\spad{e * s} returns \\spad{e} times \\spad{s}.")) (+ (($ |#1| $) "\\spad{s + x} returns the sum of \\spad{s} and \\spad{x}."))) @@ -1138,19 +1138,19 @@ NIL ((|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158)))) (-302 R E) ((|constructor| (NIL "This category is similar to AbelianMonoidRing,{} except that the sum is assumed to be finite. It is a useful model for polynomials,{} but is somewhat more general.")) (|primitivePart| (($ $) "\\spad{primitivePart(p)} returns the unit normalized form of polynomial \\spad{p} divided by the content of \\spad{p}.")) (|content| ((|#1| $) "\\spad{content(p)} gives the \\spad{gcd} of the coefficients of polynomial \\spad{p}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(p,{}r)} returns the exact quotient of polynomial \\spad{p} by \\spad{r},{} or \"failed\" if none exists.")) (|binomThmExpt| (($ $ $ (|NonNegativeInteger|)) "\\spad{binomThmExpt(p,{}q,{}n)} returns \\spad{(x+y)^n} by means of the binomial theorem trick.")) (|pomopo!| (($ $ |#1| |#2| $) "\\spad{pomopo!(p1,{}r,{}e,{}p2)} returns \\spad{p1 + monomial(e,{}r) * p2} and may use \\spad{p1} as workspace. The constaant \\spad{r} is assumed to be nonzero.")) (|mapExponents| (($ (|Mapping| |#2| |#2|) $) "\\spad{mapExponents(fn,{}u)} maps function \\spad{fn} onto the exponents of the non-zero monomials of polynomial \\spad{u}.")) (|minimumDegree| ((|#2| $) "\\spad{minimumDegree(p)} gives the least exponent of a non-zero term of polynomial \\spad{p}. Error: if applied to 0.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(p)} gives the number of non-zero monomials in polynomial \\spad{p}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(p)} gives the list of non-zero coefficients of polynomial \\spad{p}.")) (|ground| ((|#1| $) "\\spad{ground(p)} retracts polynomial \\spad{p} to the coefficient ring.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(p)} tests if polynomial \\spad{p} is a member of the coefficient ring."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-303 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."))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-304 S -2315) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-304 S -3539) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#2|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#2|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#2| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#2| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#2|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) NIL ((|HasCategory| |#2| (QUOTE (-344)))) -(-305 -2315) +(-305 -3539) ((|constructor| (NIL "FiniteAlgebraicExtensionField {\\em F} is the category of fields which are finite algebraic extensions of the field {\\em F}. If {\\em F} is finite then any finite algebraic extension of {\\em F} is finite,{} too. Let {\\em K} be a finite algebraic extension of the finite field {\\em F}. The exponentiation of elements of {\\em K} defines a \\spad{Z}-module structure on the multiplicative group of {\\em K}. The additive group of {\\em K} becomes a module over the ring of polynomials over {\\em F} via the operation \\spadfun{linearAssociatedExp}(a:K,{}f:SparseUnivariatePolynomial \\spad{F}) which is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em K},{} {\\em c,{}d} from {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)} where {\\em q=size()\\$F}. The operations order and discreteLog associated with the multiplicative exponentiation have additive analogues associated to the operation \\spadfun{linearAssociatedExp}. These are the functions \\spadfun{linearAssociatedOrder} and \\spadfun{linearAssociatedLog},{} respectively.")) (|linearAssociatedLog| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") $ $) "\\spad{linearAssociatedLog(b,{}a)} returns a polynomial {\\em g},{} such that the \\spadfun{linearAssociatedExp}(\\spad{b},{}\\spad{g}) equals {\\em a}. If there is no such polynomial {\\em g},{} then \\spadfun{linearAssociatedLog} fails.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedLog(a)} returns a polynomial {\\em g},{} such that \\spadfun{linearAssociatedExp}(normalElement(),{}\\spad{g}) equals {\\em a}.")) (|linearAssociatedOrder| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{linearAssociatedOrder(a)} retruns the monic polynomial {\\em g} of least degree,{} such that \\spadfun{linearAssociatedExp}(a,{}\\spad{g}) is 0.")) (|linearAssociatedExp| (($ $ (|SparseUnivariatePolynomial| |#1|)) "\\spad{linearAssociatedExp(a,{}f)} is linear over {\\em F},{} \\spadignore{i.e.} for elements {\\em a} from {\\em \\$},{} {\\em c,{}d} form {\\em F} and {\\em f,{}g} univariate polynomials over {\\em F} we have \\spadfun{linearAssociatedExp}(a,{}cf+dg) equals {\\em c} times \\spadfun{linearAssociatedExp}(a,{}\\spad{f}) plus {\\em d} times \\spadfun{linearAssociatedExp}(a,{}\\spad{g}). Therefore \\spadfun{linearAssociatedExp} is defined completely by its action on monomials from {\\em F[X]}: \\spadfun{linearAssociatedExp}(a,{}monomial(1,{}\\spad{k})\\spad{\\$}SUP(\\spad{F})) is defined to be \\spadfun{Frobenius}(a,{}\\spad{k}) which is {\\em a**(q**k)},{} where {\\em q=size()\\$F}.")) (|generator| (($) "\\spad{generator()} returns a root of the defining polynomial. This element generates the field as an algebra over the ground field.")) (|normal?| (((|Boolean|) $) "\\spad{normal?(a)} tests whether the element \\spad{a} is normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i <= extensionDegree()-1} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Implementation according to Lidl/Niederreiter: Theorem 2.39.")) (|normalElement| (($) "\\spad{normalElement()} returns a element,{} normal over the ground field \\spad{F},{} \\spadignore{i.e.} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. At the first call,{} the element is computed by \\spadfunFrom{createNormalElement}{FiniteAlgebraicExtensionField} then cached in a global variable. On subsequent calls,{} the element is retrieved by referencing the global variable.")) (|createNormalElement| (($) "\\spad{createNormalElement()} computes a normal element over the ground field \\spad{F},{} that is,{} \\spad{a**(q**i),{} 0 <= i < extensionDegree()} is an \\spad{F}-basis,{} where \\spad{q = size()\\$F}. Reference: Such an element exists Lidl/Niederreiter: Theorem 2.35.")) (|trace| (($ $ (|PositiveInteger|)) "\\spad{trace(a,{}d)} computes the trace of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size \\spad{q}. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: \\spad{trace(a,{}d) = reduce(+,{}[a**(q**(d*i)) for i in 0..n/d])}.") ((|#1| $) "\\spad{trace(a)} computes the trace of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|norm| (($ $ (|PositiveInteger|)) "\\spad{norm(a,{}d)} computes the norm of \\spad{a} with respect to the field of extension degree \\spad{d} over the ground field of size. Error: if \\spad{d} does not divide the extension degree of \\spad{a}. Note: norm(a,{}\\spad{d}) = reduce(*,{}[a**(\\spad{q**}(d*i)) for \\spad{i} in 0..\\spad{n/d}])") ((|#1| $) "\\spad{norm(a)} computes the norm of \\spad{a} with respect to the field considered as an algebra with 1 over the ground field \\spad{F}.")) (|degree| (((|PositiveInteger|) $) "\\spad{degree(a)} returns the degree of the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|extensionDegree| (((|PositiveInteger|)) "\\spad{extensionDegree()} returns the degree of field extension.")) (|definingPolynomial| (((|SparseUnivariatePolynomial| |#1|)) "\\spad{definingPolynomial()} returns the polynomial used to define the field extension.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| $) $ (|PositiveInteger|)) "\\spad{minimalPolynomial(x,{}n)} computes the minimal polynomial of \\spad{x} over the field of extension degree \\spad{n} over the ground field \\spad{F}.") (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of an element \\spad{a} over the ground field \\spad{F}.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{F}-vectorspace basis.")) (|basis| (((|Vector| $) (|PositiveInteger|)) "\\spad{basis(n)} returns a fixed basis of a subfield of \\spad{\\$} as \\spad{F}-vectorspace.") (((|Vector| $)) "\\spad{basis()} returns a fixed basis of \\spad{\\$} as \\spad{F}-vectorspace."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-306) ((|constructor| (NIL "This domain builds representations of program code segments for use with the FortranProgram domain.")) (|setLabelValue| (((|SingleInteger|) (|SingleInteger|)) "\\spad{setLabelValue(i)} resets the counter which produces labels to \\spad{i}")) (|getCode| (((|SExpression|) $) "\\spad{getCode(f)} returns a Lisp list of strings representing \\spad{f} in Fortran notation. This is used by the FortranProgram domain.")) (|printCode| (((|Void|) $) "\\spad{printCode(f)} prints out \\spad{f} in FORTRAN notation.")) (|code| (((|Union| (|:| |nullBranch| "null") (|:| |assignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |arrayIndex| (|List| (|Polynomial| (|Integer|)))) (|:| |rand| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |arrayAssignmentBranch| (|Record| (|:| |var| (|Symbol|)) (|:| |rand| (|OutputForm|)) (|:| |ints2Floats?| (|Boolean|)))) (|:| |conditionalBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |thenClause| $) (|:| |elseClause| $))) (|:| |returnBranch| (|Record| (|:| |empty?| (|Boolean|)) (|:| |value| (|Record| (|:| |ints2Floats?| (|Boolean|)) (|:| |expr| (|OutputForm|)))))) (|:| |blockBranch| (|List| $)) (|:| |commentBranch| (|List| (|String|))) (|:| |callBranch| (|String|)) (|:| |forBranch| (|Record| (|:| |range| (|SegmentBinding| (|Polynomial| (|Integer|)))) (|:| |span| (|Polynomial| (|Integer|))) (|:| |body| $))) (|:| |labelBranch| (|SingleInteger|)) (|:| |loopBranch| (|Record| (|:| |switch| (|Switch|)) (|:| |body| $))) (|:| |commonBranch| (|Record| (|:| |name| (|Symbol|)) (|:| |contents| (|List| (|Symbol|))))) (|:| |printBranch| (|List| (|OutputForm|)))) $) "\\spad{code(f)} returns the internal representation of the object represented by \\spad{f}.")) (|operation| (((|Union| (|:| |Null| "null") (|:| |Assignment| "assignment") (|:| |Conditional| "conditional") (|:| |Return| "return") (|:| |Block| "block") (|:| |Comment| "comment") (|:| |Call| "call") (|:| |For| "for") (|:| |While| "while") (|:| |Repeat| "repeat") (|:| |Goto| "goto") (|:| |Continue| "continue") (|:| |ArrayAssignment| "arrayAssignment") (|:| |Save| "save") (|:| |Stop| "stop") (|:| |Common| "common") (|:| |Print| "print")) $) "\\spad{operation(f)} returns the name of the operation represented by \\spad{f}.")) (|common| (($ (|Symbol|) (|List| (|Symbol|))) "\\spad{common(name,{}contents)} creates a representation a named common block.")) (|printStatement| (($ (|List| (|OutputForm|))) "\\spad{printStatement(l)} creates a representation of a PRINT statement.")) (|save| (($) "\\spad{save()} creates a representation of a SAVE statement.")) (|stop| (($) "\\spad{stop()} creates a representation of a STOP statement.")) (|block| (($ (|List| $)) "\\spad{block(l)} creates a representation of the statements in \\spad{l} as a block.")) (|assign| (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Float|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|Integer|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Complex| (|Float|))))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|Integer|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Complex| (|Float|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Float|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|Integer|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|List| (|Polynomial| (|Integer|))) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}l,{}y)} creates a representation of the assignment of \\spad{y} to the \\spad{l}\\spad{'}th element of array \\spad{x} (\\spad{l} is a list of indices).") (($ (|Symbol|) (|Vector| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineComplex|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineFloat|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|Expression| (|MachineInteger|)))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Vector| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Matrix| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineComplex|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineFloat|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|Expression| (|MachineInteger|))) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.") (($ (|Symbol|) (|String|)) "\\spad{assign(x,{}y)} creates a representation of the FORTRAN expression x=y.")) (|cond| (($ (|Switch|) $ $) "\\spad{cond(s,{}e,{}f)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e} ELSE \\spad{f}.") (($ (|Switch|) $) "\\spad{cond(s,{}e)} creates a representation of the FORTRAN expression IF (\\spad{s}) THEN \\spad{e}.")) (|returns| (($ (|Expression| (|Complex| (|Float|)))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Integer|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|Float|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineComplex|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineInteger|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($ (|Expression| (|MachineFloat|))) "\\spad{returns(e)} creates a representation of a FORTRAN RETURN statement with a returned value.") (($) "\\spad{returns()} creates a representation of a FORTRAN RETURN statement.")) (|call| (($ (|String|)) "\\spad{call(s)} creates a representation of a FORTRAN CALL statement")) (|comment| (($ (|List| (|String|))) "\\spad{comment(s)} creates a representation of the Strings \\spad{s} as a multi-line FORTRAN comment.") (($ (|String|)) "\\spad{comment(s)} creates a representation of the String \\spad{s} as a single FORTRAN comment.")) (|continue| (($ (|SingleInteger|)) "\\spad{continue(l)} creates a representation of a FORTRAN CONTINUE labelled with \\spad{l}")) (|goto| (($ (|SingleInteger|)) "\\spad{goto(l)} creates a representation of a FORTRAN GOTO statement")) (|repeatUntilLoop| (($ (|Switch|) $) "\\spad{repeatUntilLoop(s,{}c)} creates a repeat ... until loop in FORTRAN.")) (|whileLoop| (($ (|Switch|) $) "\\spad{whileLoop(s,{}c)} creates a while loop in FORTRAN.")) (|forLoop| (($ (|SegmentBinding| (|Polynomial| (|Integer|))) (|Polynomial| (|Integer|)) $) "\\spad{forLoop(i=1..10,{}n,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10 by \\spad{n}.") (($ (|SegmentBinding| (|Polynomial| (|Integer|))) $) "\\spad{forLoop(i=1..10,{}c)} creates a representation of a FORTRAN DO loop with \\spad{i} ranging over the values 1 to 10.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(f)} returns an object of type OutputForm."))) @@ -1168,15 +1168,15 @@ NIL ((|constructor| (NIL "\\indented{1}{Lift a map to finite divisors.} Author: Manuel Bronstein Date Created: 1988 Date Last Updated: 19 May 1993")) (|map| (((|FiniteDivisor| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FiniteDivisor| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}d)} \\undocumented{}"))) NIL NIL -(-310 S -2315 UP UPUP R) +(-310 S -3539 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#5| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) (|:| |principalPart| |#5|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#5| |#3| |#3| |#3| |#2|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#2| |#2| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#2| |#2|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#5|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#3| (|Fraction| |#3|) |#4| |#5|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-311 -2315 UP UPUP R) +(-311 -3539 UP UPUP R) ((|constructor| (NIL "This category describes finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|generator| (((|Union| |#4| "failed") $) "\\spad{generator(d)} returns \\spad{f} if \\spad{(f) = d},{} \"failed\" if \\spad{d} is not principal.")) (|principal?| (((|Boolean|) $) "\\spad{principal?(D)} tests if the argument is the divisor of a function.")) (|reduce| (($ $) "\\spad{reduce(D)} converts \\spad{D} to some reduced form (the reduced forms can be differents in different implementations).")) (|decompose| (((|Record| (|:| |id| (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) (|:| |principalPart| |#4|)) $) "\\spad{decompose(d)} returns \\spad{[id,{} f]} where \\spad{d = (id) + div(f)}.")) (|divisor| (($ |#4| |#2| |#2| |#2| |#1|) "\\spad{divisor(h,{} d,{} d',{} g,{} r)} returns the sum of all the finite points where \\spad{h/d} has residue \\spad{r}. \\spad{h} must be integral. \\spad{d} must be squarefree. \\spad{d'} is some derivative of \\spad{d} (not necessarily dd/dx). \\spad{g = gcd(d,{}discriminant)} contains the ramified zeros of \\spad{d}") (($ |#1| |#1| (|Integer|)) "\\spad{divisor(a,{} b,{} n)} makes the divisor \\spad{nP} where \\spad{P:} \\spad{(x = a,{} y = b)}. \\spad{P} is allowed to be singular if \\spad{n} is a multiple of the rank.") (($ |#1| |#1|) "\\spad{divisor(a,{} b)} makes the divisor \\spad{P:} \\spad{(x = a,{} y = b)}. Error: if \\spad{P} is singular.") (($ |#4|) "\\spad{divisor(g)} returns the divisor of the function \\spad{g}.") (($ (|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|)) "\\spad{divisor(I)} makes a divisor \\spad{D} from an ideal \\spad{I}.")) (|ideal| (((|FractionalIdeal| |#2| (|Fraction| |#2|) |#3| |#4|) $) "\\spad{ideal(D)} returns the ideal corresponding to a divisor \\spad{D}."))) NIL NIL -(-312 -2315 UP UPUP R) +(-312 -3539 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on a curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve.")) (|lSpaceBasis| (((|Vector| |#4|) $) "\\spad{lSpaceBasis(d)} returns a basis for \\spad{L(d) = {f | (f) >= -d}} as a module over \\spad{K[x]}.")) (|finiteBasis| (((|Vector| |#4|) $) "\\spad{finiteBasis(d)} returns a basis for \\spad{d} as a module over {\\em K[x]}."))) NIL NIL @@ -1190,32 +1190,32 @@ NIL NIL (-315 |basicSymbols| |subscriptedSymbols| R) ((|constructor| (NIL "A domain of expressions involving functions which can be translated into standard Fortran-77,{} with some extra extensions from the NAG Fortran Library.")) (|useNagFunctions| (((|Boolean|) (|Boolean|)) "\\spad{useNagFunctions(v)} sets the flag which controls whether NAG functions \\indented{1}{are being used for mathematical and machine constants.\\space{2}The previous} \\indented{1}{value is returned.}") (((|Boolean|)) "\\spad{useNagFunctions()} indicates whether NAG functions are being used \\indented{1}{for mathematical and machine constants.}")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(e)} return a list of all the variables in \\spad{e}.")) (|pi| (($) "\\spad{\\spad{pi}(x)} represents the NAG Library function X01AAF which returns \\indented{1}{an approximation to the value of \\spad{pi}}")) (|tanh| (($ $) "\\spad{tanh(x)} represents the Fortran intrinsic function TANH")) (|cosh| (($ $) "\\spad{cosh(x)} represents the Fortran intrinsic function COSH")) (|sinh| (($ $) "\\spad{sinh(x)} represents the Fortran intrinsic function SINH")) (|atan| (($ $) "\\spad{atan(x)} represents the Fortran intrinsic function ATAN")) (|acos| (($ $) "\\spad{acos(x)} represents the Fortran intrinsic function ACOS")) (|asin| (($ $) "\\spad{asin(x)} represents the Fortran intrinsic function ASIN")) (|tan| (($ $) "\\spad{tan(x)} represents the Fortran intrinsic function TAN")) (|cos| (($ $) "\\spad{cos(x)} represents the Fortran intrinsic function COS")) (|sin| (($ $) "\\spad{sin(x)} represents the Fortran intrinsic function SIN")) (|log10| (($ $) "\\spad{log10(x)} represents the Fortran intrinsic function LOG10")) (|log| (($ $) "\\spad{log(x)} represents the Fortran intrinsic function LOG")) (|exp| (($ $) "\\spad{exp(x)} represents the Fortran intrinsic function EXP")) (|sqrt| (($ $) "\\spad{sqrt(x)} represents the Fortran intrinsic function SQRT")) (|abs| (($ $) "\\spad{abs(x)} represents the Fortran intrinsic function ABS")) (|coerce| (((|Expression| |#3|) $) "\\spad{coerce(x)} \\undocumented{}")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Symbol|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (((|Union| $ "failed") (|Expression| |#3|)) "\\spad{retractIfCan(e)} takes \\spad{e} and tries to transform it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}")) (|retract| (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Symbol|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a FortranExpression \\indented{1}{checking that it is one of the given basic symbols} \\indented{1}{or subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}") (($ (|Expression| |#3|)) "\\spad{retract(e)} takes \\spad{e} and transforms it into a \\indented{1}{FortranExpression checking that it contains no non-Fortran} \\indented{1}{functions,{} and that it only contains the given basic symbols} \\indented{1}{and subscripted symbols which correspond to scalar and array} \\indented{1}{parameters respectively.}"))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-355)))) (|HasCategory| $ (QUOTE (-973))) (|HasCategory| $ (LIST (QUOTE -964) (QUOTE (-523))))) (-316 R1 UP1 UPUP1 F1 R2 UP2 UPUP2 F2) ((|constructor| (NIL "Lifts a map from rings to function fields over them.")) (|map| ((|#8| (|Mapping| |#5| |#1|) |#4|) "\\spad{map(f,{} p)} lifts \\spad{f} to \\spad{F1} and applies it to \\spad{p}."))) NIL NIL -(-317 S -2315 UP UPUP) +(-317 S -3539 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#2|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#2|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#3|) (|:| |derivden| |#3|) (|:| |gd| |#3|)) $ (|Mapping| |#3| |#3|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#3| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#3| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#2| $ |#2| |#2|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#3| |#3|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#3|)) (|:| |den| |#3|)) (|Mapping| |#3| |#3|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#3|) |#3|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#3|)) (|:| |den| |#3|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#3|) |#3|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|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 (-344))) (|HasCategory| |#2| (QUOTE (-339)))) -(-318 -2315 UP UPUP) +(-318 -3539 UP UPUP) ((|constructor| (NIL "This category is a model for the function field of a plane algebraic curve.")) (|rationalPoints| (((|List| (|List| |#1|))) "\\spad{rationalPoints()} returns the list of all the affine rational points.")) (|nonSingularModel| (((|List| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{nonSingularModel(u)} returns the equations in u1,{}...,{}un of an affine non-singular model for the curve.")) (|algSplitSimple| (((|Record| (|:| |num| $) (|:| |den| |#2|) (|:| |derivden| |#2|) (|:| |gd| |#2|)) $ (|Mapping| |#2| |#2|)) "\\spad{algSplitSimple(f,{} D)} returns \\spad{[h,{}d,{}d',{}g]} such that \\spad{f=h/d},{} \\spad{h} is integral at all the normal places \\spad{w}.\\spad{r}.\\spad{t}. \\spad{D},{} \\spad{d' = Dd},{} \\spad{g = gcd(d,{} discriminant())} and \\spad{D} is the derivation to use. \\spad{f} must have at most simple finite poles.")) (|hyperelliptic| (((|Union| |#2| "failed")) "\\spad{hyperelliptic()} returns \\spad{p(x)} if the curve is the hyperelliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elliptic| (((|Union| |#2| "failed")) "\\spad{elliptic()} returns \\spad{p(x)} if the curve is the elliptic defined by \\spad{y**2 = p(x)},{} \"failed\" otherwise.")) (|elt| ((|#1| $ |#1| |#1|) "\\spad{elt(f,{}a,{}b)} or \\spad{f}(a,{} \\spad{b}) returns the value of \\spad{f} at the point \\spad{(x = a,{} y = b)} if it is not singular.")) (|primitivePart| (($ $) "\\spad{primitivePart(f)} removes the content of the denominator and the common content of the numerator of \\spad{f}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{differentiate(x,{} d)} extends the derivation \\spad{d} from UP to \\$ and applies it to \\spad{x}.")) (|integralDerivationMatrix| (((|Record| (|:| |num| (|Matrix| |#2|)) (|:| |den| |#2|)) (|Mapping| |#2| |#2|)) "\\spad{integralDerivationMatrix(d)} extends the derivation \\spad{d} from UP to \\$ and returns (\\spad{M},{} \\spad{Q}) such that the i^th row of \\spad{M} divided by \\spad{Q} form the coordinates of \\spad{d(\\spad{wi})} with respect to \\spad{(w1,{}...,{}wn)} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by integralBasis().")) (|integralRepresents| (($ (|Vector| |#2|) |#2|) "\\spad{integralRepresents([A1,{}...,{}An],{} D)} returns \\spad{(A1 w1+...+An wn)/D} where \\spad{(w1,{}...,{}wn)} is the integral basis of \\spad{integralBasis()}.")) (|integralCoordinates| (((|Record| (|:| |num| (|Vector| |#2|)) (|:| |den| |#2|)) $) "\\spad{integralCoordinates(f)} returns \\spad{[[A1,{}...,{}An],{} D]} such that \\spad{f = (A1 w1 +...+ An wn) / D} where \\spad{(w1,{}...,{}wn)} is the integral basis returned by \\spad{integralBasis()}.")) (|represents| (($ (|Vector| |#2|) |#2|) "\\spad{represents([A0,{}...,{}A(n-1)],{}D)} returns \\spad{(A0 + A1 y +...+ A(n-1)*y**(n-1))/D}.") (($ (|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."))) -((-4237 |has| (-383 |#2|) (-339)) (-4242 |has| (-383 |#2|) (-339)) (-4236 |has| (-383 |#2|) (-339)) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 |has| (-383 |#2|) (-339)) (-4246 |has| (-383 |#2|) (-339)) (-4240 |has| (-383 |#2|) (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-319 |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."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) (-320 GF |defpol|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtensionByPolynomial(\\spad{GF},{}defpol) implements a finite extension field of the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial {\\em defpol},{} which MUST be primitive (user responsibility). Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field it is used to perform additions in the field quickly."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-321 GF |extdeg|) ((|constructor| (NIL "FiniteFieldCyclicGroupExtension(\\spad{GF},{}\\spad{n}) implements a extension of degree \\spad{n} over the ground field {\\em GF}. Its elements are represented by powers of a primitive element,{} \\spadignore{i.e.} a generator of the multiplicative (cyclic) group. As primitive element we choose the root of the extension polynomial,{} which is created by {\\em createPrimitivePoly} from \\spadtype{FiniteFieldPolynomialPackage}. Zech logarithms are stored in a table of size half of the field size,{} and use \\spadtype{SingleInteger} for representing field elements,{} hence,{} there are restrictions on the size of the field.")) (|getZechTable| (((|PrimitiveArray| (|SingleInteger|))) "\\spad{getZechTable()} returns the zech logarithm table of the field. This table is used to perform additions in the field quickly."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-322 GF) ((|constructor| (NIL "FiniteFieldFunctions(\\spad{GF}) is a package with functions concerning finite extension fields of the finite ground field {\\em GF},{} \\spadignore{e.g.} Zech logarithms.")) (|createLowComplexityNormalBasis| (((|Union| (|SparseUnivariatePolynomial| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) (|PositiveInteger|)) "\\spad{createLowComplexityNormalBasis(n)} tries to find a a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix If no low complexity basis is found it calls \\axiomFunFrom{createNormalPoly}{FiniteFieldPolynomialPackage}(\\spad{n}) to produce a normal polynomial of degree {\\em n} over {\\em GF}")) (|createLowComplexityTable| (((|Union| (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) "failed") (|PositiveInteger|)) "\\spad{createLowComplexityTable(n)} tries to find a low complexity normal basis of degree {\\em n} over {\\em GF} and returns its multiplication matrix Fails,{} if it does not find a low complexity basis")) (|sizeMultiplication| (((|NonNegativeInteger|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{sizeMultiplication(m)} returns the number of entries of the multiplication table {\\em m}.")) (|createMultiplicationMatrix| (((|Matrix| |#1|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{createMultiplicationMatrix(m)} forms the multiplication table {\\em m} into a matrix over the ground field.")) (|createMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createMultiplicationTable(f)} generates a multiplication table for the normal basis of the field extension determined by {\\em f}. This is needed to perform multiplications between elements represented as coordinate vectors to this basis. See \\spadtype{FFNBP},{} \\spadtype{FFNBX}.")) (|createZechTable| (((|PrimitiveArray| (|SingleInteger|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{createZechTable(f)} generates a Zech logarithm table for the cyclic group representation of a extension of the ground field by the primitive polynomial {\\em f(x)},{} \\spadignore{i.e.} \\spad{Z(i)},{} defined by {\\em x**Z(i) = 1+x**i} is stored at index \\spad{i}. This is needed in particular to perform addition of field elements in finite fields represented in this way. See \\spadtype{FFCGP},{} \\spadtype{FFCGX}."))) NIL @@ -1230,33 +1230,33 @@ NIL NIL (-325) ((|constructor| (NIL "FiniteFieldCategory is the category of finite fields")) (|representationType| (((|Union| "prime" "polynomial" "normal" "cyclic")) "\\spad{representationType()} returns the type of the representation,{} one of: \\spad{prime},{} \\spad{polynomial},{} \\spad{normal},{} or \\spad{cyclic}.")) (|order| (((|PositiveInteger|) $) "\\spad{order(b)} computes the order of an element \\spad{b} in the multiplicative group of the field. Error: if \\spad{b} equals 0.")) (|discreteLog| (((|NonNegativeInteger|) $) "\\spad{discreteLog(a)} computes the discrete logarithm of \\spad{a} with respect to \\spad{primitiveElement()} of the field.")) (|primitive?| (((|Boolean|) $) "\\spad{primitive?(b)} tests whether the element \\spad{b} is a generator of the (cyclic) multiplicative group of the field,{} \\spadignore{i.e.} is a primitive element. Implementation Note: see \\spad{ch}.IX.1.3,{} th.2 in \\spad{D}. Lipson.")) (|primitiveElement| (($) "\\spad{primitiveElement()} returns a primitive element stored in a global variable in the domain. At first call,{} the primitive element is computed by calling \\spadfun{createPrimitiveElement}.")) (|createPrimitiveElement| (($) "\\spad{createPrimitiveElement()} computes a generator of the (cyclic) multiplicative group of the field.")) (|tableForDiscreteLogarithm| (((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|)) "\\spad{tableForDiscreteLogarithm(a,{}n)} returns a table of the discrete logarithms of \\spad{a**0} up to \\spad{a**(n-1)} which,{} called with key \\spad{lookup(a**i)} returns \\spad{i} for \\spad{i} in \\spad{0..n-1}. Error: if not called for prime divisors of order of \\indented{7}{multiplicative group.}")) (|factorsOfCyclicGroupSize| (((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|))))) "\\spad{factorsOfCyclicGroupSize()} returns the factorization of size()\\spad{-1}")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(mat)},{} given a matrix representing a homogeneous system of equations,{} returns a vector whose characteristic'th powers is a non-trivial solution,{} or \"failed\" if no such vector exists.")) (|charthRoot| (($ $) "\\spad{charthRoot(a)} takes the characteristic'th root of {\\em a}. Note: such a root is alway defined in finite fields."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-326 R UP -2315) +(-326 R UP -3539) ((|constructor| (NIL "In this package \\spad{R} is a Euclidean domain and \\spad{F} is a framed algebra over \\spad{R}. The package provides functions to compute the integral closure of \\spad{R} in the quotient field of \\spad{F}. It is assumed that \\spad{char(R/P) = char(R)} for any prime \\spad{P} of \\spad{R}. A typical instance of this is when \\spad{R = K[x]} and \\spad{F} is a function field over \\spad{R}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) |#1|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-327 |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."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) (-328 GF |uni|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}uni) implements a finite extension of the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to. a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element,{} where \\spad{q} is the size of {\\em GF}. The normal element is chosen as a root of the extension polynomial,{} which MUST be normal over {\\em GF} (user responsibility)")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-329 GF |extdeg|) ((|constructor| (NIL "FiniteFieldNormalBasisExtensionByPolynomial(\\spad{GF},{}\\spad{n}) implements a finite extension field of degree \\spad{n} over the ground field {\\em GF}. The elements are represented by coordinate vectors with respect to a normal basis,{} \\spadignore{i.e.} a basis consisting of the conjugates (\\spad{q}-powers) of an element,{} in this case called normal element. This is chosen as a root of the extension polynomial,{} created by {\\em createNormalPoly} from \\spadtype{FiniteFieldPolynomialPackage}")) (|sizeMultiplication| (((|NonNegativeInteger|)) "\\spad{sizeMultiplication()} returns the number of entries in the multiplication table of the field. Note: the time of multiplication of field elements depends on this size.")) (|getMultiplicationMatrix| (((|Matrix| |#1|)) "\\spad{getMultiplicationMatrix()} returns the multiplication table in form of a matrix.")) (|getMultiplicationTable| (((|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|)))))) "\\spad{getMultiplicationTable()} returns the multiplication table for the normal basis of the field. This table is used to perform multiplications between field elements."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-330 |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}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| (-841 |#1|) (QUOTE (-134))) (|HasCategory| (-841 |#1|) (QUOTE (-344)))) (|HasCategory| (-841 |#1|) (QUOTE (-136))) (|HasCategory| (-841 |#1|) (QUOTE (-344))) (|HasCategory| (-841 |#1|) (QUOTE (-134)))) (-331 GF |defpol|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} defpol) implements the extension of the finite field {\\em GF} generated by the extension polynomial {\\em defpol} which MUST be irreducible. Note: the user has the responsibility to ensure that {\\em defpol} is irreducible."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) -(-332 -2315 GF) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +(-332 -3539 GF) ((|constructor| (NIL "FiniteFieldPolynomialPackage2(\\spad{F},{}\\spad{GF}) exports some functions concerning finite fields,{} which depend on a finite field {\\em GF} and an algebraic extension \\spad{F} of {\\em GF},{} \\spadignore{e.g.} a zero of a polynomial over {\\em GF} in \\spad{F}.")) (|rootOfIrreduciblePoly| ((|#1| (|SparseUnivariatePolynomial| |#2|)) "\\spad{rootOfIrreduciblePoly(f)} computes one root of the monic,{} irreducible polynomial \\spad{f},{} which degree must divide the extension degree of {\\em F} over {\\em GF},{} \\spadignore{i.e.} \\spad{f} splits into linear factors over {\\em F}.")) (|Frobenius| ((|#1| |#1|) "\\spad{Frobenius(x)} \\undocumented{}")) (|basis| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{}")) (|lookup| (((|PositiveInteger|) |#1|) "\\spad{lookup(x)} \\undocumented{}")) (|coerce| ((|#1| |#2|) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL @@ -1264,21 +1264,21 @@ NIL ((|constructor| (NIL "This package provides a number of functions for generating,{} counting and testing irreducible,{} normal,{} primitive,{} random polynomials over finite fields.")) (|reducedQPowers| (((|PrimitiveArray| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{reducedQPowers(f)} generates \\spad{[x,{}x**q,{}x**(q**2),{}...,{}x**(q**(n-1))]} reduced modulo \\spad{f} where \\spad{q = size()\\$GF} and \\spad{n = degree f}.")) (|leastAffineMultiple| (((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{leastAffineMultiple(f)} computes the least affine polynomial which is divisible by the polynomial \\spad{f} over the finite field {\\em GF},{} \\spadignore{i.e.} a polynomial whose exponents are 0 or a power of \\spad{q},{} the size of {\\em GF}.")) (|random| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{random(m,{}n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{d} over the finite field {\\em GF},{} \\spad{d} between \\spad{m} and \\spad{n}.") (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{random(n)}\\$FFPOLY(\\spad{GF}) generates a random monic polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|nextPrimitiveNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitiveNormalPoly(f)} yields the next primitive normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or,{} in case these numbers are equal,{} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. If these numbers are equals,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g},{} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are coefficients according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextNormalPrimitivePoly(\\spad{f}).")) (|nextNormalPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPrimitivePoly(f)} yields the next normal primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g} or if {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than this number for \\spad{g}. Otherwise,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents for \\spad{f} are lexicographically less than those for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}. This operation is equivalent to nextPrimitiveNormalPoly(\\spad{f}).")) (|nextNormalPoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextNormalPoly(f)} yields the next normal polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the coefficient of the term of degree {\\em n-1} of \\spad{f} is less than that for \\spad{g}. In case these numbers are equal,{} \\spad{f < g} if if the number of monomials of \\spad{f} is less that for \\spad{g} or if the list of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextPrimitivePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextPrimitivePoly(f)} yields the next primitive polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the {\\em lookup} of the constant term of \\spad{f} is less than this number for \\spad{g}. If these values are equal,{} then \\spad{f < g} if if the number of monomials of \\spad{f} is less than that for \\spad{g} or if the lists of exponents of \\spad{f} are lexicographically less than the corresponding list for \\spad{g}. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|nextIrreduciblePoly| (((|Union| (|SparseUnivariatePolynomial| |#1|) "failed") (|SparseUnivariatePolynomial| |#1|)) "\\spad{nextIrreduciblePoly(f)} yields the next monic irreducible polynomial over a finite field {\\em GF} of the same degree as \\spad{f} in the following order,{} or \"failed\" if there are no greater ones. Error: if \\spad{f} has degree 0. Note: the input polynomial \\spad{f} is made monic. Also,{} \\spad{f < g} if the number of monomials of \\spad{f} is less than this number for \\spad{g}. If \\spad{f} and \\spad{g} have the same number of monomials,{} the lists of exponents are compared lexicographically. If these lists are also equal,{} the lists of coefficients are compared according to the lexicographic ordering induced by the ordering of the elements of {\\em GF} given by {\\em lookup}.")) (|createPrimitiveNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitiveNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. polynomial of degree \\spad{n} over the field {\\em GF}.")) (|createNormalPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal and primitive polynomial of degree \\spad{n} over the field {\\em GF}. Note: this function is equivalent to createPrimitiveNormalPoly(\\spad{n})")) (|createNormalPoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createNormalPoly(n)}\\$FFPOLY(\\spad{GF}) generates a normal polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createPrimitivePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) generates a primitive polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|createIrreduciblePoly| (((|SparseUnivariatePolynomial| |#1|) (|PositiveInteger|)) "\\spad{createIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) generates a monic irreducible univariate polynomial of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfNormalPoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfNormalPoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of normal polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfPrimitivePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfPrimitivePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of primitive polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|numberOfIrreduciblePoly| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{numberOfIrreduciblePoly(n)}\\$FFPOLY(\\spad{GF}) yields the number of monic irreducible univariate polynomials of degree \\spad{n} over the finite field {\\em GF}.")) (|normal?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{normal?(f)} tests whether the polynomial \\spad{f} over a finite field is normal,{} \\spadignore{i.e.} its roots are linearly independent over the field.")) (|primitive?| (((|Boolean|) (|SparseUnivariatePolynomial| |#1|)) "\\spad{primitive?(f)} tests whether the polynomial \\spad{f} over a finite field is primitive,{} \\spadignore{i.e.} all its roots are primitive."))) NIL NIL -(-334 -2315 FP FPP) +(-334 -3539 FP FPP) ((|constructor| (NIL "This package solves linear diophantine equations for Bivariate polynomials over finite fields")) (|solveLinearPolynomialEquation| (((|Union| (|List| |#3|) "failed") (|List| |#3|) |#3|) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL (-335 GF |n|) ((|constructor| (NIL "FiniteFieldExtensionByPolynomial(\\spad{GF},{} \\spad{n}) implements an extension of the finite field {\\em GF} of degree \\spad{n} generated by the extension polynomial constructed by \\spadfunFrom{createIrreduciblePoly}{FiniteFieldPolynomialPackage} from \\spadtype{FiniteFieldPolynomialPackage}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-134)))) (-336 R |ls|) ((|constructor| (NIL "This is just an interface between several packages and domains. The goal is to compute lexicographical Groebner bases of sets of polynomial with type \\spadtype{Polynomial R} by the {\\em FGLM} algorithm if this is possible (\\spadignore{i.e.} if the input system generates a zero-dimensional ideal).")) (|groebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|))) "\\axiom{groebner(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}}. If \\axiom{\\spad{lq1}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|Polynomial| |#1|)) "failed") (|List| (|Polynomial| |#1|))) "\\axiom{fglmIfCan(\\spad{lq1})} returns the lexicographical Groebner basis of \\axiom{\\spad{lq1}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lq1})} holds.")) (|zeroDimensional?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "\\axiom{zeroDimensional?(\\spad{lq1})} returns \\spad{true} iff \\axiom{\\spad{lq1}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables of \\axiom{\\spad{ls}}."))) NIL NIL (-337 S) ((|constructor| (NIL "The free group on a set \\spad{S} is the group of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are integers. The multiplication is not commutative.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|Integer|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|Integer|) (|Integer|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|Integer|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (** (($ |#1| (|Integer|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) -((-4241 . T)) +((-4245 . T)) NIL (-338 S) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) @@ -1286,7 +1286,7 @@ NIL NIL (-339) ((|constructor| (NIL "The category of commutative fields,{} \\spadignore{i.e.} commutative rings where all non-zero elements have multiplicative inverses. The \\spadfun{factor} operation while trivial is useful to have defined. \\blankline")) (|canonicalsClosed| ((|attribute|) "since \\spad{0*0=0},{} \\spad{1*1=1}")) (|canonicalUnitNormal| ((|attribute|) "either 0 or 1.")) (/ (($ $ $) "\\spad{x/y} divides the element \\spad{x} by the element \\spad{y}. Error: if \\spad{y} is 0."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-340 |Name| S) ((|constructor| (NIL "This category provides an interface to operate on files in the computer\\spad{'s} file system. The precise method of naming files is determined by the Name parameter. The type of the contents of the file is determined by \\spad{S}.")) (|write!| ((|#2| $ |#2|) "\\spad{write!(f,{}s)} puts the value \\spad{s} into the file \\spad{f}. The state of \\spad{f} is modified so subsequents call to \\spad{write!} will append one after another.")) (|read!| ((|#2| $) "\\spad{read!(f)} extracts a value from file \\spad{f}. The state of \\spad{f} is modified so a subsequent call to \\spadfun{read!} will return the next element.")) (|iomode| (((|String|) $) "\\spad{iomode(f)} returns the status of the file \\spad{f}. The input/output status of \\spad{f} may be \"input\",{} \"output\" or \"closed\" mode.")) (|name| ((|#1| $) "\\spad{name(f)} returns the external name of the file \\spad{f}.")) (|close!| (($ $) "\\spad{close!(f)} returns the file \\spad{f} closed to input and output.")) (|reopen!| (($ $ (|String|)) "\\spad{reopen!(f,{}mode)} returns a file \\spad{f} reopened for operation in the indicated mode: \"input\" or \"output\". \\spad{reopen!(f,{}\"input\")} will reopen the file \\spad{f} for input.")) (|open| (($ |#1| (|String|)) "\\spad{open(s,{}mode)} returns a file \\spad{s} open for operation in the indicated mode: \"input\" or \"output\".") (($ |#1|) "\\spad{open(s)} returns the file \\spad{s} open for input."))) @@ -1302,7 +1302,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-515)))) (-343 R) ((|constructor| (NIL "A FiniteRankNonAssociativeAlgebra is a non associative algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|unitsKnown| ((|attribute|) "unitsKnown means that \\spadfun{recip} truly yields reciprocal or \\spad{\"failed\"} if not a unit,{} similarly for \\spadfun{leftRecip} and \\spadfun{rightRecip}. The reason is that we use left,{} respectively right,{} minimal polynomials to decide this question.")) (|unit| (((|Union| $ "failed")) "\\spad{unit()} returns a unit of the algebra (necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnit| (((|Union| $ "failed")) "\\spad{rightUnit()} returns a right unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|leftUnit| (((|Union| $ "failed")) "\\spad{leftUnit()} returns a left unit of the algebra (not necessarily unique),{} or \\spad{\"failed\"} if there is none.")) (|rightUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{rightUnits()} returns the affine space of all right units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|leftUnits| (((|Union| (|Record| (|:| |particular| $) (|:| |basis| (|List| $))) "failed")) "\\spad{leftUnits()} returns the affine space of all left units of the algebra,{} or \\spad{\"failed\"} if there is none.")) (|rightMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of right powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|leftMinimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftMinimalPolynomial(a)} returns the polynomial determined by the smallest non-trivial linear combination of left powers of \\spad{a}. Note: the polynomial never has a constant term as in general the algebra has no unit.")) (|associatorDependence| (((|List| (|Vector| |#1|))) "\\spad{associatorDependence()} looks for the associator identities,{} \\spadignore{i.e.} finds a basis of the solutions of the linear combinations of the six permutations of \\spad{associator(a,{}b,{}c)} which yield 0,{} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. The order of the permutations is \\spad{123 231 312 132 321 213}.")) (|rightRecip| (((|Union| $ "failed") $) "\\spad{rightRecip(a)} returns an element,{} which is a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|leftRecip| (((|Union| $ "failed") $) "\\spad{leftRecip(a)} returns an element,{} which is a left inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(a)} returns an element,{} which is both a left and a right inverse of \\spad{a},{} or \\spad{\"failed\"} if there is no unit element,{} if such an element doesn\\spad{'t} exist or cannot be determined (see unitsKnown).")) (|lieAlgebra?| (((|Boolean|)) "\\spad{lieAlgebra?()} tests if the algebra is anticommutative and \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jacobi identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Lie algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := a@b-b@a}.")) (|jordanAlgebra?| (((|Boolean|)) "\\spad{jordanAlgebra?()} tests if the algebra is commutative,{} characteristic is not 2,{} and \\spad{(a*b)*a**2 - a*(b*a**2) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra (Jordan identity). Example: for every associative algebra \\spad{(A,{}+,{}@)} we can construct a Jordan algebra \\spad{(A,{}+,{}*)},{} where \\spad{a*b := (a@b+b@a)/2}.")) (|noncommutativeJordanAlgebra?| (((|Boolean|)) "\\spad{noncommutativeJordanAlgebra?()} tests if the algebra is flexible and Jordan admissible.")) (|jordanAdmissible?| (((|Boolean|)) "\\spad{jordanAdmissible?()} tests if 2 is invertible in the coefficient domain and the multiplication defined by \\spad{(1/2)(a*b+b*a)} determines a Jordan algebra,{} \\spadignore{i.e.} satisfies the Jordan identity. The property of \\spadatt{commutative(\\spad{\"*\"})} follows from by definition.")) (|lieAdmissible?| (((|Boolean|)) "\\spad{lieAdmissible?()} tests if the algebra defined by the commutators is a Lie algebra,{} \\spadignore{i.e.} satisfies the Jacobi identity. The property of anticommutativity follows from definition.")) (|jacobiIdentity?| (((|Boolean|)) "\\spad{jacobiIdentity?()} tests if \\spad{(a*b)*c + (b*c)*a + (c*a)*b = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra. For example,{} this holds for crossed products of 3-dimensional vectors.")) (|powerAssociative?| (((|Boolean|)) "\\spad{powerAssociative?()} tests if all subalgebras generated by a single element are associative.")) (|alternative?| (((|Boolean|)) "\\spad{alternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0 = 2*associator(a,{}b,{}b)} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|flexible?| (((|Boolean|)) "\\spad{flexible?()} tests if \\spad{2*associator(a,{}b,{}a) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|rightAlternative?| (((|Boolean|)) "\\spad{rightAlternative?()} tests if \\spad{2*associator(a,{}b,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|leftAlternative?| (((|Boolean|)) "\\spad{leftAlternative?()} tests if \\spad{2*associator(a,{}a,{}b) = 0} for all \\spad{a},{} \\spad{b} in the algebra. Note: we only can test this; in general we don\\spad{'t} know whether \\spad{2*a=0} implies \\spad{a=0}.")) (|antiAssociative?| (((|Boolean|)) "\\spad{antiAssociative?()} tests if multiplication in algebra is anti-associative,{} \\spadignore{i.e.} \\spad{(a*b)*c + a*(b*c) = 0} for all \\spad{a},{}\\spad{b},{}\\spad{c} in the algebra.")) (|associative?| (((|Boolean|)) "\\spad{associative?()} tests if multiplication in algebra is associative.")) (|antiCommutative?| (((|Boolean|)) "\\spad{antiCommutative?()} tests if \\spad{a*a = 0} for all \\spad{a} in the algebra. Note: this implies \\spad{a*b + b*a = 0} for all \\spad{a} and \\spad{b}.")) (|commutative?| (((|Boolean|)) "\\spad{commutative?()} tests if multiplication in the algebra is commutative.")) (|rightCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{rightCharacteristicPolynomial(a)} returns the characteristic polynomial of the right regular representation of \\spad{a} with respect to any basis.")) (|leftCharacteristicPolynomial| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{leftCharacteristicPolynomial(a)} returns the characteristic polynomial of the left regular representation of \\spad{a} with respect to any basis.")) (|rightTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{rightTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}.")) (|leftTraceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{leftTraceMatrix([v1,{}...,{}vn])} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}.")) (|rightDiscriminant| ((|#1| (|Vector| $)) "\\spad{rightDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(rightTraceMatrix([v1,{}...,{}vn]))}.")) (|leftDiscriminant| ((|#1| (|Vector| $)) "\\spad{leftDiscriminant([v1,{}...,{}vn])} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj}. Note: the same as \\spad{determinant(leftTraceMatrix([v1,{}...,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}...,{}am],{}[v1,{}...,{}vm])} returns the linear combination \\spad{a1*vm + ... + an*vm}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am],{}[v1,{}...,{}vn])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}[v1,{}...,{}vn])} returns the coordinates of \\spad{a} with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rightNorm| ((|#1| $) "\\spad{rightNorm(a)} returns the determinant of the right regular representation of \\spad{a}.")) (|leftNorm| ((|#1| $) "\\spad{leftNorm(a)} returns the determinant of the left regular representation of \\spad{a}.")) (|rightTrace| ((|#1| $) "\\spad{rightTrace(a)} returns the trace of the right regular representation of \\spad{a}.")) (|leftTrace| ((|#1| $) "\\spad{leftTrace(a)} returns the trace of the left regular representation of \\spad{a}.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{rightRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{leftRegularRepresentation(a,{}[v1,{}...,{}vn])} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{R}-module basis \\spad{[v1,{}...,{}vn]}.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|)) (|Vector| $)) "\\spad{structuralConstants([v1,{}v2,{}...,{}vm])} calculates the structural constants \\spad{[(gammaijk) for k in 1..m]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijm * vm},{} where \\spad{[v1,{}...,{}vm]} is an \\spad{R}-module basis of a subalgebra.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|)) (|Vector| $)) "\\spad{conditionsForIdempotents([v1,{}...,{}vn])} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the \\spad{R}-module basis \\spad{v1},{}...,{}\\spad{vn}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra as \\spad{R}-module.")) (|someBasis| (((|Vector| $)) "\\spad{someBasis()} returns some \\spad{R}-module basis."))) -((-4241 |has| |#1| (-515)) (-4239 . T) (-4238 . T)) +((-4245 |has| |#1| (-515)) (-4243 . T) (-4242 . T)) NIL (-344) ((|constructor| (NIL "The category of domains composed of a finite set of elements. We include the functions \\spadfun{lookup} and \\spadfun{index} to give a bijection between the finite set and an initial segment of positive integers. \\blankline")) (|random| (($) "\\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."))) @@ -1314,7 +1314,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-339)))) (-346 R UP) ((|constructor| (NIL "A FiniteRankAlgebra is an algebra over a commutative ring \\spad{R} which is a free \\spad{R}-module of finite rank.")) (|minimalPolynomial| ((|#2| $) "\\spad{minimalPolynomial(a)} returns the minimal polynomial of \\spad{a}.")) (|characteristicPolynomial| ((|#2| $) "\\spad{characteristicPolynomial(a)} returns the characteristic polynomial of the regular representation of \\spad{a} with respect to any basis.")) (|traceMatrix| (((|Matrix| |#1|) (|Vector| $)) "\\spad{traceMatrix([v1,{}..,{}vn])} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr}(\\spad{vi} * \\spad{vj}) )")) (|discriminant| ((|#1| (|Vector| $)) "\\spad{discriminant([v1,{}..,{}vn])} returns \\spad{determinant(traceMatrix([v1,{}..,{}vn]))}.")) (|represents| (($ (|Vector| |#1|) (|Vector| $)) "\\spad{represents([a1,{}..,{}an],{}[v1,{}..,{}vn])} returns \\spad{a1*v1 + ... + an*vn}.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm],{} basis)} returns the coordinates of the \\spad{vi}\\spad{'s} with to the basis \\spad{basis}. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $ (|Vector| $)) "\\spad{coordinates(a,{}basis)} returns the coordinates of \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|norm| ((|#1| $) "\\spad{norm(a)} returns the determinant of the regular representation of \\spad{a} with respect to any basis.")) (|trace| ((|#1| $) "\\spad{trace(a)} returns the trace of the regular representation of \\spad{a} with respect to any basis.")) (|regularRepresentation| (((|Matrix| |#1|) $ (|Vector| $)) "\\spad{regularRepresentation(a,{}basis)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the \\spad{basis} \\spad{basis}.")) (|rank| (((|PositiveInteger|)) "\\spad{rank()} returns the rank of the algebra."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL (-347 S A R B) ((|constructor| (NIL "FiniteLinearAggregateFunctions2 provides functions involving two FiniteLinearAggregates where the underlying domains might be different. An example of this might be creating a list of rational numbers by mapping a function across a list of integers where the function divides each integer by 1000.")) (|scan| ((|#4| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{scan(f,{}a,{}r)} successively applies \\spad{reduce(f,{}x,{}r)} to more and more leading sub-aggregates \\spad{x} of aggregrate \\spad{a}. More precisely,{} if \\spad{a} is \\spad{[a1,{}a2,{}...]},{} then \\spad{scan(f,{}a,{}r)} returns \\spad{[reduce(f,{}[a1],{}r),{}reduce(f,{}[a1,{}a2],{}r),{}...]}.")) (|reduce| ((|#3| (|Mapping| |#3| |#1| |#3|) |#2| |#3|) "\\spad{reduce(f,{}a,{}r)} applies function \\spad{f} to each successive element of the aggregate \\spad{a} and an accumulant initialized to \\spad{r}. For example,{} \\spad{reduce(_+\\$Integer,{}[1,{}2,{}3],{}0)} does \\spad{3+(2+(1+0))}. Note: third argument \\spad{r} may be regarded as the identity element for the function \\spad{f}.")) (|map| ((|#4| (|Mapping| |#3| |#1|) |#2|) "\\spad{map(f,{}a)} applies function \\spad{f} to each member of aggregate \\spad{a} resulting in a new aggregate over a possibly different underlying domain."))) @@ -1323,14 +1323,14 @@ NIL (-348 A S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#2| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#2| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#2|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#2| |#2|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) NIL -((|HasAttribute| |#1| (QUOTE -4245)) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016)))) +((|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016)))) (-349 S) ((|constructor| (NIL "A finite linear aggregate is a linear aggregate of finite length. The finite property of the aggregate adds several exports to the list of exports from \\spadtype{LinearAggregate} such as \\spadfun{reverse},{} \\spadfun{sort},{} and so on.")) (|sort!| (($ $) "\\spad{sort!(u)} returns \\spad{u} with its elements in ascending order.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort!(p,{}u)} returns \\spad{u} with its elements ordered by \\spad{p}.")) (|reverse!| (($ $) "\\spad{reverse!(u)} returns \\spad{u} with its elements in reverse order.")) (|copyInto!| (($ $ $ (|Integer|)) "\\spad{copyInto!(u,{}v,{}i)} returns aggregate \\spad{u} containing a copy of \\spad{v} inserted at element \\spad{i}.")) (|position| (((|Integer|) |#1| $ (|Integer|)) "\\spad{position(x,{}a,{}n)} returns the index \\spad{i} of the first occurrence of \\spad{x} in \\axiom{a} where \\axiom{\\spad{i} \\spad{>=} \\spad{n}},{} and \\axiom{minIndex(a) - 1} if no such \\spad{x} is found.") (((|Integer|) |#1| $) "\\spad{position(x,{}a)} returns the index \\spad{i} of the first occurrence of \\spad{x} in a,{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.") (((|Integer|) (|Mapping| (|Boolean|) |#1|) $) "\\spad{position(p,{}a)} returns the index \\spad{i} of the first \\spad{x} in \\axiom{a} such that \\axiom{\\spad{p}(\\spad{x})} is \\spad{true},{} and \\axiom{minIndex(a) - 1} if there is no such \\spad{x}.")) (|sorted?| (((|Boolean|) $) "\\spad{sorted?(u)} tests if the elements of \\spad{u} are in ascending order.") (((|Boolean|) (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sorted?(p,{}a)} tests if \\axiom{a} is sorted according to predicate \\spad{p}.")) (|sort| (($ $) "\\spad{sort(u)} returns an \\spad{u} with elements in ascending order. Note: \\axiom{sort(\\spad{u}) = sort(\\spad{<=},{}\\spad{u})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $) "\\spad{sort(p,{}a)} returns a copy of \\axiom{a} sorted using total ordering predicate \\spad{p}.")) (|reverse| (($ $) "\\spad{reverse(a)} returns a copy of \\axiom{a} with elements in reverse order.")) (|merge| (($ $ $) "\\spad{merge(u,{}v)} merges \\spad{u} and \\spad{v} in ascending order. Note: \\axiom{merge(\\spad{u},{}\\spad{v}) = merge(\\spad{<=},{}\\spad{u},{}\\spad{v})}.") (($ (|Mapping| (|Boolean|) |#1| |#1|) $ $) "\\spad{merge(p,{}a,{}b)} returns an aggregate \\spad{c} which merges \\axiom{a} and \\spad{b}. The result is produced by examining each element \\spad{x} of \\axiom{a} and \\spad{y} of \\spad{b} successively. If \\axiom{\\spad{p}(\\spad{x},{}\\spad{y})} is \\spad{true},{} then \\spad{x} is inserted into the result; otherwise \\spad{y} is inserted. If \\spad{x} is chosen,{} the next element of \\axiom{a} is examined,{} and so on. When all the elements of one aggregate are examined,{} the remaining elements of the other are appended. For example,{} \\axiom{merge(<,{}[1,{}3],{}[2,{}7,{}5])} returns \\axiom{[1,{}2,{}3,{}7,{}5]}."))) -((-4244 . T) (-3656 . T)) +((-4248 . T) (-4069 . T)) NIL (-350 |VarSet| R) ((|constructor| (NIL "The category of free Lie algebras. It is used by domains of non-commutative algebra: \\spadtype{LiePolynomial} and \\spadtype{XPBWPolynomial}. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|eval| (($ $ (|List| |#1|) (|List| $)) "\\axiom{eval(\\spad{p},{} [\\spad{x1},{}...,{}\\spad{xn}],{} [\\spad{v1},{}...,{}\\spad{vn}])} replaces \\axiom{\\spad{xi}} by \\axiom{\\spad{vi}} in \\axiom{\\spad{p}}.") (($ $ |#1| $) "\\axiom{eval(\\spad{p},{} \\spad{x},{} \\spad{v})} replaces \\axiom{\\spad{x}} by \\axiom{\\spad{v}} in \\axiom{\\spad{p}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|trunc| (($ $ (|NonNegativeInteger|)) "\\axiom{trunc(\\spad{p},{}\\spad{n})} returns the polynomial \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns \\axiom{Sum(r_i mirror(w_i))} if \\axiom{\\spad{x}} is \\axiom{Sum(r_i w_i)}.")) (|LiePoly| (($ (|LyndonWord| |#1|)) "\\axiom{LiePoly(\\spad{l})} returns the bracketed form of \\axiom{\\spad{l}} as a Lie polynomial.")) (|rquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{rquo(\\spad{x},{}\\spad{y})} returns the right simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|lquo| (((|XRecursivePolynomial| |#1| |#2|) (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{lquo(\\spad{x},{}\\spad{y})} returns the left simplification of \\axiom{\\spad{x}} by \\axiom{\\spad{y}}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{x})} returns the greatest length of a word in the support of \\axiom{\\spad{x}}.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as distributed polynomial.") (($ |#1|) "\\axiom{coerce(\\spad{x})} returns \\axiom{\\spad{x}} as a Lie polynomial.")) (|coef| ((|#2| (|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coef(\\spad{x},{}\\spad{y})} returns the scalar product of \\axiom{\\spad{x}} by \\axiom{\\spad{y}},{} the set of words being regarded as an orthogonal basis."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4239 . T) (-4238 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4243 . T) (-4242 . T)) NIL (-351 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."))) @@ -1342,15 +1342,15 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-353 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}"))) -((-4241 . T)) +((-4245 . T)) NIL (-354 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of complex solutions for} systems of equations of rational functions with complex rational coefficients. The results are expressed as either complex rational numbers or complex floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|complexRoots| (((|List| (|List| (|Complex| |#1|))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) (|List| (|Symbol|)) |#1|) "\\spad{complexRoots(lrf,{} lv,{} eps)} finds all the complex solutions of a list of rational functions with rational number coefficients with respect the the variables appearing in \\spad{lv}. Each solution is computed to precision eps and returned as list corresponding to the order of variables in \\spad{lv}.") (((|List| (|Complex| |#1|)) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexRoots(rf,{} eps)} finds all the complex solutions of a univariate rational function with rational number coefficients. The solutions are computed to precision eps.")) (|complexSolve| (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(eq,{}eps)} finds all the complex solutions of the equation \\spad{eq} of rational functions with rational rational coefficients with respect to all the variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| (|Complex| |#1|)))) (|Fraction| (|Polynomial| (|Complex| (|Integer|)))) |#1|) "\\spad{complexSolve(p,{}eps)} find all the complex solutions of the rational function \\spad{p} with complex rational coefficients with respect to all the variables appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Complex| (|Integer|)))))) |#1|) "\\spad{complexSolve(leq,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{leq} of equations of rational functions over complex rationals with respect to all the variables appearing in \\spad{lp}.") (((|List| (|List| (|Equation| (|Polynomial| (|Complex| |#1|))))) (|List| (|Fraction| (|Polynomial| (|Complex| (|Integer|))))) |#1|) "\\spad{complexSolve(lp,{}eps)} finds all the complex solutions to precision \\spad{eps} of the system \\spad{lp} of rational functions over the complex rationals with respect to all the variables appearing in \\spad{lp}."))) NIL NIL (-355) -((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\^= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) -((-4227 . T) (-4235 . T) (-2562 . T) (-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((|constructor| (NIL "\\spadtype{Float} implements arbitrary precision floating point arithmetic. The number of significant digits of each operation can be set to an arbitrary value (the default is 20 decimal digits). The operation \\spad{float(mantissa,{}exponent,{}\\spadfunFrom{base}{FloatingPointSystem})} for integer \\spad{mantissa},{} \\spad{exponent} specifies the number \\spad{mantissa * \\spadfunFrom{base}{FloatingPointSystem} ** exponent} The underlying representation for floats is binary not decimal. The implications of this are described below. \\blankline The model adopted is that arithmetic operations are rounded to to nearest unit in the last place,{} that is,{} accurate to within \\spad{2**(-\\spadfunFrom{bits}{FloatingPointSystem})}. Also,{} the elementary functions and constants are accurate to one unit in the last place. A float is represented as a record of two integers,{} the mantissa and the exponent. The \\spadfunFrom{base}{FloatingPointSystem} of the representation is binary,{} hence a \\spad{Record(m:mantissa,{}e:exponent)} represents the number \\spad{m * 2 ** e}. Though it is not assumed that the underlying integers are represented with a binary \\spadfunFrom{base}{FloatingPointSystem},{} the code will be most efficient when this is the the case (this is \\spad{true} in most implementations of Lisp). The decision to choose the \\spadfunFrom{base}{FloatingPointSystem} to be binary has some unfortunate consequences. First,{} decimal numbers like 0.3 cannot be represented exactly. Second,{} there is a further loss of accuracy during conversion to decimal for output. To compensate for this,{} if \\spad{d} digits of precision are specified,{} \\spad{1 + ceiling(log2 d)} bits are used. Two numbers that are displayed identically may therefore be not equal. On the other hand,{} a significant efficiency loss would be incurred if we chose to use a decimal \\spadfunFrom{base}{FloatingPointSystem} when the underlying integer base is binary. \\blankline Algorithms used: For the elementary functions,{} the general approach is to apply identities so that the taylor series can be used,{} and,{} so that it will converge within \\spad{O( sqrt n )} steps. For example,{} using the identity \\spad{exp(x) = exp(x/2)**2},{} we can compute \\spad{exp(1/3)} to \\spad{n} digits of precision as follows. We have \\spad{exp(1/3) = exp(2 ** (-sqrt s) / 3) ** (2 ** sqrt s)}. The taylor series will converge in less than sqrt \\spad{n} steps and the exponentiation requires sqrt \\spad{n} multiplications for a total of \\spad{2 sqrt n} multiplications. Assuming integer multiplication costs \\spad{O( n**2 )} the overall running time is \\spad{O( sqrt(n) n**2 )}. This approach is the best known approach for precisions up to about 10,{}000 digits at which point the methods of Brent which are \\spad{O( log(n) n**2 )} become competitive. Note also that summing the terms of the taylor series for the elementary functions is done using integer operations. This avoids the overhead of floating point operations and results in efficient code at low precisions. This implementation makes no attempt to reuse storage,{} relying on the underlying system to do \\spadgloss{garbage collection}. \\spad{I} estimate that the efficiency of this package at low precisions could be improved by a factor of 2 if in-place operations were available. \\blankline Running times: in the following,{} \\spad{n} is the number of bits of precision \\indented{5}{\\spad{*},{} \\spad{/},{} \\spad{sqrt},{} \\spad{\\spad{pi}},{} \\spad{exp1},{} \\spad{log2},{} \\spad{log10}: \\spad{ O( n**2 )}} \\indented{5}{\\spad{exp},{} \\spad{log},{} \\spad{sin},{} \\spad{atan}:\\space{2}\\spad{ O( sqrt(n) n**2 )}} The other elementary functions are coded in terms of the ones above.")) (|outputSpacing| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputSpacing(n)} inserts a space after \\spad{n} (default 10) digits on output; outputSpacing(0) means no spaces are inserted.")) (|outputGeneral| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputGeneral(n)} sets the output mode to general notation with \\spad{n} significant digits displayed.") (((|Void|)) "\\spad{outputGeneral()} sets the output mode (default mode) to general notation; numbers will be displayed in either fixed or floating (scientific) notation depending on the magnitude.")) (|outputFixed| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFixed(n)} sets the output mode to fixed point notation,{} with \\spad{n} digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFixed()} sets the output mode to fixed point notation; the output will contain a decimal point.")) (|outputFloating| (((|Void|) (|NonNegativeInteger|)) "\\spad{outputFloating(n)} sets the output mode to floating (scientific) notation with \\spad{n} significant digits displayed after the decimal point.") (((|Void|)) "\\spad{outputFloating()} sets the output mode to floating (scientific) notation,{} \\spadignore{i.e.} \\spad{mantissa * 10 exponent} is displayed as \\spad{0.mantissa E exponent}.")) (|convert| (($ (|DoubleFloat|)) "\\spad{convert(x)} converts a \\spadtype{DoubleFloat} \\spad{x} to a \\spadtype{Float}.")) (|atan| (($ $ $) "\\spad{atan(x,{}y)} computes the arc tangent from \\spad{x} with phase \\spad{y}.")) (|exp1| (($) "\\spad{exp1()} returns exp 1: \\spad{2.7182818284...}.")) (|log10| (($ $) "\\spad{log10(x)} computes the logarithm for \\spad{x} to base 10.") (($) "\\spad{log10()} returns \\spad{ln 10}: \\spad{2.3025809299...}.")) (|log2| (($ $) "\\spad{log2(x)} computes the logarithm for \\spad{x} to base 2.") (($) "\\spad{log2()} returns \\spad{ln 2},{} \\spadignore{i.e.} \\spad{0.6931471805...}.")) (|rationalApproximation| (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n,{} b)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< b**(-n)},{} that is \\spad{|(r-f)/f| < b**(-n)}.") (((|Fraction| (|Integer|)) $ (|NonNegativeInteger|)) "\\spad{rationalApproximation(f,{} n)} computes a rational approximation \\spad{r} to \\spad{f} with relative error \\spad{< 10**(-n)}.")) (|shift| (($ $ (|Integer|)) "\\spad{shift(x,{}n)} adds \\spad{n} to the exponent of float \\spad{x}.")) (|relerror| (((|Integer|) $ $) "\\spad{relerror(x,{}y)} computes the absolute value of \\spad{x - y} divided by \\spad{y},{} when \\spad{y \\~= 0}.")) (|normalize| (($ $) "\\spad{normalize(x)} normalizes \\spad{x} at current precision.")) (** (($ $ $) "\\spad{x ** y} computes \\spad{exp(y log x)} where \\spad{x >= 0}.")) (/ (($ $ (|Integer|)) "\\spad{x / i} computes the division from \\spad{x} by an integer \\spad{i}."))) +((-4231 . T) (-4239 . T) (-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-356 |Par|) ((|constructor| (NIL "\\indented{3}{This is a package for the approximation of real solutions for} systems of polynomial equations over the rational numbers. The results are expressed as either rational numbers or floats depending on the type of the precision parameter which can be either a rational number or a floating point number.")) (|realRoots| (((|List| |#1|) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{realRoots(rf,{} eps)} finds the real zeros of a univariate rational function with precision given by eps.") (((|List| (|List| |#1|)) (|List| (|Fraction| (|Polynomial| (|Integer|)))) (|List| (|Symbol|)) |#1|) "\\spad{realRoots(lp,{}lv,{}eps)} computes the list of the real solutions of the list \\spad{lp} of rational functions with rational coefficients with respect to the variables in \\spad{lv},{} with precision \\spad{eps}. Each solution is expressed as a list of numbers in order corresponding to the variables in \\spad{lv}.")) (|solve| (((|List| (|Equation| (|Polynomial| |#1|))) (|Equation| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(eq,{}eps)} finds all of the real solutions of the univariate equation \\spad{eq} of rational functions with respect to the unique variables appearing in \\spad{eq},{} with precision \\spad{eps}.") (((|List| (|Equation| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| (|Integer|))) |#1|) "\\spad{solve(p,{}eps)} finds all of the real solutions of the univariate rational function \\spad{p} with rational coefficients with respect to the unique variable appearing in \\spad{p},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Equation| (|Fraction| (|Polynomial| (|Integer|))))) |#1|) "\\spad{solve(leq,{}eps)} finds all of the real solutions of the system \\spad{leq} of equationas of rational functions with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}.") (((|List| (|List| (|Equation| (|Polynomial| |#1|)))) (|List| (|Fraction| (|Polynomial| (|Integer|)))) |#1|) "\\spad{solve(lp,{}eps)} finds all of the real solutions of the system \\spad{lp} of rational functions over the rational numbers with respect to all the variables appearing in \\spad{lp},{} with precision \\spad{eps}."))) @@ -1358,23 +1358,23 @@ NIL NIL (-357 R S) ((|constructor| (NIL "This domain implements linear combinations of elements from the domain \\spad{S} with coefficients in the domain \\spad{R} where \\spad{S} is an ordered set and \\spad{R} is a ring (which may be non-commutative). This domain is used by domains of non-commutative algebra such as: \\indented{4}{\\spadtype{XDistributedPolynomial},{}} \\indented{4}{\\spadtype{XRecursivePolynomial}.} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (* (($ |#2| |#1|) "\\spad{s*r} returns the product \\spad{r*s} used by \\spadtype{XRecursivePolynomial}"))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (QUOTE (-158)))) (-358 R |Basis|) ((|constructor| (NIL "A domain of this category implements formal linear combinations of elements from a domain \\spad{Basis} with coefficients in a domain \\spad{R}. The domain \\spad{Basis} needs only to belong to the category \\spadtype{SetCategory} and \\spad{R} to the category \\spadtype{Ring}. Thus the coefficient ring may be non-commutative. See the \\spadtype{XDistributedPolynomial} constructor for examples of domains built with the \\spadtype{FreeModuleCat} category constructor. Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|reductum| (($ $) "\\spad{reductum(x)} returns \\spad{x} minus its leading term.")) (|leadingTerm| (((|Record| (|:| |k| |#2|) (|:| |c| |#1|)) $) "\\spad{leadingTerm(x)} returns the first term which appears in \\spad{ListOfTerms(x)}.")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(x)} returns the first coefficient which appears in \\spad{ListOfTerms(x)}.")) (|leadingMonomial| ((|#2| $) "\\spad{leadingMonomial(x)} returns the first element from \\spad{Basis} which appears in \\spad{ListOfTerms(x)}.")) (|numberOfMonomials| (((|NonNegativeInteger|) $) "\\spad{numberOfMonomials(x)} returns the number of monomials of \\spad{x}.")) (|monomials| (((|List| $) $) "\\spad{monomials(x)} returns the list of \\spad{r_i*b_i} whose sum is \\spad{x}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(x)} returns the list of coefficients of \\spad{x}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{ListOfTerms(x)} returns a list \\spad{lt} of terms with type \\spad{Record(k: Basis,{} c: R)} such that \\spad{x} equals \\spad{reduce(+,{} map(x +-> monom(x.k,{} x.c),{} lt))}.")) (|monomial?| (((|Boolean|) $) "\\spad{monomial?(x)} returns \\spad{true} if \\spad{x} contains a single monomial.")) (|monom| (($ |#2| |#1|) "\\spad{monom(b,{}r)} returns the element with the single monomial \\indented{1}{\\spad{b} and coefficient \\spad{r}.}")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps function \\spad{fn} onto the coefficients \\indented{1}{of the non-zero monomials of \\spad{u}.}")) (|coefficient| ((|#1| $ |#2|) "\\spad{coefficient(x,{}b)} returns the coefficient of \\spad{b} in \\spad{x}.")) (* (($ |#1| |#2|) "\\spad{r*b} returns the product of \\spad{r} by \\spad{b}."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL (-359) ((|constructor| (NIL "\\axiomType{FortranMatrixCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Matrix} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Matrix| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-3656 . T)) +((-4069 . T)) NIL (-360) ((|constructor| (NIL "\\axiomType{FortranMatrixFunctionCategory} provides support for producing Functions and Subroutines representing matrices of expressions.")) (|retractIfCan| (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Matrix| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Matrix| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Matrix| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-3656 . T)) +((-4069 . T)) NIL (-361 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."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (QUOTE (-158)))) (-362 S) ((|constructor| (NIL "The free monoid on a set \\spad{S} is the monoid of finite products of the form \\spad{reduce(*,{}[\\spad{si} ** \\spad{ni}])} where the \\spad{si}\\spad{'s} are in \\spad{S},{} and the \\spad{ni}\\spad{'s} are nonnegative integers. The multiplication is not commutative.")) (|mapGen| (($ (|Mapping| |#1| |#1|) $) "\\spad{mapGen(f,{} a1\\^e1 ... an\\^en)} returns \\spad{f(a1)\\^e1 ... f(an)\\^en}.")) (|mapExpon| (($ (|Mapping| (|NonNegativeInteger|) (|NonNegativeInteger|)) $) "\\spad{mapExpon(f,{} a1\\^e1 ... an\\^en)} returns \\spad{a1\\^f(e1) ... an\\^f(en)}.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(x,{} n)} returns the factor of the n^th monomial of \\spad{x}.")) (|nthExpon| (((|NonNegativeInteger|) $ (|Integer|)) "\\spad{nthExpon(x,{} n)} returns the exponent of the n^th monomial of \\spad{x}.")) (|factors| (((|List| (|Record| (|:| |gen| |#1|) (|:| |exp| (|NonNegativeInteger|)))) $) "\\spad{factors(a1\\^e1,{}...,{}an\\^en)} returns \\spad{[[a1,{} e1],{}...,{}[an,{} en]]}.")) (|size| (((|NonNegativeInteger|) $) "\\spad{size(x)} returns the number of monomials in \\spad{x}.")) (|overlap| (((|Record| (|:| |lm| $) (|:| |mm| $) (|:| |rm| $)) $ $) "\\spad{overlap(x,{} y)} returns \\spad{[l,{} m,{} r]} such that \\spad{x = l * m},{} \\spad{y = m * r} and \\spad{l} and \\spad{r} have no overlap,{} \\spadignore{i.e.} \\spad{overlap(l,{} r) = [l,{} 1,{} r]}.")) (|divide| (((|Union| (|Record| (|:| |lm| $) (|:| |rm| $)) "failed") $ $) "\\spad{divide(x,{} y)} returns the left and right exact quotients of \\spad{x} by \\spad{y},{} \\spadignore{i.e.} \\spad{[l,{} r]} such that \\spad{x = l * y * r},{} \"failed\" if \\spad{x} is not of the form \\spad{l * y * r}.")) (|rquo| (((|Union| $ "failed") $ $) "\\spad{rquo(x,{} y)} returns the exact right quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = q * y},{} \"failed\" if \\spad{x} is not of the form \\spad{q * y}.")) (|lquo| (((|Union| $ "failed") $ $) "\\spad{lquo(x,{} y)} returns the exact left quotient of \\spad{x} by \\spad{y} \\spadignore{i.e.} \\spad{q} such that \\spad{x = y * q},{} \"failed\" if \\spad{x} is not of the form \\spad{y * q}.")) (|hcrf| (($ $ $) "\\spad{hcrf(x,{} y)} returns the highest common right factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = a d} and \\spad{y = b d}.")) (|hclf| (($ $ $) "\\spad{hclf(x,{} y)} returns the highest common left factor of \\spad{x} and \\spad{y},{} \\spadignore{i.e.} the largest \\spad{d} such that \\spad{x = d a} and \\spad{y = d b}.")) (** (($ |#1| (|NonNegativeInteger|)) "\\spad{s ** n} returns the product of \\spad{s} by itself \\spad{n} times.")) (* (($ $ |#1|) "\\spad{x * s} returns the product of \\spad{x} by \\spad{s} on the right.") (($ |#1| $) "\\spad{s * x} returns the product of \\spad{x} by \\spad{s} on the left."))) @@ -1382,7 +1382,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-786)))) (-363) ((|constructor| (NIL "A category of domains which model machine arithmetic used by machines in the AXIOM-NAG link."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-364) ((|constructor| (NIL "This domain provides an interface to names in the file system."))) @@ -1394,13 +1394,13 @@ NIL NIL (-366 |n| |class| R) ((|constructor| (NIL "Generate the Free Lie Algebra over a ring \\spad{R} with identity; A \\spad{P}. Hall basis is generated by a package call to HallBasis.")) (|generator| (($ (|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"))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL (-367) ((|constructor| (NIL "Code to manipulate Fortran Output Stack")) (|topFortranOutputStack| (((|String|)) "\\spad{topFortranOutputStack()} returns the top element of the Fortran output stack")) (|pushFortranOutputStack| (((|Void|) (|String|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack") (((|Void|) (|FileName|)) "\\spad{pushFortranOutputStack(f)} pushes \\spad{f} onto the Fortran output stack")) (|popFortranOutputStack| (((|Void|)) "\\spad{popFortranOutputStack()} pops the Fortran output stack")) (|showFortranOutputStack| (((|Stack| (|String|))) "\\spad{showFortranOutputStack()} returns the Fortran output stack")) (|clearFortranOutputStack| (((|Stack| (|String|))) "\\spad{clearFortranOutputStack()} clears the Fortran output stack"))) NIL NIL -(-368 -2315 UP UPUP R) +(-368 -3539 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 @@ -1414,27 +1414,27 @@ NIL NIL (-371) ((|constructor| (NIL "\\axiomType{FortranProgramCategory} provides various models of FORTRAN subprograms. These can be transformed into actual FORTRAN code.")) (|outputAsFortran| (((|Void|) $) "\\axiom{outputAsFortran(\\spad{u})} translates \\axiom{\\spad{u}} into a legal FORTRAN subprogram."))) -((-3656 . T)) +((-4069 . T)) NIL (-372) ((|constructor| (NIL "\\axiomType{FortranFunctionCategory} is the category of arguments to NAG Library routines which return (sets of) function values.")) (|retractIfCan| (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Polynomial| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Integer|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Expression| (|Float|))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Fraction| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Fraction| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Polynomial| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Integer|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Expression| (|Float|))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-3656 . T)) +((-4069 . T)) NIL (-373) ((|constructor| (NIL "provides an interface to the boot code for calling Fortran")) (|setLegalFortranSourceExtensions| (((|List| (|String|)) (|List| (|String|))) "\\spad{setLegalFortranSourceExtensions(l)} \\undocumented{}")) (|outputAsFortran| (((|Void|) (|FileName|)) "\\spad{outputAsFortran(fn)} \\undocumented{}")) (|linkToFortran| (((|SExpression|) (|Symbol|) (|List| (|Symbol|)) (|TheSymbolTable|) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}t,{}lv)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|)) (|Symbol|)) "\\spad{linkToFortran(s,{}l,{}ll,{}lv,{}t)} \\undocumented{}") (((|SExpression|) (|Symbol|) (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|)))) (|List| (|List| (|Union| (|:| |array| (|List| (|Symbol|))) (|:| |scalar| (|Symbol|))))) (|List| (|Symbol|))) "\\spad{linkToFortran(s,{}l,{}ll,{}lv)} \\undocumented{}"))) NIL NIL -(-374 -4038 |returnType| -2455 |symbols|) +(-374 -4198 |returnType| -2134 |symbols|) ((|constructor| (NIL "\\axiomType{FortranProgram} allows the user to build and manipulate simple models of FORTRAN subprograms. These can then be transformed into actual FORTRAN notation.")) (|coerce| (($ (|Equation| (|Expression| (|Complex| (|Float|))))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Float|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|Integer|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|Complex| (|Float|)))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Float|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|Integer|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineComplex|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineFloat|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Equation| (|Expression| (|MachineInteger|)))) "\\spad{coerce(eq)} \\undocumented{}") (($ (|Expression| (|MachineComplex|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineFloat|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Expression| (|MachineInteger|))) "\\spad{coerce(e)} \\undocumented{}") (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(r)} \\undocumented{}") (($ (|List| (|FortranCode|))) "\\spad{coerce(lfc)} \\undocumented{}") (($ (|FortranCode|)) "\\spad{coerce(fc)} \\undocumented{}"))) NIL NIL -(-375 -2315 UP) +(-375 -3539 UP) ((|constructor| (NIL "\\indented{1}{Full partial fraction expansion of rational functions} Author: Manuel Bronstein Date Created: 9 December 1992 Date Last Updated: 6 October 1993 References: \\spad{M}.Bronstein & \\spad{B}.Salvy,{} \\indented{12}{Full Partial Fraction Decomposition of Rational Functions,{}} \\indented{12}{in Proceedings of ISSAC'93,{} Kiev,{} ACM Press.}")) (D (($ $ (|NonNegativeInteger|)) "\\spad{D(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{D(f)} returns the derivative of \\spad{f}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{} n)} returns the \\spad{n}-th derivative of \\spad{f}.") (($ $) "\\spad{differentiate(f)} returns the derivative of \\spad{f}.")) (|construct| (($ (|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|)))) "\\spad{construct(l)} is the inverse of fracPart.")) (|fracPart| (((|List| (|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |center| |#2|) (|:| |num| |#2|))) $) "\\spad{fracPart(f)} returns the list of summands of the fractional part of \\spad{f}.")) (|polyPart| ((|#2| $) "\\spad{polyPart(f)} returns the polynomial part of \\spad{f}.")) (|fullPartialFraction| (($ (|Fraction| |#2|)) "\\spad{fullPartialFraction(f)} returns \\spad{[p,{} [[j,{} Dj,{} Hj]...]]} such that \\spad{f = p(x) + \\sum_{[j,{}Dj,{}Hj] in l} \\sum_{Dj(a)=0} Hj(a)/(x - a)\\^j}.")) (+ (($ |#2| $) "\\spad{p + x} returns the sum of \\spad{p} and \\spad{x}"))) NIL NIL (-376 R) ((|constructor| (NIL "A set \\spad{S} is PatternMatchable over \\spad{R} if \\spad{S} can lift the pattern-matching functions of \\spad{S} over the integers and float to itself (necessary for matching in towers)."))) -((-3656 . T)) +((-4069 . T)) NIL (-377 S) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|NonNegativeInteger|)) "\\spad{primeFrobenius(a,{}s)} returns \\spad{a**(p**s)} where \\spad{p} is the characteristic.") (($ $) "\\spad{primeFrobenius(a)} returns \\spad{a ** p} where \\spad{p} is the characteristic.")) (|discreteLog| (((|Union| (|NonNegativeInteger|) "failed") $ $) "\\spad{discreteLog(b,{}a)} computes \\spad{s} with \\spad{b**s = a} if such an \\spad{s} exists.")) (|order| (((|OnePointCompletion| (|PositiveInteger|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) @@ -1442,15 +1442,15 @@ NIL NIL (-378) ((|constructor| (NIL "FieldOfPrimeCharacteristic is the category of fields of prime characteristic,{} \\spadignore{e.g.} finite fields,{} algebraic closures of fields of prime characteristic,{} transcendental extensions of of fields of prime characteristic.")) (|primeFrobenius| (($ $ (|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|)) $) "\\spad{order(a)} computes the order of an element in the multiplicative group of the field. Error: if \\spad{a} is 0."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-379 S) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) NIL -((|HasAttribute| |#1| (QUOTE -4227)) (|HasAttribute| |#1| (QUOTE -4235))) +((|HasAttribute| |#1| (QUOTE -4231)) (|HasAttribute| |#1| (QUOTE -4239))) (-380) ((|constructor| (NIL "This category is intended as a model for floating point systems. A floating point system is a model for the real numbers. In fact,{} it is an approximation in the sense that not all real numbers are exactly representable by floating point numbers. A floating point system is characterized by the following: \\blankline \\indented{2}{1: \\spadfunFrom{base}{FloatingPointSystem} of the \\spadfunFrom{exponent}{FloatingPointSystem}.} \\indented{9}{(actual implemenations are usually binary or decimal)} \\indented{2}{2: \\spadfunFrom{precision}{FloatingPointSystem} of the \\spadfunFrom{mantissa}{FloatingPointSystem} (arbitrary or fixed)} \\indented{2}{3: rounding error for operations} \\blankline Because a Float is an approximation to the real numbers,{} even though it is defined to be a join of a Field and OrderedRing,{} some of the attributes do not hold. In particular associative(\\spad{\"+\"}) does not hold. Algorithms defined over a field need special considerations when the field is a floating point system.")) (|max| (($) "\\spad{max()} returns the maximum floating point number.")) (|min| (($) "\\spad{min()} returns the minimum floating point number.")) (|decreasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{decreasePrecision(n)} decreases the current \\spadfunFrom{precision}{FloatingPointSystem} precision by \\spad{n} decimal digits.")) (|increasePrecision| (((|PositiveInteger|) (|Integer|)) "\\spad{increasePrecision(n)} increases the current \\spadfunFrom{precision}{FloatingPointSystem} by \\spad{n} decimal digits.")) (|precision| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(n)} set the precision in the base to \\spad{n} decimal digits.") (((|PositiveInteger|)) "\\spad{precision()} returns the precision in digits base.")) (|digits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{digits(d)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{d} digits.") (((|PositiveInteger|)) "\\spad{digits()} returns ceiling\\spad{'s} precision in decimal digits.")) (|bits| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{bits(n)} set the \\spadfunFrom{precision}{FloatingPointSystem} to \\spad{n} bits.") (((|PositiveInteger|)) "\\spad{bits()} returns ceiling\\spad{'s} precision in bits.")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(x)} returns the mantissa part of \\spad{x}.")) (|exponent| (((|Integer|) $) "\\spad{exponent(x)} returns the \\spadfunFrom{exponent}{FloatingPointSystem} part of \\spad{x}.")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the \\spadfunFrom{exponent}{FloatingPointSystem}.")) (|order| (((|Integer|) $) "\\spad{order x} is the order of magnitude of \\spad{x}. Note: \\spad{base ** order x <= |x| < base ** (1 + order x)}.")) (|float| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{float(a,{}e,{}b)} returns \\spad{a * b ** e}.") (($ (|Integer|) (|Integer|)) "\\spad{float(a,{}e)} returns \\spad{a * base() ** e}.")) (|approximate| ((|attribute|) "\\spad{approximate} means \"is an approximation to the real numbers\"."))) -((-2562 . T) (-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-381 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."))) @@ -1462,15 +1462,15 @@ NIL NIL (-383 S) ((|constructor| (NIL "Fraction takes an IntegralDomain \\spad{S} and produces the domain of Fractions with numerators and denominators from \\spad{S}. If \\spad{S} is also a GcdDomain,{} then \\spad{gcd}\\spad{'s} between numerator and denominator will be cancelled during all operations.")) (|canonical| ((|attribute|) "\\spad{canonical} means that equal elements are in fact identical."))) -((-4231 -12 (|has| |#1| (-6 -4242)) (|has| |#1| (-427)) (|has| |#1| (-6 -4231))) (-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-759))) (-3262 (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-786)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-1063))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-508))) (-12 (|HasAttribute| |#1| (QUOTE -4242)) (|HasAttribute| |#1| (QUOTE -4231)) (|HasCategory| |#1| (QUOTE (-427)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +((-4235 -12 (|has| |#1| (-6 -4246)) (|has| |#1| (-427)) (|has| |#1| (-6 -4235))) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (QUOTE (-759))) (-3172 (|HasCategory| |#1| (QUOTE (-759))) (|HasCategory| |#1| (QUOTE (-786)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-1063))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-767)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-508))) (-12 (|HasAttribute| |#1| (QUOTE -4246)) (|HasAttribute| |#1| (QUOTE -4235)) (|HasCategory| |#1| (QUOTE (-427)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-384 S R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#2|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#2|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#2|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#2|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#2|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#2|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#2|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#2|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) NIL NIL (-385 R UP) ((|constructor| (NIL "A \\spadtype{FramedAlgebra} is a \\spadtype{FiniteRankAlgebra} together with a fixed \\spad{R}-module basis.")) (|regularRepresentation| (((|Matrix| |#1|) $) "\\spad{regularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed basis.")) (|discriminant| ((|#1|) "\\spad{discriminant()} = determinant(traceMatrix()).")) (|traceMatrix| (((|Matrix| |#1|)) "\\spad{traceMatrix()} is the \\spad{n}-by-\\spad{n} matrix ( \\spad{Tr(\\spad{vi} * vj)} ),{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}..,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([v1,{}...,{}vm])} returns the coordinates of the \\spad{vi}\\spad{'s} with to the fixed basis. The coordinates of \\spad{vi} are contained in the \\spad{i}th row of the matrix returned by this function.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL (-386 A S) ((|constructor| (NIL "\\indented{2}{A is fully retractable to \\spad{B} means that A is retractable to \\spad{B},{} and,{}} \\indented{2}{in addition,{} if \\spad{B} is retractable to the integers or rational} \\indented{2}{numbers then so is A.} \\indented{2}{In particular,{} what we are asserting is that there are no integers} \\indented{2}{(rationals) in A which don\\spad{'t} retract into \\spad{B}.} Date Created: March 1990 Date Last Updated: 9 April 1991"))) @@ -1484,11 +1484,11 @@ NIL ((|constructor| (NIL "\\indented{1}{Lifting of morphisms to fractional ideals.} Author: Manuel Bronstein Date Created: 1 Feb 1989 Date Last Updated: 27 Feb 1990 Keywords: ideal,{} algebra,{} module.")) (|map| (((|FractionalIdeal| |#5| |#6| |#7| |#8|) (|Mapping| |#5| |#1|) (|FractionalIdeal| |#1| |#2| |#3| |#4|)) "\\spad{map(f,{}i)} \\undocumented{}"))) NIL NIL -(-389 R -2315 UP A) +(-389 R -3539 UP A) ((|constructor| (NIL "Fractional ideals in a framed algebra.")) (|randomLC| ((|#4| (|NonNegativeInteger|) (|Vector| |#4|)) "\\spad{randomLC(n,{}x)} should be local but conditional.")) (|minimize| (($ $) "\\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)}."))) -((-4241 . T)) +((-4245 . T)) NIL -(-390 R -2315 UP A |ibasis|) +(-390 R -3539 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|) $) "\\spad{basis((f1,{}...,{}fn))} = the vector \\spad{[f1,{}...,{}fn]}."))) NIL ((|HasCategory| |#4| (LIST (QUOTE -964) (|devaluate| |#2|)))) @@ -1502,12 +1502,12 @@ NIL ((|HasCategory| |#2| (QUOTE (-339)))) (-393 R) ((|constructor| (NIL "FramedNonAssociativeAlgebra(\\spad{R}) is a \\spadtype{FiniteRankNonAssociativeAlgebra} (\\spadignore{i.e.} a non associative algebra over \\spad{R} which is a free \\spad{R}-module of finite rank) over a commutative ring \\spad{R} together with a fixed \\spad{R}-module basis.")) (|apply| (($ (|Matrix| |#1|) $) "\\spad{apply(m,{}a)} defines a left operation of \\spad{n} by \\spad{n} matrices where \\spad{n} is the rank of the algebra in terms of matrix-vector multiplication,{} this is a substitute for a left module structure. Error: if shape of matrix doesn\\spad{'t} fit.")) (|rightRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{rightRankPolynomial()} calculates the right minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|leftRankPolynomial| (((|SparseUnivariatePolynomial| (|Polynomial| |#1|))) "\\spad{leftRankPolynomial()} calculates the left minimal polynomial of the generic element in the algebra,{} defined by the same structural constants over the polynomial ring in symbolic coefficients with respect to the fixed basis.")) (|rightRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{rightRegularRepresentation(a)} returns the matrix of the linear map defined by right multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|leftRegularRepresentation| (((|Matrix| |#1|) $) "\\spad{leftRegularRepresentation(a)} returns the matrix of the linear map defined by left multiplication by \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|rightTraceMatrix| (((|Matrix| |#1|)) "\\spad{rightTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|leftTraceMatrix| (((|Matrix| |#1|)) "\\spad{leftTraceMatrix()} is the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|rightDiscriminant| ((|#1|) "\\spad{rightDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the right trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(rightTraceMatrix())}.")) (|leftDiscriminant| ((|#1|) "\\spad{leftDiscriminant()} returns the determinant of the \\spad{n}-by-\\spad{n} matrix whose element at the \\spad{i}\\spad{-}th row and \\spad{j}\\spad{-}th column is given by the left trace of the product \\spad{vi*vj},{} where \\spad{v1},{}...,{}\\spad{vn} are the elements of the fixed \\spad{R}-module basis. Note: the same as \\spad{determinant(leftTraceMatrix())}.")) (|convert| (($ (|Vector| |#1|)) "\\spad{convert([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{convert(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|represents| (($ (|Vector| |#1|)) "\\spad{represents([a1,{}...,{}an])} returns \\spad{a1*v1 + ... + an*vn},{} where \\spad{v1},{} ...,{} \\spad{vn} are the elements of the fixed \\spad{R}-module basis.")) (|conditionsForIdempotents| (((|List| (|Polynomial| |#1|))) "\\spad{conditionsForIdempotents()} determines a complete list of polynomial equations for the coefficients of idempotents with respect to the fixed \\spad{R}-module basis.")) (|structuralConstants| (((|Vector| (|Matrix| |#1|))) "\\spad{structuralConstants()} calculates the structural constants \\spad{[(gammaijk) for k in 1..rank()]} defined by \\spad{\\spad{vi} * vj = gammaij1 * v1 + ... + gammaijn * vn},{} where \\spad{v1},{}...,{}\\spad{vn} is the fixed \\spad{R}-module basis.")) (|elt| ((|#1| $ (|Integer|)) "\\spad{elt(a,{}i)} returns the \\spad{i}-th coefficient of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|coordinates| (((|Matrix| |#1|) (|Vector| $)) "\\spad{coordinates([a1,{}...,{}am])} returns a matrix whose \\spad{i}-th row is formed by the coordinates of \\spad{\\spad{ai}} with respect to the fixed \\spad{R}-module basis.") (((|Vector| |#1|) $) "\\spad{coordinates(a)} returns the coordinates of \\spad{a} with respect to the fixed \\spad{R}-module basis.")) (|basis| (((|Vector| $)) "\\spad{basis()} returns the fixed \\spad{R}-module basis."))) -((-4241 |has| |#1| (-515)) (-4239 . T) (-4238 . T)) +((-4245 |has| |#1| (-515)) (-4243 . T) (-4242 . T)) NIL (-394 R) ((|constructor| (NIL "\\spadtype{Factored} creates a domain whose objects are kept in factored form as long as possible. Thus certain operations like multiplication and \\spad{gcd} are relatively easy to do. Others,{} like addition require somewhat more work,{} and unless the argument domain provides a factor function,{} the result may not be completely factored. Each object consists of a unit and a list of factors,{} where a factor has a member of \\spad{R} (the \"base\"),{} and exponent and a flag indicating what is known about the base. A flag may be one of \"nil\",{} \"sqfr\",{} \"irred\" or \"prime\",{} which respectively mean that nothing is known about the base,{} it is square-free,{} it is irreducible,{} or it is prime. The current restriction to integral domains allows simplification to be performed without worrying about multiplication order.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(u)} returns a rational number if \\spad{u} really is one,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(u)} assumes spadvar{\\spad{u}} is actually a rational number and does the conversion to rational number (see \\spadtype{Fraction Integer}).")) (|rational?| (((|Boolean|) $) "\\spad{rational?(u)} tests if \\spadvar{\\spad{u}} is actually a rational number (see \\spadtype{Fraction Integer}).")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}u)} maps the function \\userfun{\\spad{fn}} across the factors of \\spadvar{\\spad{u}} and creates a new factored object. Note: this clears the information flags (sets them to \"nil\") because the effect of \\userfun{\\spad{fn}} is clearly not known in general.")) (|unitNormalize| (($ $) "\\spad{unitNormalize(u)} normalizes the unit part of the factorization. For example,{} when working with factored integers,{} this operation will ensure that the bases are all positive integers.")) (|unit| ((|#1| $) "\\spad{unit(u)} extracts the unit part of the factorization.")) (|flagFactor| (($ |#1| (|Integer|) (|Union| "nil" "sqfr" "irred" "prime")) "\\spad{flagFactor(base,{}exponent,{}flag)} creates a factored object with a single factor whose \\spad{base} is asserted to be properly described by the information \\spad{flag}.")) (|sqfrFactor| (($ |#1| (|Integer|)) "\\spad{sqfrFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be square-free (flag = \"sqfr\").")) (|primeFactor| (($ |#1| (|Integer|)) "\\spad{primeFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be prime (flag = \"prime\").")) (|numberOfFactors| (((|NonNegativeInteger|) $) "\\spad{numberOfFactors(u)} returns the number of factors in \\spadvar{\\spad{u}}.")) (|nthFlag| (((|Union| "nil" "sqfr" "irred" "prime") $ (|Integer|)) "\\spad{nthFlag(u,{}n)} returns the information flag of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} \"nil\" is returned.")) (|nthFactor| ((|#1| $ (|Integer|)) "\\spad{nthFactor(u,{}n)} returns the base of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 1 is returned. If \\spadvar{\\spad{u}} consists only of a unit,{} the unit is returned.")) (|nthExponent| (((|Integer|) $ (|Integer|)) "\\spad{nthExponent(u,{}n)} returns the exponent of the \\spad{n}th factor of \\spadvar{\\spad{u}}. If \\spadvar{\\spad{n}} is not a valid index for a factor (for example,{} less than 1 or too big),{} 0 is returned.")) (|irreducibleFactor| (($ |#1| (|Integer|)) "\\spad{irreducibleFactor(base,{}exponent)} creates a factored object with a single factor whose \\spad{base} is asserted to be irreducible (flag = \"irred\").")) (|factors| (((|List| (|Record| (|:| |factor| |#1|) (|:| |exponent| (|Integer|)))) $) "\\spad{factors(u)} returns a list of the factors in a form suitable for iteration. That is,{} it returns a list where each element is a record containing a base and exponent. The original object is the product of all the factors and the unit (which can be extracted by \\axiom{unit(\\spad{u})}).")) (|nilFactor| (($ |#1| (|Integer|)) "\\spad{nilFactor(base,{}exponent)} creates a factored object with a single factor with no information about the kind of \\spad{base} (flag = \"nil\").")) (|factorList| (((|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|)))) $) "\\spad{factorList(u)} returns the list of factors with flags (for use by factoring code).")) (|makeFR| (($ |#1| (|List| (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#1|) (|:| |xpnt| (|Integer|))))) "\\spad{makeFR(unit,{}listOfFactors)} creates a factored object (for use by factoring code).")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of the first factor of \\spadvar{\\spad{u}},{} or 0 if the factored form consists solely of a unit.")) (|expand| ((|#1| $) "\\spad{expand(f)} multiplies the unit and factors together,{} yielding an \"unfactored\" object. Note: this is purposely not called \\spadfun{coerce} which would cause the interpreter to do this automatically."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -263) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1126))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-1126)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-427)))) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -286) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -263) (QUOTE $) (QUOTE $))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1127))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-1127)))) (|HasCategory| |#1| (QUOTE (-949))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-427)))) (-395 R) ((|constructor| (NIL "\\spadtype{FactoredFunctionUtilities} implements some utility functions for manipulating factored objects.")) (|mergeFactors| (((|Factored| |#1|) (|Factored| |#1|) (|Factored| |#1|)) "\\spad{mergeFactors(u,{}v)} is used when the factorizations of \\spadvar{\\spad{u}} and \\spadvar{\\spad{v}} are known to be disjoint,{} \\spadignore{e.g.} resulting from a content/primitive part split. Essentially,{} it creates a new factored object by multiplying the units together and appending the lists of factors.")) (|refine| (((|Factored| |#1|) (|Factored| |#1|) (|Mapping| (|Factored| |#1|) |#1|)) "\\spad{refine(u,{}fn)} is used to apply the function \\userfun{\\spad{fn}} to each factor of \\spadvar{\\spad{u}} and then build a new factored object from the results. For example,{} if \\spadvar{\\spad{u}} were created by calling \\spad{nilFactor(10,{}2)} then \\spad{refine(u,{}factor)} would create a factored object equal to that created by \\spad{factor(100)} or \\spad{primeFactor(2,{}2) * primeFactor(5,{}2)}."))) NIL @@ -1534,17 +1534,17 @@ NIL ((|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-344)))) (-401 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|) $) "\\spad{cardinality(u)} returns the number of elements of \\spad{u}. Note: \\axiom{cardinality(\\spad{u}) = \\#u}."))) -((-4244 . T) (-4234 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4238 . T) (-4249 . T) (-4069 . T)) NIL -(-402 R -2315) +(-402 R -3539) ((|constructor| (NIL "\\spadtype{FunctionSpaceComplexIntegration} provides functions for the indefinite integration of complex-valued functions.")) (|complexIntegrate| ((|#2| |#2| (|Symbol|)) "\\spad{complexIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable.")) (|internalIntegrate0| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate0 should} be a local function,{} but is conditional.")) (|internalIntegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns the integral of \\spad{f(x)dx} where \\spad{x} is viewed as a complex variable."))) NIL NIL (-403 R E) ((|constructor| (NIL "\\indented{1}{Author: James Davenport} Date Created: 17 April 1992 Date Last Updated: Basic Functions: Related Constructors: Also See: AMS Classifications: Keywords: References: Description:")) (|makeCos| (($ |#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"))) -((-4231 -12 (|has| |#1| (-6 -4231)) (|has| |#2| (-6 -4231))) (-4238 . T) (-4239 . T) (-4241 . T)) -((-12 (|HasAttribute| |#1| (QUOTE -4231)) (|HasAttribute| |#2| (QUOTE -4231)))) -(-404 R -2315) +((-4235 -12 (|has| |#1| (-6 -4235)) (|has| |#2| (-6 -4235))) (-4242 . T) (-4243 . T) (-4245 . T)) +((-12 (|HasAttribute| |#1| (QUOTE -4235)) (|HasAttribute| |#2| (QUOTE -4235)))) +(-404 R -3539) ((|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 @@ -1554,17 +1554,17 @@ NIL ((|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-25))) (|HasCategory| |#2| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-1028))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (-406 R) ((|constructor| (NIL "A space of formal functions with arguments in an arbitrary ordered set.")) (|univariate| (((|Fraction| (|SparseUnivariatePolynomial| $)) $ (|Kernel| $)) "\\spad{univariate(f,{} k)} returns \\spad{f} viewed as a univariate fraction in \\spad{k}.")) (/ (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $)) (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{p1/p2} returns the quotient of \\spad{p1} and \\spad{p2} as an element of \\%.")) (|denominator| (($ $) "\\spad{denominator(f)} returns the denominator of \\spad{f} converted to \\%.")) (|denom| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|convert| (($ (|Factored| $)) "\\spad{convert(f1\\^e1 ... fm\\^em)} returns \\spad{(f1)\\^e1 ... (fm)\\^em} as an element of \\%,{} using formal kernels created using a \\spadfunFrom{paren}{ExpressionSpace}.")) (|isPower| (((|Union| (|Record| (|:| |val| $) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|numerator| (($ $) "\\spad{numerator(f)} returns the numerator of \\spad{f} converted to \\%.")) (|numer| (((|SparseMultivariatePolynomial| |#1| (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{R} if \\spad{R} is an integral domain. If not,{} then numer(\\spad{f}) = \\spad{f} viewed as a polynomial in the kernels over \\spad{R}.")) (|coerce| (($ (|Fraction| (|Polynomial| (|Fraction| |#1|)))) "\\spad{coerce(f)} returns \\spad{f} as an element of \\%.") (($ (|Polynomial| (|Fraction| |#1|))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.") (($ (|Fraction| |#1|)) "\\spad{coerce(q)} returns \\spad{q} as an element of \\%.") (($ (|SparseMultivariatePolynomial| |#1| (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} as an element of \\%.")) (|isMult| (((|Union| (|Record| (|:| |coef| (|Integer|)) (|:| |var| (|Kernel| $))) "failed") $) "\\spad{isMult(p)} returns \\spad{[n,{} x]} if \\spad{p = n * x} and \\spad{n <> 0}.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if \\spad{p = m1 +...+ mn} and \\spad{n > 1}.")) (|isExpt| (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|Symbol|)) "\\spad{isExpt(p,{}f)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = f(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $ (|BasicOperator|)) "\\spad{isExpt(p,{}op)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0} and \\spad{x = op(a)}.") (((|Union| (|Record| (|:| |var| (|Kernel| $)) (|:| |exponent| (|Integer|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1*...*an} and \\spad{n > 1}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{x**n} returns \\spad{x} * \\spad{x} * \\spad{x} * ... * \\spad{x} (\\spad{n} times).")) (|eval| (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ $)) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a)**n} in \\spad{x} by \\spad{f(a)} for any \\spad{a}.") (($ $ (|Symbol|) (|NonNegativeInteger|) (|Mapping| $ (|List| $))) "\\spad{eval(x,{} s,{} n,{} f)} replaces every \\spad{s(a1,{}...,{}am)**n} in \\spad{x} by \\spad{f(a1,{}...,{}am)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ (|List| $)))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a1,{}...,{}an)**ni} in \\spad{x} by \\spad{\\spad{fi}(a1,{}...,{}an)} for any a1,{}...,{}am.") (($ $ (|List| (|Symbol|)) (|List| (|NonNegativeInteger|)) (|List| (|Mapping| $ $))) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [n1,{}...,{}nm],{} [f1,{}...,{}fm])} replaces every \\spad{\\spad{si}(a)**ni} in \\spad{x} by \\spad{\\spad{fi}(a)} for any \\spad{a}.") (($ $ (|List| (|BasicOperator|)) (|List| $) (|Symbol|)) "\\spad{eval(x,{} [s1,{}...,{}sm],{} [f1,{}...,{}fm],{} y)} replaces every \\spad{\\spad{si}(a)} in \\spad{x} by \\spad{\\spad{fi}(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $ (|BasicOperator|) $ (|Symbol|)) "\\spad{eval(x,{} s,{} f,{} y)} replaces every \\spad{s(a)} in \\spad{x} by \\spad{f(y)} with \\spad{y} replaced by \\spad{a} for any \\spad{a}.") (($ $) "\\spad{eval(f)} unquotes all the quoted operators in \\spad{f}.") (($ $ (|List| (|Symbol|))) "\\spad{eval(f,{} [foo1,{}...,{}foon])} unquotes all the \\spad{fooi}\\spad{'s} in \\spad{f}.") (($ $ (|Symbol|)) "\\spad{eval(f,{} foo)} unquotes all the foo\\spad{'s} in \\spad{f}.")) (|applyQuote| (($ (|Symbol|) (|List| $)) "\\spad{applyQuote(foo,{} [x1,{}...,{}xn])} returns \\spad{'foo(x1,{}...,{}xn)}.") (($ (|Symbol|) $ $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z,{} t)} returns \\spad{'foo(x,{}y,{}z,{}t)}.") (($ (|Symbol|) $ $ $) "\\spad{applyQuote(foo,{} x,{} y,{} z)} returns \\spad{'foo(x,{}y,{}z)}.") (($ (|Symbol|) $ $) "\\spad{applyQuote(foo,{} x,{} y)} returns \\spad{'foo(x,{}y)}.") (($ (|Symbol|) $) "\\spad{applyQuote(foo,{} x)} returns \\spad{'foo(x)}.")) (|variables| (((|List| (|Symbol|)) $) "\\spad{variables(f)} returns the list of all the variables of \\spad{f}.")) (|ground| ((|#1| $) "\\spad{ground(f)} returns \\spad{f} as an element of \\spad{R}. An error occurs if \\spad{f} is not an element of \\spad{R}.")) (|ground?| (((|Boolean|) $) "\\spad{ground?(f)} tests if \\spad{f} is an element of \\spad{R}."))) -((-4241 -3262 (|has| |#1| (-973)) (|has| |#1| (-448))) (-4239 |has| |#1| (-158)) (-4238 |has| |#1| (-158)) ((-4246 "*") |has| |#1| (-515)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-515)) (-4236 |has| |#1| (-515)) (-3656 . T)) +((-4245 -3172 (|has| |#1| (-973)) (|has| |#1| (-448))) (-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) ((-4250 "*") |has| |#1| (-515)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-515)) (-4240 |has| |#1| (-515)) (-4069 . T)) NIL -(-407 R -2315) +(-407 R -3539) ((|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 -(-408 R -2315) +(-408 R -3539) ((|constructor| (NIL "FunctionsSpacePrimitiveElement provides functions to compute primitive elements in functions spaces.")) (|primitiveElement| (((|Record| (|:| |primelt| |#2|) (|:| |pol1| (|SparseUnivariatePolynomial| |#2|)) (|:| |pol2| (|SparseUnivariatePolynomial| |#2|)) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) |#2| |#2|) "\\spad{primitiveElement(a1,{} a2)} returns \\spad{[a,{} q1,{} q2,{} q]} such that \\spad{k(a1,{} a2) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The minimal polynomial for a2 may involve \\spad{a1},{} but the minimal polynomial for \\spad{a1} may not involve a2; This operations uses \\spadfun{resultant}.") (((|Record| (|:| |primelt| |#2|) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#2|))) (|:| |prim| (|SparseUnivariatePolynomial| |#2|))) (|List| |#2|)) "\\spad{primitiveElement([a1,{}...,{}an])} returns \\spad{[a,{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}."))) NIL ((|HasCategory| |#2| (QUOTE (-27)))) -(-409 R -2315) +(-409 R -3539) ((|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 @@ -1572,7 +1572,7 @@ NIL ((|constructor| (NIL "Creates and manipulates objects which correspond to the basic FORTRAN data types: REAL,{} INTEGER,{} COMPLEX,{} LOGICAL and CHARACTER")) (= (((|Boolean|) $ $) "\\spad{x=y} tests for equality")) (|logical?| (((|Boolean|) $) "\\spad{logical?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type LOGICAL.")) (|character?| (((|Boolean|) $) "\\spad{character?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type CHARACTER.")) (|doubleComplex?| (((|Boolean|) $) "\\spad{doubleComplex?(t)} tests whether \\spad{t} is equivalent to the (non-standard) FORTRAN type DOUBLE COMPLEX.")) (|complex?| (((|Boolean|) $) "\\spad{complex?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type COMPLEX.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type INTEGER.")) (|double?| (((|Boolean|) $) "\\spad{double?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type DOUBLE PRECISION")) (|real?| (((|Boolean|) $) "\\spad{real?(t)} tests whether \\spad{t} is equivalent to the FORTRAN type REAL.")) (|coerce| (((|SExpression|) $) "\\spad{coerce(x)} returns the \\spad{s}-expression associated with \\spad{x}") (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol associated with \\spad{x}") (($ (|Symbol|)) "\\spad{coerce(s)} transforms the symbol \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of real,{} complex,{}double precision,{} logical,{} integer,{} character,{} REAL,{} COMPLEX,{} LOGICAL,{} INTEGER,{} CHARACTER,{} DOUBLE PRECISION") (($ (|String|)) "\\spad{coerce(s)} transforms the string \\spad{s} into an element of FortranScalarType provided \\spad{s} is one of \"real\",{} \"double precision\",{} \"complex\",{} \"logical\",{} \"integer\",{} \"character\",{} \"REAL\",{} \"COMPLEX\",{} \"LOGICAL\",{} \"INTEGER\",{} \"CHARACTER\",{} \"DOUBLE PRECISION\""))) NIL NIL -(-411 R -2315 UP) +(-411 R -3539 UP) ((|constructor| (NIL "\\indented{1}{Used internally by IR2F} Author: Manuel Bronstein Date Created: 12 May 1988 Date Last Updated: 22 September 1993 Keywords: function,{} space,{} polynomial,{} factoring")) (|anfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) "failed") |#3|) "\\spad{anfactor(p)} tries to factor \\spad{p} over algebraic numbers,{} returning \"failed\" if it cannot")) (|UP2ifCan| (((|Union| (|:| |overq| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) (|:| |overan| (|SparseUnivariatePolynomial| (|AlgebraicNumber|))) (|:| |failed| (|Boolean|))) |#3|) "\\spad{UP2ifCan(x)} should be local but conditional.")) (|qfactor| (((|Union| (|Factored| (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "failed") |#3|) "\\spad{qfactor(p)} tries to factor \\spad{p} over fractions of integers,{} returning \"failed\" if it cannot")) (|ffactor| (((|Factored| |#3|) |#3|) "\\spad{ffactor(p)} tries to factor a univariate polynomial \\spad{p} over \\spad{F}"))) NIL ((|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-47))))) @@ -1590,17 +1590,17 @@ NIL NIL (-415) ((|constructor| (NIL "\\axiomType{FortranVectorCategory} provides support for producing Functions and Subroutines when the input to these is an AXIOM object of type \\axiomType{Vector} or in domains involving \\axiomType{FortranCode}.")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|Vector| (|MachineFloat|))) "\\spad{coerce(v)} produces an ASP which returns the value of \\spad{v}."))) -((-3656 . T)) +((-4069 . T)) NIL (-416) ((|constructor| (NIL "\\axiomType{FortranVectorFunctionCategory} is the catagory of arguments to NAG Library routines which return the values of vectors of functions.")) (|retractIfCan| (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Polynomial| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Integer|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (((|Union| $ "failed") (|Vector| (|Expression| (|Float|)))) "\\spad{retractIfCan(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|retract| (($ (|Vector| (|Fraction| (|Polynomial| (|Integer|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Fraction| (|Polynomial| (|Float|))))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Polynomial| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Integer|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}") (($ (|Vector| (|Expression| (|Float|)))) "\\spad{retract(e)} tries to convert \\spad{e} into an ASP,{} checking that \\indented{1}{legal Fortran-77 is produced.}")) (|coerce| (($ (|Record| (|:| |localSymbols| (|SymbolTable|)) (|:| |code| (|List| (|FortranCode|))))) "\\spad{coerce(e)} takes the component of \\spad{e} from \\spadtype{List FortranCode} and uses it as the body of the ASP,{} making the declarations in the \\spadtype{SymbolTable} component.") (($ (|FortranCode|)) "\\spad{coerce(e)} takes an object from \\spadtype{FortranCode} and \\indented{1}{uses it as the body of an ASP.}") (($ (|List| (|FortranCode|))) "\\spad{coerce(e)} takes an object from \\spadtype{List FortranCode} and \\indented{1}{uses it as the body of an ASP.}"))) -((-3656 . T)) +((-4069 . T)) NIL (-417 UP) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizer} provides functions to factor resolvents.")) (|btwFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|) (|Set| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{btwFact(p,{}sqf,{}pd,{}r)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors). \\spad{pd} is the \\spadtype{Set} of possible degrees. \\spad{r} is a lower bound for the number of factors of \\spad{p}. Please do not use this function in your code because its design may change.")) (|henselFact| (((|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|)))))) |#1| (|Boolean|)) "\\spad{henselFact(p,{}sqf)} returns the factorization of \\spad{p},{} the result is a Record such that \\spad{contp=}content \\spad{p},{} \\spad{factors=}List of irreducible factors of \\spad{p} with exponent. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).")) (|factorOfDegree| (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|) (|Boolean|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r,{}sqf)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors. If \\spad{sqf=true} the polynomial is assumed to be square free (\\spadignore{i.e.} without repeated factors).") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees},{} and that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorOfDegree(d,{}p,{}listOfDegrees)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1| (|NonNegativeInteger|)) "\\spad{factorOfDegree(d,{}p,{}r)} returns a factor of \\spad{p} of degree \\spad{d} knowing that \\spad{p} has at least \\spad{r} factors.") (((|Union| |#1| "failed") (|PositiveInteger|) |#1|) "\\spad{factorOfDegree(d,{}p)} returns a factor of \\spad{p} of degree \\spad{d}.")) (|factorSquareFree| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factorSquareFree(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factorSquareFree(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors. \\spad{f} is supposed not having any repeated factor (this is not checked).") (((|Factored| |#1|) |#1|) "\\spad{factorSquareFree(p)} returns the factorization of \\spad{p} which is supposed not having any repeated factor (this is not checked).")) (|factor| (((|Factored| |#1|) |#1| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{factor(p,{}d,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{d} divides the degree of all factors of \\spad{p} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|)) (|NonNegativeInteger|)) "\\spad{factor(p,{}listOfDegrees,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm,{} knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees} and that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1| (|List| (|NonNegativeInteger|))) "\\spad{factor(p,{}listOfDegrees)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has for possible splitting of its degree \\spad{listOfDegrees}.") (((|Factored| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{factor(p,{}r)} factorizes the polynomial \\spad{p} using the single factor bound algorithm and knowing that \\spad{p} has at least \\spad{r} factors.") (((|Factored| |#1|) |#1|) "\\spad{factor(p)} returns the factorization of \\spad{p} over the integers.")) (|tryFunctionalDecomposition| (((|Boolean|) (|Boolean|)) "\\spad{tryFunctionalDecomposition(b)} chooses whether factorizers have to look for functional decomposition of polynomials (\\spad{true}) or not (\\spad{false}). Returns the previous value.")) (|tryFunctionalDecomposition?| (((|Boolean|)) "\\spad{tryFunctionalDecomposition?()} returns \\spad{true} if factorizers try functional decomposition of polynomials before factoring them.")) (|eisensteinIrreducible?| (((|Boolean|) |#1|) "\\spad{eisensteinIrreducible?(p)} returns \\spad{true} if \\spad{p} can be shown to be irreducible by Eisenstein\\spad{'s} criterion,{} \\spad{false} is inconclusive.")) (|useEisensteinCriterion| (((|Boolean|) (|Boolean|)) "\\spad{useEisensteinCriterion(b)} chooses whether factorizers check Eisenstein\\spad{'s} criterion before factoring: \\spad{true} for using it,{} \\spad{false} else. Returns the previous value.")) (|useEisensteinCriterion?| (((|Boolean|)) "\\spad{useEisensteinCriterion?()} returns \\spad{true} if factorizers check Eisenstein\\spad{'s} criterion before factoring.")) (|useSingleFactorBound| (((|Boolean|) (|Boolean|)) "\\spad{useSingleFactorBound(b)} chooses the algorithm to be used by the factorizers: \\spad{true} for algorithm with single factor bound,{} \\spad{false} for algorithm with overall bound. Returns the previous value.")) (|useSingleFactorBound?| (((|Boolean|)) "\\spad{useSingleFactorBound?()} returns \\spad{true} if algorithm with single factor bound is used for factorization,{} \\spad{false} for algorithm with overall bound.")) (|modularFactor| (((|Record| (|:| |prime| (|Integer|)) (|:| |factors| (|List| |#1|))) |#1|) "\\spad{modularFactor(f)} chooses a \"good\" prime and returns the factorization of \\spad{f} modulo this prime in a form that may be used by \\spadfunFrom{completeHensel}{GeneralHenselPackage}. If prime is zero it means that \\spad{f} has been proved to be irreducible over the integers or that \\spad{f} is a unit (\\spadignore{i.e.} 1 or \\spad{-1}). \\spad{f} shall be primitive (\\spadignore{i.e.} content(\\spad{p})\\spad{=1}) and square free (\\spadignore{i.e.} without repeated factors).")) (|numberOfFactors| (((|NonNegativeInteger|) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{numberOfFactors(ddfactorization)} returns the number of factors of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|stopMusserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{stopMusserTrials(n)} sets to \\spad{n} the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**n} trials. Returns the previous value.") (((|PositiveInteger|)) "\\spad{stopMusserTrials()} returns the bound on the number of factors for which \\spadfun{modularFactor} stops to look for an other prime. You will have to remember that the step of recombining the extraneous factors may take up to \\spad{2**stopMusserTrials()} trials.")) (|musserTrials| (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{musserTrials(n)} sets to \\spad{n} the number of primes to be tried in \\spadfun{modularFactor} and returns the previous value.") (((|PositiveInteger|)) "\\spad{musserTrials()} returns the number of primes that are tried in \\spadfun{modularFactor}.")) (|degreePartition| (((|Multiset| (|NonNegativeInteger|)) (|List| (|Record| (|:| |factor| |#1|) (|:| |degree| (|Integer|))))) "\\spad{degreePartition(ddfactorization)} returns the degree partition of the polynomial \\spad{f} modulo \\spad{p} where \\spad{ddfactorization} is the distinct degree factorization of \\spad{f} computed by \\spadfunFrom{ddFact}{ModularDistinctDegreeFactorizer} for some prime \\spad{p}.")) (|makeFR| (((|Factored| |#1|) (|Record| (|:| |contp| (|Integer|)) (|:| |factors| (|List| (|Record| (|:| |irr| |#1|) (|:| |pow| (|Integer|))))))) "\\spad{makeFR(flist)} turns the final factorization of henselFact into a \\spadtype{Factored} object."))) NIL NIL -(-418 R UP -2315) +(-418 R UP -3539) ((|constructor| (NIL "\\spadtype{GaloisGroupFactorizationUtilities} provides functions that will be used by the factorizer.")) (|length| ((|#3| |#2|) "\\spad{length(p)} returns the sum of the absolute values of the coefficients of the polynomial \\spad{p}.")) (|height| ((|#3| |#2|) "\\spad{height(p)} returns the maximal absolute value of the coefficients of the polynomial \\spad{p}.")) (|infinityNorm| ((|#3| |#2|) "\\spad{infinityNorm(f)} returns the maximal absolute value of the coefficients of the polynomial \\spad{f}.")) (|quadraticNorm| ((|#3| |#2|) "\\spad{quadraticNorm(f)} returns the \\spad{l2} norm of the polynomial \\spad{f}.")) (|norm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{norm(f,{}p)} returns the \\spad{lp} norm of the polynomial \\spad{f}.")) (|singleFactorBound| (((|Integer|) |#2|) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{p} shall be of degree higher or equal to 2.") (((|Integer|) |#2| (|NonNegativeInteger|)) "\\spad{singleFactorBound(p,{}r)} returns a bound on the infinite norm of the factor of \\spad{p} with smallest Bombieri\\spad{'s} norm. \\spad{r} is a lower bound for the number of factors of \\spad{p}. \\spad{p} shall be of degree higher or equal to 2.")) (|rootBound| (((|Integer|) |#2|) "\\spad{rootBound(p)} returns a bound on the largest norm of the complex roots of \\spad{p}.")) (|bombieriNorm| ((|#3| |#2| (|PositiveInteger|)) "\\spad{bombieriNorm(p,{}n)} returns the \\spad{n}th Bombieri\\spad{'s} norm of \\spad{p}.") ((|#3| |#2|) "\\spad{bombieriNorm(p)} returns quadratic Bombieri\\spad{'s} norm of \\spad{p}.")) (|beauzamyBound| (((|Integer|) |#2|) "\\spad{beauzamyBound(p)} returns a bound on the larger coefficient of any factor of \\spad{p}."))) NIL NIL @@ -1638,16 +1638,16 @@ NIL NIL (-427) ((|constructor| (NIL "This category describes domains where \\spadfun{\\spad{gcd}} can be computed but where there is no guarantee of the existence of \\spadfun{factor} operation for factorisation into irreducibles. However,{} if such a \\spadfun{factor} operation exist,{} factorization will be unique up to order and units.")) (|lcm| (($ (|List| $)) "\\spad{lcm(l)} returns the least common multiple of the elements of the list \\spad{l}.") (($ $ $) "\\spad{lcm(x,{}y)} returns the least common multiple of \\spad{x} and \\spad{y}.")) (|gcd| (($ (|List| $)) "\\spad{gcd(l)} returns the common \\spad{gcd} of the elements in the list \\spad{l}.") (($ $ $) "\\spad{gcd(x,{}y)} returns the greatest common divisor of \\spad{x} and \\spad{y}."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-428 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"))) -((-4241 |has| (-383 (-883 |#1|)) (-515)) (-4239 . T) (-4238 . T)) +((-4245 |has| (-383 (-883 |#1|)) (-515)) (-4243 . T) (-4242 . T)) ((|HasCategory| (-383 (-883 |#1|)) (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| (-383 (-883 |#1|)) (QUOTE (-515)))) (-429 |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"))) -(((-4246 "*") |has| |#2| (-158)) (-4237 |has| |#2| (-515)) (-4242 |has| |#2| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#2| (QUOTE (-840))) (-3262 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3262 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3262 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4242)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +(((-4250 "*") |has| |#2| (-158)) (-4241 |has| |#2| (-515)) (-4246 |has| |#2| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#2| (QUOTE (-840))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3172 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) (-430 R BP) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni.} January 1990 The equation \\spad{Af+Bg=h} and its generalization to \\spad{n} polynomials is solved for solutions over the \\spad{R},{} euclidean domain. A table containing the solutions of \\spad{Af+Bg=x**k} is used. The operations are performed modulus a prime which are in principle big enough,{} but the solutions are tested and,{} in case of failure,{} a hensel lifting process is used to get to the right solutions. It will be used in the factorization of multivariate polynomials over finite field,{} with \\spad{R=F[x]}.")) (|testModulus| (((|Boolean|) |#1| (|List| |#2|)) "\\spad{testModulus(p,{}lp)} returns \\spad{true} if the the prime \\spad{p} is valid for the list of polynomials \\spad{lp},{} \\spadignore{i.e.} preserves the degree and they remain relatively prime.")) (|solveid| (((|Union| (|List| |#2|) "failed") |#2| |#1| (|Vector| (|List| |#2|))) "\\spad{solveid(h,{}table)} computes the coefficients of the extended euclidean algorithm for a list of polynomials whose tablePow is \\spad{table} and with right side \\spad{h}.")) (|tablePow| (((|Union| (|Vector| (|List| |#2|)) "failed") (|NonNegativeInteger|) |#1| (|List| |#2|)) "\\spad{tablePow(maxdeg,{}prime,{}lpol)} constructs the table with the coefficients of the Extended Euclidean Algorithm for \\spad{lpol}. Here the right side is \\spad{x**k},{} for \\spad{k} less or equal to \\spad{maxdeg}. The operation returns \"failed\" when the elements are not coprime modulo \\spad{prime}.")) (|compBound| (((|NonNegativeInteger|) |#2| (|List| |#2|)) "\\spad{compBound(p,{}lp)} computes a bound for the coefficients of the solution polynomials. Given a polynomial right hand side \\spad{p},{} and a list \\spad{lp} of left hand side polynomials. Exported because it depends on the valuation.")) (|reduction| ((|#2| |#2| |#1|) "\\spad{reduction(p,{}prime)} reduces the polynomial \\spad{p} modulo \\spad{prime} of \\spad{R}. Note: this function is exported only because it\\spad{'s} conditional."))) NIL @@ -1674,7 +1674,7 @@ NIL NIL (-436 |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| $) "\\spad{leadingCoefficient(x)} \\undocumented"))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL (-437 E V R P Q) ((|constructor| (NIL "Gosper\\spad{'s} summation algorithm.")) (|GospersMethod| (((|Union| |#5| "failed") |#5| |#2| (|Mapping| |#2|)) "\\spad{GospersMethod(b,{} n,{} new)} returns a rational function \\spad{rf(n)} such that \\spad{a(n) * rf(n)} is the indefinite sum of \\spad{a(n)} with respect to upward difference on \\spad{n},{} \\spadignore{i.e.} \\spad{a(n+1) * rf(n+1) - a(n) * rf(n) = a(n)},{} where \\spad{b(n) = a(n)/a(n-1)} is a rational function. Returns \"failed\" if no such rational function \\spad{rf(n)} exists. Note: \\spad{new} is a nullary function returning a new \\spad{V} every time. The condition on \\spad{a(n)} is that \\spad{a(n)/a(n-1)} is a rational function of \\spad{n}."))) @@ -1682,7 +1682,7 @@ NIL NIL (-438 R E |VarSet| P) ((|constructor| (NIL "A domain for polynomial sets.")) (|convert| (($ (|List| |#4|)) "\\axiom{convert(\\spad{lp})} returns the polynomial set whose members are the polynomials of \\axiom{\\spad{lp}}."))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#4| (LIST (QUOTE -286) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#4| (LIST (QUOTE -563) (QUOTE (-794))))) (-439 S R E) ((|constructor| (NIL "GradedAlgebra(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-algebra\\spad{''}. A graded algebra is a graded module together with a degree preserving \\spad{R}-linear map,{} called the {\\em product}. \\blankline The name ``product\\spad{''} is written out in full so inner and outer products with the same mapping type can be distinguished by name.")) (|product| (($ $ $) "\\spad{product(a,{}b)} is the degree-preserving \\spad{R}-linear product: \\blankline \\indented{2}{\\spad{degree product(a,{}b) = degree a + degree b}} \\indented{2}{\\spad{product(a1+a2,{}b) = product(a1,{}b) + product(a2,{}b)}} \\indented{2}{\\spad{product(a,{}b1+b2) = product(a,{}b1) + product(a,{}b2)}} \\indented{2}{\\spad{product(r*a,{}b) = product(a,{}r*b) = r*product(a,{}b)}} \\indented{2}{\\spad{product(a,{}product(b,{}c)) = product(product(a,{}b),{}c)}}")) ((|One|) (($) "1 is the identity for \\spad{product}."))) @@ -1712,7 +1712,7 @@ NIL ((|constructor| (NIL "GradedModule(\\spad{R},{}\\spad{E}) denotes ``E-graded \\spad{R}-module\\spad{''},{} \\spadignore{i.e.} collection of \\spad{R}-modules indexed by an abelian monoid \\spad{E}. An element \\spad{g} of \\spad{G[s]} for some specific \\spad{s} in \\spad{E} is said to be an element of \\spad{G} with {\\em degree} \\spad{s}. Sums are defined in each module \\spad{G[s]} so two elements of \\spad{G} have a sum if they have the same degree. \\blankline Morphisms can be defined and composed by degree to give the mathematical category of graded modules.")) (+ (($ $ $) "\\spad{g+h} is the sum of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.")) (- (($ $ $) "\\spad{g-h} is the difference of \\spad{g} and \\spad{h} in the module of elements of the same degree as \\spad{g} and \\spad{h}. Error: if \\spad{g} and \\spad{h} have different degrees.") (($ $) "\\spad{-g} is the additive inverse of \\spad{g} in the module of elements of the same grade as \\spad{g}.")) (* (($ $ |#1|) "\\spad{g*r} is right module multiplication.") (($ |#1| $) "\\spad{r*g} is left module multiplication.")) ((|Zero|) (($) "0 denotes the zero of degree 0.")) (|degree| ((|#2| $) "\\spad{degree(g)} names the degree of \\spad{g}. The set of all elements of a given degree form an \\spad{R}-module."))) NIL NIL -(-446 |lv| -2315 R) +(-446 |lv| -3539 R) ((|constructor| (NIL "\\indented{1}{Author : \\spad{P}.Gianni,{} Summer \\spad{'88},{} revised November \\spad{'89}} Solve systems of polynomial equations using Groebner bases Total order Groebner bases are computed and then converted to lex ones This package is mostly intended for internal use.")) (|genericPosition| (((|Record| (|:| |dpolys| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|:| |coords| (|List| (|Integer|)))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{genericPosition(lp,{}lv)} puts a radical zero dimensional ideal in general position,{} for system \\spad{lp} in variables \\spad{lv}.")) (|testDim| (((|Union| (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) "failed") (|List| (|HomogeneousDistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{testDim(lp,{}lv)} tests if the polynomial system \\spad{lp} in variables \\spad{lv} is zero dimensional.")) (|groebSolve| (((|List| (|List| (|DistributedMultivariatePolynomial| |#1| |#2|))) (|List| (|DistributedMultivariatePolynomial| |#1| |#2|)) (|List| (|OrderedVariableList| |#1|))) "\\spad{groebSolve(lp,{}lv)} reduces the polynomial system \\spad{lp} in variables \\spad{lv} to triangular form. Algorithm based on groebner bases algorithm with linear algebra for change of ordering. Preprocessing for the general solver. The polynomials in input are of type \\spadtype{DMP}."))) NIL NIL @@ -1722,45 +1722,45 @@ NIL NIL (-448) ((|constructor| (NIL "The class of multiplicative groups,{} \\spadignore{i.e.} monoids with multiplicative inverses. \\blankline")) (|commutator| (($ $ $) "\\spad{commutator(p,{}q)} computes \\spad{inv(p) * inv(q) * p * q}.")) (|conjugate| (($ $ $) "\\spad{conjugate(p,{}q)} computes \\spad{inv(q) * p * q}; this is 'right action by conjugation'.")) (|unitsKnown| ((|attribute|) "unitsKnown asserts that recip only returns \"failed\" for non-units.")) (^ (($ $ (|Integer|)) "\\spad{x^n} returns \\spad{x} raised to the integer power \\spad{n}.")) (** (($ $ (|Integer|)) "\\spad{x**n} returns \\spad{x} raised to the integer power \\spad{n}.")) (/ (($ $ $) "\\spad{x/y} is the same as \\spad{x} times the inverse of \\spad{y}.")) (|inv| (($ $) "\\spad{inv(x)} returns the inverse of \\spad{x}."))) -((-4241 . T)) +((-4245 . T)) NIL (-449 |Coef| |var| |cen|) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x\\^r)}.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|UnivariatePuiseuxSeries| |#1| |#2| |#3|)) "\\spad{coerce(f)} converts a Puiseux series to a general power series.") (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . 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T)) -((-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-451 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)}"))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#4| (LIST (QUOTE -286) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#4| (LIST (QUOTE -563) (QUOTE (-794))))) (-452) ((|constructor| (NIL "\\indented{1}{Symbolic fractions in \\%\\spad{pi} with integer coefficients;} \\indented{1}{The point for using \\spad{Pi} as the default domain for those fractions} \\indented{1}{is that \\spad{Pi} is coercible to the float types,{} and not Expression.} Date Created: 21 Feb 1990 Date Last Updated: 12 Mai 1992")) (|pi| (($) "\\spad{\\spad{pi}()} returns the symbolic \\%\\spad{pi}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-453 |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."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-454) ((|constructor| (NIL "\\indented{1}{Author : Larry Lambe} Date Created : August 1988 Date Last Updated : March 9 1990 Related Constructors: OrderedSetInts,{} Commutator,{} FreeNilpotentLie AMS Classification: Primary 17B05,{} 17B30; Secondary 17A50 Keywords: free Lie algebra,{} Hall basis,{} basic commutators Description : Generate a basis for the free Lie algebra on \\spad{n} generators over a ring \\spad{R} with identity up to basic commutators of length \\spad{c} using the algorithm of \\spad{P}. Hall as given in Serre\\spad{'s} book Lie Groups \\spad{--} Lie Algebras")) (|generate| (((|Vector| (|List| (|Integer|))) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{generate(numberOfGens,{} maximalWeight)} generates a vector of elements of the form [left,{}weight,{}right] which represents a \\spad{P}. Hall basis element for the free lie algebra on \\spad{numberOfGens} generators. We only generate those basis elements of weight less than or equal to maximalWeight")) (|inHallBasis?| (((|Boolean|) (|Integer|) (|Integer|) (|Integer|) (|Integer|)) "\\spad{inHallBasis?(numberOfGens,{} leftCandidate,{} rightCandidate,{} left)} tests to see if a new element should be added to the \\spad{P}. Hall basis being constructed. The list \\spad{[leftCandidate,{}wt,{}rightCandidate]} is included in the basis if in the unique factorization of \\spad{rightCandidate},{} we have left factor leftOfRight,{} and leftOfRight \\spad{<=} \\spad{leftCandidate}")) (|lfunc| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{lfunc(d,{}n)} computes the rank of the \\spad{n}th factor in the lower central series of the free \\spad{d}-generated free Lie algebra; This rank is \\spad{d} if \\spad{n} = 1 and binom(\\spad{d},{}2) if \\spad{n} = 2"))) NIL NIL (-455 |vl| R) ((|constructor| (NIL "\\indented{2}{This type supports distributed multivariate polynomials} whose variables are from a user specified list of symbols. The coefficient ring may be non commutative,{} but the variables are assumed to commute. The term ordering is total degree ordering refined by reverse lexicographic ordering with respect to the position that the variables appear in the list of variables parameter.")) 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((|constructor| (NIL "Heap implemented in a flexible array to allow for insertions")) (|heap| (($ (|List| |#1|)) "\\spad{heap(ls)} creates a heap of elements consisting of the elements of \\spad{ls}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-458 -2315 UP UPUP R) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-458 -3539 UP UPUP R) ((|constructor| (NIL "This domains implements finite rational divisors on an hyperelliptic curve,{} that is finite formal sums SUM(\\spad{n} * \\spad{P}) where the \\spad{n}\\spad{'s} are integers and the \\spad{P}\\spad{'s} are finite rational points on the curve. The equation of the curve must be \\spad{y^2} = \\spad{f}(\\spad{x}) and \\spad{f} must have odd degree."))) NIL NIL @@ -1770,15 +1770,15 @@ NIL NIL (-460) ((|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.")) (|coerce| (((|RadixExpansion| 16) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a radix expansion with base 16.") (((|Fraction| (|Integer|)) $) "\\spad{coerce(h)} converts a hexadecimal expansion to a rational number."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3262 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) (-461 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 -4244)) (|HasAttribute| |#1| (QUOTE -4245)) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) +((|HasAttribute| |#1| (QUOTE -4248)) (|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (-462 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|) $) "\\spad{map(f,{}u)} returns a copy of \\spad{u} with each element \\spad{x} replaced by \\spad{f}(\\spad{x}). For collections,{} \\axiom{map(\\spad{f},{}\\spad{u}) = [\\spad{f}(\\spad{x}) for \\spad{x} in \\spad{u}]}."))) -((-3656 . T)) +((-4069 . T)) NIL (-463 S) ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) @@ -1788,33 +1788,33 @@ NIL ((|constructor| (NIL "Category for the hyperbolic trigonometric functions.")) (|tanh| (($ $) "\\spad{tanh(x)} returns the hyperbolic tangent of \\spad{x}.")) (|sinh| (($ $) "\\spad{sinh(x)} returns the hyperbolic sine of \\spad{x}.")) (|sech| (($ $) "\\spad{sech(x)} returns the hyperbolic secant of \\spad{x}.")) (|csch| (($ $) "\\spad{csch(x)} returns the hyperbolic cosecant of \\spad{x}.")) (|coth| (($ $) "\\spad{coth(x)} returns the hyperbolic cotangent of \\spad{x}.")) (|cosh| (($ $) "\\spad{cosh(x)} returns the hyperbolic cosine of \\spad{x}."))) NIL NIL -(-465 -2315 UP |AlExt| |AlPol|) +(-465 -3539 UP |AlExt| |AlPol|) ((|constructor| (NIL "Factorization of univariate polynomials with coefficients in an algebraic extension of a field over which we can factor UP\\spad{'s}.")) (|factor| (((|Factored| |#4|) |#4| (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{factor(p,{} f)} returns a prime factorisation of \\spad{p}; \\spad{f} is a factorisation map for elements of UP."))) NIL NIL (-466) ((|constructor| (NIL "Algebraic closure of the rational numbers.")) (|norm| (($ $ (|List| (|Kernel| $))) "\\spad{norm(f,{}l)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernels \\spad{l}") (($ $ (|Kernel| $)) "\\spad{norm(f,{}k)} computes the norm of the algebraic number \\spad{f} with respect to the extension generated by kernel \\spad{k}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|List| (|Kernel| $))) "\\spad{norm(p,{}l)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernels \\spad{l}") (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|Kernel| $)) "\\spad{norm(p,{}k)} computes the norm of the polynomial \\spad{p} with respect to the extension generated by kernel \\spad{k}")) (|trueEqual| (((|Boolean|) $ $) "\\spad{trueEqual(x,{}y)} tries to determine if the two numbers are equal")) (|reduce| (($ $) "\\spad{reduce(f)} simplifies all the unreduced algebraic numbers present in \\spad{f} by applying their defining relations.")) (|denom| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{denom(f)} returns the denominator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|numer| (((|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $)) $) "\\spad{numer(f)} returns the numerator of \\spad{f} viewed as a polynomial in the kernels over \\spad{Z}.")) (|coerce| (($ (|SparseMultivariatePolynomial| (|Integer|) (|Kernel| $))) "\\spad{coerce(p)} returns \\spad{p} viewed as an algebraic number."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| $ (QUOTE (-973))) (|HasCategory| $ (LIST (QUOTE -964) (QUOTE (-523))))) (-467 S |mn|) ((|constructor| (NIL "\\indented{1}{Author Micheal Monagan Aug/87} This is the basic one dimensional array data type."))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-468 R |mnRow| |mnCol|) ((|constructor| (NIL "\\indented{1}{An IndexedTwoDimensionalArray is a 2-dimensional array where} the minimal row and column indices are parameters of the type. Rows and columns are returned as IndexedOneDimensionalArray\\spad{'s} with minimal indices matching those of the IndexedTwoDimensionalArray. The index of the 'first' row may be obtained by calling the function 'minRowIndex'. The index of the 'first' column may be obtained by calling the function 'minColIndex'. The index of the first element of a 'Row' is the same as the index of the first column in an array and vice versa."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-469 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 -(-470 R UP -2315) +(-470 R UP -3539) ((|constructor| (NIL "This package contains functions used in the packages FunctionFieldIntegralBasis and NumberFieldIntegralBasis.")) (|moduleSum| (((|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|))) (|Record| (|:| |basis| (|Matrix| |#1|)) (|:| |basisDen| |#1|) (|:| |basisInv| (|Matrix| |#1|)))) "\\spad{moduleSum(m1,{}m2)} returns the sum of two modules in the framed algebra \\spad{F}. Each module \\spad{\\spad{mi}} is represented as follows: \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn} and \\spad{\\spad{mi}} is a record \\spad{[basis,{}basisDen,{}basisInv]}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then a basis \\spad{v1,{}...,{}vn} for \\spad{\\spad{mi}} is given by \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|idealiserMatrix| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiserMatrix(m1,{} m2)} returns the matrix representing the linear conditions on the Ring associatied with an ideal defined by \\spad{m1} and \\spad{m2}.")) (|idealiser| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{idealiser(m1,{}m2,{}d)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2} where \\spad{d} is the known part of the denominator") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{idealiser(m1,{}m2)} computes the order of an ideal defined by \\spad{m1} and \\spad{m2}")) (|leastPower| (((|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{leastPower(p,{}n)} returns \\spad{e},{} where \\spad{e} is the smallest integer such that \\spad{p **e >= n}")) (|divideIfCan!| ((|#1| (|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Integer|)) "\\spad{divideIfCan!(matrix,{}matrixOut,{}prime,{}n)} attempts to divide the entries of \\spad{matrix} by \\spad{prime} and store the result in \\spad{matrixOut}. If it is successful,{} 1 is returned and if not,{} \\spad{prime} is returned. Here both \\spad{matrix} and \\spad{matrixOut} are \\spad{n}-by-\\spad{n} upper triangular matrices.")) (|matrixGcd| ((|#1| (|Matrix| |#1|) |#1| (|NonNegativeInteger|)) "\\spad{matrixGcd(mat,{}sing,{}n)} is \\spad{gcd(sing,{}g)} where \\spad{g} is the \\spad{gcd} of the entries of the \\spad{n}-by-\\spad{n} upper-triangular matrix \\spad{mat}.")) (|diagonalProduct| ((|#1| (|Matrix| |#1|)) "\\spad{diagonalProduct(m)} returns the product of the elements on the diagonal of the matrix \\spad{m}")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns a square-free factorisation of \\spad{x}"))) NIL NIL (-471 |mn|) ((|constructor| (NIL "\\spadtype{IndexedBits} is a domain to compactly represent large quantities of Boolean data.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em And} of \\spad{n} and \\spad{m}.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em Or} of \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em Not} of \\spad{n}."))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| (-108) (QUOTE (-1016))) (|HasCategory| (-108) (LIST (QUOTE -286) (QUOTE (-108))))) (|HasCategory| (-108) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-108) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-108) (QUOTE (-1016))) (|HasCategory| (-108) (LIST (QUOTE -563) (QUOTE (-794))))) (-472 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)}."))) @@ -1828,7 +1828,7 @@ NIL ((|constructor| (NIL "InnerCommonDenominator provides functions to compute the common denominator of a finite linear aggregate of elements of the quotient field of an integral domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#4|) "\\spad{splitDenominator([q1,{}...,{}qn])} returns \\spad{[[p1,{}...,{}pn],{} d]} such that \\spad{\\spad{qi} = pi/d} and \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|clearDenominator| ((|#3| |#4|) "\\spad{clearDenominator([q1,{}...,{}qn])} returns \\spad{[p1,{}...,{}pn]} such that \\spad{\\spad{qi} = pi/d} where \\spad{d} is a common denominator for the \\spad{qi}\\spad{'s}.")) (|commonDenominator| ((|#1| |#4|) "\\spad{commonDenominator([q1,{}...,{}qn])} returns a common denominator \\spad{d} for \\spad{q1},{}...,{}\\spad{qn}."))) NIL NIL -(-475 -2315 |Expon| |VarSet| |DPoly|) +(-475 -3539 |Expon| |VarSet| |DPoly|) ((|constructor| (NIL "This domain represents polynomial ideals with coefficients in any field and supports the basic ideal operations,{} including intersection sum and quotient. An ideal is represented by a list of polynomials (the generators of the ideal) and a boolean that is \\spad{true} if the generators are a Groebner basis. The algorithms used are based on Groebner basis computations. The ordering is determined by the datatype of the input polynomials. Users may use refinements of total degree orderings.")) (|relationsIdeal| (((|SuchThat| (|List| (|Polynomial| |#1|)) (|List| (|Equation| (|Polynomial| |#1|)))) (|List| |#4|)) "\\spad{relationsIdeal(polyList)} returns the ideal of relations among the polynomials in \\spad{polyList}.")) (|saturate| (($ $ |#4| (|List| |#3|)) "\\spad{saturate(I,{}f,{}lvar)} is the saturation with respect to the prime principal ideal which is generated by \\spad{f} in the polynomial ring \\spad{F[lvar]}.") (($ $ |#4|) "\\spad{saturate(I,{}f)} is the saturation of the ideal \\spad{I} with respect to the multiplicative set generated by the polynomial \\spad{f}.")) (|coerce| (($ (|List| |#4|)) "\\spad{coerce(polyList)} converts the list of polynomials \\spad{polyList} to an ideal.")) (|generators| (((|List| |#4|) $) "\\spad{generators(I)} returns a list of generators for the ideal \\spad{I}.")) (|groebner?| (((|Boolean|) $) "\\spad{groebner?(I)} tests if the generators of the ideal \\spad{I} are a Groebner basis.")) (|groebnerIdeal| (($ (|List| |#4|)) "\\spad{groebnerIdeal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList} which are assumed to be a Groebner basis. Note: this operation avoids a Groebner basis computation.")) (|ideal| (($ (|List| |#4|)) "\\spad{ideal(polyList)} constructs the ideal generated by the list of polynomials \\spad{polyList}.")) (|leadingIdeal| (($ $) "\\spad{leadingIdeal(I)} is the ideal generated by the leading terms of the elements of the ideal \\spad{I}.")) (|dimension| (((|Integer|) $) "\\spad{dimension(I)} gives the dimension of the ideal \\spad{I}. in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Integer|) $ (|List| |#3|)) "\\spad{dimension(I,{}lvar)} gives the dimension of the ideal \\spad{I},{} in the ring \\spad{F[lvar]}")) (|backOldPos| (($ (|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $))) "\\spad{backOldPos(genPos)} takes the result produced by \\spadfunFrom{generalPosition}{PolynomialIdeals} and performs the inverse transformation,{} returning the original ideal \\spad{backOldPos(generalPosition(I,{}listvar))} = \\spad{I}.")) (|generalPosition| (((|Record| (|:| |mval| (|Matrix| |#1|)) (|:| |invmval| (|Matrix| |#1|)) (|:| |genIdeal| $)) $ (|List| |#3|)) "\\spad{generalPosition(I,{}listvar)} perform a random linear transformation on the variables in \\spad{listvar} and returns the transformed ideal along with the change of basis matrix.")) (|groebner| (($ $) "\\spad{groebner(I)} returns a set of generators of \\spad{I} that are a Groebner basis for \\spad{I}.")) (|quotient| (($ $ |#4|) "\\spad{quotient(I,{}f)} computes the quotient of the ideal \\spad{I} by the principal ideal generated by the polynomial \\spad{f},{} \\spad{(I:(f))}.") (($ $ $) "\\spad{quotient(I,{}J)} computes the quotient of the ideals \\spad{I} and \\spad{J},{} \\spad{(I:J)}.")) (|intersect| (($ (|List| $)) "\\spad{intersect(LI)} computes the intersection of the list of ideals \\spad{LI}.") (($ $ $) "\\spad{intersect(I,{}J)} computes the intersection of the ideals \\spad{I} and \\spad{J}.")) (|zeroDim?| (((|Boolean|) $) "\\spad{zeroDim?(I)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]},{} where lvar are the variables appearing in \\spad{I}") (((|Boolean|) $ (|List| |#3|)) "\\spad{zeroDim?(I,{}lvar)} tests if the ideal \\spad{I} is zero dimensional,{} \\spadignore{i.e.} all its associated primes are maximal,{} in the ring \\spad{F[lvar]}")) (|inRadical?| (((|Boolean|) |#4| $) "\\spad{inRadical?(f,{}I)} tests if some power of the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|in?| (((|Boolean|) $ $) "\\spad{in?(I,{}J)} tests if the ideal \\spad{I} is contained in the ideal \\spad{J}.")) (|element?| (((|Boolean|) |#4| $) "\\spad{element?(f,{}I)} tests whether the polynomial \\spad{f} belongs to the ideal \\spad{I}.")) (|zero?| (((|Boolean|) $) "\\spad{zero?(I)} tests whether the ideal \\spad{I} is the zero ideal")) (|one?| (((|Boolean|) $) "\\spad{one?(I)} tests whether the ideal \\spad{I} is the unit ideal,{} \\spadignore{i.e.} contains 1.")) (+ (($ $ $) "\\spad{I+J} computes the ideal generated by the union of \\spad{I} and \\spad{J}.")) (** (($ $ (|NonNegativeInteger|)) "\\spad{I**n} computes the \\spad{n}th power of the ideal \\spad{I}.")) (* (($ $ $) "\\spad{I*J} computes the product of the ideal \\spad{I} and \\spad{J}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-1087))))) @@ -1874,32 +1874,32 @@ NIL ((|HasCategory| |#2| (QUOTE (-731)))) (-486 S |mn|) ((|constructor| (NIL "\\indented{1}{Author: Michael Monagan July/87,{} modified \\spad{SMW} June/91} A FlexibleArray is the notion of an array intended to allow for growth at the end only. Hence the following efficient operations \\indented{2}{\\spad{append(x,{}a)} meaning append item \\spad{x} at the end of the array \\spad{a}} \\indented{2}{\\spad{delete(a,{}n)} meaning delete the last item from the array \\spad{a}} Flexible arrays support the other operations inherited from \\spadtype{ExtensibleLinearAggregate}. However,{} these are not efficient. Flexible arrays combine the \\spad{O(1)} access time property of arrays with growing and shrinking at the end in \\spad{O(1)} (average) time. This is done by using an ordinary array which may have zero or more empty slots at the end. When the array becomes full it is copied into a new larger (50\\% larger) array. Conversely,{} when the array becomes less than 1/2 full,{} it is copied into a smaller array. Flexible arrays provide for an efficient implementation of many data structures in particular heaps,{} stacks and sets.")) (|shrinkable| (((|Boolean|) (|Boolean|)) "\\spad{shrinkable(b)} sets the shrinkable attribute of flexible arrays to \\spad{b} and returns the previous value")) (|physicalLength!| (($ $ (|Integer|)) "\\spad{physicalLength!(x,{}n)} changes the physical length of \\spad{x} to be \\spad{n} and returns the new array.")) (|physicalLength| (((|NonNegativeInteger|) $) "\\spad{physicalLength(x)} returns the number of elements \\spad{x} can accomodate before growing")) (|flexibleArray| (($ (|List| |#1|)) "\\spad{flexibleArray(l)} creates a flexible array from the list of elements \\spad{l}"))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-487 |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}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| (-536 |#1|) (QUOTE (-134))) (|HasCategory| (-536 |#1|) (QUOTE (-344)))) (|HasCategory| (-536 |#1|) (QUOTE (-136))) (|HasCategory| (-536 |#1|) (QUOTE (-344))) (|HasCategory| (-536 |#1|) (QUOTE (-134)))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((-3172 (|HasCategory| (-536 |#1|) (QUOTE (-134))) (|HasCategory| (-536 |#1|) (QUOTE (-344)))) (|HasCategory| (-536 |#1|) (QUOTE (-136))) (|HasCategory| (-536 |#1|) (QUOTE (-344))) (|HasCategory| (-536 |#1|) (QUOTE (-134)))) (-488 R |mnRow| |mnCol| |Row| |Col|) ((|constructor| (NIL "\\indented{1}{This is an internal type which provides an implementation of} 2-dimensional arrays as PrimitiveArray\\spad{'s} of PrimitiveArray\\spad{'s}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-489 S |mn|) ((|constructor| (NIL "\\spadtype{IndexedList} is a basic implementation of the functions in \\spadtype{ListAggregate},{} often using functions in the underlying LISP system. The second parameter to the constructor (\\spad{mn}) is the beginning index of the list. That is,{} if \\spad{l} is a list,{} then \\spad{elt(l,{}mn)} is the first value. This constructor is probably best viewed as the implementation of singly-linked lists that are addressable by index rather than as a mere wrapper for LISP lists."))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-490 R |Row| |Col| M) ((|constructor| (NIL "\\spadtype{InnerMatrixLinearAlgebraFunctions} is an internal package which provides standard linear algebra functions on domains in \\spad{MatrixCategory}")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix \\spad{m}. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|generalizedInverse| ((|#4| |#4|) "\\spad{generalizedInverse(m)} returns the generalized (Moore--Penrose) inverse of the matrix \\spad{m},{} \\spadignore{i.e.} the matrix \\spad{h} such that m*h*m=h,{} h*m*h=m,{} \\spad{m*h} and \\spad{h*m} are both symmetric matrices.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}."))) NIL -((|HasAttribute| |#3| (QUOTE -4245))) +((|HasAttribute| |#3| (QUOTE -4249))) (-491 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 -4245))) +((|HasAttribute| |#7| (QUOTE -4249))) (-492 R |mnRow| |mnCol|) ((|constructor| (NIL "An \\spad{IndexedMatrix} is a matrix where the minimal row and column indices are parameters of the type. The domains Row and Col are both IndexedVectors. The index of the 'first' row may be obtained by calling the function \\spadfun{minRowIndex}. The index of the 'first' column may be obtained by calling the function \\spadfun{minColIndex}. The index of the first element of a 'Row' is the same as the index of the first column in a matrix and vice versa."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4246 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-493 GF) ((|constructor| (NIL "InnerNormalBasisFieldFunctions(\\spad{GF}) (unexposed): This package has functions used by every normal basis finite field extension domain.")) (|minimalPolynomial| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{minimalPolynomial(x)} \\undocumented{} See \\axiomFunFrom{minimalPolynomial}{FiniteAlgebraicExtensionField}")) (|normalElement| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{normalElement(n)} \\undocumented{} See \\axiomFunFrom{normalElement}{FiniteAlgebraicExtensionField}")) (|basis| (((|Vector| (|Vector| |#1|)) (|PositiveInteger|)) "\\spad{basis(n)} \\undocumented{} See \\axiomFunFrom{basis}{FiniteAlgebraicExtensionField}")) (|normal?| (((|Boolean|) (|Vector| |#1|)) "\\spad{normal?(x)} \\undocumented{} See \\axiomFunFrom{normal?}{FiniteAlgebraicExtensionField}")) (|lookup| (((|PositiveInteger|) (|Vector| |#1|)) "\\spad{lookup(x)} \\undocumented{} See \\axiomFunFrom{lookup}{Finite}")) (|inv| (((|Vector| |#1|) (|Vector| |#1|)) "\\spad{inv x} \\undocumented{} See \\axiomFunFrom{inv}{DivisionRing}")) (|trace| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{trace(x,{}n)} \\undocumented{} See \\axiomFunFrom{trace}{FiniteAlgebraicExtensionField}")) (|norm| (((|Vector| |#1|) (|Vector| |#1|) (|PositiveInteger|)) "\\spad{norm(x,{}n)} \\undocumented{} See \\axiomFunFrom{norm}{FiniteAlgebraicExtensionField}")) (/ (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x/y} \\undocumented{} See \\axiomFunFrom{/}{Field}")) (* (((|Vector| |#1|) (|Vector| |#1|) (|Vector| |#1|)) "\\spad{x*y} \\undocumented{} See \\axiomFunFrom{*}{SemiGroup}")) (** (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{x**n} \\undocumented{} See \\axiomFunFrom{\\spad{**}}{DivisionRing}")) (|qPot| (((|Vector| |#1|) (|Vector| |#1|) (|Integer|)) "\\spad{qPot(v,{}e)} computes \\spad{v**(q**e)},{} interpreting \\spad{v} as an element of normal basis field,{} \\spad{q} the size of the ground field. This is done by a cyclic \\spad{e}-shift of the vector \\spad{v}.")) (|expPot| (((|Vector| |#1|) (|Vector| |#1|) (|SingleInteger|) (|SingleInteger|)) "\\spad{expPot(v,{}e,{}d)} returns the sum from \\spad{i = 0} to \\spad{e - 1} of \\spad{v**(q**i*d)},{} interpreting \\spad{v} as an element of a normal basis field and where \\spad{q} is the size of the ground field. Note: for a description of the algorithm,{} see \\spad{T}.Itoh and \\spad{S}.Tsujii,{} \"A fast algorithm for computing multiplicative inverses in \\spad{GF}(2^m) using normal bases\",{} Information and Computation 78,{} \\spad{pp}.171-177,{} 1988.")) (|repSq| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|)) "\\spad{repSq(v,{}e)} computes \\spad{v**e} by repeated squaring,{} interpreting \\spad{v} as an element of a normal basis field.")) (|dAndcExp| (((|Vector| |#1|) (|Vector| |#1|) (|NonNegativeInteger|) (|SingleInteger|)) "\\spad{dAndcExp(v,{}n,{}k)} computes \\spad{v**e} interpreting \\spad{v} as an element of normal basis field. A divide and conquer algorithm similar to the one from \\spad{D}.\\spad{R}.Stinson,{} \"Some observations on parallel Algorithms for fast exponentiation in \\spad{GF}(2^n)\",{} Siam \\spad{J}. Computation,{} Vol.19,{} No.4,{} \\spad{pp}.711-717,{} August 1990 is used. Argument \\spad{k} is a parameter of this algorithm.")) (|xn| (((|SparseUnivariatePolynomial| |#1|) (|NonNegativeInteger|)) "\\spad{xn(n)} returns the polynomial \\spad{x**n-1}.")) (|pol| (((|SparseUnivariatePolynomial| |#1|) (|Vector| |#1|)) "\\spad{pol(v)} turns the vector \\spad{[v0,{}...,{}vn]} into the polynomial \\spad{v0+v1*x+ ... + vn*x**n}.")) (|index| (((|Vector| |#1|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{index(n,{}m)} is a index function for vectors of length \\spad{n} over the ground field.")) (|random| (((|Vector| |#1|) (|PositiveInteger|)) "\\spad{random(n)} creates a vector over the ground field with random entries.")) (|setFieldInfo| (((|Void|) (|Vector| (|List| (|Record| (|:| |value| |#1|) (|:| |index| (|SingleInteger|))))) |#1|) "\\spad{setFieldInfo(m,{}p)} initializes the field arithmetic,{} where \\spad{m} is the multiplication table and \\spad{p} is the respective normal element of the ground field \\spad{GF}."))) NIL @@ -1912,7 +1912,7 @@ NIL ((|constructor| (NIL "converts entire exponents to OutputForm"))) NIL NIL -(-496 K -2315 |Par|) +(-496 K -3539 |Par|) ((|constructor| (NIL "This package is the inner package to be used by NumericRealEigenPackage and NumericComplexEigenPackage for the computation of numeric eigenvalues and eigenvectors.")) (|innerEigenvectors| (((|List| (|Record| (|:| |outval| |#2|) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| |#2|))))) (|Matrix| |#1|) |#3| (|Mapping| (|Factored| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|))) "\\spad{innerEigenvectors(m,{}eps,{}factor)} computes explicitly the eigenvalues and the correspondent eigenvectors of the matrix \\spad{m}. The parameter \\spad{eps} determines the type of the output,{} \\spad{factor} is the univariate factorizer to \\spad{br} used to reduce the characteristic polynomial into irreducible factors.")) (|solve1| (((|List| |#2|) (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{solve1(pol,{} eps)} finds the roots of the univariate polynomial polynomial \\spad{pol} to precision eps. If \\spad{K} is \\spad{Fraction Integer} then only the real roots are returned,{} if \\spad{K} is \\spad{Complex Fraction Integer} then all roots are found.")) (|charpol| (((|SparseUnivariatePolynomial| |#1|) (|Matrix| |#1|)) "\\spad{charpol(m)} computes the characteristic polynomial of a matrix \\spad{m} with entries in \\spad{K}. This function returns a polynomial over \\spad{K},{} while the general one (that is in EiegenPackage) returns Fraction \\spad{P} \\spad{K}"))) NIL NIL @@ -1932,7 +1932,7 @@ NIL ((|constructor| (NIL "This package computes infinite products of univariate Taylor series over an integral domain of characteristic 0.")) (|generalInfiniteProduct| ((|#2| |#2| (|Integer|) (|Integer|)) "\\spad{generalInfiniteProduct(f(x),{}a,{}d)} computes \\spad{product(n=a,{}a+d,{}a+2*d,{}...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|oddInfiniteProduct| ((|#2| |#2|) "\\spad{oddInfiniteProduct(f(x))} computes \\spad{product(n=1,{}3,{}5...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|evenInfiniteProduct| ((|#2| |#2|) "\\spad{evenInfiniteProduct(f(x))} computes \\spad{product(n=2,{}4,{}6...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1.")) (|infiniteProduct| ((|#2| |#2|) "\\spad{infiniteProduct(f(x))} computes \\spad{product(n=1,{}2,{}3...,{}f(x**n))}. The series \\spad{f(x)} should have constant coefficient 1."))) NIL NIL -(-501 K -2315 |Par|) +(-501 K -3539 |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 @@ -1962,17 +1962,17 @@ NIL NIL (-508) ((|constructor| (NIL "An \\spad{IntegerNumberSystem} is a model for the integers.")) (|invmod| (($ $ $) "\\spad{invmod(a,{}b)},{} \\spad{0<=a<b>1},{} \\spad{(a,{}b)=1} means \\spad{1/a mod b}.")) (|powmod| (($ $ $ $) "\\spad{powmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a**b mod p}.")) (|mulmod| (($ $ $ $) "\\spad{mulmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a*b mod p}.")) (|submod| (($ $ $ $) "\\spad{submod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a-b mod p}.")) (|addmod| (($ $ $ $) "\\spad{addmod(a,{}b,{}p)},{} \\spad{0<=a,{}b<p>1},{} means \\spad{a+b mod p}.")) (|mask| (($ $) "\\spad{mask(n)} returns \\spad{2**n-1} (an \\spad{n} bit mask).")) (|dec| (($ $) "\\spad{dec(x)} returns \\spad{x - 1}.")) (|inc| (($ $) "\\spad{inc(x)} returns \\spad{x + 1}.")) (|copy| (($ $) "\\spad{copy(n)} gives a copy of \\spad{n}.")) (|hash| (($ $) "\\spad{hash(n)} returns the hash code of \\spad{n}.")) (|random| (($ $) "\\spad{random(a)} creates a random element from 0 to \\spad{n-1}.") (($) "\\spad{random()} creates a random element.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(n)} creates a rational number,{} or returns \"failed\" if this is not possible.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(n)} creates a rational number (see \\spadtype{Fraction Integer})..")) (|rational?| (((|Boolean|) $) "\\spad{rational?(n)} tests if \\spad{n} is a rational number (see \\spadtype{Fraction Integer}).")) (|symmetricRemainder| (($ $ $) "\\spad{symmetricRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{ -b/2 <= r < b/2 }.")) (|positiveRemainder| (($ $ $) "\\spad{positiveRemainder(a,{}b)} (where \\spad{b > 1}) yields \\spad{r} where \\spad{0 <= r < b} and \\spad{r == a rem b}.")) (|bit?| (((|Boolean|) $ $) "\\spad{bit?(n,{}i)} returns \\spad{true} if and only if \\spad{i}-th bit of \\spad{n} is a 1.")) (|shift| (($ $ $) "\\spad{shift(a,{}i)} shift \\spad{a} by \\spad{i} digits.")) (|length| (($ $) "\\spad{length(a)} length of \\spad{a} in digits.")) (|base| (($) "\\spad{base()} returns the base for the operations of \\spad{IntegerNumberSystem}.")) (|multiplicativeValuation| ((|attribute|) "euclideanSize(a*b) returns \\spad{euclideanSize(a)*euclideanSize(b)}.")) (|even?| (((|Boolean|) $) "\\spad{even?(n)} returns \\spad{true} if and only if \\spad{n} is even.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(n)} returns \\spad{true} if and only if \\spad{n} is odd."))) -((-4242 . T) (-4243 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4246 . T) (-4247 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-509 |Key| |Entry| |addDom|) ((|constructor| (NIL "This domain is used to provide a conditional \"add\" domain for the implementation of \\spadtype{Table}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) -(-510 R -2315) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +(-510 R -3539) ((|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 -(-511 R0 -2315 UP UPUP R) +(-511 R0 -3539 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 @@ -1982,7 +1982,7 @@ NIL NIL (-513 R) ((|constructor| (NIL "\\indented{1}{+ Author: Mike Dewar} + Date Created: November 1996 + Date Last Updated: + Basic Functions: + Related Constructors: + Also See: + AMS Classifications: + Keywords: + References: + Description: + This category implements of interval arithmetic and transcendental + functions over intervals.")) (|contains?| (((|Boolean|) $ |#1|) "\\spad{contains?(i,{}f)} returns \\spad{true} if \\axiom{\\spad{f}} is contained within the interval \\axiom{\\spad{i}},{} \\spad{false} otherwise.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is negative,{} \\axiom{\\spad{false}} otherwise.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(u)} returns \\axiom{\\spad{true}} if every element of \\spad{u} is positive,{} \\axiom{\\spad{false}} otherwise.")) (|width| ((|#1| $) "\\spad{width(u)} returns \\axiom{sup(\\spad{u}) - inf(\\spad{u})}.")) (|sup| ((|#1| $) "\\spad{sup(u)} returns the supremum of \\axiom{\\spad{u}}.")) (|inf| ((|#1| $) "\\spad{inf(u)} returns the infinum of \\axiom{\\spad{u}}.")) (|qinterval| (($ |#1| |#1|) "\\spad{qinterval(inf,{}sup)} creates a new interval \\axiom{[\\spad{inf},{}\\spad{sup}]},{} without checking the ordering on the elements.")) (|interval| (($ (|Fraction| (|Integer|))) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1|) "\\spad{interval(f)} creates a new interval around \\spad{f}.") (($ |#1| |#1|) "\\spad{interval(inf,{}sup)} creates a new interval,{} either \\axiom{[\\spad{inf},{}\\spad{sup}]} if \\axiom{\\spad{inf} \\spad{<=} \\spad{sup}} or \\axiom{[\\spad{sup},{}in]} otherwise."))) -((-2562 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4108 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-514 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."))) @@ -1990,9 +1990,9 @@ NIL NIL (-515) ((|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."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-516 R -2315) +(-516 R -3539) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for elemntary functions.")) (|lfextlimint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) (|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{lfextlimint(f,{}x,{}k,{}[k1,{}...,{}kn])} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - c dk/dx}. Value \\spad{h} is looked for in a field containing \\spad{f} and \\spad{k1},{}...,{}\\spad{kn} (the \\spad{ki}\\spad{'s} must be logs).")) (|lfintegrate| (((|IntegrationResult| |#2|) |#2| (|Symbol|)) "\\spad{lfintegrate(f,{} x)} = \\spad{g} such that \\spad{dg/dx = f}.")) (|lfinfieldint| (((|Union| |#2| "failed") |#2| (|Symbol|)) "\\spad{lfinfieldint(f,{} x)} returns a function \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|lflimitedint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Symbol|) (|List| |#2|)) "\\spad{lflimitedint(f,{}x,{}[g1,{}...,{}gn])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} and \\spad{d(h+sum(\\spad{ci} log(\\spad{gi})))/dx = f},{} if possible,{} \"failed\" otherwise.")) (|lfextendedint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Symbol|) |#2|) "\\spad{lfextendedint(f,{} x,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f - cg},{} if (\\spad{h},{} \\spad{c}) exist,{} \"failed\" otherwise."))) NIL NIL @@ -2004,39 +2004,39 @@ NIL ((|constructor| (NIL "\\blankline")) (|entry| (((|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{entry(n)} \\undocumented{}")) (|entries| (((|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) $) "\\spad{entries(x)} \\undocumented{}")) (|showAttributes| (((|Union| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))) "failed") (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showAttributes(x)} \\undocumented{}")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated"))))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|fTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |endPointContinuity| (|Union| (|:| |continuous| "Continuous at the end points") (|:| |lowerSingular| "There is a singularity at the lower end point") (|:| |upperSingular| "There is a singularity at the upper end point") (|:| |bothSingular| "There are singularities at both end points") (|:| |notEvaluated| "End point continuity not yet evaluated"))) (|:| |singularitiesStream| (|Union| (|:| |str| (|Stream| (|DoubleFloat|))) (|:| |notEvaluated| "Internal singularities not yet evaluated"))) (|:| |range| (|Union| (|:| |finite| "The range is finite") (|:| |lowerInfinite| "The bottom of range is infinite") (|:| |upperInfinite| "The top of range is infinite") (|:| |bothInfinite| "Both top and bottom points are infinite") (|:| |notEvaluated| "Range not yet evaluated")))))))) "\\spad{fTable(l)} creates a functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |var| (|Symbol|)) (|:| |fn| (|Expression| (|DoubleFloat|))) (|:| |range| (|Segment| (|OrderedCompletion| (|DoubleFloat|)))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(f)} returns the list of keys of \\spad{f}")) (|clearTheFTable| (((|Void|)) "\\spad{clearTheFTable()} clears the current table of functions.")) (|showTheFTable| (($) "\\spad{showTheFTable()} returns the current table of functions."))) NIL NIL -(-519 R -2315 L) +(-519 R -3539 L) ((|constructor| (NIL "This internal package rationalises integrands on curves of the form: \\indented{2}{\\spad{y\\^2 = a x\\^2 + b x + c}} \\indented{2}{\\spad{y\\^2 = (a x + b) / (c x + d)}} \\indented{2}{\\spad{f(x,{} y) = 0} where \\spad{f} has degree 1 in \\spad{x}} The rationalization is done for integration,{} limited integration,{} extended integration and the risch differential equation.")) (|palgLODE0| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgLODE0(op,{}g,{}x,{}y,{}z,{}t,{}c)} returns the solution of \\spad{op f = g} Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgLODE0(op,{} g,{} x,{} y,{} d,{} p)} returns the solution of \\spad{op f = g}. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|lift| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|SparseUnivariatePolynomial| |#2|) (|Kernel| |#2|)) "\\spad{lift(u,{}k)} \\undocumented")) (|multivariate| ((|#2| (|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) (|Kernel| |#2|) |#2|) "\\spad{multivariate(u,{}k,{}f)} \\undocumented")) (|univariate| (((|SparseUnivariatePolynomial| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|SparseUnivariatePolynomial| |#2|)) "\\spad{univariate(f,{}k,{}k,{}p)} \\undocumented")) (|palgRDE0| (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} t,{} c)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.") (((|Union| |#2| "failed") |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|)) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgRDE0(f,{} g,{} x,{} y,{} foo,{} d,{} p)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}. Argument \\spad{foo},{} called by \\spad{foo(a,{} b,{} x)},{} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}.")) (|palglimint0| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} z,{} t,{} c)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}.") (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palglimint0(f,{} x,{} y,{} [u1,{}...,{}un],{} d,{} p)} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} and \"failed\" otherwise. Argument \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2y(x)\\^2 = P(x)}.")) (|palgextint0| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgextint0(f,{} x,{} y,{} g,{} z,{} t,{} c)} returns functions \\spad{[h,{} d]} such that \\spad{dh/dx = f(x,{}y) - d g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy},{} and \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}. The operation returns \"failed\" if no such functions exist.") (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgextint0(f,{} x,{} y,{} g,{} d,{} p)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)},{} or \"failed\" if no such functions exist.")) (|palgint0| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|Fraction| (|SparseUnivariatePolynomial| |#2|))) "\\spad{palgint0(f,{} x,{} y,{} z,{} t,{} c)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{f(x,{}y)dx = c f(t,{}y) dy}; \\spad{c} and \\spad{t} are rational functions of \\spad{y}. Argument \\spad{z} is a dummy variable not appearing in \\spad{f(x,{}y)}.") (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) "\\spad{palgint0(f,{} x,{} y,{} d,{} p)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x} satisfying \\spad{d(x)\\^2 y(x)\\^2 = P(x)}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -599) (|devaluate| |#2|)))) (-520) -((|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."))) +((|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 -(-521 -2315 UP UPUP R) +(-521 -3539 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 -(-522 -2315 UP) +(-522 -3539 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 (-523) ((|constructor| (NIL "\\spadtype{Integer} provides the domain of arbitrary precision integers.")) (|infinite| ((|attribute|) "nextItem never returns \"failed\".")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality.")) (|random| (($ $) "\\spad{random(n)} returns a random integer from 0 to \\spad{n-1}."))) -((-4226 . T) (-4232 . T) (-4236 . T) (-4231 . T) (-4242 . T) (-4243 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4230 . T) (-4236 . T) (-4240 . T) (-4235 . T) (-4246 . T) (-4247 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-524) ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|))) (|:| |extra| (|Result|))) (|NumericalIntegrationProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine for solving the numerical integration problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{NumericalIntegrationCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information.")) (|integrate| (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|Symbol|)) "\\spad{integrate(exp,{} x = a..b,{} numerical)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error if the last argument is not {\\spad{\\tt} numerical}.") (((|Union| (|Result|) "failed") (|Expression| (|Float|)) (|SegmentBinding| (|OrderedCompletion| (|Float|))) (|String|)) "\\spad{integrate(exp,{} x = a..b,{} \"numerical\")} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range,{} {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.\\newline \\blankline Default values for the absolute and relative error are used. \\blankline It is an error of the last argument is not {\\spad{\\tt} \"numerical\"}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel,{} routines)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy,{} using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsabs,{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|)))) (|Float|)) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...],{} epsrel)} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|List| (|Segment| (|OrderedCompletion| (|Float|))))) "\\spad{integrate(exp,{} [a..b,{}c..d,{}...])} is a top level ANNA function to integrate a multivariate expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given set of ranges. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|)))) "\\spad{integrate(exp,{} a..b)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline Default values for the absolute and relative error are used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}. \\blankline If epsrel = 0,{} a default absolute accuracy is used.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|)) "\\spad{integrate(exp,{} a..b,{} epsabs,{} epsrel)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|NumericalIntegrationProblem|)) "\\spad{integrate(IntegrationProblem)} is a top level ANNA function to integrate an expression over a given range or ranges to the required absolute and relative accuracy. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}.") (((|Result|) (|Expression| (|Float|)) (|Segment| (|OrderedCompletion| (|Float|))) (|Float|) (|Float|) (|RoutinesTable|)) "\\spad{integrate(exp,{} a..b,{} epsrel,{} routines)} is a top level ANNA function to integrate an expression,{} {\\spad{\\tt} \\spad{exp}},{} over a given range {\\spad{\\tt} a} to {\\spad{\\tt} \\spad{b}} to the required absolute and relative accuracy using the routines available in the RoutinesTable provided. \\blankline It iterates over the \\axiom{domains} of \\axiomType{NumericalIntegrationCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline It then performs the integration of the given expression on that \\axiom{domain}."))) NIL NIL -(-525 R -2315 L) +(-525 R -3539 L) ((|constructor| (NIL "This package provides functions for integration,{} limited integration,{} extended integration and the risch differential equation for pure algebraic integrands.")) (|palgLODE| (((|Record| (|:| |particular| (|Union| |#2| "failed")) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Symbol|)) "\\spad{palgLODE(op,{} g,{} kx,{} y,{} x)} returns the solution of \\spad{op f = g}. \\spad{y} is an algebraic function of \\spad{x}.")) (|palgRDE| (((|Union| |#2| "failed") |#2| |#2| |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|Mapping| (|Union| |#2| "failed") |#2| |#2| (|Symbol|))) "\\spad{palgRDE(nfp,{} f,{} g,{} x,{} y,{} foo)} returns a function \\spad{z(x,{}y)} such that \\spad{dz/dx + n * df/dx z(x,{}y) = g(x,{}y)} if such a \\spad{z} exists,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}; \\spad{foo(a,{} b,{} x)} is a function that solves \\spad{du/dx + n * da/dx u(x) = u(x)} for an unknown \\spad{u(x)} not involving \\spad{y}. \\spad{nfp} is \\spad{n * df/dx}.")) (|palglimint| (((|Union| (|Record| (|:| |mainpart| |#2|) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| |#2|) (|:| |logand| |#2|))))) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) (|List| |#2|)) "\\spad{palglimint(f,{} x,{} y,{} [u1,{}...,{}un])} returns functions \\spad{[h,{}[[\\spad{ci},{} \\spad{ui}]]]} such that the \\spad{ui}\\spad{'s} are among \\spad{[u1,{}...,{}un]} and \\spad{d(h + sum(\\spad{ci} log(\\spad{ui})))/dx = f(x,{}y)} if such functions exist,{} \"failed\" otherwise; \\spad{y} is an algebraic function of \\spad{x}.")) (|palgextint| (((|Union| (|Record| (|:| |ratpart| |#2|) (|:| |coeff| |#2|)) "failed") |#2| (|Kernel| |#2|) (|Kernel| |#2|) |#2|) "\\spad{palgextint(f,{} x,{} y,{} g)} returns functions \\spad{[h,{} c]} such that \\spad{dh/dx = f(x,{}y) - c g},{} where \\spad{y} is an algebraic function of \\spad{x}; returns \"failed\" if no such functions exist.")) (|palgint| (((|IntegrationResult| |#2|) |#2| (|Kernel| |#2|) (|Kernel| |#2|)) "\\spad{palgint(f,{} x,{} y)} returns the integral of \\spad{f(x,{}y)dx} where \\spad{y} is an algebraic function of \\spad{x}."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -599) (|devaluate| |#2|)))) -(-526 R -2315) +(-526 R -3539) ((|constructor| (NIL "\\spadtype{PatternMatchIntegration} provides functions that use the pattern matcher to find some indefinite and definite integrals involving special functions and found in the litterature.")) (|pmintegrate| (((|Union| |#2| "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|) (|OrderedCompletion| |#2|)) "\\spad{pmintegrate(f,{} x = a..b)} returns the integral of \\spad{f(x)dx} from a to \\spad{b} if it can be found by the built-in pattern matching rules.") (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}.")) (|pmComplexintegrate| (((|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|)) "\\spad{pmComplexintegrate(f,{} x)} returns either \"failed\" or \\spad{[g,{}h]} such that \\spad{integrate(f,{}x) = g + integrate(h,{}x)}. It only looks for special complex integrals that pmintegrate does not return.")) (|splitConstant| (((|Record| (|:| |const| |#2|) (|:| |nconst| |#2|)) |#2| (|Symbol|)) "\\spad{splitConstant(f,{} x)} returns \\spad{[c,{} g]} such that \\spad{f = c * g} and \\spad{c} does not involve \\spad{t}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1051)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-575))))) -(-527 -2315 UP) +(-527 -3539 UP) ((|constructor| (NIL "This package provides functions for the base case of the Risch algorithm.")) (|limitedint| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|List| (|Fraction| |#2|))) "\\spad{limitedint(f,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{}[[\\spad{ci},{} \\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{ci' = 0},{} and \\spad{(h+sum(\\spad{ci} log(\\spad{gi})))' = f},{} if possible,{} \"failed\" otherwise.")) (|extendedint| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{extendedint(f,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{c' = 0} and \\spad{h' = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|infieldint| (((|Union| (|Fraction| |#2|) "failed") (|Fraction| |#2|)) "\\spad{infieldint(f)} returns \\spad{g} such that \\spad{g' = f} or \"failed\" if the integral of \\spad{f} is not a rational function.")) (|integrate| (((|IntegrationResult| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{integrate(f)} returns \\spad{g} such that \\spad{g' = f}."))) NIL NIL @@ -2044,53 +2044,53 @@ NIL ((|constructor| (NIL "Provides integer testing and retraction functions. Date Created: March 1990 Date Last Updated: 9 April 1991")) (|integerIfCan| (((|Union| (|Integer|) "failed") |#1|) "\\spad{integerIfCan(x)} returns \\spad{x} as an integer,{} \"failed\" if \\spad{x} is not an integer.")) (|integer?| (((|Boolean|) |#1|) "\\spad{integer?(x)} is \\spad{true} if \\spad{x} is an integer,{} \\spad{false} otherwise.")) (|integer| (((|Integer|) |#1|) "\\spad{integer(x)} returns \\spad{x} as an integer; error if \\spad{x} is not an integer."))) NIL NIL -(-529 -2315) +(-529 -3539) ((|constructor| (NIL "This package provides functions for the integration of rational functions.")) (|extendedIntegrate| (((|Union| (|Record| (|:| |ratpart| (|Fraction| (|Polynomial| |#1|))) (|:| |coeff| (|Fraction| (|Polynomial| |#1|)))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|Fraction| (|Polynomial| |#1|))) "\\spad{extendedIntegrate(f,{} x,{} g)} returns fractions \\spad{[h,{} c]} such that \\spad{dc/dx = 0} and \\spad{dh/dx = f - cg},{} if \\spad{(h,{} c)} exist,{} \"failed\" otherwise.")) (|limitedIntegrate| (((|Union| (|Record| (|:| |mainpart| (|Fraction| (|Polynomial| |#1|))) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| (|Polynomial| |#1|))) (|:| |logand| (|Fraction| (|Polynomial| |#1|))))))) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|) (|List| (|Fraction| (|Polynomial| |#1|)))) "\\spad{limitedIntegrate(f,{} x,{} [g1,{}...,{}gn])} returns fractions \\spad{[h,{} [[\\spad{ci},{}\\spad{gi}]]]} such that the \\spad{gi}\\spad{'s} are among \\spad{[g1,{}...,{}gn]},{} \\spad{dci/dx = 0},{} and \\spad{d(h + sum(\\spad{ci} log(\\spad{gi})))/dx = f} if possible,{} \"failed\" otherwise.")) (|infieldIntegrate| (((|Union| (|Fraction| (|Polynomial| |#1|)) "failed") (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{infieldIntegrate(f,{} x)} returns a fraction \\spad{g} such that \\spad{dg/dx = f} if \\spad{g} exists,{} \"failed\" otherwise.")) (|internalIntegrate| (((|IntegrationResult| (|Fraction| (|Polynomial| |#1|))) (|Fraction| (|Polynomial| |#1|)) (|Symbol|)) "\\spad{internalIntegrate(f,{} x)} returns \\spad{g} such that \\spad{dg/dx = f}."))) NIL NIL (-530 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."))) -((-2562 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4108 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-531) ((|constructor| (NIL "This package provides the implementation for the \\spadfun{solveLinearPolynomialEquation} operation over the integers. It uses a lifting technique from the package GenExEuclid")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| (|Integer|))) "failed") (|List| (|SparseUnivariatePolynomial| (|Integer|))) (|SparseUnivariatePolynomial| (|Integer|))) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists."))) NIL NIL -(-532 R -2315) +(-532 R -3539) ((|constructor| (NIL "\\indented{1}{Tools for the integrator} Author: Manuel Bronstein Date Created: 25 April 1990 Date Last Updated: 9 June 1993 Keywords: elementary,{} function,{} integration.")) (|intPatternMatch| (((|IntegrationResult| |#2|) |#2| (|Symbol|) (|Mapping| (|IntegrationResult| |#2|) |#2| (|Symbol|)) (|Mapping| (|Union| (|Record| (|:| |special| |#2|) (|:| |integrand| |#2|)) "failed") |#2| (|Symbol|))) "\\spad{intPatternMatch(f,{} x,{} int,{} pmint)} tries to integrate \\spad{f} first by using the integration function \\spad{int},{} and then by using the pattern match intetgration function \\spad{pmint} on any remaining unintegrable part.")) (|mkPrim| ((|#2| |#2| (|Symbol|)) "\\spad{mkPrim(f,{} x)} makes the logs in \\spad{f} which are linear in \\spad{x} primitive with respect to \\spad{x}.")) (|removeConstantTerm| ((|#2| |#2| (|Symbol|)) "\\spad{removeConstantTerm(f,{} x)} returns \\spad{f} minus any additive constant with respect to \\spad{x}.")) (|vark| (((|List| (|Kernel| |#2|)) (|List| |#2|) (|Symbol|)) "\\spad{vark([f1,{}...,{}fn],{}x)} returns the set-theoretic union of \\spad{(varselect(f1,{}x),{}...,{}varselect(fn,{}x))}.")) (|union| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|))) "\\spad{union(l1,{} l2)} returns set-theoretic union of \\spad{l1} and \\spad{l2}.")) (|ksec| (((|Kernel| |#2|) (|Kernel| |#2|) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{ksec(k,{} [k1,{}...,{}kn],{} x)} returns the second top-level \\spad{ki} after \\spad{k} involving \\spad{x}.")) (|kmax| (((|Kernel| |#2|) (|List| (|Kernel| |#2|))) "\\spad{kmax([k1,{}...,{}kn])} returns the top-level \\spad{ki} for integration.")) (|varselect| (((|List| (|Kernel| |#2|)) (|List| (|Kernel| |#2|)) (|Symbol|)) "\\spad{varselect([k1,{}...,{}kn],{} x)} returns the \\spad{ki} which involve \\spad{x}."))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-261))) (|HasCategory| |#2| (QUOTE (-575))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087))))) (-12 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-261)))) (|HasCategory| |#1| (QUOTE (-515)))) -(-533 -2315 UP) +(-533 -3539 UP) ((|constructor| (NIL "This package provides functions for the transcendental case of the Risch algorithm.")) (|monomialIntPoly| (((|Record| (|:| |answer| |#2|) (|:| |polypart| |#2|)) |#2| (|Mapping| |#2| |#2|)) "\\spad{monomialIntPoly(p,{} ')} returns [\\spad{q},{} \\spad{r}] such that \\spad{p = q' + r} and \\spad{degree(r) < degree(t')}. Error if \\spad{degree(t') < 2}.")) (|monomialIntegrate| (((|Record| (|:| |ir| (|IntegrationResult| (|Fraction| |#2|))) (|:| |specpart| (|Fraction| |#2|)) (|:| |polypart| |#2|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|)) "\\spad{monomialIntegrate(f,{} ')} returns \\spad{[ir,{} s,{} p]} such that \\spad{f = ir' + s + p} and all the squarefree factors of the denominator of \\spad{s} are special \\spad{w}.\\spad{r}.\\spad{t} the derivation '.")) (|expintfldpoly| (((|Union| (|LaurentPolynomial| |#1| |#2|) "failed") (|LaurentPolynomial| |#1| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintfldpoly(p,{} foo)} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument foo is a Risch differential equation function on \\spad{F}.")) (|primintfldpoly| (((|Union| |#2| "failed") |#2| (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) |#1|) "\\spad{primintfldpoly(p,{} ',{} t')} returns \\spad{q} such that \\spad{p' = q} or \"failed\" if no such \\spad{q} exists. Argument \\spad{t'} is the derivative of the primitive generating the extension.")) (|primlimintfrac| (((|Union| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|)))))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|List| (|Fraction| |#2|))) "\\spad{primlimintfrac(f,{} ',{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn]]} such that \\spad{ci' = 0} and \\spad{f = v' + +/[\\spad{ci} * ui'/ui]}. Error: if \\spad{degree numer f >= degree denom f}.")) (|primextintfrac| (((|Union| (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Fraction| |#2|)) "\\spad{primextintfrac(f,{} ',{} g)} returns \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0}. Error: if \\spad{degree numer f >= degree denom f} or if \\spad{degree numer g >= degree denom g} or if \\spad{denom g} is not squarefree.")) (|explimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|List| (|Fraction| |#2|))) "\\spad{explimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primlimitedint| (((|Union| (|Record| (|:| |answer| (|Record| (|:| |mainpart| (|Fraction| |#2|)) (|:| |limitedlogs| (|List| (|Record| (|:| |coeff| (|Fraction| |#2|)) (|:| |logand| (|Fraction| |#2|))))))) (|:| |a0| |#1|)) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|List| (|Fraction| |#2|))) "\\spad{primlimitedint(f,{} ',{} foo,{} [u1,{}...,{}un])} returns \\spad{[v,{} [c1,{}...,{}cn],{} a]} such that \\spad{ci' = 0},{} \\spad{f = v' + a + reduce(+,{}[\\spad{ci} * ui'/ui])},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if no such \\spad{v},{} \\spad{ci},{} a exist. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|expextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|) (|Fraction| |#2|)) "\\spad{expextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is a Risch differential equation function on \\spad{F}.")) (|primextendedint| (((|Union| (|Record| (|:| |answer| (|Fraction| |#2|)) (|:| |a0| |#1|)) (|Record| (|:| |ratpart| (|Fraction| |#2|)) (|:| |coeff| (|Fraction| |#2|))) "failed") (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|) (|Fraction| |#2|)) "\\spad{primextendedint(f,{} ',{} foo,{} g)} returns either \\spad{[v,{} c]} such that \\spad{f = v' + c g} and \\spad{c' = 0},{} or \\spad{[v,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Returns \"failed\" if neither case can hold. Argument \\spad{foo} is an extended integration function on \\spad{F}.")) (|tanintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|List| |#1|) "failed") (|Integer|) |#1| |#1|)) "\\spad{tanintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential system solver on \\spad{F}.")) (|expintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Record| (|:| |ans| |#1|) (|:| |right| |#1|) (|:| |sol?| (|Boolean|))) (|Integer|) |#1|)) "\\spad{expintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in \\spad{F}; Argument foo is a Risch differential equation solver on \\spad{F}.")) (|primintegrate| (((|Record| (|:| |answer| (|IntegrationResult| (|Fraction| |#2|))) (|:| |a0| |#1|)) (|Fraction| |#2|) (|Mapping| |#2| |#2|) (|Mapping| (|Union| (|Record| (|:| |ratpart| |#1|) (|:| |coeff| |#1|)) "failed") |#1|)) "\\spad{primintegrate(f,{} ',{} foo)} returns \\spad{[g,{} a]} such that \\spad{f = g' + a},{} and \\spad{a = 0} or \\spad{a} has no integral in UP. Argument foo is an extended integration function on \\spad{F}."))) NIL NIL -(-534 R -2315) +(-534 R -3539) ((|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 (-535 |p| |unBalanced?|) ((|constructor| (NIL "This domain implements \\spad{Zp},{} the \\spad{p}-adic completion of the integers. This is an internal domain."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-536 |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."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-344)))) (-537) ((|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 -(-538 R -2315) +(-538 R -3539) ((|constructor| (NIL "This package allows a sum of logs over the roots of a polynomial to be expressed as explicit logarithms and arc tangents,{} provided that the indexing polynomial can be factored into quadratics.")) (|complexExpand| ((|#2| (|IntegrationResult| |#2|)) "\\spad{complexExpand(i)} returns the expanded complex function corresponding to \\spad{i}.")) (|expand| (((|List| |#2|) (|IntegrationResult| |#2|)) "\\spad{expand(i)} returns the list of possible real functions corresponding to \\spad{i}.")) (|split| (((|IntegrationResult| |#2|) (|IntegrationResult| |#2|)) "\\spad{split(u(x) + sum_{P(a)=0} Q(a,{}x))} returns \\spad{u(x) + sum_{P1(a)=0} Q(a,{}x) + ... + sum_{Pn(a)=0} Q(a,{}x)} where \\spad{P1},{}...,{}\\spad{Pn} are the factors of \\spad{P}."))) NIL NIL -(-539 E -2315) +(-539 E -3539) ((|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 -(-540 -2315) +(-540 -3539) ((|constructor| (NIL "If a function \\spad{f} has an elementary integral \\spad{g},{} then \\spad{g} can be written in the form \\spad{g = h + c1 log(u1) + c2 log(u2) + ... + cn log(un)} where \\spad{h},{} which is in the same field than \\spad{f},{} is called the rational part of the integral,{} and \\spad{c1 log(u1) + ... cn log(un)} is called the logarithmic part of the integral. This domain manipulates integrals represented in that form,{} by keeping both parts separately. The logs are not explicitly computed.")) (|differentiate| ((|#1| $ (|Symbol|)) "\\spad{differentiate(ir,{}x)} differentiates \\spad{ir} with respect to \\spad{x}") ((|#1| $ (|Mapping| |#1| |#1|)) "\\spad{differentiate(ir,{}D)} differentiates \\spad{ir} with respect to the derivation \\spad{D}.")) (|integral| (($ |#1| (|Symbol|)) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}") (($ |#1| |#1|) "\\spad{integral(f,{}x)} returns the formal integral of \\spad{f} with respect to \\spad{x}")) (|elem?| (((|Boolean|) $) "\\spad{elem?(ir)} tests if an integration result is elementary over \\spad{F?}")) (|notelem| (((|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|))) $) "\\spad{notelem(ir)} returns the non-elementary part of an integration result")) (|logpart| (((|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) $) "\\spad{logpart(ir)} returns the logarithmic part of an integration result")) (|ratpart| ((|#1| $) "\\spad{ratpart(ir)} returns the rational part of an integration result")) (|mkAnswer| (($ |#1| (|List| (|Record| (|:| |scalar| (|Fraction| (|Integer|))) (|:| |coeff| (|SparseUnivariatePolynomial| |#1|)) (|:| |logand| (|SparseUnivariatePolynomial| |#1|)))) (|List| (|Record| (|:| |integrand| |#1|) (|:| |intvar| |#1|)))) "\\spad{mkAnswer(r,{}l,{}ne)} creates an integration result from a rational part \\spad{r},{} a logarithmic part \\spad{l},{} and a non-elementary part \\spad{ne}."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-1087))))) (-541 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"))) @@ -2114,19 +2114,19 @@ NIL NIL (-546 |mn|) ((|constructor| (NIL "This domain implements low-level strings")) (|hash| (((|Integer|) $) "\\spad{hash(x)} provides a hashing function for strings"))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (-3262 (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (-3172 (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) (-547 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 (-548 |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}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|)))) (|HasCategory| (-523) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -1458) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523)))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-523)) (|devaluate| |#1|)))) (|HasCategory| (-523) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-523)))))) (-549 |Coef|) ((|constructor| (NIL "Internal package for dense Taylor series. This is an internal Taylor series type in which Taylor series are represented by a \\spadtype{Stream} of \\spadtype{Ring} elements. For univariate series,{} the \\spad{Stream} elements are the Taylor coefficients. For multivariate series,{} the \\spad{n}th Stream element is a form of degree \\spad{n} in the power series variables.")) (* (($ $ (|Integer|)) "\\spad{x*i} returns the product of integer \\spad{i} and the series \\spad{x}.") (($ $ |#1|) "\\spad{x*c} returns the product of \\spad{c} and the series \\spad{x}.") (($ |#1| $) "\\spad{c*x} returns the product of \\spad{c} and the series \\spad{x}.")) (|order| (((|NonNegativeInteger|) $ (|NonNegativeInteger|)) "\\spad{order(x,{}n)} returns the minimum of \\spad{n} and the order of \\spad{x}.") (((|NonNegativeInteger|) $) "\\spad{order(x)} returns the order of a power series \\spad{x},{} \\indented{1}{\\spadignore{i.e.} the degree of the first non-zero term of the series.}")) (|pole?| (((|Boolean|) $) "\\spad{pole?(x)} tests if the series \\spad{x} has a pole. \\indented{1}{Note: this is \\spad{false} when \\spad{x} is a Taylor series.}")) (|series| (($ (|Stream| |#1|)) "\\spad{series(s)} creates a power series from a stream of \\indented{1}{ring elements.} \\indented{1}{For univariate series types,{} the stream \\spad{s} should be a stream} \\indented{1}{of Taylor coefficients. For multivariate series types,{} the} \\indented{1}{stream \\spad{s} should be a stream of forms the \\spad{n}th element} \\indented{1}{of which is a} \\indented{1}{form of degree \\spad{n} in the power series variables.}")) (|coefficients| (((|Stream| |#1|) $) "\\spad{coefficients(x)} returns a stream of ring elements. \\indented{1}{When \\spad{x} is a univariate series,{} this is a stream of Taylor} \\indented{1}{coefficients. When \\spad{x} is a multivariate series,{} the} \\indented{1}{\\spad{n}th element of the stream is a form of} \\indented{1}{degree \\spad{n} in the power series variables.}"))) -((-4239 |has| |#1| (-515)) (-4238 |has| |#1| (-515)) ((-4246 "*") |has| |#1| (-515)) (-4237 |has| |#1| (-515)) (-4241 . T)) +((-4243 |has| |#1| (-515)) (-4242 |has| |#1| (-515)) ((-4250 "*") |has| |#1| (-515)) (-4241 |has| |#1| (-515)) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-515)))) (-550 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),{}..]}."))) @@ -2136,7 +2136,7 @@ NIL ((|constructor| (NIL "Functions defined on streams with entries in two sets.")) (|map| (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|Stream| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|Stream| |#3|) (|Mapping| |#3| |#1| |#2|) (|Stream| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented") (((|InfiniteTuple| |#3|) (|Mapping| |#3| |#1| |#2|) (|InfiniteTuple| |#1|) (|InfiniteTuple| |#2|)) "\\spad{map(f,{}a,{}b)} \\undocumented"))) NIL NIL -(-552 R -2315 FG) +(-552 R -3539 FG) ((|constructor| (NIL "This package provides transformations from trigonometric functions to exponentials and logarithms,{} and back. \\spad{F} and \\spad{FG} should be the same type of function space.")) (|trigs2explogs| ((|#3| |#3| (|List| (|Kernel| |#3|)) (|List| (|Symbol|))) "\\spad{trigs2explogs(f,{} [k1,{}...,{}kn],{} [x1,{}...,{}xm])} rewrites all the trigonometric functions appearing in \\spad{f} and involving one of the \\spad{\\spad{xi}'s} in terms of complex logarithms and exponentials. A kernel of the form \\spad{tan(u)} is expressed using \\spad{exp(u)**2} if it is one of the \\spad{\\spad{ki}'s},{} in terms of \\spad{exp(2*u)} otherwise.")) (|explogs2trigs| (((|Complex| |#2|) |#3|) "\\spad{explogs2trigs(f)} rewrites all the complex logs and exponentials appearing in \\spad{f} in terms of trigonometric functions.")) (F2FG ((|#3| |#2|) "\\spad{F2FG(a + sqrt(-1) b)} returns \\spad{a + i b}.")) (FG2F ((|#2| |#3|) "\\spad{FG2F(a + i b)} returns \\spad{a + sqrt(-1) b}.")) (GF2FG ((|#3| (|Complex| |#2|)) "\\spad{GF2FG(a + i b)} returns \\spad{a + i b} viewed as a function with the \\spad{i} pushed down into the coefficient domain."))) NIL NIL @@ -2146,31 +2146,31 @@ NIL NIL (-554 R |mn|) ((|constructor| (NIL "\\indented{2}{This type represents vector like objects with varying lengths} and a user-specified initial index."))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-555 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 -4245)) (|HasCategory| |#2| (QUOTE (-786))) (|HasAttribute| |#1| (QUOTE -4244)) (|HasCategory| |#3| (QUOTE (-1016)))) +((|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (QUOTE (-786))) (|HasAttribute| |#1| (QUOTE -4248)) (|HasCategory| |#3| (QUOTE (-1016)))) (-556 |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|) $) "\\spad{entries(u)} returns a list of all the entries of aggregate \\spad{u} in no assumed order."))) -((-3656 . T)) +((-4069 . T)) NIL (-557 R A) ((|constructor| (NIL "\\indented{1}{AssociatedJordanAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4241 -3262 (-4099 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4239 . T) (-4238 . T)) -((-3262 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) +((-4245 -3172 (-3147 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4243 . T) (-4242 . T)) +((-3172 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-558 |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."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#1|)))))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-559 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 (-560 |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}."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL (-561 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"))) @@ -2188,7 +2188,7 @@ NIL ((|constructor| (NIL "A is convertible to \\spad{B} means any element of A can be converted into an element of \\spad{B},{} but not automatically by the interpreter.")) (|convert| ((|#1| $) "\\spad{convert(a)} transforms a into an element of \\spad{S}."))) NIL NIL -(-565 -2315 UP) +(-565 -3539 UP) ((|constructor| (NIL "\\spadtype{Kovacic} provides a modified Kovacic\\spad{'s} algorithm for solving explicitely irreducible 2nd order linear ordinary differential equations.")) (|kovacic| (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2,{}ezfactor)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{\\$a_2 y'' + a_1 y' + a0 y = 0\\$}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|Union| (|SparseUnivariatePolynomial| (|Fraction| |#2|)) "failed") (|Fraction| |#2|) (|Fraction| |#2|) (|Fraction| |#2|)) "\\spad{kovacic(a_0,{}a_1,{}a_2)} returns either \"failed\" or \\spad{P}(\\spad{u}) such that \\spad{\\$e^{\\int(-a_1/2a_2)} e^{\\int u}\\$} is a solution of \\indented{5}{\\spad{a_2 y'' + a_1 y' + a0 y = 0}} whenever \\spad{u} is a solution of \\spad{P u = 0}. The equation must be already irreducible over the rational functions."))) NIL NIL @@ -2198,19 +2198,19 @@ NIL NIL (-567 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."))) -((-4241 . T)) +((-4245 . T)) NIL (-568 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}."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-784)))) -(-569 R -2315) +(-569 R -3539) ((|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 (-570 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"))) -((-4239 . T) (-4238 . T) ((-4246 "*") . T) (-4237 . T) (-4241 . T)) +((-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4241 . T) (-4245 . T)) ((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (-571 R E V P TS ST) ((|constructor| (NIL "A package for solving polynomial systems by means of Lazard triangular sets [1]. This package provides two operations. One for solving in the sense of the regular zeros,{} and the other for solving in the sense of the Zariski closure. Both produce square-free regular sets. Moreover,{} the decompositions do not contain any redundant component. However,{} only zero-dimensional regular sets are normalized,{} since normalization may be time consumming in positive dimension. The decomposition process is that of [2].\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| |#6|) (|List| |#4|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?)} has the same specifications as \\axiomOpFrom{zeroSetSplit(\\spad{lp},{}clos?)}{RegularTriangularSetCategory}.")) (|normalizeIfCan| ((|#6| |#6|) "\\axiom{normalizeIfCan(\\spad{ts})} returns \\axiom{\\spad{ts}} in an normalized shape if \\axiom{\\spad{ts}} is zero-dimensional."))) @@ -2222,7 +2222,7 @@ NIL NIL (-573 |VarSet| R |Order|) ((|constructor| (NIL "Management of the Lie Group associated with a free nilpotent Lie algebra. Every Lie bracket with length greater than \\axiom{Order} are assumed to be null. The implementation inherits from the \\spadtype{XPBWPolynomial} domain constructor: Lyndon coordinates are exponential coordinates of the second kind. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|identification| (((|List| (|Equation| |#2|)) $ $) "\\axiom{identification(\\spad{g},{}\\spad{h})} returns the list of equations \\axiom{g_i = h_i},{} where \\axiom{g_i} (resp. \\axiom{h_i}) are exponential coordinates of \\axiom{\\spad{g}} (resp. \\axiom{\\spad{h}}).")) (|LyndonCoordinates| (((|List| (|Record| (|:| |k| (|LyndonWord| |#1|)) (|:| |c| |#2|))) $) "\\axiom{LyndonCoordinates(\\spad{g})} returns the exponential coordinates of \\axiom{\\spad{g}}.")) (|LyndonBasis| (((|List| (|LiePolynomial| |#1| |#2|)) (|List| |#1|)) "\\axiom{LyndonBasis(\\spad{lv})} returns the Lyndon basis of the nilpotent free Lie algebra.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{g})} returns the list of variables of \\axiom{\\spad{g}}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{g})} is the mirror of the internal representation of \\axiom{\\spad{g}}.")) (|coerce| (((|XPBWPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{g})} returns the internal representation of \\axiom{\\spad{g}}.")) (|ListOfTerms| (((|List| (|Record| (|:| |k| (|PoincareBirkhoffWittLyndonBasis| |#1|)) (|:| |c| |#2|))) $) "\\axiom{ListOfTerms(\\spad{p})} returns the internal representation of \\axiom{\\spad{p}}.")) (|log| (((|LiePolynomial| |#1| |#2|) $) "\\axiom{log(\\spad{p})} returns the logarithm of \\axiom{\\spad{p}}.")) (|exp| (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{exp(\\spad{p})} returns the exponential of \\axiom{\\spad{p}}."))) -((-4241 . T)) +((-4245 . T)) NIL (-574 R |ls|) ((|constructor| (NIL "A package for solving polynomial systems with finitely many solutions. The decompositions are given by means of regular triangular sets. The computations use lexicographical Groebner bases. The main operations are \\axiomOpFrom{lexTriangular}{LexTriangularPackage} and \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage}. The second one provide decompositions by means of square-free regular triangular sets. Both are based on the {\\em lexTriangular} method described in [1]. They differ from the algorithm described in [2] by the fact that multiciplities of the roots are not kept. With the \\axiomOpFrom{squareFreeLexTriangular}{LexTriangularPackage} operation all multiciplities are removed. With the other operation some multiciplities may remain. Both operations admit an optional argument to produce normalized triangular sets. \\newline")) (|zeroSetSplit| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{} norm?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|squareFreeLexTriangular| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#2|)) (|OrderedVariableList| |#2|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{squareFreeLexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into square-free regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|lexTriangular| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|)) "\\axiom{lexTriangular(base,{} norm?)} decomposes the variety associated with \\axiom{base} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{base} needs to be a lexicographical Groebner basis of a zero-dimensional ideal. If \\axiom{norm?} is \\axiom{\\spad{true}} then the regular sets are normalized.")) (|groebner| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{groebner(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}}. If \\axiom{\\spad{lp}} generates a zero-dimensional ideal then the {\\em FGLM} strategy is used,{} otherwise the {\\em Sugar} strategy is used.")) (|fglmIfCan| (((|Union| (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "failed") (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{fglmIfCan(\\spad{lp})} returns the lexicographical Groebner basis of \\axiom{\\spad{lp}} by using the {\\em FGLM} strategy,{} if \\axiom{zeroDimensional?(\\spad{lp})} holds .")) (|zeroDimensional?| (((|Boolean|) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|)))) "\\axiom{zeroDimensional?(\\spad{lp})} returns \\spad{true} iff \\axiom{\\spad{lp}} generates a zero-dimensional ideal \\spad{w}.\\spad{r}.\\spad{t}. the variables involved in \\axiom{\\spad{lp}}."))) @@ -2232,30 +2232,30 @@ NIL ((|constructor| (NIL "Category for the transcendental Liouvillian functions.")) (|erf| (($ $) "\\spad{erf(x)} returns the error function of \\spad{x},{} \\spadignore{i.e.} \\spad{2 / sqrt(\\%\\spad{pi})} times the integral of \\spad{exp(-x**2) dx}.")) (|dilog| (($ $) "\\spad{dilog(x)} returns the dilogarithm of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{log(x) / (1 - x) dx}.")) (|li| (($ $) "\\spad{\\spad{li}(x)} returns the logarithmic integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{dx / log(x)}.")) (|Ci| (($ $) "\\spad{\\spad{Ci}(x)} returns the cosine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{cos(x) / x dx}.")) (|Si| (($ $) "\\spad{\\spad{Si}(x)} returns the sine integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{sin(x) / x dx}.")) (|Ei| (($ $) "\\spad{\\spad{Ei}(x)} returns the exponential integral of \\spad{x},{} \\spadignore{i.e.} the integral of \\spad{exp(x)/x dx}."))) NIL NIL -(-576 R -2315) +(-576 R -3539) ((|constructor| (NIL "This package provides liouvillian functions over an integral domain.")) (|integral| ((|#2| |#2| (|SegmentBinding| |#2|)) "\\spad{integral(f,{}x = a..b)} denotes the definite integral of \\spad{f} with respect to \\spad{x} from \\spad{a} to \\spad{b}.") ((|#2| |#2| (|Symbol|)) "\\spad{integral(f,{}x)} indefinite integral of \\spad{f} with respect to \\spad{x}.")) (|dilog| ((|#2| |#2|) "\\spad{dilog(f)} denotes the dilogarithm")) (|erf| ((|#2| |#2|) "\\spad{erf(f)} denotes the error function")) (|li| ((|#2| |#2|) "\\spad{\\spad{li}(f)} denotes the logarithmic integral")) (|Ci| ((|#2| |#2|) "\\spad{\\spad{Ci}(f)} denotes the cosine integral")) (|Si| ((|#2| |#2|) "\\spad{\\spad{Si}(f)} denotes the sine integral")) (|Ei| ((|#2| |#2|) "\\spad{\\spad{Ei}(f)} denotes the exponential integral")) (|operator| (((|BasicOperator|) (|BasicOperator|)) "\\spad{operator(op)} returns the Liouvillian operator based on \\spad{op}")) (|belong?| (((|Boolean|) (|BasicOperator|)) "\\spad{belong?(op)} checks if \\spad{op} is Liouvillian"))) NIL NIL -(-577 |lv| -2315) +(-577 |lv| -3539) ((|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 (-578) ((|constructor| (NIL "This domain provides a simple way to save values in files.")) (|setelt| (((|Any|) $ (|Symbol|) (|Any|)) "\\spad{lib.k := v} saves the value \\spad{v} in the library \\spad{lib}. It can later be extracted using the key \\spad{k}.")) (|elt| (((|Any|) $ (|Symbol|)) "\\spad{elt(lib,{}k)} or \\spad{lib}.\\spad{k} extracts the value corresponding to the key \\spad{k} from the library \\spad{lib}.")) (|pack!| (($ $) "\\spad{pack!(f)} reorganizes the file \\spad{f} on disk to recover unused space.")) (|library| (($ (|FileName|)) "\\spad{library(ln)} creates a new library file."))) -((-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2433) (QUOTE (-51))))))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-1070) (QUOTE (-786))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2482) (QUOTE (-51))))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-1070) (QUOTE (-786))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) (-579 S R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#2|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) NIL ((|HasCategory| |#2| (QUOTE (-339)))) (-580 R) ((|constructor| (NIL "\\axiom{JacobiIdentity} means that \\axiom{[\\spad{x},{}[\\spad{y},{}\\spad{z}]]+[\\spad{y},{}[\\spad{z},{}\\spad{x}]]+[\\spad{z},{}[\\spad{x},{}\\spad{y}]] = 0} holds.")) (/ (($ $ |#1|) "\\axiom{\\spad{x/r}} returns the division of \\axiom{\\spad{x}} by \\axiom{\\spad{r}}.")) (|construct| (($ $ $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket of \\axiom{\\spad{x}} and \\axiom{\\spad{y}}."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4239 . T) (-4238 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4243 . T) (-4242 . T)) NIL (-581 R A) ((|constructor| (NIL "AssociatedLieAlgebra takes an algebra \\spad{A} and uses \\spadfun{*\\$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)."))) -((-4241 -3262 (-4099 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4239 . T) (-4238 . T)) -((-3262 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) +((-4245 -3172 (-3147 (|has| |#2| (-343 |#1|)) (|has| |#1| (-515))) (-12 (|has| |#2| (-393 |#1|)) (|has| |#1| (-515)))) (-4243 . T) (-4242 . T)) +((-3172 (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -393) (|devaluate| |#1|))))) (|HasCategory| |#2| (LIST (QUOTE -343) (|devaluate| |#1|)))) (-582 R FE) ((|constructor| (NIL "PowerSeriesLimitPackage implements limits of expressions in one or more variables as one of the variables approaches a limiting value. Included are two-sided limits,{} left- and right- hand limits,{} and limits at plus or minus infinity.")) (|complexLimit| (((|Union| (|OnePointCompletion| |#2|) "failed") |#2| (|Equation| (|OnePointCompletion| |#2|))) "\\spad{complexLimit(f(x),{}x = a)} computes the complex limit \\spad{lim(x -> a,{}f(x))}.")) (|limit| (((|Union| (|OrderedCompletion| |#2|) "failed") |#2| (|Equation| |#2|) (|String|)) "\\spad{limit(f(x),{}x=a,{}\"left\")} computes the left hand real limit \\spad{lim(x -> a-,{}f(x))}; \\spad{limit(f(x),{}x=a,{}\"right\")} computes the right hand real limit \\spad{lim(x -> a+,{}f(x))}.") (((|Union| (|OrderedCompletion| |#2|) (|Record| (|:| |leftHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed")) (|:| |rightHandLimit| (|Union| (|OrderedCompletion| |#2|) "failed"))) "failed") |#2| (|Equation| (|OrderedCompletion| |#2|))) "\\spad{limit(f(x),{}x = a)} computes the real limit \\spad{lim(x -> a,{}f(x))}."))) NIL @@ -2267,10 +2267,10 @@ NIL (-584 S R) ((|constructor| (NIL "Test for linear dependence.")) (|solveLinear| (((|Union| (|Vector| (|Fraction| |#1|)) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in the quotient field of \\spad{S}.") (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|) |#2|) "\\spad{solveLinear([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such \\spad{ci}\\spad{'s} exist in \\spad{S}.")) (|linearDependence| (((|Union| (|Vector| |#1|) "failed") (|Vector| |#2|)) "\\spad{linearDependence([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over \\spad{S}.")) (|linearlyDependent?| (((|Boolean|) (|Vector| |#2|)) "\\spad{linearlyDependent?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over \\spad{S},{} \\spad{false} otherwise."))) NIL -((-3900 (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-339)))) +((-4179 (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-339)))) (-585 R) ((|constructor| (NIL "An extension ring with an explicit linear dependence test.")) (|reducedSystem| (((|Record| (|:| |mat| (|Matrix| |#1|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| $) (|Vector| $)) "\\spad{reducedSystem(A,{} v)} returns a matrix \\spad{B} and a vector \\spad{w} such that \\spad{A x = v} and \\spad{B x = w} have the same solutions in \\spad{R}.") (((|Matrix| |#1|) (|Matrix| $)) "\\spad{reducedSystem(A)} returns a matrix \\spad{B} such that \\spad{A x = 0} and \\spad{B x = 0} have the same solutions in \\spad{R}."))) -((-4241 . T)) +((-4245 . T)) NIL (-586 A B) ((|constructor| (NIL "\\spadtype{ListToMap} allows mappings to be described by a pair of lists of equal lengths. The image of an element \\spad{x},{} which appears in position \\spad{n} in the first list,{} is then the \\spad{n}th element of the second list. A default value or default function can be specified to be used when \\spad{x} does not appear in the first list. In the absence of defaults,{} an error will occur in that case.")) (|match| ((|#2| (|List| |#1|) (|List| |#2|) |#1| (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} a,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is a default function to call if a is not in \\spad{la}. The value returned is then obtained by applying \\spad{f} to argument a.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) (|Mapping| |#2| |#1|)) "\\spad{match(la,{} lb,{} f)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{f} is used as the function to call when the given function argument is not in \\spad{la}. The value returned is \\spad{f} applied to that argument.") ((|#2| (|List| |#1|) (|List| |#2|) |#1| |#2|) "\\spad{match(la,{} lb,{} a,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length. and applies this map to a. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Argument \\spad{b} is the default target value if a is not in \\spad{la}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|) |#2|) "\\spad{match(la,{} lb,{} b)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{b} is used as the default target value if the given function argument is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") ((|#2| (|List| |#1|) (|List| |#2|) |#1|) "\\spad{match(la,{} lb,{} a)} creates a map defined by lists \\spad{la} and \\spad{lb} of equal length,{} where \\spad{a} is used as the default source value if the given one is not in \\spad{la}. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length.") (((|Mapping| |#2| |#1|) (|List| |#1|) (|List| |#2|)) "\\spad{match(la,{} lb)} creates a map with no default source or target values defined by lists \\spad{la} and \\spad{lb} of equal length. The target of a source value \\spad{x} in \\spad{la} is the value \\spad{y} with the same index \\spad{lb}. Error: if \\spad{la} and \\spad{lb} are not of equal length. Note: when this map is applied,{} an error occurs when applied to a value missing from \\spad{la}."))) @@ -2286,12 +2286,12 @@ NIL NIL (-589 S) ((|constructor| (NIL "\\spadtype{List} implements singly-linked lists that are addressable by indices; the index of the first element is 1. In addition to the operations provided by \\spadtype{IndexedList},{} this constructor provides some LISP-like functions such as \\spadfun{null} and \\spadfun{cons}.")) (|setDifference| (($ $ $) "\\spad{setDifference(u1,{}u2)} returns a list of the elements of \\spad{u1} that are not also in \\spad{u2}. The order of elements in the resulting list is unspecified.")) (|setIntersection| (($ $ $) "\\spad{setIntersection(u1,{}u2)} returns a list of the elements that lists \\spad{u1} and \\spad{u2} have in common. The order of elements in the resulting list is unspecified.")) (|setUnion| (($ $ $) "\\spad{setUnion(u1,{}u2)} appends the two lists \\spad{u1} and \\spad{u2},{} then removes all duplicates. The order of elements in the resulting list is unspecified.")) (|append| (($ $ $) "\\spad{append(u1,{}u2)} appends the elements of list \\spad{u1} onto the front of list \\spad{u2}. This new list and \\spad{u2} will share some structure.")) (|cons| (($ |#1| $) "\\spad{cons(element,{}u)} appends \\spad{element} onto the front of list \\spad{u} and returns the new list. This new list and the old one will share some structure.")) (|null| (((|Boolean|) $) "\\spad{null(u)} tests if list \\spad{u} is the empty list.")) (|nil| (($) "\\spad{nil()} returns the empty list."))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-767))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-590 S) ((|substitute| (($ |#1| |#1| $) "\\spad{substitute(x,{}y,{}d)} replace \\spad{x}\\spad{'s} with \\spad{y}\\spad{'s} in dictionary \\spad{d}.")) (|duplicates?| (((|Boolean|) $) "\\spad{duplicates?(d)} tests if dictionary \\spad{d} has duplicate entries."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-591 R) ((|constructor| (NIL "The category of left modules over an \\spad{rng} (ring not necessarily with unit). This is an abelian group which supports left multiplation by elements of the \\spad{rng}. \\blankline")) (* (($ |#1| $) "\\spad{r*x} returns the left multiplication of the module element \\spad{x} by the ring element \\spad{r}."))) NIL @@ -2303,22 +2303,22 @@ NIL (-593 A S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#2| $ (|UniversalSegment| (|Integer|)) |#2|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#2| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#2|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#2|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) NIL -((|HasAttribute| |#1| (QUOTE -4245))) +((|HasAttribute| |#1| (QUOTE -4249))) (-594 S) ((|constructor| (NIL "A linear aggregate is an aggregate whose elements are indexed by integers. Examples of linear aggregates are strings,{} lists,{} and arrays. Most of the exported operations for linear aggregates are non-destructive but are not always efficient for a particular aggregate. For example,{} \\spadfun{concat} of two lists needs only to copy its first argument,{} whereas \\spadfun{concat} of two arrays needs to copy both arguments. Most of the operations exported here apply to infinite objects (\\spadignore{e.g.} streams) as well to finite ones. For finite linear aggregates,{} see \\spadtype{FiniteLinearAggregate}.")) (|setelt| ((|#1| $ (|UniversalSegment| (|Integer|)) |#1|) "\\spad{setelt(u,{}i..j,{}x)} (also written: \\axiom{\\spad{u}(\\spad{i}..\\spad{j}) \\spad{:=} \\spad{x}}) destructively replaces each element in the segment \\axiom{\\spad{u}(\\spad{i}..\\spad{j})} by \\spad{x}. The value \\spad{x} is returned. Note: \\spad{u} is destructively change so that \\axiom{\\spad{u}.\\spad{k} \\spad{:=} \\spad{x} for \\spad{k} in \\spad{i}..\\spad{j}}; its length remains unchanged.")) (|insert| (($ $ $ (|Integer|)) "\\spad{insert(v,{}u,{}k)} returns a copy of \\spad{u} having \\spad{v} inserted beginning at the \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{v},{}\\spad{u},{}\\spad{k}) = concat( \\spad{u}(0..\\spad{k}-1),{} \\spad{v},{} \\spad{u}(\\spad{k}..) )}.") (($ |#1| $ (|Integer|)) "\\spad{insert(x,{}u,{}i)} returns a copy of \\spad{u} having \\spad{x} as its \\axiom{\\spad{i}}th element. Note: \\axiom{insert(\\spad{x},{}a,{}\\spad{k}) = concat(concat(a(0..\\spad{k}-1),{}\\spad{x}),{}a(\\spad{k}..))}.")) (|delete| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{delete(u,{}i..j)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th through \\axiom{\\spad{j}}th element deleted. Note: \\axiom{delete(a,{}\\spad{i}..\\spad{j}) = concat(a(0..\\spad{i}-1),{}a(\\spad{j+1}..))}.") (($ $ (|Integer|)) "\\spad{delete(u,{}i)} returns a copy of \\spad{u} with the \\axiom{\\spad{i}}th element deleted. Note: for lists,{} \\axiom{delete(a,{}\\spad{i}) \\spad{==} concat(a(0..\\spad{i} - 1),{}a(\\spad{i} + 1,{}..))}.")) (|elt| (($ $ (|UniversalSegment| (|Integer|))) "\\spad{elt(u,{}i..j)} (also written: \\axiom{a(\\spad{i}..\\spad{j})}) returns the aggregate of elements \\axiom{\\spad{u}} for \\spad{k} from \\spad{i} to \\spad{j} in that order. Note: in general,{} \\axiom{a.\\spad{s} = [a.\\spad{k} for \\spad{i} in \\spad{s}]}.")) (|map| (($ (|Mapping| |#1| |#1| |#1|) $ $) "\\spad{map(f,{}u,{}v)} returns a new collection \\spad{w} with elements \\axiom{\\spad{z} = \\spad{f}(\\spad{x},{}\\spad{y})} for corresponding elements \\spad{x} and \\spad{y} from \\spad{u} and \\spad{v}. Note: for linear aggregates,{} \\axiom{\\spad{w}.\\spad{i} = \\spad{f}(\\spad{u}.\\spad{i},{}\\spad{v}.\\spad{i})}.")) (|concat| (($ (|List| $)) "\\spad{concat(u)},{} where \\spad{u} is a lists of aggregates \\axiom{[a,{}\\spad{b},{}...,{}\\spad{c}]},{} returns a single aggregate consisting of the elements of \\axiom{a} followed by those of \\spad{b} followed ... by the elements of \\spad{c}. Note: \\axiom{concat(a,{}\\spad{b},{}...,{}\\spad{c}) = concat(a,{}concat(\\spad{b},{}...,{}\\spad{c}))}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} then \\axiom{\\spad{w}.\\spad{i} = \\spad{u}.\\spad{i} for \\spad{i} in indices \\spad{u}} and \\axiom{\\spad{w}.(\\spad{j} + maxIndex \\spad{u}) = \\spad{v}.\\spad{j} for \\spad{j} in indices \\spad{v}}.") (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate \\spad{u} with additional element at the front. Note: for lists: \\axiom{concat(\\spad{x},{}\\spad{u}) \\spad{==} concat([\\spad{x}],{}\\spad{u})}.") (($ $ |#1|) "\\spad{concat(u,{}x)} returns aggregate \\spad{u} with additional element \\spad{x} at the end. Note: for lists,{} \\axiom{concat(\\spad{u},{}\\spad{x}) \\spad{==} concat(\\spad{u},{}[\\spad{x}])}")) (|new| (($ (|NonNegativeInteger|) |#1|) "\\spad{new(n,{}x)} returns \\axiom{fill!(new \\spad{n},{}\\spad{x})}."))) -((-3656 . T)) +((-4069 . T)) NIL -(-595 R -2315 L) +(-595 R -3539 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 (-596 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}}"))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-339)))) (-597 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| (($ $) "\\spad{differentiate(x)} returns the derivative of \\spad{x}"))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-339)))) (-598 S A) ((|constructor| (NIL "\\spad{LinearOrdinaryDifferentialOperatorCategory} is the category of differential operators with coefficients in a ring A with a given derivation. Multiplication of operators corresponds to functional composition: \\indented{4}{\\spad{(L1 * L2).(f) = L1 L2 f}}")) (|directSum| (($ $ $) "\\spad{directSum(a,{}b)} computes an operator \\spad{c} of minimal order such that the nullspace of \\spad{c} is generated by all the sums of a solution of \\spad{a} by a solution of \\spad{b}.")) (|symmetricSquare| (($ $) "\\spad{symmetricSquare(a)} computes \\spad{symmetricProduct(a,{}a)} using a more efficient method.")) (|symmetricPower| (($ $ (|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}."))) @@ -2326,15 +2326,15 @@ NIL ((|HasCategory| |#2| (QUOTE (-339)))) (-599 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}."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-600 -2315 UP) +(-600 -3539 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)))) -(-601 A -4168) +(-601 A -2576) ((|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}}"))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-339)))) (-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."))) @@ -2350,7 +2350,7 @@ NIL NIL (-605 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}."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) ((|HasCategory| |#1| (QUOTE (-730)))) (-606 R) ((|constructor| (NIL "Given a PolynomialFactorizationExplicit ring,{} this package provides a defaulting rule for the \\spad{solveLinearPolynomialEquation} operation,{} by moving into the field of fractions,{} and solving it there via the \\spad{multiEuclidean} operation.")) (|solveLinearPolynomialEquationByFractions| (((|Union| (|List| (|SparseUnivariatePolynomial| |#1|)) "failed") (|List| (|SparseUnivariatePolynomial| |#1|)) (|SparseUnivariatePolynomial| |#1|)) "\\spad{solveLinearPolynomialEquationByFractions([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such exists."))) @@ -2358,7 +2358,7 @@ NIL NIL (-607 |VarSet| R) ((|constructor| (NIL "This type supports Lie polynomials in Lyndon basis see Free Lie Algebras by \\spad{C}. Reutenauer (Oxford science publications). \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|construct| (($ $ (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) $) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.") (($ (|LyndonWord| |#1|) (|LyndonWord| |#1|)) "\\axiom{construct(\\spad{x},{}\\spad{y})} returns the Lie bracket \\axiom{[\\spad{x},{}\\spad{y}]}.")) (|LiePolyIfCan| (((|Union| $ "failed") (|XDistributedPolynomial| |#1| |#2|)) "\\axiom{LiePolyIfCan(\\spad{p})} returns \\axiom{\\spad{p}} in Lyndon basis if \\axiom{\\spad{p}} is a Lie polynomial,{} otherwise \\axiom{\"failed\"} is returned."))) -((|JacobiIdentity| . T) (|NullSquare| . T) (-4239 . T) (-4238 . T)) +((|JacobiIdentity| . T) (|NullSquare| . T) (-4243 . T) (-4242 . T)) ((|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-158)))) (-608 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}."))) @@ -2366,13 +2366,13 @@ NIL NIL (-609 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}."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL -(-610 -2315) +(-610 -3539) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}. It is essentially a particular instantiation of the package \\spadtype{LinearSystemMatrixPackage} for Matrix and Vector. This package\\spad{'s} existence makes it easier to use \\spadfun{solve} in the AXIOM interpreter.")) (|rank| (((|NonNegativeInteger|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|List| (|List| |#1|)) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|List| (|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|))))) (|Matrix| |#1|) (|List| (|Vector| |#1|))) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|List| (|List| |#1|)) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}.") (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#1|) (|Vector| |#1|)) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL -(-611 -2315 |Row| |Col| M) +(-611 -3539 |Row| |Col| M) ((|constructor| (NIL "This package solves linear system in the matrix form \\spad{AX = B}.")) (|rank| (((|NonNegativeInteger|) |#4| |#3|) "\\spad{rank(A,{}B)} computes the rank of the complete matrix \\spad{(A|B)} of the linear system \\spad{AX = B}.")) (|hasSolution?| (((|Boolean|) |#4| |#3|) "\\spad{hasSolution?(A,{}B)} tests if the linear system \\spad{AX = B} has a solution.")) (|particularSolution| (((|Union| |#3| "failed") |#4| |#3|) "\\spad{particularSolution(A,{}B)} finds a particular solution of the linear system \\spad{AX = B}.")) (|solve| (((|List| (|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|)))) |#4| (|List| |#3|)) "\\spad{solve(A,{}LB)} finds a particular soln of the systems \\spad{AX = B} and a basis of the associated homogeneous systems \\spad{AX = 0} where \\spad{B} varies in the list of column vectors \\spad{LB}.") (((|Record| (|:| |particular| (|Union| |#3| "failed")) (|:| |basis| (|List| |#3|))) |#4| |#3|) "\\spad{solve(A,{}B)} finds a particular solution of the system \\spad{AX = B} and a basis of the associated homogeneous system \\spad{AX = 0}."))) NIL NIL @@ -2382,8 +2382,8 @@ NIL NIL (-613 |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."))) -((-4241 . T) (-4244 . T) (-4238 . T) (-4239 . T)) -((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4246 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3262 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515))) (-3262 (|HasAttribute| |#2| (QUOTE (-4246 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) +((-4245 . T) (-4248 . T) (-4242 . T) (-4243 . T)) +((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3172 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515))) (-3172 (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) (-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{<=} \\spad{b}} holds. Lyndon words are internally represented by binary trees using the \\spadtype{Magma} domain constructor. Two ordering are provided: lexicographic and length-lexicographic. \\newline Author : Michel Petitot (petitot@lifl.\\spad{fr}).")) (|LyndonWordsList| (((|List| $) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList(\\spad{vl},{} \\spad{n})} returns the list of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|LyndonWordsList1| (((|OneDimensionalArray| (|List| $)) (|List| |#1|) (|PositiveInteger|)) "\\axiom{LyndonWordsList1(\\spad{vl},{} \\spad{n})} returns an array of lists of Lyndon words over the alphabet \\axiom{\\spad{vl}},{} up to order \\axiom{\\spad{n}}.")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|lyndonIfCan| (((|Union| $ "failed") (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndonIfCan(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word.")) (|lyndon| (($ (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon(\\spad{w})} convert \\axiom{\\spad{w}} into a Lyndon word,{} error if \\axiom{\\spad{w}} is not a Lyndon word.")) (|lyndon?| (((|Boolean|) (|OrderedFreeMonoid| |#1|)) "\\axiom{lyndon?(\\spad{w})} test if \\axiom{\\spad{w}} is a Lyndon word.")) (|factor| (((|List| $) (|OrderedFreeMonoid| |#1|)) "\\axiom{factor(\\spad{x})} returns the decreasing factorization into Lyndon words.")) (|coerce| (((|Magma| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{Magma}(VarSet) corresponding to \\axiom{\\spad{x}}.") (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{LyndonWord}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry."))) NIL @@ -2394,12 +2394,12 @@ NIL NIL (-616 S) ((|constructor| (NIL "LazyStreamAggregate is the category of streams with lazy evaluation. It is understood that the function 'empty?' will cause lazy evaluation if necessary to determine if there are entries. Functions which call 'empty?',{} \\spadignore{e.g.} 'first' and 'rest',{} will also cause lazy evaluation if necessary.")) (|complete| (($ $) "\\spad{complete(st)} causes all entries of 'st' to be computed. this function should only be called on streams which are known to be finite.")) (|extend| (($ $ (|Integer|)) "\\spad{extend(st,{}n)} causes entries to be computed,{} if necessary,{} so that 'st' will have at least \\spad{'n'} explicit entries or so that all entries of 'st' will be computed if 'st' is finite with length \\spad{<=} \\spad{n}.")) (|numberOfComputedEntries| (((|NonNegativeInteger|) $) "\\spad{numberOfComputedEntries(st)} returns the number of explicitly computed entries of stream \\spad{st} which exist immediately prior to the time this function is called.")) (|rst| (($ $) "\\spad{rst(s)} returns a pointer to the next node of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|frst| ((|#1| $) "\\spad{frst(s)} returns the first element of stream \\spad{s}. Caution: this function should only be called after a \\spad{empty?} test has been made since there no error check.")) (|lazyEvaluate| (($ $) "\\spad{lazyEvaluate(s)} causes one lazy evaluation of stream \\spad{s}. Caution: the first node must be a lazy evaluation mechanism (satisfies \\spad{lazy?(s) = true}) as there is no error check. Note: a call to this function may or may not produce an explicit first entry")) (|lazy?| (((|Boolean|) $) "\\spad{lazy?(s)} returns \\spad{true} if the first node of the stream \\spad{s} is a lazy evaluation mechanism which could produce an additional entry to \\spad{s}.")) (|explicitlyEmpty?| (((|Boolean|) $) "\\spad{explicitlyEmpty?(s)} returns \\spad{true} if the stream is an (explicitly) empty stream. Note: this is a null test which will not cause lazy evaluation.")) (|explicitEntries?| (((|Boolean|) $) "\\spad{explicitEntries?(s)} returns \\spad{true} if the stream \\spad{s} has explicitly computed entries,{} and \\spad{false} otherwise.")) (|select| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{select(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} satisfying the predicate \\spad{f}. Note: \\spad{select(f,{}st) = [x for x in st | f(x)]}.")) (|remove| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{remove(f,{}st)} returns a stream consisting of those elements of stream \\spad{st} which do not satisfy the predicate \\spad{f}. Note: \\spad{remove(f,{}st) = [x for x in st | not f(x)]}."))) -((-3656 . T)) +((-4069 . T)) NIL (-617 R) ((|constructor| (NIL "This domain represents three dimensional matrices over a general object type")) (|matrixDimensions| (((|Vector| (|NonNegativeInteger|)) $) "\\spad{matrixDimensions(x)} returns the dimensions of a matrix")) (|matrixConcat3D| (($ (|Symbol|) $ $) "\\spad{matrixConcat3D(s,{}x,{}y)} concatenates two 3-\\spad{D} matrices along a specified axis")) (|coerce| (((|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|))) $) "\\spad{coerce(x)} moves from the domain to the representation type") (($ (|PrimitiveArray| (|PrimitiveArray| (|PrimitiveArray| |#1|)))) "\\spad{coerce(p)} moves from the representation type (PrimitiveArray PrimitiveArray PrimitiveArray \\spad{R}) to the domain")) (|setelt!| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|) |#1|) "\\spad{setelt!(x,{}i,{}j,{}k,{}s)} (or \\spad{x}.\\spad{i}.\\spad{j}.k:=s) sets a specific element of the array to some value of type \\spad{R}")) (|elt| ((|#1| $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{elt(x,{}i,{}j,{}k)} extract an element from the matrix \\spad{x}")) (|construct| (($ (|List| (|List| (|List| |#1|)))) "\\spad{construct(lll)} creates a 3-\\spad{D} matrix from a List List List \\spad{R} \\spad{lll}")) (|plus| (($ $ $) "\\spad{plus(x,{}y)} adds two matrices,{} term by term we note that they must be the same size")) (|identityMatrix| (($ (|NonNegativeInteger|)) "\\spad{identityMatrix(n)} create an identity matrix we note that this must be square")) (|zeroMatrix| (($ (|NonNegativeInteger|) (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zeroMatrix(i,{}j,{}k)} create a matrix with all zero terms"))) NIL -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-973))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-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.\\spad{fr}).")) (|varList| (((|List| |#1|) $) "\\axiom{varList(\\spad{x})} returns the list of distinct entries of \\axiom{\\spad{x}}.")) (|right| (($ $) "\\axiom{right(\\spad{x})} returns right subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|retractable?| (((|Boolean|) $) "\\axiom{retractable?(\\spad{x})} tests if \\axiom{\\spad{x}} is a tree with only one entry.")) (|rest| (($ $) "\\axiom{rest(\\spad{x})} return \\axiom{\\spad{x}} without the first entry or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|mirror| (($ $) "\\axiom{mirror(\\spad{x})} returns the reversed word of \\axiom{\\spad{x}}. That is \\axiom{\\spad{x}} itself if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true} and \\axiom{mirror(\\spad{z}) * mirror(\\spad{y})} if \\axiom{\\spad{x}} is \\axiom{\\spad{y*z}}.")) (|lexico| (((|Boolean|) $ $) "\\axiom{lexico(\\spad{x},{}\\spad{y})} returns \\axiom{\\spad{true}} iff \\axiom{\\spad{x}} is smaller than \\axiom{\\spad{y}} \\spad{w}.\\spad{r}.\\spad{t}. the lexicographical ordering induced by \\axiom{VarSet}. \\spad{N}.\\spad{B}. This operation does not take into account the tree structure of its arguments. Thus this is not a total ordering.")) (|length| (((|PositiveInteger|) $) "\\axiom{length(\\spad{x})} returns the number of entries in \\axiom{\\spad{x}}.")) (|left| (($ $) "\\axiom{left(\\spad{x})} returns left subtree of \\axiom{\\spad{x}} or error if \\axiomOpFrom{retractable?}{Magma}(\\axiom{\\spad{x}}) is \\spad{true}.")) (|first| ((|#1| $) "\\axiom{first(\\spad{x})} returns the first entry of the tree \\axiom{\\spad{x}}.")) (|coerce| (((|OrderedFreeMonoid| |#1|) $) "\\axiom{coerce(\\spad{x})} returns the element of \\axiomType{OrderedFreeMonoid}(VarSet) corresponding to \\axiom{\\spad{x}} by removing parentheses.")) (* (($ $ $) "\\axiom{x*y} returns the tree \\axiom{[\\spad{x},{}\\spad{y}]}."))) NIL @@ -2435,24 +2435,24 @@ NIL (-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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#2|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#2|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#2|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) NIL -((|HasAttribute| |#2| (QUOTE (-4246 "*"))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515)))) +((|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-515)))) (-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| $)) "\\spad{diagonalMatrix([m1,{}...,{}mk])} creates a block diagonal matrix \\spad{M} with block matrices {\\em m1},{}...,{}{\\em mk} down the diagonal,{} with 0 block matrices elsewhere. More precisly: if \\spad{\\spad{ri} := nrows \\spad{mi}},{} \\spad{\\spad{ci} := ncols \\spad{mi}},{} then \\spad{m} is an (\\spad{r1+}..\\spad{+rk}) by (\\spad{c1+}..\\spad{+ck}) - matrix with entries \\spad{m.i.j = ml.(i-r1-..-r(l-1)).(j-n1-..-n(l-1))},{} if \\spad{(r1+..+r(l-1)) < i <= r1+..+rl} and \\spad{(c1+..+c(l-1)) < i <= c1+..+cl},{} \\spad{m.i.j} = 0 otherwise.") (($ (|List| |#1|)) "\\spad{diagonalMatrix(l)} returns a diagonal matrix with the elements of \\spad{l} on the diagonal.")) (|scalarMatrix| (($ (|NonNegativeInteger|) |#1|) "\\spad{scalarMatrix(n,{}r)} returns an \\spad{n}-by-\\spad{n} matrix with \\spad{r}\\spad{'s} on the diagonal and zeroes elsewhere.")) (|matrix| (($ (|List| (|List| |#1|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|zero| (($ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{zero(m,{}n)} returns an \\spad{m}-by-\\spad{n} zero matrix.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|finiteAggregate| ((|attribute|) "matrices are finite")) (|shallowlyMutable| ((|attribute|) "One may destructively alter matrices"))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-628 R |Row| |Col| M) -((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{^=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{^=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) +((|constructor| (NIL "\\spadtype{MatrixLinearAlgebraFunctions} provides functions to compute inverses and canonical forms.")) (|inverse| (((|Union| |#4| "failed") |#4|) "\\spad{inverse(m)} returns the inverse of the matrix. If the matrix is not invertible,{} \"failed\" is returned. Error: if the matrix is not square.")) (|normalizedDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{normalizedDivide(n,{}d)} returns a normalized quotient and remainder such that consistently unique representatives for the residue class are chosen,{} \\spadignore{e.g.} positive remainders")) (|rowEchelon| ((|#4| |#4|) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (|adjoint| (((|Record| (|:| |adjMat| |#4|) (|:| |detMat| |#1|)) |#4|) "\\spad{adjoint(m)} returns the ajoint matrix of \\spad{m} (\\spadignore{i.e.} the matrix \\spad{n} such that \\spad{m*n} = determinant(\\spad{m})*id) and the detrminant of \\spad{m}.")) (|invertIfCan| (((|Union| |#4| "failed") |#4|) "\\spad{invertIfCan(m)} returns the inverse of \\spad{m} over \\spad{R}")) (|fractionFreeGauss!| ((|#4| |#4|) "\\spad{fractionFreeGauss(m)} performs the fraction free gaussian elimination on the matrix \\spad{m}.")) (|nullSpace| (((|List| |#3|) |#4|) "\\spad{nullSpace(m)} returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) |#4|) "\\spad{nullity(m)} returns the mullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) |#4|) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|elColumn2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elColumn2!(m,{}a,{}i,{}j)} adds to column \\spad{i} a*column(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow2!| ((|#4| |#4| |#1| (|Integer|) (|Integer|)) "\\spad{elRow2!(m,{}a,{}i,{}j)} adds to row \\spad{i} a*row(\\spad{m},{}\\spad{j}) : elementary operation of second kind. (\\spad{i} \\spad{~=j})")) (|elRow1!| ((|#4| |#4| (|Integer|) (|Integer|)) "\\spad{elRow1!(m,{}i,{}j)} swaps rows \\spad{i} and \\spad{j} of matrix \\spad{m} : elementary operation of first kind")) (|minordet| ((|#1| |#4|) "\\spad{minordet(m)} computes the determinant of the matrix \\spad{m} using minors. Error: if the matrix is not square.")) (|determinant| ((|#1| |#4|) "\\spad{determinant(m)} returns the determinant of the matrix \\spad{m}. an error message is returned if the matrix is not square."))) NIL ((|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515)))) (-629 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."))) -((-4244 . T) (-4245 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4246 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-284))) (|HasCategory| |#1| (QUOTE (-515))) (|HasAttribute| |#1| (QUOTE (-4250 "*"))) (|HasCategory| |#1| (QUOTE (-339))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-630 R) ((|constructor| (NIL "This package provides standard arithmetic operations on matrices. The functions in this package store the results of computations in existing matrices,{} rather than creating new matrices. This package works only for matrices of type Matrix and uses the internal representation of this type.")) (** (((|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{x ** n} computes the \\spad{n}-th power of a square matrix. The power \\spad{n} is assumed greater than 1.")) (|power!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|NonNegativeInteger|)) "\\spad{power!(a,{}b,{}c,{}m,{}n)} computes \\spad{m} \\spad{**} \\spad{n} and stores the result in \\spad{a}. The matrices \\spad{b} and \\spad{c} are used to store intermediate results. Error: if \\spad{a},{} \\spad{b},{} \\spad{c},{} and \\spad{m} are not square and of the same dimensions.")) (|times!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{times!(c,{}a,{}b)} computes the matrix product \\spad{a * b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have compatible dimensions.")) (|rightScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) |#1|) "\\spad{rightScalarTimes!(c,{}a,{}r)} computes the scalar product \\spad{a * r} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|leftScalarTimes!| (((|Matrix| |#1|) (|Matrix| |#1|) |#1| (|Matrix| |#1|)) "\\spad{leftScalarTimes!(c,{}r,{}a)} computes the scalar product \\spad{r * a} and stores the result in the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions.")) (|minus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{!minus!(c,{}a,{}b)} computes the matrix difference \\spad{a - b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{minus!(c,{}a)} computes \\spad{-a} and stores the result in the matrix \\spad{c}. Error: if a and \\spad{c} do not have the same dimensions.")) (|plus!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{plus!(c,{}a,{}b)} computes the matrix sum \\spad{a + b} and stores the result in the matrix \\spad{c}. Error: if \\spad{a},{} \\spad{b},{} and \\spad{c} do not have the same dimensions.")) (|copy!| (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{copy!(c,{}a)} copies the matrix \\spad{a} into the matrix \\spad{c}. Error: if \\spad{a} and \\spad{c} do not have the same dimensions."))) NIL NIL -(-631 S -2315 FLAF FLAS) +(-631 S -3539 FLAF FLAS) ((|constructor| (NIL "\\indented{1}{\\spadtype{MultiVariableCalculusFunctions} Package provides several} \\indented{1}{functions for multivariable calculus.} These include gradient,{} hessian and jacobian,{} divergence and laplacian. Various forms for banded and sparse storage of matrices are included.")) (|bandedJacobian| (((|Matrix| |#2|) |#3| |#4| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{bandedJacobian(vf,{}xlist,{}kl,{}ku)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist},{} \\spad{kl} is the number of nonzero subdiagonals,{} \\spad{ku} is the number of nonzero superdiagonals,{} kl+ku+1 being actual bandwidth. Stores the nonzero band in a matrix,{} dimensions kl+ku+1 by \\#xlist. The upper triangle is in the top \\spad{ku} rows,{} the diagonal is in row ku+1,{} the lower triangle in the last \\spad{kl} rows. Entries in a column in the band store correspond to entries in same column of full store. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|jacobian| (((|Matrix| |#2|) |#3| |#4|) "\\spad{jacobian(vf,{}xlist)} computes the jacobian,{} the matrix of first partial derivatives,{} of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|bandedHessian| (((|Matrix| |#2|) |#2| |#4| (|NonNegativeInteger|)) "\\spad{bandedHessian(v,{}xlist,{}k)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist},{} \\spad{k} is the semi-bandwidth,{} the number of nonzero subdiagonals,{} 2*k+1 being actual bandwidth. Stores the nonzero band in lower triangle in a matrix,{} dimensions \\spad{k+1} by \\#xlist,{} whose rows are the vectors formed by diagonal,{} subdiagonal,{} etc. of the real,{} full-matrix,{} hessian. (The notation conforms to LAPACK/NAG-\\spad{F07} conventions.)")) (|hessian| (((|Matrix| |#2|) |#2| |#4|) "\\spad{hessian(v,{}xlist)} computes the hessian,{} the matrix of second partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|laplacian| ((|#2| |#2| |#4|) "\\spad{laplacian(v,{}xlist)} computes the laplacian of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}.")) (|divergence| ((|#2| |#3| |#4|) "\\spad{divergence(vf,{}xlist)} computes the divergence of the vector field \\spad{vf},{} \\spad{vf} a vector function of the variables listed in \\spad{xlist}.")) (|gradient| (((|Vector| |#2|) |#2| |#4|) "\\spad{gradient(v,{}xlist)} computes the gradient,{} the vector of first partial derivatives,{} of the scalar field \\spad{v},{} \\spad{v} a function of the variables listed in \\spad{xlist}."))) NIL NIL @@ -2462,11 +2462,11 @@ NIL NIL (-633) ((|constructor| (NIL "A domain which models the complex number representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Complex| (|Float|)) $) "\\spad{coerce(u)} transforms \\spad{u} into a COmplex Float") (($ (|Complex| (|MachineInteger|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|MachineFloat|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Integer|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex") (($ (|Complex| (|Float|))) "\\spad{coerce(u)} transforms \\spad{u} into a MachineComplex"))) -((-4237 . T) (-4242 |has| (-638) (-339)) (-4236 |has| (-638) (-339)) (-2571 . T) (-4243 |has| (-638) (-6 -4243)) (-4240 |has| (-638) (-6 -4240)) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-638) (QUOTE (-136))) (|HasCategory| (-638) (QUOTE (-134))) (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-344))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-211))) (-3262 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (LIST (QUOTE -263) (QUOTE (-638)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -286) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3262 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-638) (QUOTE (-949))) (|HasCategory| (-638) (QUOTE (-1108))) (-12 (|HasCategory| (-638) (QUOTE (-930))) (|HasCategory| (-638) (QUOTE (-1108)))) (-3262 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (-3262 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (|HasCategory| (-638) (QUOTE (-508))) (-12 (|HasCategory| (-638) (QUOTE (-982))) (|HasCategory| (-638) (QUOTE (-1108)))) (|HasCategory| (-638) (QUOTE (-982))) (-3262 (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840))) (-3262 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339)))) (-3262 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-515)))) (-12 (|HasCategory| (-638) (QUOTE (-211))) (|HasCategory| (-638) (QUOTE (-339)))) (-12 (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-786))) (|HasCategory| (-638) (QUOTE (-515))) (|HasAttribute| (-638) (QUOTE -4243)) (|HasAttribute| (-638) (QUOTE -4240)) (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-134)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-325))))) +((-4241 . T) (-4246 |has| (-638) (-339)) (-4240 |has| (-638) (-339)) (-4115 . T) (-4247 |has| (-638) (-6 -4247)) (-4244 |has| (-638) (-6 -4244)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-638) (QUOTE (-136))) (|HasCategory| (-638) (QUOTE (-134))) (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-344))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-211))) (-3172 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (LIST (QUOTE -263) (QUOTE (-638)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -286) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-638)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-638) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-638) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (-3172 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-325)))) (|HasCategory| (-638) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-638) (QUOTE (-949))) (|HasCategory| (-638) (QUOTE (-1109))) (-12 (|HasCategory| (-638) (QUOTE (-930))) (|HasCategory| (-638) (QUOTE (-1109)))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-339))) (|HasCategory| (-638) (QUOTE (-840)))) (-12 (|HasCategory| (-638) (QUOTE (-325))) (|HasCategory| (-638) (QUOTE (-840))))) (|HasCategory| (-638) (QUOTE (-508))) (-12 (|HasCategory| (-638) (QUOTE (-982))) (|HasCategory| (-638) (QUOTE (-1109)))) (|HasCategory| (-638) (QUOTE (-982))) (-3172 (|HasCategory| (-638) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-339)))) (-3172 (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-515)))) (-12 (|HasCategory| (-638) (QUOTE (-211))) (|HasCategory| (-638) (QUOTE (-339)))) (-12 (|HasCategory| (-638) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-638) (QUOTE (-339)))) (|HasCategory| (-638) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-638) (QUOTE (-786))) (|HasCategory| (-638) (QUOTE (-515))) (|HasAttribute| (-638) (QUOTE -4247)) (|HasAttribute| (-638) (QUOTE -4244)) (-12 (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-134)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-638) (QUOTE (-284))) (|HasCategory| (-638) (QUOTE (-840)))) (|HasCategory| (-638) (QUOTE (-325))))) (-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}."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL (-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 \\spad{gcd} of the univariate polynomials \\spad{f1} and \\spad{f2} modulo the integer prime \\spad{p}."))) @@ -2476,13 +2476,13 @@ NIL ((|constructor| (NIL "\\indented{1}{<description of package>} Author: Jim Wen Date Created: \\spad{??} Date Last Updated: October 1991 by Jon Steinbach Keywords: Examples: References:")) (|ptFunc| (((|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|))) "\\spad{ptFunc(a,{}b,{}c,{}d)} is an internal function exported in order to compile packages.")) (|meshPar1Var| (((|ThreeSpace| (|DoubleFloat|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Expression| (|Integer|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar1Var(s,{}t,{}u,{}f,{}s1,{}l)} \\undocumented")) (|meshFun2Var| (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshFun2Var(f,{}g,{}s1,{}s2,{}l)} \\undocumented")) (|meshPar2Var| (((|ThreeSpace| (|DoubleFloat|)) (|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(sp,{}f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|Point| (|DoubleFloat|)) (|DoubleFloat|) (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}s1,{}s2,{}l)} \\undocumented") (((|ThreeSpace| (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) (|Union| (|Mapping| (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|)) "undefined") (|Segment| (|DoubleFloat|)) (|Segment| (|DoubleFloat|)) (|List| (|DrawOption|))) "\\spad{meshPar2Var(f,{}g,{}h,{}j,{}s1,{}s2,{}l)} \\undocumented"))) NIL NIL -(-637 OV E -2315 PG) +(-637 OV E -3539 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 (-638) ((|constructor| (NIL "A domain which models the floating point representation used by machines in the AXIOM-NAG link.")) (|changeBase| (($ (|Integer|) (|Integer|) (|PositiveInteger|)) "\\spad{changeBase(exp,{}man,{}base)} \\undocumented{}")) (|exponent| (((|Integer|) $) "\\spad{exponent(u)} returns the exponent of \\spad{u}")) (|mantissa| (((|Integer|) $) "\\spad{mantissa(u)} returns the mantissa of \\spad{u}")) (|coerce| (($ (|MachineInteger|)) "\\spad{coerce(u)} transforms a MachineInteger into a MachineFloat") (((|Float|) $) "\\spad{coerce(u)} transforms a MachineFloat to a standard Float")) (|minimumExponent| (((|Integer|)) "\\spad{minimumExponent()} returns the minimum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{minimumExponent(e)} sets the minimum exponent in the model to \\spad{e}")) (|maximumExponent| (((|Integer|)) "\\spad{maximumExponent()} returns the maximum exponent in the model") (((|Integer|) (|Integer|)) "\\spad{maximumExponent(e)} sets the maximum exponent in the model to \\spad{e}")) (|base| (((|PositiveInteger|)) "\\spad{base()} returns the base of the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{base(b)} sets the base of the model to \\spad{b}")) (|precision| (((|PositiveInteger|)) "\\spad{precision()} returns the number of digits in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{precision(p)} sets the number of digits in the model to \\spad{p}"))) -((-2562 . T) (-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4108 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-639 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."))) @@ -2490,7 +2490,7 @@ NIL NIL (-640) ((|constructor| (NIL "A domain which models the integer representation used by machines in the AXIOM-NAG link.")) (|coerce| (((|Expression| $) (|Expression| (|Integer|))) "\\spad{coerce(x)} returns \\spad{x} with coefficients in the domain")) (|maxint| (((|PositiveInteger|)) "\\spad{maxint()} returns the maximum integer in the model") (((|PositiveInteger|) (|PositiveInteger|)) "\\spad{maxint(u)} sets the maximum integer in the model to \\spad{u}"))) -((-4243 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4247 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-641 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"))) @@ -2512,7 +2512,7 @@ NIL ((|constructor| (NIL "MakeRecord is used internally by the interpreter to create record types which are used for doing parallel iterations on streams.")) (|makeRecord| (((|Record| (|:| |part1| |#1|) (|:| |part2| |#2|)) |#1| |#2|) "\\spad{makeRecord(a,{}b)} creates a record object with type Record(part1:S,{} part2:R),{} where part1 is \\spad{a} and part2 is \\spad{b}."))) NIL NIL -(-646 S -2862 I) +(-646 S -2909 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 @@ -2521,8 +2521,8 @@ NIL NIL NIL (-648 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|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((|constructor| (NIL "This is the category of linear operator rings with one generator. The generator is not named by the category but can always be constructed as \\spad{monomial(1,{}1)}. \\blankline For convenience,{} call the generator \\spad{G}. Then each value is equal to \\indented{4}{\\spad{sum(a(i)*G**i,{} i = 0..n)}} for some unique \\spad{n} and \\spad{a(i)} in \\spad{R}. \\blankline Note that multiplication is not necessarily commutative. In fact,{} if \\spad{a} is in \\spad{R},{} it is quite normal to have \\spad{a*G \\~= G*a}.")) (|monomial| (($ |#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)}.}"))) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL (-649 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}."))) @@ -2532,25 +2532,25 @@ NIL ((|constructor| (NIL "\\spadtype{MathMLFormat} provides a coercion from \\spadtype{OutputForm} to MathML format.")) (|display| (((|Void|) (|String|)) "prints the string returned by coerce,{} adding <math ...> tags.")) (|exprex| (((|String|) (|OutputForm|)) "coverts \\spadtype{OutputForm} to \\spadtype{String} with the structure preserved with braces. Actually this is not quite accurate. The function \\spadfun{precondition} is first applied to the \\spadtype{OutputForm} expression before \\spadfun{exprex}. The raw \\spadtype{OutputForm} and the nature of the \\spadfun{precondition} function is still obscure to me at the time of this writing (2007-02-14).")) (|coerceL| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format and displays result as one long string.")) (|coerceS| (((|String|) (|OutputForm|)) "\\spad{coerceS(o)} changes \\spad{o} in the standard output format to MathML format and displays formatted result.")) (|coerce| (((|String|) (|OutputForm|)) "coerceS(\\spad{o}) changes \\spad{o} in the standard output format to MathML format."))) NIL NIL -(-651 R |Mod| -2227 -2178 |exactQuo|) +(-651 R |Mod| -1327 -3780 |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| $) "\\spad{modulus(x)} \\undocumented"))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-652 R |Rep|) ((|constructor| (NIL "This package \\undocumented")) (|frobenius| (($ $) "\\spad{frobenius(x)} \\undocumented")) (|computePowers| (((|PrimitiveArray| $)) "\\spad{computePowers()} \\undocumented")) (|pow| (((|PrimitiveArray| $)) "\\spad{pow()} \\undocumented")) (|An| (((|Vector| |#1|) $) "\\spad{An(x)} \\undocumented")) (|UnVectorise| (($ (|Vector| |#1|)) "\\spad{UnVectorise(v)} \\undocumented")) (|Vectorise| (((|Vector| |#1|) $) "\\spad{Vectorise(x)} \\undocumented")) (|coerce| (($ |#2|) "\\spad{coerce(x)} \\undocumented")) (|lift| ((|#2| $) "\\spad{lift(x)} \\undocumented")) (|reduce| (($ |#2|) "\\spad{reduce(x)} \\undocumented")) (|modulus| ((|#2|) "\\spad{modulus()} \\undocumented")) (|setPoly| ((|#2| |#2|) "\\spad{setPoly(x)} \\undocumented"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4240 |has| |#1| (-339)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-325))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4244 |has| |#1| (-339)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-325))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-653 IS E |ff|) ((|constructor| (NIL "This package \\undocumented")) (|construct| (($ |#1| |#2|) "\\spad{construct(i,{}e)} \\undocumented")) (|coerce| (((|Record| (|:| |index| |#1|) (|:| |exponent| |#2|)) $) "\\spad{coerce(x)} \\undocumented") (($ (|Record| (|:| |index| |#1|) (|:| |exponent| |#2|))) "\\spad{coerce(x)} \\undocumented")) (|index| ((|#1| $) "\\spad{index(x)} \\undocumented")) (|exponent| ((|#2| $) "\\spad{exponent(x)} \\undocumented"))) NIL NIL (-654 R M) ((|constructor| (NIL "Algebra of ADDITIVE operators on a module.")) (|makeop| (($ |#1| (|FreeGroup| (|BasicOperator|))) "\\spad{makeop should} be local but conditional")) (|opeval| ((|#2| (|BasicOperator|) |#2|) "\\spad{opeval should} be local but conditional")) (** (($ $ (|Integer|)) "\\spad{op**n} \\undocumented") (($ (|BasicOperator|) (|Integer|)) "\\spad{op**n} \\undocumented")) (|evaluateInverse| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluateInverse(x,{}f)} \\undocumented")) (|evaluate| (($ $ (|Mapping| |#2| |#2|)) "\\spad{evaluate(f,{} u +-> g u)} attaches the map \\spad{g} to \\spad{f}. \\spad{f} must be a basic operator \\spad{g} MUST be additive,{} \\spadignore{i.e.} \\spad{g(a + b) = g(a) + g(b)} for any \\spad{a},{} \\spad{b} in \\spad{M}. This implies that \\spad{g(n a) = n g(a)} for any \\spad{a} in \\spad{M} and integer \\spad{n > 0}.")) (|conjug| ((|#1| |#1|) "\\spad{conjug(x)}should be local but conditional")) (|adjoint| (($ $ $) "\\spad{adjoint(op1,{} op2)} sets the adjoint of \\spad{op1} to be op2. \\spad{op1} must be a basic operator") (($ $) "\\spad{adjoint(op)} returns the adjoint of the operator \\spad{op}."))) -((-4239 |has| |#1| (-158)) (-4238 |has| |#1| (-158)) (-4241 . T)) +((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136)))) -(-655 R |Mod| -2227 -2178 |exactQuo|) +(-655 R |Mod| -1327 -3780 |exactQuo|) ((|constructor| (NIL "These domains are used for the factorization and gcds of univariate polynomials over the integers in order to work modulo different primes. See \\spadtype{EuclideanModularRing} ,{}\\spadtype{ModularField}")) (|inv| (($ $) "\\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"))) -((-4241 . T)) +((-4245 . T)) NIL (-656 S R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) @@ -2558,11 +2558,11 @@ NIL NIL (-657 R) ((|constructor| (NIL "The category of modules over a commutative ring. \\blankline"))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL -(-658 -2315) +(-658 -3539) ((|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]]}."))) -((-4241 . T)) +((-4245 . T)) NIL (-659 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."))) @@ -2586,7 +2586,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-325))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-344)))) (-664 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."))) -((-4237 |has| |#1| (-339)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 |has| |#1| (-339)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-665 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.")) (** (($ $ (|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."))) @@ -2596,7 +2596,7 @@ NIL ((|constructor| (NIL "The class of multiplicative monoids,{} \\spadignore{i.e.} semigroups with a multiplicative identity element. \\blankline")) (|recip| (((|Union| $ "failed") $) "\\spad{recip(x)} tries to compute the multiplicative inverse for \\spad{x} or \"failed\" if it cannot find the inverse (see unitsKnown).")) (^ (($ $ (|NonNegativeInteger|)) "\\spad{x^n} returns the repeated product of \\spad{x} \\spad{n} times,{} \\spadignore{i.e.} exponentiation.")) (** (($ $ (|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 -(-667 -2315 UP) +(-667 -3539 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 @@ -2614,8 +2614,8 @@ NIL NIL (-671 |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."))) -(((-4246 "*") |has| |#2| (-158)) (-4237 |has| |#2| (-515)) (-4242 |has| |#2| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#2| (QUOTE (-840))) (-3262 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3262 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3262 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4242)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +(((-4250 "*") |has| |#2| (-158)) (-4241 |has| |#2| (-515)) (-4246 |has| |#2| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#2| (QUOTE (-840))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-796 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (-3172 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) (-672 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|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL @@ -2630,15 +2630,15 @@ NIL NIL (-675 R M) ((|constructor| (NIL "\\spadtype{MonoidRing}(\\spad{R},{}\\spad{M}),{} implements the algebra of all maps from the monoid \\spad{M} to the commutative ring \\spad{R} with finite support. Multiplication of two maps \\spad{f} and \\spad{g} is defined to map an element \\spad{c} of \\spad{M} to the (convolution) sum over {\\em f(a)g(b)} such that {\\em ab = c}. Thus \\spad{M} can be identified with a canonical basis and the maps can also be considered as formal linear combinations of the elements in \\spad{M}. Scalar multiples of a basis element are called monomials. A prominent example is the class of polynomials where the monoid is a direct product of the natural numbers with pointwise addition. When \\spad{M} is \\spadtype{FreeMonoid Symbol},{} one gets polynomials in infinitely many non-commuting variables. Another application area is representation theory of finite groups \\spad{G},{} where modules over \\spadtype{MonoidRing}(\\spad{R},{}\\spad{G}) are studied.")) (|reductum| (($ $) "\\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}."))) -((-4239 |has| |#1| (-158)) (-4238 |has| |#1| (-158)) (-4241 . T)) +((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-344)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-786)))) (-676 S) ((|constructor| (NIL "A multi-set aggregate is a set which keeps track of the multiplicity of its elements."))) -((-4234 . T) (-4245 . T) (-3656 . T)) +((-4238 . T) (-4249 . T) (-4069 . T)) NIL (-677 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}."))) -((-4244 . T) (-4234 . T) (-4245 . T)) +((-4248 . T) (-4238 . T) (-4249 . T)) ((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-678) ((|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."))) @@ -2650,7 +2650,7 @@ NIL NIL (-680 |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}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4239 . T) (-4238 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL (-681 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"))) @@ -2666,7 +2666,7 @@ NIL NIL (-684 R) ((|constructor| (NIL "NonAssociativeAlgebra is the category of non associative algebras (modules which are themselves non associative rngs). Axioms \\indented{3}{\\spad{r*}(a*b) = (r*a)\\spad{*b} = a*(\\spad{r*b})}")) (|plenaryPower| (($ $ (|PositiveInteger|)) "\\spad{plenaryPower(a,{}n)} is recursively defined to be \\spad{plenaryPower(a,{}n-1)*plenaryPower(a,{}n-1)} for \\spad{n>1} and \\spad{a} for \\spad{n=1}."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL (-685) ((|constructor| (NIL "This package uses the NAG Library to compute the zeros of a polynomial with real or complex coefficients. See \\downlink{Manual Page}{manpageXXc02}.")) (|c02agf| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02agf(a,{}n,{}scale,{}ifail)} finds all the roots of a real polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02agf}.")) (|c02aff| (((|Result|) (|Matrix| (|DoubleFloat|)) (|Integer|) (|Boolean|) (|Integer|)) "\\spad{c02aff(a,{}n,{}scale,{}ifail)} finds all the roots of a complex polynomial equation,{} using a variant of Laguerre\\spad{'s} Method. See \\downlink{Manual Page}{manpageXXc02aff}."))) @@ -2748,15 +2748,15 @@ NIL ((|constructor| (NIL "This package computes explicitly eigenvalues and eigenvectors of matrices with entries over the complex rational numbers. The results are expressed either as complex floating numbers or as complex rational numbers depending on the type of the precision parameter.")) (|complexEigenvectors| (((|List| (|Record| (|:| |outval| (|Complex| |#1|)) (|:| |outmult| (|Integer|)) (|:| |outvect| (|List| (|Matrix| (|Complex| |#1|)))))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvectors(m,{}eps)} returns a list of records each one containing a complex eigenvalue,{} its algebraic multiplicity,{} and a list of associated eigenvectors. All these results are computed to precision \\spad{eps} and are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|complexEigenvalues| (((|List| (|Complex| |#1|)) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) |#1|) "\\spad{complexEigenvalues(m,{}eps)} computes the eigenvalues of the matrix \\spad{m} to precision \\spad{eps}. The eigenvalues are expressed as complex floats or complex rational numbers depending on the type of \\spad{eps} (float or rational).")) (|characteristicPolynomial| (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|)))) (|Symbol|)) "\\spad{characteristicPolynomial(m,{}x)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over Complex Rationals with variable \\spad{x}.") (((|Polynomial| (|Complex| (|Fraction| (|Integer|)))) (|Matrix| (|Complex| (|Fraction| (|Integer|))))) "\\spad{characteristicPolynomial(m)} returns the characteristic polynomial of the matrix \\spad{m} expressed as polynomial over complex rationals with a new symbol as variable."))) NIL NIL -(-705 -2315) +(-705 -3539) ((|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 -(-706 P -2315) +(-706 P -3539) ((|constructor| (NIL "This package provides a division and related operations for \\spadtype{MonogenicLinearOperator}\\spad{s} over a \\spadtype{Field}. Since the multiplication is in general non-commutative,{} these operations all have left- and right-hand versions. This package provides the operations based on left-division.")) (|leftLcm| ((|#1| |#1| |#1|) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftGcd| ((|#1| |#1| |#1|) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| |#1| "failed") |#1| |#1|) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| ((|#1| |#1| |#1|) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| ((|#1| |#1| |#1|) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| |#1|) (|:| |remainder| |#1|)) |#1| |#1|) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}."))) NIL NIL -(-707 UP -2315) +(-707 UP -3539) ((|constructor| (NIL "In this package \\spad{F} is a framed algebra over the integers (typically \\spad{F = Z[a]} for some algebraic integer a). The package provides functions to compute the integral closure of \\spad{Z} in the quotient quotient field of \\spad{F}.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|)))) (|Integer|)) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{Z} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| (|Integer|))) (|:| |basisDen| (|Integer|)) (|:| |basisInv| (|Matrix| (|Integer|))))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{Z} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{Z}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|discriminant| (((|Integer|)) "\\spad{discriminant()} returns the discriminant of the integral closure of \\spad{Z} in the quotient field of the framed algebra \\spad{F}."))) NIL NIL @@ -2770,9 +2770,9 @@ NIL NIL (-710) ((|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."))) -(((-4246 "*") . T)) +(((-4250 "*") . T)) NIL -(-711 R -2315) +(-711 R -3539) ((|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 @@ -2792,7 +2792,7 @@ NIL ((|constructor| (NIL "A package for computing normalized assocites of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}")) (|normInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normInvertible?(\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|outputArgs| (((|Void|) (|String|) (|String|) |#4| |#5|) "\\axiom{outputArgs(\\spad{s1},{}\\spad{s2},{}\\spad{p},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|normalize| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{normalize(\\spad{p},{}\\spad{ts})} normalizes \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|normalizedAssociate| ((|#4| |#4| |#5|) "\\axiom{normalizedAssociate(\\spad{p},{}\\spad{ts})} returns a normalized polynomial \\axiom{\\spad{n}} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts} such that \\axiom{\\spad{n}} and \\axiom{\\spad{p}} are associates \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} and assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}.")) (|recip| (((|Record| (|:| |num| |#4|) (|:| |den| |#4|)) |#4| |#5|) "\\axiom{recip(\\spad{p},{}\\spad{ts})} returns the inverse of \\axiom{\\spad{p}} \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts} assuming that \\axiom{\\spad{p}} is invertible \\spad{w}.\\spad{r}.\\spad{t} \\spad{ts}."))) NIL NIL -(-716 -2315 |ExtF| |SUEx| |ExtP| |n|) +(-716 -3539 |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 @@ -2806,23 +2806,23 @@ NIL NIL (-719 R |VarSet|) ((|constructor| (NIL "A post-facto extension for \\axiomType{\\spad{SMP}} in order to speed up operations related to pseudo-division and \\spad{gcd}. This domain is based on the \\axiomType{NSUP} constructor which is itself a post-facto extension of the \\axiomType{SUP} constructor."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . 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Note that the mapping is assumed to send zero to zero,{} since it will only be applied to the non-zero coefficients of the polynomial.")) (|map| (((|NewSparseUnivariatePolynomial| |#2|) (|Mapping| |#2| |#1|) (|NewSparseUnivariatePolynomial| |#1|)) "\\axiom{map(func,{} poly)} creates a new polynomial by applying func to every non-zero coefficient of the polynomial poly."))) NIL NIL (-721 R) ((|constructor| (NIL "A post-facto extension for \\axiomType{SUP} in order to speed up operations related to pseudo-division and \\spad{gcd} for both \\axiomType{SUP} and,{} consequently,{} \\axiomType{NSMP}.")) (|halfExtendedResultant2| (((|Record| (|:| |resultant| |#1|) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedResultant2(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|halfExtendedResultant1| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedResultant1(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca]} such that \\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{} \\spad{cb}]}")) (|extendedResultant| (((|Record| (|:| |resultant| |#1|) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedResultant(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}ca,{}\\spad{cb}]} such that \\axiom{\\spad{r}} is the resultant of \\axiom{a} and \\axiom{\\spad{b}} and \\axiom{\\spad{r} = ca * a + \\spad{cb} * \\spad{b}}")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} such that \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]}")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{} \\spad{cb}]} such that \\axiom{\\spad{g}} is a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{g} = ca * a + \\spad{cb} * \\spad{b}}")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns \\axiom{resultant(a,{}\\spad{b})} if \\axiom{a} and \\axiom{\\spad{b}} has no non-trivial \\spad{gcd} in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} otherwise the non-zero sub-resultant with smallest index.")) (|subResultantsChain| (((|List| $) $ $) "\\axiom{subResultantsChain(a,{}\\spad{b})} returns the list of the non-zero sub-resultants of \\axiom{a} and \\axiom{\\spad{b}} sorted by increasing degree.")) (|lazyPseudoQuotient| (($ $ $) "\\axiom{lazyPseudoQuotient(a,{}\\spad{b})} returns \\axiom{\\spad{q}} if \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}")) (|lazyPseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{c^n} * a = \\spad{q*b} \\spad{+r}} and \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} where \\axiom{\\spad{n} + \\spad{g} = max(0,{} degree(\\spad{b}) - degree(a) + 1)}.")) (|lazyPseudoRemainder| (($ $ $) "\\axiom{lazyPseudoRemainder(a,{}\\spad{b})} returns \\axiom{\\spad{r}} if \\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]}. This lazy pseudo-remainder is computed by means of the \\axiomOpFrom{fmecg}{NewSparseUnivariatePolynomial} operation.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| |#1|) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{r},{}\\spad{c},{}\\spad{n}]} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{\\spad{c^n} * a - \\spad{r}} where \\axiom{\\spad{c}} is \\axiom{leadingCoefficient(\\spad{b})} and \\axiom{\\spad{n}} is as small as possible with the previous properties.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} returns \\axiom{\\spad{r}} such that \\axiom{\\spad{r}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{b}} divides \\axiom{a \\spad{-r}} where \\axiom{\\spad{b}} is monic.")) (|fmecg| (($ $ (|NonNegativeInteger|) |#1| $) "\\axiom{fmecg(\\spad{p1},{}\\spad{e},{}\\spad{r},{}\\spad{p2})} returns \\axiom{\\spad{p1} - \\spad{r} * X**e * \\spad{p2}} where \\axiom{\\spad{X}} is \\axiom{monomial(1,{}1)}"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4240 |has| |#1| (-339)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4244 |has| |#1| (-339)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-1063))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-722 R) ((|constructor| (NIL "This package provides polynomials as functions on a ring.")) (|eulerE| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{eulerE(n,{}r)} \\undocumented")) (|bernoulliB| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{bernoulliB(n,{}r)} \\undocumented")) (|cyclotomic| ((|#1| (|NonNegativeInteger|) |#1|) "\\spad{cyclotomic(n,{}r)} \\undocumented"))) NIL ((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-723 R E V P) ((|constructor| (NIL "The category of normalized triangular sets. A triangular set \\spad{ts} is said normalized if for every algebraic variable \\spad{v} of \\spad{ts} the polynomial \\spad{select(ts,{}v)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. every polynomial in \\spad{collectUnder(ts,{}v)}. A polynomial \\spad{p} is said normalized \\spad{w}.\\spad{r}.\\spad{t}. a non-constant polynomial \\spad{q} if \\spad{p} is constant or \\spad{degree(p,{}mdeg(q)) = 0} and \\spad{init(p)} is normalized \\spad{w}.\\spad{r}.\\spad{t}. \\spad{q}. One of the important features of normalized triangular sets is that they are regular sets.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[3] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.}"))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-724 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}."))) @@ -2874,25 +2874,25 @@ NIL ((|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-344)))) (-736 R) ((|constructor| (NIL "OctonionCategory gives the categorial frame for the octonions,{} and eight-dimensional non-associative algebra,{} doubling the the quaternions in the same way as doubling the Complex numbers to get the quaternions.")) (|inv| (($ $) "\\spad{inv(o)} returns the inverse of \\spad{o} if it exists.")) (|rationalIfCan| (((|Union| (|Fraction| (|Integer|)) "failed") $) "\\spad{rationalIfCan(o)} returns the real part if all seven imaginary parts are 0,{} and \"failed\" otherwise.")) (|rational| (((|Fraction| (|Integer|)) $) "\\spad{rational(o)} returns the real part if all seven imaginary parts are 0. Error: if \\spad{o} is not rational.")) (|rational?| (((|Boolean|) $) "\\spad{rational?(o)} tests if \\spad{o} is rational,{} \\spadignore{i.e.} that all seven imaginary parts are 0.")) (|abs| ((|#1| $) "\\spad{abs(o)} computes the absolute value of an octonion,{} equal to the square root of the \\spadfunFrom{norm}{Octonion}.")) (|octon| (($ |#1| |#1| |#1| |#1| |#1| |#1| |#1| |#1|) "\\spad{octon(re,{}\\spad{ri},{}rj,{}rk,{}rE,{}rI,{}rJ,{}rK)} constructs an octonion from scalars.")) (|norm| ((|#1| $) "\\spad{norm(o)} returns the norm of an octonion,{} equal to the sum of the squares of its coefficients.")) (|imagK| ((|#1| $) "\\spad{imagK(o)} extracts the imaginary \\spad{K} part of octonion \\spad{o}.")) (|imagJ| ((|#1| $) "\\spad{imagJ(o)} extracts the imaginary \\spad{J} part of octonion \\spad{o}.")) (|imagI| ((|#1| $) "\\spad{imagI(o)} extracts the imaginary \\spad{I} part of octonion \\spad{o}.")) (|imagE| ((|#1| $) "\\spad{imagE(o)} extracts the imaginary \\spad{E} part of octonion \\spad{o}.")) (|imagk| ((|#1| $) "\\spad{imagk(o)} extracts the \\spad{k} part of octonion \\spad{o}.")) (|imagj| ((|#1| $) "\\spad{imagj(o)} extracts the \\spad{j} part of octonion \\spad{o}.")) (|imagi| ((|#1| $) "\\spad{imagi(o)} extracts the \\spad{i} part of octonion \\spad{o}.")) (|real| ((|#1| $) "\\spad{real(o)} extracts real part of octonion \\spad{o}.")) (|conjugate| (($ $) "\\spad{conjugate(o)} negates the imaginary parts \\spad{i},{}\\spad{j},{}\\spad{k},{}\\spad{E},{}\\spad{I},{}\\spad{J},{}\\spad{K} of octonian \\spad{o}."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-737 -3262 R OS S) +(-737 -3172 R OS S) ((|constructor| (NIL "OctonionCategoryFunctions2 implements functions between two octonion domains defined over different rings. The function map is used to coerce between octonion types.")) (|map| ((|#3| (|Mapping| |#4| |#2|) |#1|) "\\spad{map(f,{}u)} maps \\spad{f} onto the component parts of the octonion \\spad{u}."))) NIL NIL (-738 R) ((|constructor| (NIL "Octonion implements octonions (Cayley-Dixon algebra) over a commutative ring,{} an eight-dimensional non-associative algebra,{} doubling the quaternions in the same way as doubling the complex numbers to get the quaternions the main constructor function is {\\em octon} which takes 8 arguments: the real part,{} the \\spad{i} imaginary part,{} the \\spad{j} imaginary part,{} the \\spad{k} imaginary part,{} (as with quaternions) and in addition the imaginary parts \\spad{E},{} \\spad{I},{} \\spad{J},{} \\spad{K}.")) (|octon| (($ (|Quaternion| |#1|) (|Quaternion| |#1|)) "\\spad{octon(qe,{}qE)} constructs an octonion from two quaternions using the relation {\\em O = Q + QE}."))) -((-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-3262 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3262 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) +((-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (-3172 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-927 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (-739) ((|ODESolve| (((|Result|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{ODESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-740 R -2315 L) +(-740 R -3539 L) ((|constructor| (NIL "Solution of linear ordinary differential equations,{} constant coefficient case.")) (|constDsolve| (((|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#3| |#2| (|Symbol|)) "\\spad{constDsolve(op,{} g,{} x)} returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular solution of the equation \\spad{op y = g},{} and the \\spad{\\spad{yi}}\\spad{'s} form a basis for the solutions of \\spad{op y = 0}."))) NIL NIL -(-741 R -2315) +(-741 R -3539) ((|constructor| (NIL "\\spad{ElementaryFunctionODESolver} provides the top-level functions for finding closed form solutions of ordinary differential equations and initial value problems.")) (|solve| (((|Union| |#2| "failed") |#2| (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Equation| |#2|) (|List| |#2|)) "\\spad{solve(eq,{} y,{} x = a,{} [y0,{}...,{}ym])} returns either the solution of the initial value problem \\spad{eq,{} y(a) = y0,{} y'(a) = y1,{}...} or \"failed\" if the solution cannot be found; error if the equation is not one linear ordinary or of the form \\spad{dy/dx = f(x,{}y)}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") |#2| (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}.") (((|Union| (|Record| (|:| |particular| |#2|) (|:| |basis| (|List| |#2|))) |#2| "failed") (|Equation| |#2|) (|BasicOperator|) (|Symbol|)) "\\spad{solve(eq,{} y,{} x)} returns either a solution of the ordinary differential equation \\spad{eq} or \"failed\" if no non-trivial solution can be found; If the equation is linear ordinary,{} a solution is of the form \\spad{[h,{} [b1,{}...,{}bm]]} where \\spad{h} is a particular solution and \\spad{[b1,{}...bm]} are linearly independent solutions of the associated homogenuous equation \\spad{f(x,{}y) = 0}; A full basis for the solutions of the homogenuous equation is not always returned,{} only the solutions which were found; If the equation is of the form {dy/dx = \\spad{f}(\\spad{x},{}\\spad{y})},{} a solution is of the form \\spad{h(x,{}y)} where \\spad{h(x,{}y) = c} is a first integral of the equation for any constant \\spad{c}; error if the equation is not one of those 2 forms.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| |#2|) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|List| (|Equation| |#2|)) (|List| (|BasicOperator|)) (|Symbol|)) "\\spad{solve([eq_1,{}...,{}eq_n],{} [y_1,{}...,{}y_n],{} x)} returns either \"failed\" or,{} if the equations form a fist order linear system,{} a solution of the form \\spad{[y_p,{} [b_1,{}...,{}b_n]]} where \\spad{h_p} is a particular solution and \\spad{[b_1,{}...b_m]} are linearly independent solutions of the associated homogenuous system. error if the equations do not form a first order linear system") (((|Union| (|List| (|Vector| |#2|)) "failed") (|Matrix| |#2|) (|Symbol|)) "\\spad{solve(m,{} x)} returns a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable.") (((|Union| (|Record| (|:| |particular| (|Vector| |#2|)) (|:| |basis| (|List| (|Vector| |#2|)))) "failed") (|Matrix| |#2|) (|Vector| |#2|) (|Symbol|)) "\\spad{solve(m,{} v,{} x)} returns \\spad{[v_p,{} [v_1,{}...,{}v_m]]} such that the solutions of the system \\spad{D y = m y + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D y = m y}. \\spad{x} is the dependent variable."))) NIL NIL @@ -2900,7 +2900,7 @@ NIL ((|constructor| (NIL "\\axiom{ODEIntensityFunctionsTable()} provides a dynamic table and a set of functions to store details found out about sets of ODE\\spad{'s}.")) (|showIntensityFunctions| (((|Union| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))) "failed") (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{showIntensityFunctions(k)} returns the entries in the table of intensity functions \\spad{k}.")) (|insert!| (($ (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|)))))) "\\spad{insert!(r)} inserts an entry \\spad{r} into theIFTable")) (|iFTable| (($ (|List| (|Record| (|:| |key| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) (|:| |entry| (|Record| (|:| |stiffness| (|Float|)) (|:| |stability| (|Float|)) (|:| |expense| (|Float|)) (|:| |accuracy| (|Float|)) (|:| |intermediateResults| (|Float|))))))) "\\spad{iFTable(l)} creates an intensity-functions table from the elements of \\spad{l}.")) (|keys| (((|List| (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) $) "\\spad{keys(tab)} returns the list of keys of \\spad{f}")) (|clearTheIFTable| (((|Void|)) "\\spad{clearTheIFTable()} clears the current table of intensity functions.")) (|showTheIFTable| (($) "\\spad{showTheIFTable()} returns the current table of intensity functions."))) NIL NIL -(-743 R -2315) +(-743 R -3539) ((|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 @@ -2908,11 +2908,11 @@ NIL ((|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{measure(prob,{}R)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} listed in \\axiom{\\spad{R}} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.") (((|Record| (|:| |measure| (|Float|)) (|:| |name| (|String|)) (|:| |explanations| (|List| (|String|)))) (|NumericalODEProblem|)) "\\spad{measure(prob)} is a top level ANNA function for identifying the most appropriate numerical routine from those in the routines table provided for solving the numerical ODE problem defined by \\axiom{\\spad{prob}}. \\blankline It calls each \\axiom{domain} of \\axiom{category} \\axiomType{OrdinaryDifferentialEquationsSolverCategory} in turn to calculate all measures and returns the best \\spadignore{i.e.} the name of the most appropriate domain and any other relevant information. It predicts the likely most effective NAG numerical Library routine to solve the input set of ODEs by checking various attributes of the system of ODEs and calculating a measure of compatibility of each routine to these attributes.")) (|solve| (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}epsabs,{}epsrel)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to an absolute error requirement \\axiom{\\spad{epsabs}} and relative error \\axiom{\\spad{epsrel}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}intVals,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The values of \\spad{Y}[1]..\\spad{Y}[\\spad{n}] will be output for the values of \\spad{X} in \\axiom{\\spad{intVals}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Expression| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}G,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. The calculation will stop if the function \\spad{G}(\\spad{X},{}\\spad{Y}[1],{}..,{}\\spad{Y}[\\spad{n}]) evaluates to zero before \\spad{X} = \\spad{xEnd}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|)) (|Float|)) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial,{}tol)} is a top level ANNA function to solve numerically a system of ordinary differential equations,{} \\axiom{\\spad{f}},{} \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}] from \\axiom{\\spad{xStart}} to \\axiom{\\spad{xEnd}} with the initial values for \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (\\axiom{\\spad{yInitial}}) to a tolerance \\axiom{\\spad{tol}}. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|Vector| (|Expression| (|Float|))) (|Float|) (|Float|) (|List| (|Float|))) "\\spad{solve(f,{}xStart,{}xEnd,{}yInitial)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with a starting value for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions) and a final value of \\spad{X}. A default value is used for the accuracy requirement. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|) (|RoutinesTable|)) "\\spad{solve(odeProblem,{}R)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} contained in the table of routines \\axiom{\\spad{R}} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine.") (((|Result|) (|NumericalODEProblem|)) "\\spad{solve(odeProblem)} is a top level ANNA function to solve numerically a system of ordinary differential equations \\spadignore{i.e.} equations for the derivatives \\spad{Y}[1]'..\\spad{Y}[\\spad{n}]' defined in terms of \\spad{X},{}\\spad{Y}[1]..\\spad{Y}[\\spad{n}],{} together with starting values for \\spad{X} and \\spad{Y}[1]..\\spad{Y}[\\spad{n}] (called the initial conditions),{} a final value of \\spad{X},{} an accuracy requirement and any intermediate points at which the result is required. \\blankline It iterates over the \\axiom{domains} of \\axiomType{OrdinaryDifferentialEquationsSolverCategory} to get the name and other relevant information of the the (domain of the) numerical routine likely to be the most appropriate,{} \\spadignore{i.e.} have the best \\axiom{measure}. \\blankline The method used to perform the numerical process will be one of the routines contained in the NAG numerical Library. The function predicts the likely most effective routine by checking various attributes of the system of ODE\\spad{'s} and calculating a measure of compatibility of each routine to these attributes. \\blankline It then calls the resulting `best' routine."))) NIL NIL -(-745 -2315 UP UPUP R) +(-745 -3539 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 -(-746 -2315 UP L LQ) +(-746 -3539 UP L LQ) ((|constructor| (NIL "\\spad{PrimitiveRatDE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the transcendental case.} \\indented{1}{The derivation to use is given by the parameter \\spad{L}.}")) (|splitDenominator| (((|Record| (|:| |eq| |#3|) (|:| |rh| (|List| (|Fraction| |#2|)))) |#4| (|List| (|Fraction| |#2|))) "\\spad{splitDenominator(op,{} [g1,{}...,{}gm])} returns \\spad{op0,{} [h1,{}...,{}hm]} such that the equations \\spad{op y = c1 g1 + ... + cm gm} and \\spad{op0 y = c1 h1 + ... + cm hm} have the same solutions.")) (|indicialEquation| ((|#2| |#4| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.") ((|#2| |#3| |#1|) "\\spad{indicialEquation(op,{} a)} returns the indicial equation of \\spad{op} at \\spad{a}.")) (|indicialEquations| (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#4|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3| |#2|) "\\spad{indicialEquations(op,{} p)} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op} above the roots of \\spad{p},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.") (((|List| (|Record| (|:| |center| |#2|) (|:| |equation| |#2|))) |#3|) "\\spad{indicialEquations op} returns \\spad{[[d1,{}e1],{}...,{}[dq,{}eq]]} where the \\spad{d_i}\\spad{'s} are the affine singularities of \\spad{op},{} and the \\spad{e_i}\\spad{'s} are the indicial equations at each \\spad{d_i}.")) (|denomLODE| ((|#2| |#3| (|List| (|Fraction| |#2|))) "\\spad{denomLODE(op,{} [g1,{}...,{}gm])} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{p/d} for some polynomial \\spad{p}.") (((|Union| |#2| "failed") |#3| (|Fraction| |#2|)) "\\spad{denomLODE(op,{} g)} returns a polynomial \\spad{d} such that any rational solution of \\spad{op y = g} is of the form \\spad{p/d} for some polynomial \\spad{p},{} and \"failed\",{} if the equation has no rational solution."))) NIL NIL @@ -2920,41 +2920,41 @@ NIL ((|retract| (((|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|))) $) "\\spad{retract(x)} \\undocumented{}")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(x)} \\undocumented{}") (($ (|Record| (|:| |xinit| (|DoubleFloat|)) (|:| |xend| (|DoubleFloat|)) (|:| |fn| (|Vector| (|Expression| (|DoubleFloat|)))) (|:| |yinit| (|List| (|DoubleFloat|))) (|:| |intvals| (|List| (|DoubleFloat|))) (|:| |g| (|Expression| (|DoubleFloat|))) (|:| |abserr| (|DoubleFloat|)) (|:| |relerr| (|DoubleFloat|)))) "\\spad{coerce(x)} \\undocumented{}"))) NIL NIL -(-748 -2315 UP L LQ) +(-748 -3539 UP L LQ) ((|constructor| (NIL "In-field solution of Riccati equations,{} primitive case.")) (|changeVar| ((|#3| |#3| (|Fraction| |#2|)) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.") ((|#3| |#3| |#2|) "\\spad{changeVar(+/[\\spad{ai} D^i],{} a)} returns the operator \\spad{+/[\\spad{ai} (D+a)\\spad{^i}]}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#2|) |#2| (|SparseUnivariatePolynomial| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} zeros,{} ezfactor)} returns \\spad{[[f1,{} L1],{} [f2,{} L2],{} ... ,{} [fk,{} Lk]]} such that the singular part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z=0}. \\spad{zeros(C(x),{}H(x,{}y))} returns all the \\spad{P_i(x)}\\spad{'s} such that \\spad{H(x,{}P_i(x)) = 0 modulo C(x)}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{} Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y=0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z=y e^{-int p}} is \\spad{\\spad{Li} z =0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|constantCoefficientRicDE| (((|List| (|Record| (|:| |constant| |#1|) (|:| |eq| |#3|))) |#3| (|Mapping| (|List| |#1|) |#2|)) "\\spad{constantCoefficientRicDE(op,{} ric)} returns \\spad{[[a1,{} L1],{} [a2,{} L2],{} ... ,{} [ak,{} Lk]]} such that any rational solution with no polynomial part of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{ai}\\spad{'s} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. \\spad{ric} is a Riccati equation solver over \\spad{F},{} whose input is the associated linear equation.")) (|leadingCoefficientRicDE| (((|List| (|Record| (|:| |deg| (|NonNegativeInteger|)) (|:| |eq| |#2|))) |#3|) "\\spad{leadingCoefficientRicDE(op)} returns \\spad{[[m1,{} p1],{} [m2,{} p2],{} ... ,{} [mk,{} pk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must have degree \\spad{mj} for some \\spad{j},{} and its leading coefficient is then a zero of \\spad{pj}. In addition,{}\\spad{m1>m2> ... >mk}.")) (|denomRicDE| ((|#2| |#3|) "\\spad{denomRicDE(op)} returns a polynomial \\spad{d} such that any rational solution of the associated Riccati equation of \\spad{op y = 0} is of the form \\spad{p/d + q'/q + r} for some polynomials \\spad{p} and \\spad{q} and a reduced \\spad{r}. Also,{} \\spad{deg(p) < deg(d)} and {\\spad{gcd}(\\spad{d},{}\\spad{q}) = 1}."))) NIL NIL -(-749 -2315 UP) +(-749 -3539 UP) ((|constructor| (NIL "\\spad{RationalLODE} provides functions for in-field solutions of linear \\indented{1}{ordinary differential equations,{} in the rational case.}")) (|indicialEquationAtInfinity| ((|#2| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.") ((|#2| (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{indicialEquationAtInfinity op} returns the indicial equation of \\spad{op} at infinity.")) (|ratDsolve| (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation.") (((|Record| (|:| |basis| (|List| (|Fraction| |#2|))) (|:| |mat| (|Matrix| |#1|))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|List| (|Fraction| |#2|))) "\\spad{ratDsolve(op,{} [g1,{}...,{}gm])} returns \\spad{[[h1,{}...,{}hq],{} M]} such that any rational solution of \\spad{op y = c1 g1 + ... + cm gm} is of the form \\spad{d1 h1 + ... + dq hq} where \\spad{M [d1,{}...,{}dq,{}c1,{}...,{}cm] = 0}.") (((|Record| (|:| |particular| (|Union| (|Fraction| |#2|) "failed")) (|:| |basis| (|List| (|Fraction| |#2|)))) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Fraction| |#2|)) "\\spad{ratDsolve(op,{} g)} returns \\spad{[\"failed\",{} []]} if the equation \\spad{op y = g} has no rational solution. Otherwise,{} it returns \\spad{[f,{} [y1,{}...,{}ym]]} where \\spad{f} is a particular rational solution and the \\spad{yi}\\spad{'s} form a basis for the rational solutions of the homogeneous equation."))) NIL NIL -(-750 -2315 L UP A LO) +(-750 -3539 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 -(-751 -2315 UP) +(-751 -3539 UP) ((|constructor| (NIL "In-field solution of Riccati equations,{} rational case.")) (|polyRicDE| (((|List| (|Record| (|:| |poly| |#2|) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{polyRicDE(op,{} zeros)} returns \\spad{[[p1,{} L1],{} [p2,{} L2],{} ... ,{} [pk,{}Lk]]} such that the polynomial part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{pi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int p}} is \\spad{\\spad{Li} z = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.")) (|singRicDE| (((|List| (|Record| (|:| |frac| (|Fraction| |#2|)) (|:| |eq| (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))))) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{singRicDE(op,{} ezfactor)} returns \\spad{[[f1,{}L1],{} [f2,{}L2],{}...,{} [fk,{}Lk]]} such that the singular \\spad{++} part of any rational solution of the associated Riccati equation of \\spad{op y = 0} must be one of the \\spad{fi}\\spad{'s} (up to the constant coefficient),{} in which case the equation for \\spad{z = y e^{-int \\spad{ai}}} is \\spad{\\spad{Li} z = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.")) (|ricDsolve| (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|))) "\\spad{ricDsolve(op)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator2| |#2| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|) (|Mapping| (|Factored| |#2|) |#2|)) "\\spad{ricDsolve(op,{} zeros,{} ezfactor)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}. Argument \\spad{ezfactor} is a factorisation in \\spad{UP},{} not necessarily into irreducibles.") (((|List| (|Fraction| |#2|)) (|LinearOrdinaryDifferentialOperator1| (|Fraction| |#2|)) (|Mapping| (|List| |#1|) |#2|)) "\\spad{ricDsolve(op,{} zeros)} returns the rational solutions of the associated Riccati equation of \\spad{op y = 0}. \\spad{zeros} is a zero finder in \\spad{UP}."))) NIL ((|HasCategory| |#1| (QUOTE (-27)))) -(-752 -2315 LO) +(-752 -3539 LO) ((|constructor| (NIL "SystemODESolver provides tools for triangulating and solving some systems of linear ordinary differential equations.")) (|solveInField| (((|Record| (|:| |particular| (|Union| (|Vector| |#1|) "failed")) (|:| |basis| (|List| (|Vector| |#1|)))) (|Matrix| |#2|) (|Vector| |#1|) (|Mapping| (|Record| (|:| |particular| (|Union| |#1| "failed")) (|:| |basis| (|List| |#1|))) |#2| |#1|)) "\\spad{solveInField(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{m x = v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{m x = 0}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|solve| (((|Union| (|Record| (|:| |particular| (|Vector| |#1|)) (|:| |basis| (|Matrix| |#1|))) "failed") (|Matrix| |#1|) (|Vector| |#1|) (|Mapping| (|Union| (|Record| (|:| |particular| |#1|) (|:| |basis| (|List| |#1|))) "failed") |#2| |#1|)) "\\spad{solve(m,{} v,{} solve)} returns \\spad{[[v_1,{}...,{}v_m],{} v_p]} such that the solutions in \\spad{F} of the system \\spad{D x = m x + v} are \\spad{v_p + c_1 v_1 + ... + c_m v_m} where the \\spad{c_i's} are constants,{} and the \\spad{v_i's} form a basis for the solutions of \\spad{D x = m x}. Argument \\spad{solve} is a function for solving a single linear ordinary differential equation in \\spad{F}.")) (|triangulate| (((|Record| (|:| |mat| (|Matrix| |#2|)) (|:| |vec| (|Vector| |#1|))) (|Matrix| |#2|) (|Vector| |#1|)) "\\spad{triangulate(m,{} v)} returns \\spad{[m_0,{} v_0]} such that \\spad{m_0} is upper triangular and the system \\spad{m_0 x = v_0} is equivalent to \\spad{m x = v}.") 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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(\\spad{fi})=0}. The value \"failed\" is returned if \\spad{m < n} and no particular solution is found.")) (|wronskianMatrix| (((|Matrix| |#1|) (|List| |#1|) (|NonNegativeInteger|)) "\\spad{wronskianMatrix([f1,{}...,{}fn],{} q,{} D)} returns the \\spad{q x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}.") (((|Matrix| |#1|) (|List| |#1|)) "\\spad{wronskianMatrix([f1,{}...,{}fn])} returns the \\spad{n x n} matrix \\spad{m} whose i^th row is \\spad{[f1^(i-1),{}...,{}fn^(i-1)]}."))) 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(-523)))))) (|HasCategory| (-523) (QUOTE (-786))) (-12 (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (QUOTE (-973)))) (-12 (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087))))) (|HasCategory| |#2| (QUOTE (-666))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523))))) (-3172 (|HasCategory| |#2| (QUOTE (-973))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-1016)))) (|HasAttribute| |#2| (QUOTE -4245)) (|HasCategory| |#2| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-25))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (-755 R) ((|constructor| (NIL "\\spadtype{OrderlyDifferentialPolynomial} implements an ordinary differential polynomial ring in arbitrary number of differential indeterminates,{} with coefficients in a ring. The ranking on the differential indeterminate is orderly. This is analogous to the domain \\spadtype{Polynomial}. \\blankline"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-757 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-756 |Kernels| R |var|) ((|constructor| (NIL "This constructor produces an ordinary differential ring from a partial differential ring by specifying a variable.")) (|coerce| ((|#2| $) "\\spad{coerce(p)} views \\spad{p} as a valie in the partial differential ring.") (($ |#2|) "\\spad{coerce(r)} views \\spad{r} as a value in the ordinary differential ring."))) -(((-4246 "*") |has| |#2| (-339)) (-4237 |has| |#2| (-339)) (-4242 |has| |#2| (-339)) (-4236 |has| |#2| (-339)) (-4241 . T) (-4239 . T) (-4238 . T)) +(((-4250 "*") |has| |#2| (-339)) (-4241 |has| |#2| (-339)) (-4246 |has| |#2| (-339)) (-4240 |has| |#2| (-339)) (-4245 . T) (-4243 . T) (-4242 . T)) ((|HasCategory| |#2| (QUOTE (-339)))) (-757 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}))."))) @@ -2966,7 +2966,7 @@ NIL NIL (-759) ((|constructor| (NIL "The category of ordered commutative integral domains,{} where ordering and the arithmetic operations are compatible \\blankline"))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-760) ((|constructor| (NIL "\\spadtype{OpenMathConnection} provides low-level functions for handling connections to and from \\spadtype{OpenMathDevice}\\spad{s}.")) (|OMbindTCP| (((|Boolean|) $ (|SingleInteger|)) "\\spad{OMbindTCP}")) (|OMconnectTCP| (((|Boolean|) $ (|String|) (|SingleInteger|)) "\\spad{OMconnectTCP}")) (|OMconnOutDevice| (((|OpenMathDevice|) $) "\\spad{OMconnOutDevice:}")) (|OMconnInDevice| (((|OpenMathDevice|) $) "\\spad{OMconnInDevice:}")) (|OMcloseConn| (((|Void|) $) "\\spad{OMcloseConn}")) (|OMmakeConn| (($ (|SingleInteger|)) "\\spad{OMmakeConn}"))) @@ -2994,7 +2994,7 @@ NIL NIL (-766 P R) ((|constructor| (NIL "This constructor creates the \\spadtype{MonogenicLinearOperator} domain which is ``opposite\\spad{''} in the ring sense to \\spad{P}. That is,{} as sets \\spad{P = \\$} but \\spad{a * b} in \\spad{\\$} is equal to \\spad{b * a} in \\spad{P}.")) (|po| ((|#1| $) "\\spad{po(q)} creates a value in \\spad{P} equal to \\spad{q} in \\$.")) (|op| (($ |#1|) "\\spad{op(p)} creates a value in \\$ equal to \\spad{p} in \\spad{P}."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-211)))) (-767) ((|constructor| (NIL "\\spadtype{OpenMath} provides operations for exporting an object in OpenMath format.")) (|OMwrite| (((|Void|) (|OpenMathDevice|) $ (|Boolean|)) "\\spad{OMwrite(dev,{} u,{} true)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object; OMwrite(\\spad{dev},{} \\spad{u},{} \\spad{false}) writes the object as an OpenMath fragment.") (((|Void|) (|OpenMathDevice|) $) "\\spad{OMwrite(dev,{} u)} writes the OpenMath form of \\axiom{\\spad{u}} to the OpenMath device \\axiom{\\spad{dev}} as a complete OpenMath object.") (((|String|) $ (|Boolean|)) "\\spad{OMwrite(u,{} true)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object; OMwrite(\\spad{u},{} \\spad{false}) returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as an OpenMath fragment.") (((|String|) $) "\\spad{OMwrite(u)} returns the OpenMath \\spad{XML} encoding of \\axiom{\\spad{u}} as a complete OpenMath object."))) @@ -3006,7 +3006,7 @@ NIL NIL (-769 S) ((|constructor| (NIL "to become an in order iterator")) (|min| ((|#1| $) "\\spad{min(u)} returns the smallest entry in the multiset aggregate \\spad{u}."))) -((-4244 . T) (-4234 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4238 . T) (-4249 . T) (-4069 . T)) NIL (-770) ((|constructor| (NIL "\\spadtype{OpenMathServerPackage} provides the necessary operations to run AXIOM as an OpenMath server,{} reading/writing objects to/from a port. Please note the facilities available here are very basic. The idea is that a user calls \\spadignore{e.g.} \\axiom{Omserve(4000,{}60)} and then another process sends OpenMath objects to port 4000 and reads the result.")) (|OMserve| (((|Void|) (|SingleInteger|) (|SingleInteger|)) "\\spad{OMserve(portnum,{}timeout)} puts AXIOM into server mode on port number \\axiom{\\spad{portnum}}. The parameter \\axiom{\\spad{timeout}} specifies the \\spad{timeout} period for the connection.")) (|OMsend| (((|Void|) (|OpenMathConnection|) (|Any|)) "\\spad{OMsend(c,{}u)} attempts to output \\axiom{\\spad{u}} on \\aciom{\\spad{c}} in OpenMath.")) (|OMreceive| (((|Any|) (|OpenMathConnection|)) "\\spad{OMreceive(c)} reads an OpenMath object from connection \\axiom{\\spad{c}} and returns the appropriate AXIOM object."))) @@ -3018,11 +3018,11 @@ NIL NIL (-772 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."))) -((-4241 |has| |#1| (-784))) -((|HasCategory| |#1| (QUOTE (-784))) (-3262 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3262 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4245 |has| |#1| (-784))) +((|HasCategory| |#1| (QUOTE (-784))) (-3172 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) (-773 R) ((|constructor| (NIL "Algebra of ADDITIVE operators over a ring."))) -((-4239 |has| |#1| (-158)) (-4238 |has| |#1| (-158)) (-4241 . T)) +((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136)))) (-774) ((|constructor| (NIL "This package exports tools to create AXIOM Library information databases.")) (|getDatabase| (((|Database| (|IndexCard|)) (|String|)) "\\spad{getDatabase(\"char\")} returns a list of appropriate entries in the browser database. The legal values for \\spad{\"char\"} are \"o\" (operations),{} \\spad{\"k\"} (constructors),{} \\spad{\"d\"} (domains),{} \\spad{\"c\"} (categories) or \\spad{\"p\"} (packages)."))) @@ -3046,13 +3046,13 @@ NIL NIL (-779 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."))) -((-4241 |has| |#1| (-784))) -((|HasCategory| |#1| (QUOTE (-784))) (-3262 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3262 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) +((-4245 |has| |#1| (-784))) +((|HasCategory| |#1| (QUOTE (-784))) (-3172 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-784)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-21)))) (-780) ((|constructor| (NIL "Ordered finite sets."))) NIL NIL -(-781 -1346 S) +(-781 -1996 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 @@ -3066,7 +3066,7 @@ NIL NIL (-784) ((|constructor| (NIL "Ordered sets which are also rings,{} that is,{} domains where the ring operations are compatible with the ordering. \\blankline")) (|abs| (($ $) "\\spad{abs(x)} returns the absolute value of \\spad{x}.")) (|sign| (((|Integer|) $) "\\spad{sign(x)} is 1 if \\spad{x} is positive,{} \\spad{-1} if \\spad{x} is negative,{} 0 if \\spad{x} equals 0.")) (|negative?| (((|Boolean|) $) "\\spad{negative?(x)} tests whether \\spad{x} is strictly less than 0.")) (|positive?| (((|Boolean|) $) "\\spad{positive?(x)} tests whether \\spad{x} is strictly greater than 0."))) -((-4241 . T)) +((-4245 . T)) NIL (-785 S) ((|constructor| (NIL "The class of totally ordered sets,{} that is,{} sets such that for each pair of elements \\spad{(a,{}b)} exactly one of the following relations holds \\spad{a<b or a=b or b<a} and the relation is transitive,{} \\spadignore{i.e.} \\spad{a<b and b<c => a<c}.")) (|min| (($ $ $) "\\spad{min(x,{}y)} returns the minimum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (|max| (($ $ $) "\\spad{max(x,{}y)} returns the maximum of \\spad{x} and \\spad{y} relative to \\spad{\"<\"}.")) (<= (((|Boolean|) $ $) "\\spad{x <= y} is a less than or equal test.")) (>= (((|Boolean|) $ $) "\\spad{x >= y} is a greater than or equal test.")) (> (((|Boolean|) $ $) "\\spad{x > y} is a greater than test.")) (< (((|Boolean|) $ $) "\\spad{x < y} is a strict total ordering on the elements of the set."))) @@ -3077,24 +3077,24 @@ NIL NIL NIL (-787 S R) -((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) +((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#2| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#2|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#2| $ |#2| |#2|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#2|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#2| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#2| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#2| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) NIL ((|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158)))) (-788 R) -((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ^= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((|constructor| (NIL "This is the category of univariate skew polynomials over an Ore coefficient ring. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}. This category is an evolution of the types \\indented{2}{MonogenicLinearOperator,{} OppositeMonogenicLinearOperator,{} and} \\indented{2}{NonCommutativeOperatorDivision} developped by Jean Della Dora and Stephen \\spad{M}. Watt.")) (|leftLcm| (($ $ $) "\\spad{leftLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = aa*a = bb*b} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using right-division.")) (|rightExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{rightExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = c * a + d * b = rightGcd(a,{} b)}.")) (|rightGcd| (($ $ $) "\\spad{rightGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = aa*g}} \\indented{3}{\\spad{b = bb*g}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using right-division.")) (|rightExactQuotient| (((|Union| $ "failed") $ $) "\\spad{rightExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists such that \\spad{a = q*b}.")) (|rightRemainder| (($ $ $) "\\spad{rightRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|rightQuotient| (($ $ $) "\\spad{rightQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|rightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{rightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}.")) (|rightLcm| (($ $ $) "\\spad{rightLcm(a,{}b)} computes the value \\spad{m} of lowest degree such that \\spad{m = a*aa = b*bb} for some values \\spad{aa} and \\spad{bb}. The value \\spad{m} is computed using left-division.")) (|leftExtendedGcd| (((|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) $ $) "\\spad{leftExtendedGcd(a,{}b)} returns \\spad{[c,{}d]} such that \\spad{g = a * c + b * d = leftGcd(a,{} b)}.")) (|leftGcd| (($ $ $) "\\spad{leftGcd(a,{}b)} computes the value \\spad{g} of highest degree such that \\indented{3}{\\spad{a = g*aa}} \\indented{3}{\\spad{b = g*bb}} for some values \\spad{aa} and \\spad{bb}. The value \\spad{g} is computed using left-division.")) (|leftExactQuotient| (((|Union| $ "failed") $ $) "\\spad{leftExactQuotient(a,{}b)} computes the value \\spad{q},{} if it exists,{} \\indented{1}{such that \\spad{a = b*q}.}")) (|leftRemainder| (($ $ $) "\\spad{leftRemainder(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{r} is returned.")) (|leftQuotient| (($ $ $) "\\spad{leftQuotient(a,{}b)} computes the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. The value \\spad{q} is returned.")) (|leftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{leftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}.")) (|primitivePart| (($ $) "\\spad{primitivePart(l)} returns \\spad{l0} such that \\spad{l = a * l0} for some a in \\spad{R},{} and \\spad{content(l0) = 1}.")) (|content| ((|#1| $) "\\spad{content(l)} returns the \\spad{gcd} of all the coefficients of \\spad{l}.")) (|monicRightDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicRightDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}.")) (|monicLeftDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicLeftDivide(a,{}b)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}.")) (|exquo| (((|Union| $ "failed") $ |#1|) "\\spad{exquo(l,{} a)} returns the exact quotient of \\spad{l} by a,{} returning \\axiom{\"failed\"} if this is not possible.")) (|apply| ((|#1| $ |#1| |#1|) "\\spad{apply(p,{} c,{} m)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|coefficients| (((|List| |#1|) $) "\\spad{coefficients(l)} returns the list of all the nonzero coefficients of \\spad{l}.")) (|monomial| (($ |#1| (|NonNegativeInteger|)) "\\spad{monomial(c,{}k)} produces \\spad{c} times the \\spad{k}-th power of the generating operator,{} \\spad{monomial(1,{}1)}.")) (|coefficient| ((|#1| $ (|NonNegativeInteger|)) "\\spad{coefficient(l,{}k)} is \\spad{a(k)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|reductum| (($ $) "\\spad{reductum(l)} is \\spad{l - monomial(a(n),{}n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|leadingCoefficient| ((|#1| $) "\\spad{leadingCoefficient(l)} is \\spad{a(n)} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|minimumDegree| (((|NonNegativeInteger|) $) "\\spad{minimumDegree(l)} is the smallest \\spad{k} such that \\spad{a(k) ~= 0} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(l)} is \\spad{n} if \\indented{2}{\\spad{l = sum(monomial(a(i),{}i),{} i = 0..n)}.}"))) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL (-789 R C) ((|constructor| (NIL "\\spad{UnivariateSkewPolynomialCategoryOps} provides products and \\indented{1}{divisions of univariate skew polynomials.}")) (|rightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{rightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|leftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{leftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicRightDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicRightDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = q*b + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``right division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|monicLeftDivide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2| (|Automorphism| |#1|)) "\\spad{monicLeftDivide(a,{} b,{} sigma)} returns the pair \\spad{[q,{}r]} such that \\spad{a = b*q + r} and the degree of \\spad{r} is less than the degree of \\spad{b}. \\spad{b} must be monic. This process is called ``left division\\spad{''}. \\spad{\\sigma} is the morphism to use.")) (|apply| ((|#1| |#2| |#1| |#1| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{apply(p,{} c,{} m,{} sigma,{} delta)} returns \\spad{p(m)} where the action is given by \\spad{x m = c sigma(m) + delta(m)}.")) (|times| ((|#2| |#2| |#2| (|Automorphism| |#1|) (|Mapping| |#1| |#1|)) "\\spad{times(p,{} q,{} sigma,{} delta)} returns \\spad{p * q}. \\spad{\\sigma} and \\spad{\\delta} are the maps to use."))) NIL ((|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) -(-790 R |sigma| -2594) +(-790 R |sigma| -1566) ((|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."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-339)))) -(-791 |x| R |sigma| -2594) +(-791 |x| R |sigma| -1566) ((|constructor| (NIL "This is the domain of univariate skew polynomials over an Ore coefficient field in a named variable. The multiplication is given by \\spad{x a = \\sigma(a) x + \\delta a}.")) (|coerce| (($ (|Variable| |#1|)) "\\spad{coerce(x)} returns \\spad{x} as a skew-polynomial."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-339)))) (-792 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..)}."))) @@ -3105,7 +3105,7 @@ NIL NIL NIL (-794) -((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (^= (($ $ $) "\\spad{f ^= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) +((|constructor| (NIL "This domain is used to create and manipulate mathematical expressions for output. It is intended to provide an insulating layer between the expression rendering software (\\spadignore{e.g.} TeX,{} or Script) and the output coercions in the various domains.")) (SEGMENT (($ $) "\\spad{SEGMENT(x)} creates the prefix form: \\spad{x..}.") (($ $ $) "\\spad{SEGMENT(x,{}y)} creates the infix form: \\spad{x..y}.")) (|not| (($ $) "\\spad{not f} creates the equivalent prefix form.")) (|or| (($ $ $) "\\spad{f or g} creates the equivalent infix form.")) (|and| (($ $ $) "\\spad{f and g} creates the equivalent infix form.")) (|exquo| (($ $ $) "\\spad{exquo(f,{}g)} creates the equivalent infix form.")) (|quo| (($ $ $) "\\spad{f quo g} creates the equivalent infix form.")) (|rem| (($ $ $) "\\spad{f rem g} creates the equivalent infix form.")) (|div| (($ $ $) "\\spad{f div g} creates the equivalent infix form.")) (** (($ $ $) "\\spad{f ** g} creates the equivalent infix form.")) (/ (($ $ $) "\\spad{f / g} creates the equivalent infix form.")) (* (($ $ $) "\\spad{f * g} creates the equivalent infix form.")) (- (($ $) "\\spad{- f} creates the equivalent prefix form.") (($ $ $) "\\spad{f - g} creates the equivalent infix form.")) (+ (($ $ $) "\\spad{f + g} creates the equivalent infix form.")) (>= (($ $ $) "\\spad{f >= g} creates the equivalent infix form.")) (<= (($ $ $) "\\spad{f <= g} creates the equivalent infix form.")) (> (($ $ $) "\\spad{f > g} creates the equivalent infix form.")) (< (($ $ $) "\\spad{f < g} creates the equivalent infix form.")) (~= (($ $ $) "\\spad{f ~= g} creates the equivalent infix form.")) (= (($ $ $) "\\spad{f = g} creates the equivalent infix form.")) (|blankSeparate| (($ (|List| $)) "\\spad{blankSeparate(l)} creates the form separating the elements of \\spad{l} by blanks.")) (|semicolonSeparate| (($ (|List| $)) "\\spad{semicolonSeparate(l)} creates the form separating the elements of \\spad{l} by semicolons.")) (|commaSeparate| (($ (|List| $)) "\\spad{commaSeparate(l)} creates the form separating the elements of \\spad{l} by commas.")) (|pile| (($ (|List| $)) "\\spad{pile(l)} creates the form consisting of the elements of \\spad{l} which displays as a pile,{} \\spadignore{i.e.} the elements begin on a new line and are indented right to the same margin.")) (|paren| (($ (|List| $)) "\\spad{paren(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in parentheses.") (($ $) "\\spad{paren(f)} creates the form enclosing \\spad{f} in parentheses.")) (|bracket| (($ (|List| $)) "\\spad{bracket(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in square brackets.") (($ $) "\\spad{bracket(f)} creates the form enclosing \\spad{f} in square brackets.")) (|brace| (($ (|List| $)) "\\spad{brace(lf)} creates the form separating the elements of \\spad{lf} by commas and encloses the result in curly brackets.") (($ $) "\\spad{brace(f)} creates the form enclosing \\spad{f} in braces (curly brackets).")) (|int| (($ $ $ $) "\\spad{int(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by an integral sign with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{int(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by an integral sign with a \\spad{lowerlimit}.") (($ $) "\\spad{int(expr)} creates the form prefixing \\spad{expr} with an integral sign.")) (|prod| (($ $ $ $) "\\spad{prod(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{prod(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital \\spad{pi} with a \\spad{lowerlimit}.") (($ $) "\\spad{prod(expr)} creates the form prefixing \\spad{expr} by a capital \\spad{pi}.")) (|sum| (($ $ $ $) "\\spad{sum(expr,{}lowerlimit,{}upperlimit)} creates the form prefixing \\spad{expr} by a capital sigma with both a \\spad{lowerlimit} and \\spad{upperlimit}.") (($ $ $) "\\spad{sum(expr,{}lowerlimit)} creates the form prefixing \\spad{expr} by a capital sigma with a \\spad{lowerlimit}.") (($ $) "\\spad{sum(expr)} creates the form prefixing \\spad{expr} by a capital sigma.")) (|overlabel| (($ $ $) "\\spad{overlabel(x,{}f)} creates the form \\spad{f} with \\spad{\"x} overbar\" over the top.")) (|overbar| (($ $) "\\spad{overbar(f)} creates the form \\spad{f} with an overbar.")) (|prime| (($ $ (|NonNegativeInteger|)) "\\spad{prime(f,{}n)} creates the form \\spad{f} followed by \\spad{n} primes.") (($ $) "\\spad{prime(f)} creates the form \\spad{f} followed by a suffix prime (single quote).")) (|dot| (($ $ (|NonNegativeInteger|)) "\\spad{dot(f,{}n)} creates the form \\spad{f} with \\spad{n} dots overhead.") (($ $) "\\spad{dot(f)} creates the form with a one dot overhead.")) (|quote| (($ $) "\\spad{quote(f)} creates the form \\spad{f} with a prefix quote.")) (|supersub| (($ $ (|List| $)) "\\spad{supersub(a,{}[sub1,{}super1,{}sub2,{}super2,{}...])} creates a form with each subscript aligned under each superscript.")) (|scripts| (($ $ (|List| $)) "\\spad{scripts(f,{} [sub,{} super,{} presuper,{} presub])} \\indented{1}{creates a form for \\spad{f} with scripts on all 4 corners.}")) (|presuper| (($ $ $) "\\spad{presuper(f,{}n)} creates a form for \\spad{f} presuperscripted by \\spad{n}.")) (|presub| (($ $ $) "\\spad{presub(f,{}n)} creates a form for \\spad{f} presubscripted by \\spad{n}.")) (|super| (($ $ $) "\\spad{super(f,{}n)} creates a form for \\spad{f} superscripted by \\spad{n}.")) (|sub| (($ $ $) "\\spad{sub(f,{}n)} creates a form for \\spad{f} subscripted by \\spad{n}.")) (|binomial| (($ $ $) "\\spad{binomial(n,{}m)} creates a form for the binomial coefficient of \\spad{n} and \\spad{m}.")) (|differentiate| (($ $ (|NonNegativeInteger|)) "\\spad{differentiate(f,{}n)} creates a form for the \\spad{n}th derivative of \\spad{f},{} \\spadignore{e.g.} \\spad{f'},{} \\spad{f''},{} \\spad{f'''},{} \\spad{\"f} super \\spad{iv}\".")) (|rarrow| (($ $ $) "\\spad{rarrow(f,{}g)} creates a form for the mapping \\spad{f -> g}.")) (|assign| (($ $ $) "\\spad{assign(f,{}g)} creates a form for the assignment \\spad{f := g}.")) (|slash| (($ $ $) "\\spad{slash(f,{}g)} creates a form for the horizontal fraction of \\spad{f} over \\spad{g}.")) (|over| (($ $ $) "\\spad{over(f,{}g)} creates a form for the vertical fraction of \\spad{f} over \\spad{g}.")) (|root| (($ $ $) "\\spad{root(f,{}n)} creates a form for the \\spad{n}th root of form \\spad{f}.") (($ $) "\\spad{root(f)} creates a form for the square root of form \\spad{f}.")) (|zag| (($ $ $) "\\spad{zag(f,{}g)} creates a form for the continued fraction form for \\spad{f} over \\spad{g}.")) (|matrix| (($ (|List| (|List| $))) "\\spad{matrix(llf)} makes \\spad{llf} (a list of lists of forms) into a form which displays as a matrix.")) (|box| (($ $) "\\spad{box(f)} encloses \\spad{f} in a box.")) (|label| (($ $ $) "\\spad{label(n,{}f)} gives form \\spad{f} an equation label \\spad{n}.")) (|string| (($ $) "\\spad{string(f)} creates \\spad{f} with string quotes.")) (|elt| (($ $ (|List| $)) "\\spad{elt(op,{}l)} creates a form for application of \\spad{op} to list of arguments \\spad{l}.")) (|infix?| (((|Boolean|) $) "\\spad{infix?(op)} returns \\spad{true} if \\spad{op} is an infix operator,{} and \\spad{false} otherwise.")) (|postfix| (($ $ $) "\\spad{postfix(op,{} a)} creates a form which prints as: a \\spad{op}.")) (|infix| (($ $ $ $) "\\spad{infix(op,{} a,{} b)} creates a form which prints as: a \\spad{op} \\spad{b}.") (($ $ (|List| $)) "\\spad{infix(f,{}l)} creates a form depicting the \\spad{n}-ary application of infix operation \\spad{f} to a tuple of arguments \\spad{l}.")) (|prefix| (($ $ (|List| $)) "\\spad{prefix(f,{}l)} creates a form depicting the \\spad{n}-ary prefix application of \\spad{f} to a tuple of arguments given by list \\spad{l}.")) (|vconcat| (($ (|List| $)) "\\spad{vconcat(u)} vertically concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{vconcat(f,{}g)} vertically concatenates forms \\spad{f} and \\spad{g}.")) (|hconcat| (($ (|List| $)) "\\spad{hconcat(u)} horizontally concatenates all forms in list \\spad{u}.") (($ $ $) "\\spad{hconcat(f,{}g)} horizontally concatenate forms \\spad{f} and \\spad{g}.")) (|center| (($ $) "\\spad{center(f)} centers form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{center(f,{}n)} centers form \\spad{f} within space of width \\spad{n}.")) (|right| (($ $) "\\spad{right(f)} right-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{right(f,{}n)} right-justifies form \\spad{f} within space of width \\spad{n}.")) (|left| (($ $) "\\spad{left(f)} left-justifies form \\spad{f} in total space.") (($ $ (|Integer|)) "\\spad{left(f,{}n)} left-justifies form \\spad{f} within space of width \\spad{n}.")) (|rspace| (($ (|Integer|) (|Integer|)) "\\spad{rspace(n,{}m)} creates rectangular white space,{} \\spad{n} wide by \\spad{m} high.")) (|vspace| (($ (|Integer|)) "\\spad{vspace(n)} creates white space of height \\spad{n}.")) (|hspace| (($ (|Integer|)) "\\spad{hspace(n)} creates white space of width \\spad{n}.")) (|superHeight| (((|Integer|) $) "\\spad{superHeight(f)} returns the height of form \\spad{f} above the base line.")) (|subHeight| (((|Integer|) $) "\\spad{subHeight(f)} returns the height of form \\spad{f} below the base line.")) (|height| (((|Integer|)) "\\spad{height()} returns the height of the display area (an integer).") (((|Integer|) $) "\\spad{height(f)} returns the height of form \\spad{f} (an integer).")) (|width| (((|Integer|)) "\\spad{width()} returns the width of the display area (an integer).") (((|Integer|) $) "\\spad{width(f)} returns the width of form \\spad{f} (an integer).")) (|empty| (($) "\\spad{empty()} creates an empty form.")) (|outputForm| (($ (|DoubleFloat|)) "\\spad{outputForm(sf)} creates an form for small float \\spad{sf}.") (($ (|String|)) "\\spad{outputForm(s)} creates an form for string \\spad{s}.") (($ (|Symbol|)) "\\spad{outputForm(s)} creates an form for symbol \\spad{s}.") (($ (|Integer|)) "\\spad{outputForm(n)} creates an form for integer \\spad{n}.")) (|messagePrint| (((|Void|) (|String|)) "\\spad{messagePrint(s)} prints \\spad{s} without string quotes. Note: \\spad{messagePrint(s)} is equivalent to \\spad{print message(s)}.")) (|message| (($ (|String|)) "\\spad{message(s)} creates an form with no string quotes from string \\spad{s}.")) (|print| (((|Void|) $) "\\spad{print(u)} prints the form \\spad{u}."))) NIL NIL (-795) @@ -3118,7 +3118,7 @@ NIL NIL (-797 R |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over the \"Polynomial\" type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} This changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ (|Polynomial| |#1|)) "\\spad{coerce(p)} coerces a Polynomial(\\spad{R}) into Weighted form,{} applying weights and ignoring terms") (((|Polynomial| |#1|) $) "\\spad{coerce(p)} converts back into a Polynomial(\\spad{R}),{} ignoring weights"))) -((-4239 |has| |#1| (-158)) (-4238 |has| |#1| (-158)) (-4241 . T)) +((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339)))) (-798 R PS UP) ((|constructor| (NIL "\\indented{1}{This package computes reliable Pad&ea. approximants using} a generalized Viskovatov continued fraction algorithm. Authors: Burge,{} Hassner & Watt. Date Created: April 1987 Date Last Updated: 12 April 1990 Keywords: Pade,{} series Examples: References: \\indented{2}{\"Pade Approximants,{} Part I: Basic Theory\",{} Baker & Graves-Morris.}")) (|padecf| (((|Union| (|ContinuedFraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{padecf(nd,{}dd,{}ns,{}ds)} computes the approximant as a continued fraction of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function).")) (|pade| (((|Union| (|Fraction| |#3|) "failed") (|NonNegativeInteger|) (|NonNegativeInteger|) |#2| |#2|) "\\spad{pade(nd,{}dd,{}ns,{}ds)} computes the approximant as a quotient of polynomials (if it exists) for arguments \\spad{nd} (numerator degree of approximant),{} \\spad{dd} (denominator degree of approximant),{} \\spad{ns} (numerator series of function),{} and \\spad{ds} (denominator series of function)."))) @@ -3130,24 +3130,24 @@ NIL NIL (-800 |p|) ((|constructor| (NIL "This is the catefory of stream-based representations of \\indented{2}{the \\spad{p}-adic integers.}")) (|root| (($ (|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}."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-801 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Zp:} \\spad{p}-adic numbers are represented as sum(\\spad{i} = 0..,{} a[\\spad{i}] * p^i),{} where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-802 |p|) ((|constructor| (NIL "Stream-based implementation of \\spad{Qp:} numbers are represented as sum(\\spad{i} = \\spad{k}..,{} a[\\spad{i}] * p^i) where the a[\\spad{i}] lie in 0,{}1,{}...,{}(\\spad{p} - 1)."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-801 |#1|) (QUOTE (-840))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-136))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-801 |#1|) (QUOTE (-949))) (|HasCategory| (-801 |#1|) (QUOTE (-759))) (-3262 (|HasCategory| (-801 |#1|) (QUOTE (-759))) (|HasCategory| (-801 |#1|) (QUOTE (-786)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-1063))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-211))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -801) (|devaluate| |#1|)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (QUOTE (-284))) (|HasCategory| (-801 |#1|) (QUOTE (-508))) (|HasCategory| (-801 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-801 |#1|) (QUOTE (-840))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-136))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-801 |#1|) (QUOTE (-949))) (|HasCategory| (-801 |#1|) (QUOTE (-759))) (-3172 (|HasCategory| (-801 |#1|) (QUOTE (-759))) (|HasCategory| (-801 |#1|) (QUOTE (-786)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-1063))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-801 |#1|) (QUOTE (-211))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -484) (QUOTE (-1087)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -286) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (LIST (QUOTE -263) (LIST (QUOTE -801) (|devaluate| |#1|)) (LIST (QUOTE -801) (|devaluate| |#1|)))) (|HasCategory| (-801 |#1|) (QUOTE (-284))) (|HasCategory| (-801 |#1|) (QUOTE (-508))) (|HasCategory| (-801 |#1|) (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-801 |#1|) (QUOTE (-840)))) (|HasCategory| (-801 |#1|) (QUOTE (-134))))) (-803 |p| PADIC) ((|constructor| (NIL "This is the category of stream-based representations of \\spad{Qp}.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}x)} removes up to \\spad{n} leading zeroes from the \\spad{p}-adic rational \\spad{x}.") (($ $) "\\spad{removeZeroes(x)} removes leading zeroes from the representation of the \\spad{p}-adic rational \\spad{x}. A \\spad{p}-adic rational is represented by (1) an exponent and (2) a \\spad{p}-adic integer which may have leading zero digits. When the \\spad{p}-adic integer has a leading zero digit,{} a 'leading zero' is removed from the \\spad{p}-adic rational as follows: the number is rewritten by increasing the exponent by 1 and dividing the \\spad{p}-adic integer by \\spad{p}. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}.")) (|continuedFraction| (((|ContinuedFraction| (|Fraction| (|Integer|))) $) "\\spad{continuedFraction(x)} converts the \\spad{p}-adic rational number \\spad{x} to a continued fraction.")) (|approximate| (((|Fraction| (|Integer|)) $ (|Integer|)) "\\spad{approximate(x,{}n)} returns a rational number \\spad{y} such that \\spad{y = x (mod p^n)}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-759))) (-3262 (|HasCategory| |#2| (QUOTE (-759))) (|HasCategory| |#2| (QUOTE (-786)))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -263) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-759))) (-3172 (|HasCategory| |#2| (QUOTE (-759))) (|HasCategory| |#2| (QUOTE (-786)))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -263) (|devaluate| |#2|) (|devaluate| |#2|))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-786))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) (-804 S T$) ((|constructor| (NIL "\\indented{1}{This domain provides a very simple representation} of the notion of `pair of objects'. It does not try to achieve all possible imaginable things.")) (|second| ((|#2| $) "\\spad{second(p)} extracts the second components of \\spad{`p'}.")) (|first| ((|#1| $) "\\spad{first(p)} extracts the first component of \\spad{`p'}.")) (|construct| (($ |#1| |#2|) "\\spad{construct(s,{}t)} is same as pair(\\spad{s},{}\\spad{t}),{} with syntactic sugar.")) (|pair| (($ |#1| |#2|) "\\spad{pair(s,{}t)} returns a pair object composed of \\spad{`s'} and \\spad{`t'}."))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))))) (-805) ((|constructor| (NIL "This domain describes four groups of color shades (palettes).")) (|coerce| (($ (|Color|)) "\\spad{coerce(c)} sets the average shade for the palette to that of the indicated color \\spad{c}.")) (|shade| (((|Integer|) $) "\\spad{shade(p)} returns the shade index of the indicated palette \\spad{p}.")) (|hue| (((|Color|) $) "\\spad{hue(p)} returns the hue field of the indicated palette \\spad{p}.")) (|light| (($ (|Color|)) "\\spad{light(c)} sets the shade of a hue,{} \\spad{c},{} to it\\spad{'s} highest value.")) (|pastel| (($ (|Color|)) "\\spad{pastel(c)} sets the shade of a hue,{} \\spad{c},{} above bright,{} but below light.")) (|bright| (($ (|Color|)) "\\spad{bright(c)} sets the shade of a hue,{} \\spad{c},{} above dim,{} but below pastel.")) (|dim| (($ (|Color|)) "\\spad{dim(c)} sets the shade of a hue,{} \\spad{c},{} above dark,{} but below bright.")) (|dark| (($ (|Color|)) "\\spad{dark(c)} sets the shade of the indicated hue of \\spad{c} to it\\spad{'s} lowest value."))) NIL @@ -3203,7 +3203,7 @@ NIL (-818 |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 (-3900 (|HasCategory| |#2| (QUOTE (-973)))) (-3900 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (-12 (|HasCategory| |#2| (QUOTE (-973))) (-3900 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087))))) +((-12 (-4179 (|HasCategory| |#2| (QUOTE (-973)))) (-4179 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (-12 (|HasCategory| |#2| (QUOTE (-973))) (-4179 (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087))))) (-819 R A B) ((|constructor| (NIL "Lifts maps to pattern matching results.")) (|map| (((|PatternMatchResult| |#1| |#3|) (|Mapping| |#3| |#2|) (|PatternMatchResult| |#1| |#2|)) "\\spad{map(f,{} [(v1,{}a1),{}...,{}(vn,{}an)])} returns the matching result [(\\spad{v1},{}\\spad{f}(a1)),{}...,{}(\\spad{vn},{}\\spad{f}(an))]."))) NIL @@ -3212,7 +3212,7 @@ NIL ((|constructor| (NIL "A PatternMatchResult is an object internally returned by the pattern matcher; It is either a failed match,{} or a list of matches of the form (var,{} expr) meaning that the variable var matches the expression expr.")) (|satisfy?| (((|Union| (|Boolean|) "failed") $ (|Pattern| |#1|)) "\\spad{satisfy?(r,{} p)} returns \\spad{true} if the matches satisfy the top-level predicate of \\spad{p},{} \\spad{false} if they don\\spad{'t},{} and \"failed\" if not enough variables of \\spad{p} are matched in \\spad{r} to decide.")) (|construct| (($ (|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|)))) "\\spad{construct([v1,{}e1],{}...,{}[vn,{}en])} returns the match result containing the matches (\\spad{v1},{}e1),{}...,{}(\\spad{vn},{}en).")) (|destruct| (((|List| (|Record| (|:| |key| (|Symbol|)) (|:| |entry| |#2|))) $) "\\spad{destruct(r)} returns the list of matches (var,{} expr) in \\spad{r}. Error: if \\spad{r} is a failed match.")) (|addMatchRestricted| (($ (|Pattern| |#1|) |#2| $ |#2|) "\\spad{addMatchRestricted(var,{} expr,{} r,{} val)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} that \\spad{var} is not matched to another expression already,{} and that either \\spad{var} is an optional pattern variable or that \\spad{expr} is not equal to val (usually an identity).")) (|insertMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{insertMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} without checking predicates or previous matches for \\spad{var}.")) (|addMatch| (($ (|Pattern| |#1|) |#2| $) "\\spad{addMatch(var,{} expr,{} r)} adds the match (\\spad{var},{} \\spad{expr}) in \\spad{r},{} provided that \\spad{expr} satisfies the predicates attached to \\spad{var},{} and that \\spad{var} is not matched to another expression already.")) (|getMatch| (((|Union| |#2| "failed") (|Pattern| |#1|) $) "\\spad{getMatch(var,{} r)} returns the expression that \\spad{var} matches in the result \\spad{r},{} and \"failed\" if \\spad{var} is not matched in \\spad{r}.")) (|union| (($ $ $) "\\spad{union(a,{} b)} makes the set-union of two match results.")) (|new| (($) "\\spad{new()} returns a new empty match result.")) (|failed| (($) "\\spad{failed()} returns a failed match.")) (|failed?| (((|Boolean|) $) "\\spad{failed?(r)} tests if \\spad{r} is a failed match."))) NIL NIL -(-821 R -2862) +(-821 R -2909) ((|constructor| (NIL "Tools for patterns.")) (|badValues| (((|List| |#2|) (|Pattern| |#1|)) "\\spad{badValues(p)} returns the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|addBadValue| (((|Pattern| |#1|) (|Pattern| |#1|) |#2|) "\\spad{addBadValue(p,{} v)} adds \\spad{v} to the list of \"bad values\" for \\spad{p}; \\spad{p} is not allowed to match any of its \"bad values\".")) (|satisfy?| (((|Boolean|) (|List| |#2|) (|Pattern| |#1|)) "\\spad{satisfy?([v1,{}...,{}vn],{} p)} returns \\spad{f(v1,{}...,{}vn)} where \\spad{f} is the top-level predicate attached to \\spad{p}.") (((|Boolean|) |#2| (|Pattern| |#1|)) "\\spad{satisfy?(v,{} p)} returns \\spad{f}(\\spad{v}) where \\spad{f} is the predicate attached to \\spad{p}.")) (|predicate| (((|Mapping| (|Boolean|) |#2|) (|Pattern| |#1|)) "\\spad{predicate(p)} returns the predicate attached to \\spad{p},{} the constant function \\spad{true} if \\spad{p} has no predicates attached to it.")) (|suchThat| (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#2|))) "\\spad{suchThat(p,{} [a1,{}...,{}an],{} f)} returns a copy of \\spad{p} with the top-level predicate set to \\spad{f(a1,{}...,{}an)}.") (((|Pattern| |#1|) (|Pattern| |#1|) (|List| (|Mapping| (|Boolean|) |#2|))) "\\spad{suchThat(p,{} [f1,{}...,{}fn])} makes a copy of \\spad{p} and adds the predicate \\spad{f1} and ... and \\spad{fn} to the copy,{} which is returned.") (((|Pattern| |#1|) (|Pattern| |#1|) (|Mapping| (|Boolean|) |#2|)) "\\spad{suchThat(p,{} f)} makes a copy of \\spad{p} and adds the predicate \\spad{f} to the copy,{} which is returned."))) NIL NIL @@ -3236,7 +3236,7 @@ NIL ((|PDESolve| (((|Result|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{PDESolve(args)} performs the integration of the function given the strategy or method returned by \\axiomFun{measure}.")) (|measure| (((|Record| (|:| |measure| (|Float|)) (|:| |explanations| (|String|))) (|RoutinesTable|) (|Record| (|:| |pde| (|List| (|Expression| (|DoubleFloat|)))) (|:| |constraints| (|List| (|Record| (|:| |start| (|DoubleFloat|)) (|:| |finish| (|DoubleFloat|)) (|:| |grid| (|NonNegativeInteger|)) (|:| |boundaryType| (|Integer|)) (|:| |dStart| (|Matrix| (|DoubleFloat|))) (|:| |dFinish| (|Matrix| (|DoubleFloat|)))))) (|:| |f| (|List| (|List| (|Expression| (|DoubleFloat|))))) (|:| |st| (|String|)) (|:| |tol| (|DoubleFloat|)))) "\\spad{measure(R,{}args)} calculates an estimate of the ability of a particular method to solve a problem. \\blankline This method may be either a specific NAG routine or a strategy (such as transforming the function from one which is difficult to one which is easier to solve). \\blankline It will call whichever agents are needed to perform analysis on the problem in order to calculate the measure. There is a parameter,{} labelled \\axiom{sofar},{} which would contain the best compatibility found so far."))) NIL NIL -(-827 UP -2315) +(-827 UP -3539) ((|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 @@ -3254,19 +3254,19 @@ NIL NIL (-831 S) ((|constructor| (NIL "A partial differential ring with differentiations indexed by a parameter type \\spad{S}. \\blankline")) (D (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{D(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1,{} n1)...,{} sn,{} nn)}.") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{D(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{D(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{D(...D(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{D(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}.")) (|differentiate| (($ $ (|List| |#1|) (|List| (|NonNegativeInteger|))) "\\spad{differentiate(x,{} [s1,{}...,{}sn],{} [n1,{}...,{}nn])} computes multiple partial derivatives,{} \\spadignore{i.e.}") (($ $ |#1| (|NonNegativeInteger|)) "\\spad{differentiate(x,{} s,{} n)} computes multiple partial derivatives,{} \\spadignore{i.e.} \\spad{n}-th derivative of \\spad{x} with respect to \\spad{s}.") (($ $ (|List| |#1|)) "\\spad{differentiate(x,{}[s1,{}...sn])} computes successive partial derivatives,{} \\spadignore{i.e.} \\spad{differentiate(...differentiate(x,{} s1)...,{} sn)}.") (($ $ |#1|) "\\spad{differentiate(x,{}v)} computes the partial derivative of \\spad{x} with respect to \\spad{v}."))) -((-4241 . T)) +((-4245 . T)) NIL (-832 S) ((|constructor| (NIL "\\indented{1}{A PendantTree(\\spad{S})is either a leaf? and is an \\spad{S} or has} a left and a right both PendantTree(\\spad{S})\\spad{'s}")) (|coerce| (((|Tree| |#1|) $) "\\spad{coerce(x)} \\undocumented")) (|ptree| (($ $ $) "\\spad{ptree(x,{}y)} \\undocumented") (($ |#1|) "\\spad{ptree(s)} is a leaf? pendant tree"))) NIL -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-833 |n| R) -((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ^= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) +((|constructor| (NIL "Permanent implements the functions {\\em permanent},{} the permanent for square matrices.")) (|permanent| ((|#2| (|SquareMatrix| |#1| |#2|)) "\\spad{permanent(x)} computes the permanent of a square matrix \\spad{x}. The {\\em permanent} is equivalent to the \\spadfun{determinant} except that coefficients have no change of sign. This function is much more difficult to compute than the {\\em determinant}. The formula used is by \\spad{H}.\\spad{J}. Ryser,{} improved by [Nijenhuis and Wilf,{} \\spad{Ch}. 19]. Note: permanent(\\spad{x}) choose one of three algorithms,{} depending on the underlying ring \\spad{R} and on \\spad{n},{} the number of rows (and columns) of \\spad{x:}\\begin{items} \\item 1. if 2 has an inverse in \\spad{R} we can use the algorithm of \\indented{3}{[Nijenhuis and Wilf,{} \\spad{ch}.19,{}\\spad{p}.158]; if 2 has no inverse,{}} \\indented{3}{some modifications are necessary:} \\item 2. if {\\em n > 6} and \\spad{R} is an integral domain with characteristic \\indented{3}{different from 2 (the algorithm works if and only 2 is not a} \\indented{3}{zero-divisor of \\spad{R} and {\\em characteristic()\\$R ~= 2},{}} \\indented{3}{but how to check that for any given \\spad{R} ?),{}} \\indented{3}{the local function {\\em permanent2} is called;} \\item 3. else,{} the local function {\\em permanent3} is called \\indented{3}{(works for all commutative rings \\spad{R}).} \\end{items}"))) NIL NIL (-834 S) ((|constructor| (NIL "PermutationCategory provides a categorial environment \\indented{1}{for subgroups of bijections of a set (\\spadignore{i.e.} permutations)}")) (< (((|Boolean|) $ $) "\\spad{p < q} is an order relation on permutations. Note: this order is only total if and only if \\spad{S} is totally ordered or \\spad{S} is finite.")) (|orbit| (((|Set| |#1|) $ |#1|) "\\spad{orbit(p,{} el)} returns the orbit of {\\em el} under the permutation \\spad{p},{} \\spadignore{i.e.} the set which is given by applications of the powers of \\spad{p} to {\\em el}.")) (|elt| ((|#1| $ |#1|) "\\spad{elt(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|eval| ((|#1| $ |#1|) "\\spad{eval(p,{} el)} returns the image of {\\em el} under the permutation \\spad{p}.")) (|cycles| (($ (|List| (|List| |#1|))) "\\spad{cycles(lls)} coerces a list list of cycles {\\em lls} to a permutation,{} each cycle being a list with not repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|cycle| (($ (|List| |#1|)) "\\spad{cycle(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur."))) -((-4241 . T)) +((-4245 . T)) NIL (-835 S) ((|constructor| (NIL "PermutationGroup implements permutation groups acting on a set \\spad{S},{} \\spadignore{i.e.} all subgroups of the symmetric group of \\spad{S},{} represented as a list of permutations (generators). Note that therefore the objects are not members of the \\Language category \\spadtype{Group}. Using the idea of base and strong generators by Sims,{} basic routines and algorithms are implemented so that the word problem for permutation groups can be solved.")) (|initializeGroupForWordProblem| (((|Void|) $ (|Integer|) (|Integer|)) "\\spad{initializeGroupForWordProblem(gp,{}m,{}n)} initializes the group {\\em gp} for the word problem. Notes: (1) with a small integer you get shorter words,{} but the routine takes longer than the standard routine for longer words. (2) be careful: invoking this routine will destroy the possibly stored information about your group (but will recompute it again). (3) users need not call this function normally for the soultion of the word problem.") (((|Void|) $) "\\spad{initializeGroupForWordProblem(gp)} initializes the group {\\em gp} for the word problem. Notes: it calls the other function of this name with parameters 0 and 1: {\\em initializeGroupForWordProblem(gp,{}0,{}1)}. Notes: (1) be careful: invoking this routine will destroy the possibly information about your group (but will recompute it again) (2) users need not call this function normally for the soultion of the word problem.")) (<= (((|Boolean|) $ $) "\\spad{gp1 <= gp2} returns \\spad{true} if and only if {\\em gp1} is a subgroup of {\\em gp2}. Note: because of a bug in the parser you have to call this function explicitly by {\\em gp1 <=\\$(PERMGRP S) gp2}.")) (< (((|Boolean|) $ $) "\\spad{gp1 < gp2} returns \\spad{true} if and only if {\\em gp1} is a proper subgroup of {\\em gp2}.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(gp)} returns the points moved by the group {\\em gp}.")) (|wordInGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the original generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em generators}.")) (|wordInStrongGenerators| (((|List| (|NonNegativeInteger|)) (|Permutation| |#1|) $) "\\spad{wordInStrongGenerators(p,{}gp)} returns the word for the permutation \\spad{p} in the strong generators of the group {\\em gp},{} represented by the indices of the list,{} given by {\\em strongGenerators}.")) (|member?| (((|Boolean|) (|Permutation| |#1|) $) "\\spad{member?(pp,{}gp)} answers the question,{} whether the permutation {\\em pp} is in the group {\\em gp} or not.")) (|orbits| (((|Set| (|Set| |#1|)) $) "\\spad{orbits(gp)} returns the orbits of the group {\\em gp},{} \\spadignore{i.e.} it partitions the (finite) of all moved points.")) (|orbit| (((|Set| (|List| |#1|)) $ (|List| |#1|)) "\\spad{orbit(gp,{}ls)} returns the orbit of the ordered list {\\em ls} under the group {\\em gp}. Note: return type is \\spad{L} \\spad{L} \\spad{S} temporarily because FSET \\spad{L} \\spad{S} has an error.") (((|Set| (|Set| |#1|)) $ (|Set| |#1|)) "\\spad{orbit(gp,{}els)} returns the orbit of the unordered set {\\em els} under the group {\\em gp}.") (((|Set| |#1|) $ |#1|) "\\spad{orbit(gp,{}el)} returns the orbit of the element {\\em el} under the group {\\em gp},{} \\spadignore{i.e.} the set of all points gained by applying each group element to {\\em el}.")) (|permutationGroup| (($ (|List| (|Permutation| |#1|))) "\\spad{permutationGroup(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.")) (|wordsForStrongGenerators| (((|List| (|List| (|NonNegativeInteger|))) $) "\\spad{wordsForStrongGenerators(gp)} returns the words for the strong generators of the group {\\em gp} in the original generators of {\\em gp},{} represented by their indices in the list,{} given by {\\em generators}.")) (|strongGenerators| (((|List| (|Permutation| |#1|)) $) "\\spad{strongGenerators(gp)} returns strong generators for the group {\\em gp}.")) (|base| (((|List| |#1|) $) "\\spad{base(gp)} returns a base for the group {\\em gp}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(gp)} returns the number of points moved by all permutations of the group {\\em gp}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(gp)} returns the order of the group {\\em gp}.")) (|random| (((|Permutation| |#1|) $) "\\spad{random(gp)} returns a random product of maximal 20 generators of the group {\\em gp}. Note: {\\em random(gp)=random(gp,{}20)}.") (((|Permutation| |#1|) $ (|Integer|)) "\\spad{random(gp,{}i)} returns a random product of maximal \\spad{i} generators of the group {\\em gp}.")) (|elt| (((|Permutation| |#1|) $ (|NonNegativeInteger|)) "\\spad{elt(gp,{}i)} returns the \\spad{i}-th generator of the group {\\em gp}.")) (|generators| (((|List| (|Permutation| |#1|)) $) "\\spad{generators(gp)} returns the generators of the group {\\em gp}.")) (|coerce| (($ (|List| (|Permutation| |#1|))) "\\spad{coerce(ls)} coerces a list of permutations {\\em ls} to the group generated by this list.") (((|List| (|Permutation| |#1|)) $) "\\spad{coerce(gp)} returns the generators of the group {\\em gp}."))) @@ -3274,8 +3274,8 @@ NIL NIL (-836 S) ((|constructor| (NIL "Permutation(\\spad{S}) implements the group of all bijections \\indented{2}{on a set \\spad{S},{} which move only a finite number of points.} \\indented{2}{A permutation is considered as a map from \\spad{S} into \\spad{S}. In particular} \\indented{2}{multiplication is defined as composition of maps:} \\indented{2}{{\\em pi1 * pi2 = pi1 o pi2}.} \\indented{2}{The internal representation of permuatations are two lists} \\indented{2}{of equal length representing preimages and images.}")) (|coerceImages| (($ (|List| |#1|)) "\\spad{coerceImages(ls)} coerces the list {\\em ls} to a permutation whose image is given by {\\em ls} and the preimage is fixed to be {\\em [1,{}...,{}n]}. Note: {coerceImages(\\spad{ls})=coercePreimagesImages([1,{}...,{}\\spad{n}],{}\\spad{ls})}. We assume that both preimage and image do not contain repetitions.")) (|fixedPoints| (((|Set| |#1|) $) "\\spad{fixedPoints(p)} returns the points fixed by the permutation \\spad{p}.")) (|sort| (((|List| $) (|List| $)) "\\spad{sort(lp)} sorts a list of permutations {\\em lp} according to cycle structure first according to length of cycles,{} second,{} if \\spad{S} has \\spadtype{Finite} or \\spad{S} has \\spadtype{OrderedSet} according to lexicographical order of entries in cycles of equal length.")) (|odd?| (((|Boolean|) $) "\\spad{odd?(p)} returns \\spad{true} if and only if \\spad{p} is an odd permutation \\spadignore{i.e.} {\\em sign(p)} is {\\em -1}.")) (|even?| (((|Boolean|) $) "\\spad{even?(p)} returns \\spad{true} if and only if \\spad{p} is an even permutation,{} \\spadignore{i.e.} {\\em sign(p)} is 1.")) (|sign| (((|Integer|) $) "\\spad{sign(p)} returns the signum of the permutation \\spad{p},{} \\spad{+1} or \\spad{-1}.")) (|numberOfCycles| (((|NonNegativeInteger|) $) "\\spad{numberOfCycles(p)} returns the number of non-trivial cycles of the permutation \\spad{p}.")) (|order| (((|NonNegativeInteger|) $) "\\spad{order(p)} returns the order of a permutation \\spad{p} as a group element.")) (|cyclePartition| (((|Partition|) $) "\\spad{cyclePartition(p)} returns the cycle structure of a permutation \\spad{p} including cycles of length 1 only if \\spad{S} is finite.")) (|movedPoints| (((|Set| |#1|) $) "\\spad{movedPoints(p)} returns the set of points moved by the permutation \\spad{p}.")) (|degree| (((|NonNegativeInteger|) $) "\\spad{degree(p)} retuns the number of points moved by the permutation \\spad{p}.")) (|coerceListOfPairs| (($ (|List| (|List| |#1|))) "\\spad{coerceListOfPairs(lls)} coerces a list of pairs {\\em lls} to a permutation. Error: if not consistent,{} \\spadignore{i.e.} the set of the first elements coincides with the set of second elements. coerce(\\spad{p}) generates output of the permutation \\spad{p} with domain OutputForm.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(ls)} coerces a cycle {\\em ls},{} \\spadignore{i.e.} a list with not repetitions to a permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list. Error: if repetitions occur.") (($ (|List| (|List| |#1|))) "\\spad{coerce(lls)} coerces a list of cycles {\\em lls} to a permutation,{} each cycle being a list with no repetitions,{} is coerced to the permutation,{} which maps {\\em ls.i} to {\\em ls.i+1},{} indices modulo the length of the list,{} then these permutations are mutiplied. Error: if repetitions occur in one cycle.")) (|coercePreimagesImages| (($ (|List| (|List| |#1|))) "\\spad{coercePreimagesImages(lls)} coerces the representation {\\em lls} of a permutation as a list of preimages and images to a permutation. We assume that both preimage and image do not contain repetitions.")) (|listRepresentation| (((|Record| (|:| |preimage| (|List| |#1|)) (|:| |image| (|List| |#1|))) $) "\\spad{listRepresentation(p)} produces a representation {\\em rep} of the permutation \\spad{p} as a list of preimages and images,{} \\spad{i}.\\spad{e} \\spad{p} maps {\\em (rep.preimage).k} to {\\em (rep.image).k} for all indices \\spad{k}. Elements of \\spad{S} not in {\\em (rep.preimage).k} are fixed points,{} and these are the only fixed points of the permutation."))) -((-4241 . T)) -((-3262 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) +((-4245 . T)) +((-3172 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-786)))) (-837 R E |VarSet| S) ((|constructor| (NIL "PolynomialFactorizationByRecursion(\\spad{R},{}\\spad{E},{}\\spad{VarSet},{}\\spad{S}) is used for factorization of sparse univariate polynomials over a domain \\spad{S} of multivariate polynomials over \\spad{R}.")) (|factorSFBRlcUnit| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|List| |#3|) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSFBRlcUnit(p)} returns the square free factorization of polynomial \\spad{p} (see \\spadfun{factorSquareFreeByRecursion}{PolynomialFactorizationByRecursionUnivariate}) in the case where the leading coefficient of \\spad{p} is a unit.")) (|bivariateSLPEBR| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|) |#3|) "\\spad{bivariateSLPEBR(lp,{}p,{}v)} implements the bivariate case of \\spadfunFrom{solveLinearPolynomialEquationByRecursion}{PolynomialFactorizationByRecursionUnivariate}; its implementation depends on \\spad{R}")) (|randomR| ((|#1|) "\\spad{randomR produces} a random element of \\spad{R}")) (|factorSquareFreeByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorSquareFreeByRecursion(p)} returns the square free factorization of \\spad{p}. This functions performs the recursion step for factorSquareFreePolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorSquareFreePolynomial}).")) (|factorByRecursion| (((|Factored| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{factorByRecursion(p)} factors polynomial \\spad{p}. This function performs the recursion step for factorPolynomial,{} as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{factorPolynomial})")) (|solveLinearPolynomialEquationByRecursion| (((|Union| (|List| (|SparseUnivariatePolynomial| |#4|)) "failed") (|List| (|SparseUnivariatePolynomial| |#4|)) (|SparseUnivariatePolynomial| |#4|)) "\\spad{solveLinearPolynomialEquationByRecursion([p1,{}...,{}pn],{}p)} returns the list of polynomials \\spad{[q1,{}...,{}qn]} such that \\spad{sum qi/pi = p / prod \\spad{pi}},{} a recursion step for solveLinearPolynomialEquation as defined in \\spadfun{PolynomialFactorizationExplicit} category (see \\spadfun{solveLinearPolynomialEquation}). If no such list of \\spad{qi} exists,{} then \"failed\" is returned."))) NIL @@ -3290,13 +3290,13 @@ NIL ((|HasCategory| |#1| (QUOTE (-134)))) (-840) ((|constructor| (NIL "This is the category of domains that know \"enough\" about themselves in order to factor univariate polynomials over themselves. This will be used in future releases for supporting factorization over finitely generated coefficient fields,{} it is not yet available in the current release of axiom.")) (|charthRoot| (((|Union| $ "failed") $) "\\spad{charthRoot(r)} returns the \\spad{p}\\spad{-}th root of \\spad{r},{} or \"failed\" if none exists in the domain.")) (|conditionP| (((|Union| (|Vector| $) "failed") (|Matrix| $)) "\\spad{conditionP(m)} returns a vector of elements,{} not all zero,{} whose \\spad{p}\\spad{-}th powers (\\spad{p} is the characteristic of the domain) are a solution of the homogenous linear system represented by \\spad{m},{} or \"failed\" is there is no such vector.")) (|solveLinearPolynomialEquation| (((|Union| (|List| (|SparseUnivariatePolynomial| $)) "failed") (|List| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{solveLinearPolynomialEquation([f1,{} ...,{} fn],{} g)} (where the \\spad{fi} are relatively prime to each other) returns a list of \\spad{ai} such that \\spad{g/prod \\spad{fi} = sum ai/fi} or returns \"failed\" if no such list of \\spad{ai}\\spad{'s} exists.")) (|gcdPolynomial| (((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $)) "\\spad{gcdPolynomial(p,{}q)} returns the \\spad{gcd} of the univariate polynomials \\spad{p} \\spad{qnd} \\spad{q}.")) (|factorSquareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorSquareFreePolynomial(p)} factors the univariate polynomial \\spad{p} into irreducibles where \\spad{p} is known to be square free and primitive with respect to its main variable.")) (|factorPolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{factorPolynomial(p)} returns the factorization into irreducibles of the univariate polynomial \\spad{p}.")) (|squareFreePolynomial| (((|Factored| (|SparseUnivariatePolynomial| $)) (|SparseUnivariatePolynomial| $)) "\\spad{squareFreePolynomial(p)} returns the square-free factorization of the univariate polynomial \\spad{p}."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-841 |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."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) ((|HasCategory| $ (QUOTE (-136))) (|HasCategory| $ (QUOTE (-134))) (|HasCategory| $ (QUOTE (-344)))) -(-842 R0 -2315 UP UPUP R) +(-842 R0 -3539 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 @@ -3310,7 +3310,7 @@ NIL NIL (-845 R) ((|constructor| (NIL "The domain \\spadtype{PartialFraction} implements partial fractions over a euclidean domain \\spad{R}. This requirement on the argument domain allows us to normalize the fractions. Of particular interest are the 2 forms for these fractions. The ``compact\\spad{''} form has only one fractional term per prime in the denominator,{} while the \\spad{``p}-adic\\spad{''} form expands each numerator \\spad{p}-adically via the prime \\spad{p} in the denominator. For computational efficiency,{} the compact form is used,{} though the \\spad{p}-adic form may be gotten by calling the function \\spadfunFrom{padicFraction}{PartialFraction}. For a general euclidean domain,{} it is not known how to factor the denominator. Thus the function \\spadfunFrom{partialFraction}{PartialFraction} takes as its second argument an element of \\spadtype{Factored(R)}.")) (|wholePart| ((|#1| $) "\\spad{wholePart(p)} extracts the whole part of the partial fraction \\spad{p}.")) (|partialFraction| (($ |#1| (|Factored| |#1|)) "\\spad{partialFraction(numer,{}denom)} is the main function for constructing partial fractions. The second argument is the denominator and should be factored.")) (|padicFraction| (($ $) "\\spad{padicFraction(q)} expands the fraction \\spad{p}-adically in the primes \\spad{p} in the denominator of \\spad{q}. For example,{} \\spad{padicFraction(3/(2**2)) = 1/2 + 1/(2**2)}. Use \\spadfunFrom{compactFraction}{PartialFraction} to return to compact form.")) (|padicallyExpand| (((|SparseUnivariatePolynomial| |#1|) |#1| |#1|) "\\spad{padicallyExpand(p,{}x)} is a utility function that expands the second argument \\spad{x} \\spad{``p}-adically\\spad{''} in the first.")) (|numberOfFractionalTerms| (((|Integer|) $) "\\spad{numberOfFractionalTerms(p)} computes the number of fractional terms in \\spad{p}. This returns 0 if there is no fractional part.")) (|nthFractionalTerm| (($ $ (|Integer|)) "\\spad{nthFractionalTerm(p,{}n)} extracts the \\spad{n}th fractional term from the partial fraction \\spad{p}. This returns 0 if the index \\spad{n} is out of range.")) (|firstNumer| ((|#1| $) "\\spad{firstNumer(p)} extracts the numerator of the first fractional term. This returns 0 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|firstDenom| (((|Factored| |#1|) $) "\\spad{firstDenom(p)} extracts the denominator of the first fractional term. This returns 1 if there is no fractional part (use \\spadfunFrom{wholePart}{PartialFraction} to get the whole part).")) (|compactFraction| (($ $) "\\spad{compactFraction(p)} normalizes the partial fraction \\spad{p} to the compact representation. In this form,{} the partial fraction has only one fractional term per prime in the denominator.")) (|coerce| (($ (|Fraction| (|Factored| |#1|))) "\\spad{coerce(f)} takes a fraction with numerator and denominator in factored form and creates a partial fraction. It is necessary for the parts to be factored because it is not known in general how to factor elements of \\spad{R} and this is needed to decompose into partial fractions.") (((|Fraction| |#1|) $) "\\spad{coerce(p)} sums up the components of the partial fraction and returns a single fraction."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-846 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."))) @@ -3324,7 +3324,7 @@ NIL ((|constructor| (NIL "PermutationGroupExamples provides permutation groups for some classes of groups: symmetric,{} alternating,{} dihedral,{} cyclic,{} direct products of cyclic,{} which are in fact the finite abelian groups of symmetric groups called Young subgroups. Furthermore,{} Rubik\\spad{'s} group as permutation group of 48 integers and a list of sporadic simple groups derived from the atlas of finite groups.")) (|youngGroup| (((|PermutationGroup| (|Integer|)) (|Partition|)) "\\spad{youngGroup(lambda)} constructs the direct product of the symmetric groups given by the parts of the partition {\\em lambda}.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{youngGroup([n1,{}...,{}nk])} constructs the direct product of the symmetric groups {\\em Sn1},{}...,{}{\\em Snk}.")) (|rubiksGroup| (((|PermutationGroup| (|Integer|))) "\\spad{rubiksGroup constructs} the permutation group representing Rubic\\spad{'s} Cube acting on integers {\\em 10*i+j} for {\\em 1 <= i <= 6},{} {\\em 1 <= j <= 8}. The faces of Rubik\\spad{'s} Cube are labelled in the obvious way Front,{} Right,{} Up,{} Down,{} Left,{} Back and numbered from 1 to 6 in this given ordering,{} the pieces on each face (except the unmoveable center piece) are clockwise numbered from 1 to 8 starting with the piece in the upper left corner. The moves of the cube are represented as permutations on these pieces,{} represented as a two digit integer {\\em ij} where \\spad{i} is the numer of theface (1 to 6) and \\spad{j} is the number of the piece on this face. The remaining ambiguities are resolved by looking at the 6 generators,{} which represent a 90 degree turns of the faces,{} or from the following pictorial description. Permutation group representing Rubic\\spad{'s} Cube acting on integers 10*i+j for 1 \\spad{<=} \\spad{i} \\spad{<=} 6,{} 1 \\spad{<=} \\spad{j} \\spad{<=8}. \\blankline\\begin{verbatim}Rubik's Cube: +-----+ +-- B where: marks Side # : / U /|/ / / | F(ront) <-> 1 L --> +-----+ R| R(ight) <-> 2 | | + U(p) <-> 3 | F | / D(own) <-> 4 | |/ L(eft) <-> 5 +-----+ B(ack) <-> 6 ^ | DThe Cube's surface: The pieces on each side +---+ (except the unmoveable center |567| piece) are clockwise numbered |4U8| from 1 to 8 starting with the |321| piece in the upper left +---+---+---+ corner (see figure on the |781|123|345| left). The moves of the cube |6L2|8F4|2R6| are represented as |543|765|187| permutations on these pieces. +---+---+---+ Each of the pieces is |123| represented as a two digit |8D4| integer ij where i is the |765| # of the side ( 1 to 6 for +---+ F to B (see table above )) |567| and j is the # of the piece. |4B8| |321| +---+\\end{verbatim}")) (|janko2| (((|PermutationGroup| (|Integer|))) "\\spad{janko2 constructs} the janko group acting on the integers 1,{}...,{}100.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{janko2(\\spad{li})} constructs the janko group acting on the 100 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 100 different entries")) (|mathieu24| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu24 constructs} the mathieu group acting on the integers 1,{}...,{}24.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu24(\\spad{li})} constructs the mathieu group acting on the 24 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 24 different entries.")) (|mathieu23| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu23 constructs} the mathieu group acting on the integers 1,{}...,{}23.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu23(\\spad{li})} constructs the mathieu group acting on the 23 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 23 different entries.")) (|mathieu22| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu22 constructs} the mathieu group acting on the integers 1,{}...,{}22.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu22(\\spad{li})} constructs the mathieu group acting on the 22 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. Error: if {\\em \\spad{li}} has less or more than 22 different entries.")) (|mathieu12| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu12 constructs} the mathieu group acting on the integers 1,{}...,{}12.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu12(\\spad{li})} constructs the mathieu group acting on the 12 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed Error: if {\\em \\spad{li}} has less or more than 12 different entries.")) (|mathieu11| (((|PermutationGroup| (|Integer|))) "\\spad{mathieu11 constructs} the mathieu group acting on the integers 1,{}...,{}11.") (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{mathieu11(\\spad{li})} constructs the mathieu group acting on the 11 integers given in the list {\\em \\spad{li}}. Note: duplicates in the list will be removed. error,{} if {\\em \\spad{li}} has less or more than 11 different entries.")) (|dihedralGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{dihedralGroup([i1,{}...,{}ik])} constructs the dihedral group of order 2k acting on the integers out of {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{dihedralGroup(n)} constructs the dihedral group of order 2n acting on integers 1,{}...,{}\\spad{N}.")) (|cyclicGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{cyclicGroup([i1,{}...,{}ik])} constructs the cyclic group of order \\spad{k} acting on the integers {\\em i1},{}...,{}{\\em ik}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{cyclicGroup(n)} constructs the cyclic group of order \\spad{n} acting on the integers 1,{}...,{}\\spad{n}.")) (|abelianGroup| (((|PermutationGroup| (|Integer|)) (|List| (|PositiveInteger|))) "\\spad{abelianGroup([n1,{}...,{}nk])} constructs the abelian group that is the direct product of cyclic groups with order {\\em \\spad{ni}}.")) (|alternatingGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{alternatingGroup(\\spad{li})} constructs the alternating group acting on the integers in the list {\\em \\spad{li}},{} generators are in general the {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is odd and product of the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)} with {\\em n-2}-cycle {\\em (\\spad{li}.3,{}...,{}\\spad{li}.n)} and the 3-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2,{}\\spad{li}.3)},{} if \\spad{n} is even. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{alternatingGroup(n)} constructs the alternating group {\\em An} acting on the integers 1,{}...,{}\\spad{n},{} generators are in general the {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is odd and the product of the 2-cycle {\\em (1,{}2)} with {\\em n-2}-cycle {\\em (3,{}...,{}n)} and the 3-cycle {\\em (1,{}2,{}3)} if \\spad{n} is even.")) (|symmetricGroup| (((|PermutationGroup| (|Integer|)) (|List| (|Integer|))) "\\spad{symmetricGroup(\\spad{li})} constructs the symmetric group acting on the integers in the list {\\em \\spad{li}},{} generators are the cycle given by {\\em \\spad{li}} and the 2-cycle {\\em (\\spad{li}.1,{}\\spad{li}.2)}. Note: duplicates in the list will be removed.") (((|PermutationGroup| (|Integer|)) (|PositiveInteger|)) "\\spad{symmetricGroup(n)} constructs the symmetric group {\\em Sn} acting on the integers 1,{}...,{}\\spad{n},{} generators are the {\\em n}-cycle {\\em (1,{}...,{}n)} and the 2-cycle {\\em (1,{}2)}."))) NIL NIL -(-849 -2315) +(-849 -3539) ((|constructor| (NIL "Groebner functions for \\spad{P} \\spad{F} \\indented{2}{This package is an interface package to the groebner basis} package which allows you to compute groebner bases for polynomials in either lexicographic ordering or total degree ordering refined by reverse lex. The input is the ordinary polynomial type which is internally converted to a type with the required ordering. The resulting grobner basis is converted back to ordinary polynomials. The ordering among the variables is controlled by an explicit list of variables which is passed as a second argument. The coefficient domain is allowed to be any \\spad{gcd} domain,{} but the groebner basis is computed as if the polynomials were over a field.")) (|totalGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{totalGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} with the terms ordered first by total degree and then refined by reverse lexicographic ordering. The variables are ordered by their position in the list \\spad{lv}.")) (|lexGroebner| (((|List| (|Polynomial| |#1|)) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{lexGroebner(lp,{}lv)} computes Groebner basis for the list of polynomials \\spad{lp} in lexicographic order. The variables are ordered by their position in the list \\spad{lv}."))) NIL NIL @@ -3334,22 +3334,22 @@ NIL NIL (-851) ((|constructor| (NIL "The category of constructive principal ideal domains,{} \\spadignore{i.e.} where a single generator can be constructively found for any ideal given by a finite set of generators. Note that this constructive definition only implies that finitely generated ideals are principal. It is not clear what we would mean by an infinitely generated ideal.")) (|expressIdealMember| (((|Union| (|List| $) "failed") (|List| $) $) "\\spad{expressIdealMember([f1,{}...,{}fn],{}h)} returns a representation of \\spad{h} as a linear combination of the \\spad{fi} or \"failed\" if \\spad{h} is not in the ideal generated by the \\spad{fi}.")) (|principalIdeal| (((|Record| (|:| |coef| (|List| $)) (|:| |generator| $)) (|List| $)) "\\spad{principalIdeal([f1,{}...,{}fn])} returns a record whose generator component is a generator of the ideal generated by \\spad{[f1,{}...,{}fn]} whose coef component satisfies \\spad{generator = sum (input.i * coef.i)}"))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-852) ((|constructor| (NIL "\\spadtype{PositiveInteger} provides functions for \\indented{2}{positive integers.}")) (|commutative| ((|attribute| "*") "\\spad{commutative(\"*\")} means multiplication is commutative : x*y = \\spad{y*x}")) (|gcd| (($ $ $) "\\spad{gcd(a,{}b)} computes the greatest common divisor of two positive integers \\spad{a} and \\spad{b}."))) -(((-4246 "*") . T)) +(((-4250 "*") . T)) NIL -(-853 -2315 P) +(-853 -3539 P) ((|constructor| (NIL "This package exports interpolation algorithms")) (|LagrangeInterpolation| ((|#2| (|List| |#1|) (|List| |#1|)) "\\spad{LagrangeInterpolation(l1,{}l2)} \\undocumented"))) NIL NIL -(-854 |xx| -2315) +(-854 |xx| -3539) ((|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 (-855 R |Var| |Expon| GR) -((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{^=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) +((|constructor| (NIL "Author: William Sit,{} spring 89")) (|inconsistent?| (((|Boolean|) (|List| (|Polynomial| |#1|))) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.") (((|Boolean|) (|List| |#4|)) "inconsistant?(\\spad{pl}) returns \\spad{true} if the system of equations \\spad{p} = 0 for \\spad{p} in \\spad{pl} is inconsistent. It is assumed that \\spad{pl} is a groebner basis.")) (|sqfree| ((|#4| |#4|) "\\spad{sqfree(p)} returns the product of square free factors of \\spad{p}")) (|regime| (((|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))) (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|List| |#4|)) (|NonNegativeInteger|) (|NonNegativeInteger|) (|Integer|)) "\\spad{regime(y,{}c,{} w,{} p,{} r,{} rm,{} m)} returns a regime,{} a list of polynomials specifying the consistency conditions,{} a particular solution and basis representing the general solution of the parametric linear system \\spad{c} \\spad{z} = \\spad{w} on that regime. The regime returned depends on the subdeterminant \\spad{y}.det and the row and column indices. The solutions are simplified using the assumption that the system has rank \\spad{r} and maximum rank \\spad{rm}. The list \\spad{p} represents a list of list of factors of polynomials in a groebner basis of the ideal generated by higher order subdeterminants,{} and ius used for the simplification. The mode \\spad{m} distinguishes the cases when the system is homogeneous,{} or the right hand side is arbitrary,{} or when there is no new right hand side variables.")) (|redmat| (((|Matrix| |#4|) (|Matrix| |#4|) (|List| |#4|)) "\\spad{redmat(m,{}g)} returns a matrix whose entries are those of \\spad{m} modulo the ideal generated by the groebner basis \\spad{g}")) (|ParCond| (((|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCond(m,{}k)} returns the list of all \\spad{k} by \\spad{k} subdeterminants in the matrix \\spad{m}")) (|overset?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\spad{overset?(s,{}sl)} returns \\spad{true} if \\spad{s} properly a sublist of a member of \\spad{sl}; otherwise it returns \\spad{false}")) (|nextSublist| (((|List| (|List| (|Integer|))) (|Integer|) (|Integer|)) "\\spad{nextSublist(n,{}k)} returns a list of \\spad{k}-subsets of {1,{} ...,{} \\spad{n}}.")) (|minset| (((|List| (|List| |#4|)) (|List| (|List| |#4|))) "\\spad{minset(sl)} returns the sublist of \\spad{sl} consisting of the minimal lists (with respect to inclusion) in the list \\spad{sl} of lists")) (|minrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{minrank(r)} returns the minimum rank in the list \\spad{r} of regimes")) (|maxrank| (((|NonNegativeInteger|) (|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|))))) "\\spad{maxrank(r)} returns the maximum rank in the list \\spad{r} of regimes")) (|factorset| (((|List| |#4|) |#4|) "\\spad{factorset(p)} returns the set of irreducible factors of \\spad{p}.")) (|B1solve| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |mat| (|Matrix| (|Fraction| (|Polynomial| |#1|)))) (|:| |vec| (|List| (|Fraction| (|Polynomial| |#1|)))) (|:| |rank| (|NonNegativeInteger|)) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|))))) "\\spad{B1solve(s)} solves the system (\\spad{s}.mat) \\spad{z} = \\spad{s}.vec for the variables given by the column indices of \\spad{s}.cols in terms of the other variables and the right hand side \\spad{s}.vec by assuming that the rank is \\spad{s}.rank,{} that the system is consistent,{} with the linearly independent equations indexed by the given row indices \\spad{s}.rows; the coefficients in \\spad{s}.mat involving parameters are treated as polynomials. B1solve(\\spad{s}) returns a particular solution to the system and a basis of the homogeneous system (\\spad{s}.mat) \\spad{z} = 0.")) (|redpps| (((|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))) (|List| |#4|)) "\\spad{redpps(s,{}g)} returns the simplified form of \\spad{s} after reducing modulo a groebner basis \\spad{g}")) (|ParCondList| (((|List| (|Record| (|:| |rank| (|NonNegativeInteger|)) (|:| |eqns| (|List| (|Record| (|:| |det| |#4|) (|:| |rows| (|List| (|Integer|))) (|:| |cols| (|List| (|Integer|)))))) (|:| |fgb| (|List| |#4|)))) (|Matrix| |#4|) (|NonNegativeInteger|)) "\\spad{ParCondList(c,{}r)} computes a list of subdeterminants of each rank \\spad{>=} \\spad{r} of the matrix \\spad{c} and returns a groebner basis for the ideal they generate")) (|hasoln| (((|Record| (|:| |sysok| (|Boolean|)) (|:| |z0| (|List| |#4|)) (|:| |n0| (|List| |#4|))) (|List| |#4|) (|List| |#4|)) "\\spad{hasoln(g,{} l)} tests whether the quasi-algebraic set defined by \\spad{p} = 0 for \\spad{p} in \\spad{g} and \\spad{q} \\spad{~=} 0 for \\spad{q} in \\spad{l} is empty or not and returns a simplified definition of the quasi-algebraic set")) (|pr2dmp| ((|#4| (|Polynomial| |#1|)) "\\spad{pr2dmp(p)} converts \\spad{p} to target domain")) (|se2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| (|Symbol|))) "\\spad{se2rfi(l)} converts \\spad{l} to target domain")) (|dmp2rfi| (((|List| (|Fraction| (|Polynomial| |#1|))) (|List| |#4|)) "\\spad{dmp2rfi(l)} converts \\spad{l} to target domain") (((|Matrix| (|Fraction| (|Polynomial| |#1|))) (|Matrix| |#4|)) "\\spad{dmp2rfi(m)} converts \\spad{m} to target domain") (((|Fraction| (|Polynomial| |#1|)) |#4|) "\\spad{dmp2rfi(p)} converts \\spad{p} to target domain")) (|bsolve| (((|Record| (|:| |rgl| (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|)))))))))) (|:| |rgsz| (|Integer|))) (|Matrix| |#4|) (|List| (|Fraction| (|Polynomial| |#1|))) (|NonNegativeInteger|) (|String|) (|Integer|)) "\\spad{bsolve(c,{} w,{} r,{} s,{} m)} returns a list of regimes and solutions of the system \\spad{c} \\spad{z} = \\spad{w} for ranks at least \\spad{r}; depending on the mode \\spad{m} chosen,{} it writes the output to a file given by the string \\spad{s}.")) (|rdregime| (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{rdregime(s)} reads in a list from a file with name \\spad{s}")) (|wrregime| (((|Integer|) (|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|String|)) "\\spad{wrregime(l,{}s)} writes a list of regimes to a file named \\spad{s} and returns the number of regimes written")) (|psolve| (((|Integer|) (|Matrix| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}k,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|) (|String|)) "\\spad{psolve(c,{}w,{}k,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|String|)) "\\spad{psolve(c,{}s)} solves \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| (|Symbol|)) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|Integer|) (|Matrix| |#4|) (|List| |#4|) (|String|)) "\\spad{psolve(c,{}w,{}s)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w},{} writes the results to a file named \\spad{s},{} and returns the number of regimes") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|PositiveInteger|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|)) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|) (|PositiveInteger|)) "\\spad{psolve(c,{}w,{}k)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks \\spad{>=} \\spad{k} of the matrix \\spad{c} and given right hand side vector \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|)) "\\spad{psolve(c)} solves the homogeneous linear system \\spad{c} \\spad{z} = 0 for all possible ranks of the matrix \\spad{c}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| (|Symbol|))) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and indeterminate right hand side \\spad{w}") (((|List| (|Record| (|:| |eqzro| (|List| |#4|)) (|:| |neqzro| (|List| |#4|)) (|:| |wcond| (|List| (|Polynomial| |#1|))) (|:| |bsoln| (|Record| (|:| |partsol| (|Vector| (|Fraction| (|Polynomial| |#1|)))) (|:| |basis| (|List| (|Vector| (|Fraction| (|Polynomial| |#1|))))))))) (|Matrix| |#4|) (|List| |#4|)) "\\spad{psolve(c,{}w)} solves \\spad{c} \\spad{z} = \\spad{w} for all possible ranks of the matrix \\spad{c} and given right hand side vector \\spad{w}"))) NIL NIL (-856 S) @@ -3368,7 +3368,7 @@ NIL ((|constructor| (NIL "This package exports plotting tools")) (|calcRanges| (((|List| (|Segment| (|DoubleFloat|))) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{calcRanges(l)} \\undocumented"))) NIL NIL -(-860 R -2315) +(-860 R -3539) ((|constructor| (NIL "Attaching assertions to symbols for pattern matching; Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|multiple| ((|#2| |#2|) "\\spad{multiple(x)} tells the pattern matcher that \\spad{x} should preferably match a multi-term quantity in a sum or product. For matching on lists,{} multiple(\\spad{x}) tells the pattern matcher that \\spad{x} should match a list instead of an element of a list. Error: if \\spad{x} is not a symbol.")) (|optional| ((|#2| |#2|) "\\spad{optional(x)} tells the pattern matcher that \\spad{x} can match an identity (0 in a sum,{} 1 in a product or exponentiation). Error: if \\spad{x} is not a symbol.")) (|constant| ((|#2| |#2|) "\\spad{constant(x)} tells the pattern matcher that \\spad{x} should match only the symbol \\spad{'x} and no other quantity. Error: if \\spad{x} is not a symbol.")) (|assert| ((|#2| |#2| (|String|)) "\\spad{assert(x,{} s)} makes the assertion \\spad{s} about \\spad{x}. Error: if \\spad{x} is not a symbol."))) NIL NIL @@ -3380,7 +3380,7 @@ NIL ((|constructor| (NIL "This packages provides tools for matching recursively in type towers.")) (|patternMatch| (((|PatternMatchResult| |#1| |#3|) |#2| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#3|)) "\\spad{patternMatch(expr,{} pat,{} res)} matches the pattern \\spad{pat} to the expression \\spad{expr}; res contains the variables of \\spad{pat} which are already matched and their matches. Note: this function handles type towers by changing the predicates and calling the matching function provided by \\spad{A}.")) (|fixPredicate| (((|Mapping| (|Boolean|) |#2|) (|Mapping| (|Boolean|) |#3|)) "\\spad{fixPredicate(f)} returns \\spad{g} defined by \\spad{g}(a) = \\spad{f}(a::B)."))) NIL NIL -(-863 S R -2315) +(-863 S R -3539) ((|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 @@ -3400,11 +3400,11 @@ NIL ((|constructor| (NIL "This package provides pattern matching functions on polynomials.")) (|patternMatch| (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|)) "\\spad{patternMatch(p,{} pat,{} res)} matches the pattern \\spad{pat} to the polynomial \\spad{p}; res contains the variables of \\spad{pat} which are already matched and their matches.") (((|PatternMatchResult| |#1| |#5|) |#5| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|) (|Mapping| (|PatternMatchResult| |#1| |#5|) |#3| (|Pattern| |#1|) (|PatternMatchResult| |#1| |#5|))) "\\spad{patternMatch(p,{} pat,{} res,{} vmatch)} matches the pattern \\spad{pat} to the polynomial \\spad{p}. \\spad{res} contains the variables of \\spad{pat} which are already matched and their matches; vmatch is the matching function to use on the variables."))) NIL ((|HasCategory| |#3| (LIST (QUOTE -817) (|devaluate| |#1|)))) -(-868 R -2315 -2862) +(-868 R -3539 -2909) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| ((|#2| |#2| (|List| (|Mapping| (|Boolean|) |#3|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}. Error: if \\spad{x} is not a symbol.") ((|#2| |#2| (|Mapping| (|Boolean|) |#3|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}; error if \\spad{x} is not a symbol."))) NIL NIL -(-869 -2862) +(-869 -2909) ((|constructor| (NIL "Attaching predicates to symbols for pattern matching. Date Created: 21 Mar 1989 Date Last Updated: 23 May 1990")) (|suchThat| (((|Expression| (|Integer|)) (|Symbol|) (|List| (|Mapping| (|Boolean|) |#1|))) "\\spad{suchThat(x,{} [f1,{} f2,{} ...,{} fn])} attaches the predicate \\spad{f1} and \\spad{f2} and ... and \\spad{fn} to \\spad{x}.") (((|Expression| (|Integer|)) (|Symbol|) (|Mapping| (|Boolean|) |#1|)) "\\spad{suchThat(x,{} foo)} attaches the predicate foo to \\spad{x}."))) NIL NIL @@ -3426,8 +3426,8 @@ NIL NIL (-874 R) ((|constructor| (NIL "This domain implements points in coordinate space"))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-875 |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 @@ -3447,12 +3447,12 @@ NIL (-879 S R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#4|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#4|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#4|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#4|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#4|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#4|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#4|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#2|) |#4|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#4|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#4| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#4|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#4|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#4| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#4|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#4|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) NIL -((|HasCategory| |#2| (QUOTE (-840))) (|HasAttribute| |#2| (QUOTE -4242)) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#4| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#4| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#4| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#4| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-786)))) +((|HasCategory| |#2| (QUOTE (-840))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#4| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#4| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#4| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#4| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-786)))) (-880 R E |VarSet|) ((|constructor| (NIL "The category for general multi-variate polynomials over a ring \\spad{R},{} in variables from VarSet,{} with exponents from the \\spadtype{OrderedAbelianMonoidSup}.")) (|canonicalUnitNormal| ((|attribute|) "we can choose a unique representative for each associate class. This normalization is chosen to be normalization of leading coefficient (by default).")) (|squareFreePart| (($ $) "\\spad{squareFreePart(p)} returns product of all the irreducible factors of polynomial \\spad{p} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(p)} returns the square free factorization of the polynomial \\spad{p}.")) (|primitivePart| (($ $ |#3|) "\\spad{primitivePart(p,{}v)} returns the unitCanonical associate of the polynomial \\spad{p} with its content with respect to the variable \\spad{v} divided out.") (($ $) "\\spad{primitivePart(p)} returns the unitCanonical associate of the polynomial \\spad{p} with its content divided out.")) (|content| (($ $ |#3|) "\\spad{content(p,{}v)} is the \\spad{gcd} of the coefficients of the polynomial \\spad{p} when \\spad{p} is viewed as a univariate polynomial with respect to the variable \\spad{v}. Thus,{} for polynomial 7*x**2*y + 14*x*y**2,{} the \\spad{gcd} of the coefficients with respect to \\spad{x} is 7*y.")) (|discriminant| (($ $ |#3|) "\\spad{discriminant(p,{}v)} returns the disriminant of the polynomial \\spad{p} with respect to the variable \\spad{v}.")) (|resultant| (($ $ $ |#3|) "\\spad{resultant(p,{}q,{}v)} returns the resultant of the polynomials \\spad{p} and \\spad{q} with respect to the variable \\spad{v}.")) (|primitiveMonomials| (((|List| $) $) "\\spad{primitiveMonomials(p)} gives the list of monomials of the polynomial \\spad{p} with their coefficients removed. Note: \\spad{primitiveMonomials(sum(a_(i) X^(i))) = [X^(1),{}...,{}X^(n)]}.")) (|variables| (((|List| |#3|) $) "\\spad{variables(p)} returns the list of those variables actually appearing in the polynomial \\spad{p}.")) (|totalDegree| (((|NonNegativeInteger|) $ (|List| |#3|)) "\\spad{totalDegree(p,{} lv)} returns the maximum sum (over all monomials of polynomial \\spad{p}) of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $) "\\spad{totalDegree(p)} returns the largest sum over all monomials of all exponents of a monomial.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#3|) (|:| |exponent| (|NonNegativeInteger|))) "failed") $) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if polynomial \\spad{p} has the form \\spad{x**n} and \\spad{n > 0}.")) (|isTimes| (((|Union| (|List| $) "failed") $) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if polynomial \\spad{p = a1 ... an} and \\spad{n >= 2},{} and,{} for each \\spad{i},{} \\spad{ai} is either a nontrivial constant in \\spad{R} or else of the form \\spad{x**e},{} where \\spad{e > 0} is an integer and \\spad{x} in a member of VarSet.")) (|isPlus| (((|Union| (|List| $) "failed") $) "\\spad{isPlus(p)} returns \\spad{[m1,{}...,{}mn]} if polynomial \\spad{p = m1 + ... + mn} and \\spad{n >= 2} and each \\spad{mi} is a nonzero monomial.")) (|multivariate| (($ (|SparseUnivariatePolynomial| $) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.") (($ (|SparseUnivariatePolynomial| |#1|) |#3|) "\\spad{multivariate(sup,{}v)} converts an anonymous univariable polynomial \\spad{sup} to a polynomial in the variable \\spad{v}.")) (|monomial| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{monomial(a,{}[v1..vn],{}[e1..en])} returns \\spad{a*prod(vi**ei)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{monomial(a,{}x,{}n)} creates the monomial \\spad{a*x**n} where \\spad{a} is a polynomial,{} \\spad{x} is a variable and \\spad{n} is a nonnegative integer.")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\spad{monicDivide(a,{}b,{}v)} divides the polynomial a by the polynomial \\spad{b},{} with each viewed as a univariate polynomial in \\spad{v} returning both the quotient and remainder. Error: if \\spad{b} is not monic with respect to \\spad{v}.")) (|minimumDegree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{minimumDegree(p,{} lv)} gives the list of minimum degrees of the polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}") (((|NonNegativeInteger|) $ |#3|) "\\spad{minimumDegree(p,{}v)} gives the minimum degree of polynomial \\spad{p} with respect to \\spad{v},{} \\spadignore{i.e.} viewed a univariate polynomial in \\spad{v}")) (|mainVariable| (((|Union| |#3| "failed") $) "\\spad{mainVariable(p)} returns the biggest variable which actually occurs in the polynomial \\spad{p},{} or \"failed\" if no variables are present. fails precisely if polynomial satisfies ground?")) (|univariate| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{univariate(p)} converts the multivariate polynomial \\spad{p},{} which should actually involve only one variable,{} into a univariate polynomial in that variable,{} whose coefficients are in the ground ring. Error: if polynomial is genuinely multivariate") (((|SparseUnivariatePolynomial| $) $ |#3|) "\\spad{univariate(p,{}v)} converts the multivariate polynomial \\spad{p} into a univariate polynomial in \\spad{v},{} whose coefficients are still multivariate polynomials (in all the other variables).")) (|monomials| (((|List| $) $) "\\spad{monomials(p)} returns the list of non-zero monomials of polynomial \\spad{p},{} \\spadignore{i.e.} \\spad{monomials(sum(a_(i) X^(i))) = [a_(1) X^(1),{}...,{}a_(n) X^(n)]}.")) (|coefficient| (($ $ (|List| |#3|) (|List| (|NonNegativeInteger|))) "\\spad{coefficient(p,{} lv,{} ln)} views the polynomial \\spad{p} as a polynomial in the variables of \\spad{lv} and returns the coefficient of the term \\spad{lv**ln},{} \\spadignore{i.e.} \\spad{prod(lv_i ** ln_i)}.") (($ $ |#3| (|NonNegativeInteger|)) "\\spad{coefficient(p,{}v,{}n)} views the polynomial \\spad{p} as a univariate polynomial in \\spad{v} and returns the coefficient of the \\spad{v**n} term.")) (|degree| (((|List| (|NonNegativeInteger|)) $ (|List| |#3|)) "\\spad{degree(p,{}lv)} gives the list of degrees of polynomial \\spad{p} with respect to each of the variables in the list \\spad{lv}.") (((|NonNegativeInteger|) $ |#3|) "\\spad{degree(p,{}v)} gives the degree of polynomial \\spad{p} with respect to the variable \\spad{v}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL -(-881 E V R P -2315) +(-881 E V R P -3539) ((|constructor| (NIL "This package transforms multivariate polynomials or fractions into univariate polynomials or fractions,{} and back.")) (|isPower| (((|Union| (|Record| (|:| |val| |#5|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isPower(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isExpt| (((|Union| (|Record| (|:| |var| |#2|) (|:| |exponent| (|Integer|))) "failed") |#5|) "\\spad{isExpt(p)} returns \\spad{[x,{} n]} if \\spad{p = x**n} and \\spad{n <> 0},{} \"failed\" otherwise.")) (|isTimes| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isTimes(p)} returns \\spad{[a1,{}...,{}an]} if \\spad{p = a1 ... an} and \\spad{n > 1},{} \"failed\" otherwise.")) (|isPlus| (((|Union| (|List| |#5|) "failed") |#5|) "\\spad{isPlus(p)} returns [\\spad{m1},{}...,{}\\spad{mn}] if \\spad{p = m1 + ... + mn} and \\spad{n > 1},{} \"failed\" otherwise.")) (|multivariate| ((|#5| (|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#2|) "\\spad{multivariate(f,{} v)} applies both the numerator and denominator of \\spad{f} to \\spad{v}.")) (|univariate| (((|SparseUnivariatePolynomial| |#5|) |#5| |#2| (|SparseUnivariatePolynomial| |#5|)) "\\spad{univariate(f,{} x,{} p)} returns \\spad{f} viewed as a univariate polynomial in \\spad{x},{} using the side-condition \\spad{p(x) = 0}.") (((|Fraction| (|SparseUnivariatePolynomial| |#5|)) |#5| |#2|) "\\spad{univariate(f,{} v)} returns \\spad{f} viewed as a univariate rational function in \\spad{v}.")) (|mainVariable| (((|Union| |#2| "failed") |#5|) "\\spad{mainVariable(f)} returns the highest variable appearing in the numerator or the denominator of \\spad{f},{} \"failed\" if \\spad{f} has no variables.")) (|variables| (((|List| |#2|) |#5|) "\\spad{variables(f)} returns the list of variables appearing in the numerator or the denominator of \\spad{f}."))) NIL NIL @@ -3462,9 +3462,9 @@ NIL NIL (-883 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}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) -(-884 E V R P -2315) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1087) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(-884 E V R P -3539) ((|constructor| (NIL "computes \\spad{n}-th roots of quotients of multivariate polynomials")) (|nthr| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#4|) (|:| |radicand| (|List| |#4|))) |#4| (|NonNegativeInteger|)) "\\spad{nthr(p,{}n)} should be local but conditional")) (|froot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#5| (|NonNegativeInteger|)) "\\spad{froot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|qroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) (|Fraction| (|Integer|)) (|NonNegativeInteger|)) "\\spad{qroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|rroot| (((|Record| (|:| |exponent| (|NonNegativeInteger|)) (|:| |coef| |#5|) (|:| |radicand| |#5|)) |#3| (|NonNegativeInteger|)) "\\spad{rroot(f,{} n)} returns \\spad{[m,{}c,{}r]} such that \\spad{f**(1/n) = c * r**(1/m)}.")) (|coerce| (($ |#4|) "\\spad{coerce(p)} \\undocumented")) (|denom| ((|#4| $) "\\spad{denom(x)} \\undocumented")) (|numer| ((|#4| $) "\\spad{numer(x)} \\undocumented"))) NIL ((|HasCategory| |#3| (QUOTE (-427)))) @@ -3482,13 +3482,13 @@ NIL NIL (-888 S) ((|constructor| (NIL "\\indented{1}{This provides a fast array type with no bound checking on elt\\spad{'s}.} Minimum index is 0 in this type,{} cannot be changed"))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-889) ((|constructor| (NIL "Category for the functions defined by integrals.")) (|integral| (($ $ (|SegmentBinding| $)) "\\spad{integral(f,{} x = a..b)} returns the formal definite integral of \\spad{f} \\spad{dx} for \\spad{x} between \\spad{a} and \\spad{b}.") (($ $ (|Symbol|)) "\\spad{integral(f,{} x)} returns the formal integral of \\spad{f} \\spad{dx}."))) NIL NIL -(-890 -2315) +(-890 -3539) ((|constructor| (NIL "PrimitiveElement provides functions to compute primitive elements in algebraic extensions.")) (|primitiveElement| (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|)) (|Symbol|)) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an],{} a)} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef| (|List| (|Integer|))) (|:| |poly| (|List| (|SparseUnivariatePolynomial| |#1|))) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|List| (|Polynomial| |#1|)) (|List| (|Symbol|))) "\\spad{primitiveElement([p1,{}...,{}pn],{} [a1,{}...,{}an])} returns \\spad{[[c1,{}...,{}cn],{} [q1,{}...,{}qn],{} q]} such that then \\spad{k(a1,{}...,{}an) = k(a)},{} where \\spad{a = a1 c1 + ... + an cn},{} \\spad{\\spad{ai} = \\spad{qi}(a)},{} and \\spad{q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. This operation uses the technique of \\spadglossSee{groebner bases}{Groebner basis}.") (((|Record| (|:| |coef1| (|Integer|)) (|:| |coef2| (|Integer|)) (|:| |prim| (|SparseUnivariatePolynomial| |#1|))) (|Polynomial| |#1|) (|Symbol|) (|Polynomial| |#1|) (|Symbol|)) "\\spad{primitiveElement(p1,{} a1,{} p2,{} a2)} returns \\spad{[c1,{} c2,{} q]} such that \\spad{k(a1,{} a2) = k(a)} where \\spad{a = c1 a1 + c2 a2,{} and q(a) = 0}. The \\spad{pi}\\spad{'s} are the defining polynomials for the \\spad{ai}\\spad{'s}. The \\spad{p2} may involve \\spad{a1},{} but \\spad{p1} must not involve a2. This operation uses \\spadfun{resultant}."))) NIL NIL @@ -3502,12 +3502,12 @@ NIL NIL (-893 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}"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-124)))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-124)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246))) (-894 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"))) -((-4241 -12 (|has| |#2| (-448)) (|has| |#1| (-448)))) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666))))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-344)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) +((-4245 -12 (|has| |#2| (-448)) (|has| |#1| (-448)))) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666))))) (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-344)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-21)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-448))) (|HasCategory| |#2| (QUOTE (-448)))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-732))) (|HasCategory| |#2| (QUOTE (-732))))) (-12 (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-666)))) (-12 (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-23)))) (-12 (|HasCategory| |#1| (QUOTE (-124))) (|HasCategory| |#2| (QUOTE (-124)))) (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-786))))) (-895) ((|constructor| (NIL "\\indented{1}{Author: Gabriel Dos Reis} Date Created: October 24,{} 2007 Date Last Modified: January 18,{} 2008. An `Property' is a pair of name and value.")) (|property| (($ (|Symbol|) (|SExpression|)) "\\spad{property(n,{}val)} constructs a property with name \\spad{`n'} and value `val'.")) (|value| (((|SExpression|) $) "\\spad{value(p)} returns value of property \\spad{p}")) (|name| (((|Symbol|) $) "\\spad{name(p)} returns the name of property \\spad{p}"))) NIL @@ -3522,7 +3522,7 @@ NIL NIL (-898 S) ((|constructor| (NIL "A priority queue is a bag of items from an ordered set where the item extracted is always the maximum element.")) (|merge!| (($ $ $) "\\spad{merge!(q,{}q1)} destructively changes priority queue \\spad{q} to include the values from priority queue \\spad{q1}.")) (|merge| (($ $ $) "\\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}."))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-899 R |polR|) ((|constructor| (NIL "This package contains some functions: \\axiomOpFrom{discriminant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultant}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcd}{PseudoRemainderSequence},{} \\axiomOpFrom{chainSubResultants}{PseudoRemainderSequence},{} \\axiomOpFrom{degreeSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{lastSubResultant}{PseudoRemainderSequence},{} \\axiomOpFrom{resultantEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{subResultantGcdEuclidean}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean1}{PseudoRemainderSequence},{} \\axiomOpFrom{semiSubResultantGcdEuclidean2}{PseudoRemainderSequence},{} etc. This procedures are coming from improvements of the subresultants algorithm. \\indented{2}{Version : 7} \\indented{2}{References : Lionel Ducos \"Optimizations of the subresultant algorithm\"} \\indented{2}{to appear in the Journal of Pure and Applied Algebra.} \\indented{2}{Author : Ducos Lionel \\axiom{Lionel.Ducos@mathlabo.univ-poitiers.\\spad{fr}}}")) (|semiResultantEuclideannaif| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the semi-extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantEuclideannaif| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the extended resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|resultantnaif| ((|#1| |#2| |#2|) "\\axiom{resultantEuclidean_naif(\\spad{P},{}\\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}} computed by means of the naive algorithm.")) (|nextsousResultant2| ((|#2| |#2| |#2| |#2| |#1|) "\\axiom{nextsousResultant2(\\spad{P},{} \\spad{Q},{} \\spad{Z},{} \\spad{s})} returns the subresultant \\axiom{\\spad{S_}{\\spad{e}-1}} where \\axiom{\\spad{P} ~ \\spad{S_d},{} \\spad{Q} = \\spad{S_}{\\spad{d}-1},{} \\spad{Z} = S_e,{} \\spad{s} = \\spad{lc}(\\spad{S_d})}")) (|Lazard2| ((|#2| |#2| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard2(\\spad{F},{} \\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{(x/y)\\spad{**}(\\spad{n}-1) * \\spad{F}}")) (|Lazard| ((|#1| |#1| |#1| (|NonNegativeInteger|)) "\\axiom{Lazard(\\spad{x},{} \\spad{y},{} \\spad{n})} computes \\axiom{x**n/y**(\\spad{n}-1)}")) (|divide| (((|Record| (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{divide(\\spad{F},{}\\spad{G})} computes quotient and rest of the exact euclidean division of \\axiom{\\spad{F}} by \\axiom{\\spad{G}}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| |#2|) (|:| |remainder| |#2|)) |#2| |#2|) "\\axiom{pseudoDivide(\\spad{P},{}\\spad{Q})} computes the pseudoDivide of \\axiom{\\spad{P}} by \\axiom{\\spad{Q}}.")) (|exquo| (((|Vector| |#2|) (|Vector| |#2|) |#1|) "\\axiom{\\spad{v} exquo \\spad{r}} computes the exact quotient of \\axiom{\\spad{v}} by \\axiom{\\spad{r}}")) (* (((|Vector| |#2|) |#1| (|Vector| |#2|)) "\\axiom{\\spad{r} * \\spad{v}} computes the product of \\axiom{\\spad{r}} and \\axiom{\\spad{v}}")) (|gcd| ((|#2| |#2| |#2|) "\\axiom{\\spad{gcd}(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiResultantReduitEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{semiResultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduitEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultantReduit| |#1|)) |#2| |#2|) "\\axiom{resultantReduitEuclidean(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" and carries out the equality \\axiom{coef1*P + coef2*Q = resultantReduit(\\spad{P},{}\\spad{Q})}.")) (|resultantReduit| ((|#1| |#2| |#2|) "\\axiom{resultantReduit(\\spad{P},{}\\spad{Q})} returns the \"reduce resultant\" of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|schema| (((|List| (|NonNegativeInteger|)) |#2| |#2|) "\\axiom{schema(\\spad{P},{}\\spad{Q})} returns the list of degrees of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|chainSubResultants| (((|List| |#2|) |#2| |#2|) "\\axiom{chainSubResultants(\\spad{P},{} \\spad{Q})} computes the list of non zero subresultants of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiDiscriminantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{...\\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|discriminantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |discriminant| |#1|)) |#2|) "\\axiom{discriminantEuclidean(\\spad{P})} carries out the equality \\axiom{coef1 * \\spad{P} + coef2 * \\spad{D}(\\spad{P}) = discriminant(\\spad{P})}.")) (|discriminant| ((|#1| |#2|) "\\axiom{discriminant(\\spad{P},{} \\spad{Q})} returns the discriminant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiSubResultantGcdEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + ? \\spad{Q} = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|semiSubResultantGcdEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{semiSubResultantGcdEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|subResultantGcdEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |gcd| |#2|)) |#2| |#2|) "\\axiom{subResultantGcdEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{+/-} S_i(\\spad{P},{}\\spad{Q})} where the degree (not the indice) of the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} is the smaller as possible.")) (|subResultantGcd| ((|#2| |#2| |#2|) "\\axiom{subResultantGcd(\\spad{P},{} \\spad{Q})} returns the \\spad{gcd} of two primitive polynomials \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}.")) (|semiLastSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{semiLastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = \\spad{S}}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|lastSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2|) "\\axiom{lastSubResultantEuclidean(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant \\axiom{\\spad{S}} and carries out the equality \\axiom{coef1*P + coef2*Q = \\spad{S}}.")) (|lastSubResultant| ((|#2| |#2| |#2|) "\\axiom{lastSubResultant(\\spad{P},{} \\spad{Q})} computes the last non zero subresultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}")) (|semiDegreeSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|degreeSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns a subresultant \\axiom{\\spad{S}} of degree \\axiom{\\spad{d}} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i}.")) (|degreeSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{degreeSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{d})} computes a subresultant of degree \\axiom{\\spad{d}}.")) (|semiIndiceSubResultantEuclidean| (((|Record| (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{semiIndiceSubResultantEuclidean(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{...\\spad{P} + coef2*Q = S_i(\\spad{P},{}\\spad{Q})} Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|indiceSubResultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |subResultant| |#2|)) |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant \\axiom{S_i(\\spad{P},{}\\spad{Q})} and carries out the equality \\axiom{coef1*P + coef2*Q = S_i(\\spad{P},{}\\spad{Q})}")) (|indiceSubResultant| ((|#2| |#2| |#2| (|NonNegativeInteger|)) "\\axiom{indiceSubResultant(\\spad{P},{} \\spad{Q},{} \\spad{i})} returns the subresultant of indice \\axiom{\\spad{i}}")) (|semiResultantEuclidean1| (((|Record| (|:| |coef1| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean1(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1.\\spad{P} + ? \\spad{Q} = resultant(\\spad{P},{}\\spad{Q})}.")) (|semiResultantEuclidean2| (((|Record| (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{semiResultantEuclidean2(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{...\\spad{P} + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}. Warning: \\axiom{degree(\\spad{P}) \\spad{>=} degree(\\spad{Q})}.")) (|resultantEuclidean| (((|Record| (|:| |coef1| |#2|) (|:| |coef2| |#2|) (|:| |resultant| |#1|)) |#2| |#2|) "\\axiom{resultantEuclidean(\\spad{P},{}\\spad{Q})} carries out the equality \\axiom{coef1*P + coef2*Q = resultant(\\spad{P},{}\\spad{Q})}")) (|resultant| ((|#1| |#2| |#2|) "\\axiom{resultant(\\spad{P},{} \\spad{Q})} returns the resultant of \\axiom{\\spad{P}} and \\axiom{\\spad{Q}}"))) @@ -3538,7 +3538,7 @@ NIL NIL (-902 |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}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-903) ((|constructor| (NIL "PlottableSpaceCurveCategory is the category of curves in 3-space which may be plotted via the graphics facilities. Functions are provided for obtaining lists of lists of points,{} representing the branches of the curve,{} and for determining the ranges of the \\spad{x-},{} \\spad{y-},{} and \\spad{z}-coordinates of the points on the curve.")) (|zRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{zRange(c)} returns the range of the \\spad{z}-coordinates of the points on the curve \\spad{c}.")) (|yRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{yRange(c)} returns the range of the \\spad{y}-coordinates of the points on the curve \\spad{c}.")) (|xRange| (((|Segment| (|DoubleFloat|)) $) "\\spad{xRange(c)} returns the range of the \\spad{x}-coordinates of the points on the curve \\spad{c}.")) (|listBranches| (((|List| (|List| (|Point| (|DoubleFloat|)))) $) "\\spad{listBranches(c)} returns a list of lists of points,{} representing the branches of the curve \\spad{c}."))) @@ -3550,7 +3550,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-515)))) (-905 R E |VarSet| P) ((|constructor| (NIL "A category for finite subsets of a polynomial ring. Such a set is only regarded as a set of polynomials and not identified to the ideal it generates. So two distinct sets may generate the same the ideal. Furthermore,{} for \\spad{R} being an integral domain,{} a set of polynomials may be viewed as a representation of the ideal it generates in the polynomial ring \\spad{(R)^(-1) P},{} or the set of its zeros (described for instance by the radical of the previous ideal,{} or a split of the associated affine variety) and so on. So this category provides operations about those different notions.")) (|triangular?| (((|Boolean|) $) "\\axiom{triangular?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} is a triangular set,{} \\spadignore{i.e.} two distinct polynomials have distinct main variables and no constant lies in \\axiom{\\spad{ps}}.")) (|rewriteIdealWithRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that every polynomial in \\axiom{\\spad{lr}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|rewriteIdealWithHeadRemainder| (((|List| |#4|) (|List| |#4|) $) "\\axiom{rewriteIdealWithHeadRemainder(\\spad{lp},{}\\spad{cs})} returns \\axiom{\\spad{lr}} such that the leading monomial of every polynomial in \\axiom{\\spad{lr}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{cs}} and \\axiom{(\\spad{lp},{}\\spad{cs})} and \\axiom{(\\spad{lr},{}\\spad{cs})} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}.")) (|remainder| (((|Record| (|:| |rnum| |#1|) (|:| |polnum| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{remainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{c},{}\\spad{b},{}\\spad{r}]} such that \\axiom{\\spad{b}} is fully reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}},{} \\axiom{r*a - \\spad{c*b}} lies in the ideal generated by \\axiom{\\spad{ps}}. Furthermore,{} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} \\axiom{\\spad{b}} is primitive.")) (|headRemainder| (((|Record| (|:| |num| |#4|) (|:| |den| |#1|)) |#4| $) "\\axiom{headRemainder(a,{}\\spad{ps})} returns \\axiom{[\\spad{b},{}\\spad{r}]} such that the leading monomial of \\axiom{\\spad{b}} is reduced in the sense of Groebner bases \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ps}} and \\axiom{r*a - \\spad{b}} lies in the ideal generated by \\axiom{\\spad{ps}}.")) (|roughUnitIdeal?| (((|Boolean|) $) "\\axiom{roughUnitIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} contains some non null element lying in the base ring \\axiom{\\spad{R}}.")) (|roughEqualIdeals?| (((|Boolean|) $ $) "\\axiom{roughEqualIdeals?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that \\axiom{\\spad{ps1}} and \\axiom{\\spad{ps2}} generate the same ideal in \\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}} without computing Groebner bases.")) (|roughSubIdeal?| (((|Boolean|) $ $) "\\axiom{roughSubIdeal?(\\spad{ps1},{}\\spad{ps2})} returns \\spad{true} iff it can proved that all polynomials in \\axiom{\\spad{ps1}} lie in the ideal generated by \\axiom{\\spad{ps2}} in \\axiom{\\axiom{(\\spad{R})^(\\spad{-1}) \\spad{P}}} without computing Groebner bases.")) (|roughBase?| (((|Boolean|) $) "\\axiom{roughBase?(\\spad{ps})} returns \\spad{true} iff for every pair \\axiom{{\\spad{p},{}\\spad{q}}} of polynomials in \\axiom{\\spad{ps}} their leading monomials are relatively prime.")) (|trivialIdeal?| (((|Boolean|) $) "\\axiom{trivialIdeal?(\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{ps}} does not contain non-zero elements.")) (|sort| (((|Record| (|:| |under| $) (|:| |floor| $) (|:| |upper| $)) $ |#3|) "\\axiom{sort(\\spad{v},{}\\spad{ps})} returns \\axiom{us,{}\\spad{vs},{}\\spad{ws}} such that \\axiom{us} is \\axiom{collectUnder(\\spad{ps},{}\\spad{v})},{} \\axiom{\\spad{vs}} is \\axiom{collect(\\spad{ps},{}\\spad{v})} and \\axiom{\\spad{ws}} is \\axiom{collectUpper(\\spad{ps},{}\\spad{v})}.")) (|collectUpper| (($ $ |#3|) "\\axiom{collectUpper(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable greater than \\axiom{\\spad{v}}.")) (|collect| (($ $ |#3|) "\\axiom{collect(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with \\axiom{\\spad{v}} as main variable.")) (|collectUnder| (($ $ |#3|) "\\axiom{collectUnder(\\spad{ps},{}\\spad{v})} returns the set consisting of the polynomials of \\axiom{\\spad{ps}} with main variable less than \\axiom{\\spad{v}}.")) (|mainVariable?| (((|Boolean|) |#3| $) "\\axiom{mainVariable?(\\spad{v},{}\\spad{ps})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ps}}.")) (|mainVariables| (((|List| |#3|) $) "\\axiom{mainVariables(\\spad{ps})} returns the decreasingly sorted list of the variables which are main variables of some polynomial in \\axiom{\\spad{ps}}.")) (|variables| (((|List| |#3|) $) "\\axiom{variables(\\spad{ps})} returns the decreasingly sorted list of the variables which are variables of some polynomial in \\axiom{\\spad{ps}}.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{ps})} returns the main variable of the non constant polynomial with the greatest main variable,{} if any,{} else an error is returned.")) (|retract| (($ (|List| |#4|)) "\\axiom{retract(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{retractIfCan(\\spad{lp})} returns an element of the domain whose elements are the members of \\axiom{\\spad{lp}} if such an element exists,{} otherwise \\axiom{\"failed\"} is returned."))) -((-4244 . T) (-3656 . T)) +((-4248 . T) (-4069 . T)) NIL (-906 R E V P) ((|constructor| (NIL "This package provides modest routines for polynomial system solving. The aim of many of the operations of this package is to remove certain factors in some polynomials in order to avoid unnecessary computations in algorithms involving splitting techniques by partial factorization.")) (|removeIrreducibleRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeIrreducibleRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{irreducibleFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.")) (|lazyIrreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{lazyIrreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct. The algorithm tries to avoid factorization into irreducible factors as far as possible and makes previously use of \\spad{gcd} techniques over \\axiom{\\spad{R}}.")) (|irreducibleFactors| (((|List| |#4|) (|List| |#4|)) "\\axiom{irreducibleFactors(\\spad{lp})} returns \\axiom{\\spad{lf}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lf} = [\\spad{f1},{}...,{}\\spad{fm}]} then \\axiom{p1*p2*...*pn=0} means \\axiom{f1*f2*...*fm=0},{} and the \\axiom{\\spad{fi}} are irreducible over \\axiom{\\spad{R}} and are pairwise distinct.")) (|removeRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in every polynomial \\axiom{\\spad{lp}}.")) (|removeRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp} where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any non trivial factor of any polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|removeRoughlyRedundantFactorsInContents| (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInContents(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in the content of every polynomial of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. Moreover,{} squares over \\axiom{\\spad{R}} are first removed in the content of every polynomial of \\axiom{\\spad{lp}}.")) (|univariatePolynomialsGcds| (((|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp},{}opt)} returns the same as \\axiom{univariatePolynomialsGcds(\\spad{lp})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|)) "\\axiom{univariatePolynomialsGcds(\\spad{lp})} returns \\axiom{\\spad{lg}} where \\axiom{\\spad{lg}} is a list of the gcds of every pair in \\axiom{\\spad{lp}} of univariate polynomials in the same main variable.")) (|squareFreeFactors| (((|List| |#4|) |#4|) "\\axiom{squareFreeFactors(\\spad{p})} returns the square-free factors of \\axiom{\\spad{p}} over \\axiom{\\spad{R}}")) (|rewriteIdealWithQuasiMonicGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteIdealWithQuasiMonicGenerators(\\spad{lp},{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} and \\axiom{\\spad{lp}} generate the same ideal in \\axiom{\\spad{R^}(\\spad{-1}) \\spad{P}} and \\axiom{\\spad{lq}} has rank not higher than the one of \\axiom{\\spad{lp}}. Moreover,{} \\axiom{\\spad{lq}} is computed by reducing \\axiom{\\spad{lp}} \\spad{w}.\\spad{r}.\\spad{t}. some basic set of the ideal generated by the quasi-monic polynomials in \\axiom{\\spad{lp}}.")) (|rewriteSetByReducingWithParticularGenerators| (((|List| |#4|) (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{rewriteSetByReducingWithParticularGenerators(\\spad{lp},{}pred?,{}redOp?,{}redOp)} returns \\axiom{\\spad{lq}} where \\axiom{\\spad{lq}} is computed by the following algorithm. Chose a basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-test \\axiom{redOp?} among the polynomials satisfying property \\axiom{pred?},{} if it is empty then leave,{} else reduce the other polynomials by this basic set \\spad{w}.\\spad{r}.\\spad{t}. the reduction-operation \\axiom{redOp}. Repeat while another basic set with smaller rank can be computed. See code. If \\axiom{pred?} is \\axiom{quasiMonic?} the ideal is unchanged.")) (|crushedSet| (((|List| |#4|) (|List| |#4|)) "\\axiom{crushedSet(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and and \\axiom{\\spad{lq}} generate the same ideal and no rough basic sets reduce (in the sense of Groebner bases) the other polynomials in \\axiom{\\spad{lq}}.")) (|roughBasicSet| (((|Union| (|Record| (|:| |bas| (|GeneralTriangularSet| |#1| |#2| |#3| |#4|)) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|)) "\\axiom{roughBasicSet(\\spad{lp})} returns the smallest (with Ritt-Wu ordering) triangular set contained in \\axiom{\\spad{lp}}.")) (|interReduce| (((|List| |#4|) (|List| |#4|)) "\\axiom{interReduce(\\spad{lp})} returns \\axiom{\\spad{lq}} such that \\axiom{\\spad{lp}} and \\axiom{\\spad{lq}} generate the same ideal and no polynomial in \\axiom{\\spad{lq}} is reducuble by the others in the sense of Groebner bases. Since no assumptions are required the result may depend on the ordering the reductions are performed.")) (|removeRoughlyRedundantFactorsInPol| ((|#4| |#4| (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPol(\\spad{p},{}\\spad{lf})} returns the same as removeRoughlyRedundantFactorsInPols([\\spad{p}],{}\\spad{lf},{}\\spad{true})")) (|removeRoughlyRedundantFactorsInPols| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Boolean|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf},{}opt)} returns the same as \\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} if \\axiom{opt} is \\axiom{\\spad{false}} and if the previous operation does not return any non null and constant polynomial,{} else return \\axiom{[1]}.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lf})} returns \\axiom{newlp}where \\axiom{newlp} is obtained from \\axiom{\\spad{lp}} by removing in every polynomial \\axiom{\\spad{p}} of \\axiom{\\spad{lp}} any occurence of a polynomial \\axiom{\\spad{f}} in \\axiom{\\spad{lf}}. This may involve a lot of exact-quotients computations.")) (|bivariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{bivariatePolynomials(\\spad{lp})} returns \\axiom{\\spad{bps},{}nbps} where \\axiom{\\spad{bps}} is a list of the bivariate polynomials,{} and \\axiom{nbps} are the other ones.")) (|bivariate?| (((|Boolean|) |#4|) "\\axiom{bivariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves two and only two variables.")) (|linearPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{linearPolynomials(\\spad{lp})} returns \\axiom{\\spad{lps},{}nlps} where \\axiom{\\spad{lps}} is a list of the linear polynomials in \\spad{lp},{} and \\axiom{nlps} are the other ones.")) (|linear?| (((|Boolean|) |#4|) "\\axiom{linear?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} does not lie in the base ring \\axiom{\\spad{R}} and has main degree \\axiom{1}.")) (|univariatePolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{univariatePolynomials(\\spad{lp})} returns \\axiom{ups,{}nups} where \\axiom{ups} is a list of the univariate polynomials,{} and \\axiom{nups} are the other ones.")) (|univariate?| (((|Boolean|) |#4|) "\\axiom{univariate?(\\spad{p})} returns \\spad{true} iff \\axiom{\\spad{p}} involves one and only one variable.")) (|quasiMonicPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| |#4|)) "\\axiom{quasiMonicPolynomials(\\spad{lp})} returns \\axiom{qmps,{}nqmps} where \\axiom{qmps} is a list of the quasi-monic polynomials in \\axiom{\\spad{lp}} and \\axiom{nqmps} are the other ones.")) (|selectAndPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectAndPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for every \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectOrPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|List| (|Mapping| (|Boolean|) |#4|)) (|List| |#4|)) "\\axiom{selectOrPolynomials(lpred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds for some \\axiom{pred?} in \\axiom{lpred?} and \\axiom{\\spad{bps}} are the other ones.")) (|selectPolynomials| (((|Record| (|:| |goodPols| (|List| |#4|)) (|:| |badPols| (|List| |#4|))) (|Mapping| (|Boolean|) |#4|) (|List| |#4|)) "\\axiom{selectPolynomials(pred?,{}\\spad{ps})} returns \\axiom{\\spad{gps},{}\\spad{bps}} where \\axiom{\\spad{gps}} is a list of the polynomial \\axiom{\\spad{p}} in \\axiom{\\spad{ps}} such that \\axiom{pred?(\\spad{p})} holds and \\axiom{\\spad{bps}} are the other ones.")) (|probablyZeroDim?| (((|Boolean|) (|List| |#4|)) "\\axiom{probablyZeroDim?(\\spad{lp})} returns \\spad{true} iff the number of polynomials in \\axiom{\\spad{lp}} is not smaller than the number of variables occurring in these polynomials.")) (|possiblyNewVariety?| (((|Boolean|) (|List| |#4|) (|List| (|List| |#4|))) "\\axiom{possiblyNewVariety?(newlp,{}\\spad{llp})} returns \\spad{true} iff for every \\axiom{\\spad{lp}} in \\axiom{\\spad{llp}} certainlySubVariety?(newlp,{}\\spad{lp}) does not hold.")) (|certainlySubVariety?| (((|Boolean|) (|List| |#4|) (|List| |#4|)) "\\axiom{certainlySubVariety?(newlp,{}\\spad{lp})} returns \\spad{true} iff for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}} the remainder of \\axiom{\\spad{p}} by \\axiom{newlp} using the division algorithm of Groebner techniques is zero.")) (|unprotectedRemoveRedundantFactors| (((|List| |#4|) |#4| |#4|) "\\axiom{unprotectedRemoveRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} but does assume that neither \\axiom{\\spad{p}} nor \\axiom{\\spad{q}} lie in the base ring \\axiom{\\spad{R}} and assumes that \\axiom{infRittWu?(\\spad{p},{}\\spad{q})} holds. Moreover,{} if \\axiom{\\spad{R}} is \\spad{gcd}-domain,{} then \\axiom{\\spad{p}} and \\axiom{\\spad{q}} are assumed to be square free.")) (|removeSquaresIfCan| (((|List| |#4|) (|List| |#4|)) "\\axiom{removeSquaresIfCan(\\spad{lp})} returns \\axiom{removeDuplicates [squareFreePart(\\spad{p})\\$\\spad{P} for \\spad{p} in \\spad{lp}]} if \\axiom{\\spad{R}} is \\spad{gcd}-domain else returns \\axiom{\\spad{lp}}.")) (|removeRedundantFactors| (((|List| |#4|) (|List| |#4|) (|List| |#4|) (|Mapping| (|List| |#4|) (|List| |#4|))) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq},{}remOp)} returns the same as \\axiom{concat(remOp(removeRoughlyRedundantFactorsInPols(\\spad{lp},{}\\spad{lq})),{}\\spad{lq})} assuming that \\axiom{remOp(\\spad{lq})} returns \\axiom{\\spad{lq}} up to similarity.") (((|List| |#4|) (|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{lq})} returns the same as \\axiom{removeRedundantFactors(concat(\\spad{lp},{}\\spad{lq}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) (|List| |#4|) |#4|) "\\axiom{removeRedundantFactors(\\spad{lp},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors(cons(\\spad{q},{}\\spad{lp}))} assuming that \\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lp}} up to replacing some polynomial \\axiom{\\spad{pj}} in \\axiom{\\spad{lp}} by some some polynomial \\axiom{\\spad{qj}} associated to \\axiom{\\spad{pj}}.") (((|List| |#4|) |#4| |#4|) "\\axiom{removeRedundantFactors(\\spad{p},{}\\spad{q})} returns the same as \\axiom{removeRedundantFactors([\\spad{p},{}\\spad{q}])}") (((|List| |#4|) (|List| |#4|)) "\\axiom{removeRedundantFactors(\\spad{lp})} returns \\axiom{\\spad{lq}} such that if \\axiom{\\spad{lp} = [\\spad{p1},{}...,{}\\spad{pn}]} and \\axiom{\\spad{lq} = [\\spad{q1},{}...,{}\\spad{qm}]} then the product \\axiom{p1*p2*...\\spad{*pn}} vanishes iff the product \\axiom{q1*q2*...\\spad{*qm}} vanishes,{} and the product of degrees of the \\axiom{\\spad{qi}} is not greater than the one of the \\axiom{\\spad{pj}},{} and no polynomial in \\axiom{\\spad{lq}} divides another polynomial in \\axiom{\\spad{lq}}. In particular,{} polynomials lying in the base ring \\axiom{\\spad{R}} are removed. Moreover,{} \\axiom{\\spad{lq}} is sorted \\spad{w}.\\spad{r}.\\spad{t} \\axiom{infRittWu?}. Furthermore,{} if \\spad{R} is \\spad{gcd}-domain,{} the polynomials in \\axiom{\\spad{lq}} are pairwise without common non trivial factor."))) @@ -3566,7 +3566,7 @@ NIL NIL (-909 R) ((|constructor| (NIL "PointCategory is the category of points in space which may be plotted via the graphics facilities. Functions are provided for defining points and handling elements of points.")) (|extend| (($ $ (|List| |#1|)) "\\spad{extend(x,{}l,{}r)} \\undocumented")) (|cross| (($ $ $) "\\spad{cross(p,{}q)} computes the cross product of the two points \\spad{p} and \\spad{q}. Error if the \\spad{p} and \\spad{q} are not 3 dimensional")) (|convert| (($ (|List| |#1|)) "\\spad{convert(l)} takes a list of elements,{} \\spad{l},{} from the domain Ring and returns the form of point category.")) (|dimension| (((|PositiveInteger|) $) "\\spad{dimension(s)} returns the dimension of the point category \\spad{s}.")) (|point| (($ (|List| |#1|)) "\\spad{point(l)} returns a point category defined by a list \\spad{l} of elements from the domain \\spad{R}."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-910 R1 R2) ((|constructor| (NIL "This package \\undocumented")) (|map| (((|Point| |#2|) (|Mapping| |#2| |#1|) (|Point| |#1|)) "\\spad{map(f,{}p)} \\undocumented"))) @@ -3584,7 +3584,7 @@ NIL ((|constructor| (NIL "This package \\undocumented{}")) (|map| ((|#4| (|Mapping| |#4| (|Polynomial| |#1|)) |#4|) "\\spad{map(f,{}p)} \\undocumented{}")) (|pushup| ((|#4| |#4| (|List| |#3|)) "\\spad{pushup(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushup(p,{}v)} \\undocumented{}")) (|pushdown| ((|#4| |#4| (|List| |#3|)) "\\spad{pushdown(p,{}lv)} \\undocumented{}") ((|#4| |#4| |#3|) "\\spad{pushdown(p,{}v)} \\undocumented{}")) (|variable| (((|Union| $ "failed") (|Symbol|)) "\\spad{variable(s)} makes an element from symbol \\spad{s} or fails")) (|convert| (((|Symbol|) $) "\\spad{convert(x)} converts \\spad{x} to a symbol"))) NIL NIL -(-914 K R UP -2315) +(-914 K R UP -3539) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a monogenic algebra over \\spad{R}. We require that \\spad{F} is monogenic,{} \\spadignore{i.e.} that \\spad{F = K[x,{}y]/(f(x,{}y))},{} because the integral basis algorithm used will factor the polynomial \\spad{f(x,{}y)}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|reducedDiscriminant| ((|#2| |#3|) "\\spad{reducedDiscriminant(up)} \\undocumented")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv] } containing information regarding the integral closure of \\spad{R} in the quotient field of the framed algebra \\spad{F}. \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If 'basis' is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of 'basis' contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix 'basisInv' contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if 'basisInv' is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL @@ -3593,7 +3593,7 @@ NIL NIL NIL (-916 R |Var| |Expon| |Dpoly|) -((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{^=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) +((|constructor| (NIL "\\spadtype{QuasiAlgebraicSet} constructs a domain representing quasi-algebraic sets,{} which is the intersection of a Zariski closed set,{} defined as the common zeros of a given list of polynomials (the defining polynomials for equations),{} and a principal Zariski open set,{} defined as the complement of the common zeros of a polynomial \\spad{f} (the defining polynomial for the inequation). This domain provides simplification of a user-given representation using groebner basis computations. There are two simplification routines: the first function \\spadfun{idealSimplify} uses groebner basis of ideals alone,{} while the second,{} \\spadfun{simplify} uses both groebner basis and factorization. The resulting defining equations \\spad{L} always form a groebner basis,{} and the resulting defining inequation \\spad{f} is always reduced. The function \\spadfun{simplify} may be applied several times if desired. A third simplification routine \\spadfun{radicalSimplify} is provided in \\spadtype{QuasiAlgebraicSet2} for comparison study only,{} as it is inefficient compared to the other two,{} as well as is restricted to only certain coefficient domains. For detail analysis and a comparison of the three methods,{} please consult the reference cited. \\blankline A polynomial function \\spad{q} defined on the quasi-algebraic set is equivalent to its reduced form with respect to \\spad{L}. While this may be obtained using the usual normal form algorithm,{} there is no canonical form for \\spad{q}. \\blankline The ordering in groebner basis computation is determined by the data type of the input polynomials. If it is possible we suggest to use refinements of total degree orderings.")) (|simplify| (($ $) "\\spad{simplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using a heuristic algorithm based on factoring.")) (|idealSimplify| (($ $) "\\spad{idealSimplify(s)} returns a different and presumably simpler representation of \\spad{s} with the defining polynomials for the equations forming a groebner basis,{} and the defining polynomial for the inequation reduced with respect to the basis,{} using Buchberger\\spad{'s} algorithm.")) (|definingInequation| ((|#4| $) "\\spad{definingInequation(s)} returns a single defining polynomial for the inequation,{} that is,{} the Zariski open part of \\spad{s}.")) (|definingEquations| (((|List| |#4|) $) "\\spad{definingEquations(s)} returns a list of defining polynomials for equations,{} that is,{} for the Zariski closed part of \\spad{s}.")) (|empty?| (((|Boolean|) $) "\\spad{empty?(s)} returns \\spad{true} if the quasialgebraic set \\spad{s} has no points,{} and \\spad{false} otherwise.")) (|setStatus| (($ $ (|Union| (|Boolean|) "failed")) "\\spad{setStatus(s,{}t)} returns the same representation for \\spad{s},{} but asserts the following: if \\spad{t} is \\spad{true},{} then \\spad{s} is empty,{} if \\spad{t} is \\spad{false},{} then \\spad{s} is non-empty,{} and if \\spad{t} = \"failed\",{} then no assertion is made (that is,{} \"don\\spad{'t} know\"). Note: for internal use only,{} with care.")) (|status| (((|Union| (|Boolean|) "failed") $) "\\spad{status(s)} returns \\spad{true} if the quasi-algebraic set is empty,{} \\spad{false} if it is not,{} and \"failed\" if not yet known")) (|quasiAlgebraicSet| (($ (|List| |#4|) |#4|) "\\spad{quasiAlgebraicSet(pl,{}q)} returns the quasi-algebraic set with defining equations \\spad{p} = 0 for \\spad{p} belonging to the list \\spad{pl},{} and defining inequation \\spad{q} \\spad{~=} 0.")) (|empty| (($) "\\spad{empty()} returns the empty quasi-algebraic set"))) NIL ((-12 (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-284))))) (-917 R E V P TS) @@ -3614,7 +3614,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-949))) (|HasCategory| |#2| (QUOTE (-759))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-1063)))) (-921 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}."))) -((-3656 . T) (-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4069 . T) (-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-922 |n| K) ((|constructor| (NIL "This domain provides modest support for quadratic forms.")) (|elt| ((|#2| $ (|DirectProduct| |#1| |#2|)) "\\spad{elt(qf,{}v)} evaluates the quadratic form \\spad{qf} on the vector \\spad{v},{} producing a scalar.")) (|matrix| (((|SquareMatrix| |#1| |#2|) $) "\\spad{matrix(qf)} creates a square matrix from the quadratic form \\spad{qf}.")) (|quadraticForm| (($ (|SquareMatrix| |#1| |#2|)) "\\spad{quadraticForm(m)} creates a quadratic form from a symmetric,{} square matrix \\spad{m}."))) @@ -3622,7 +3622,7 @@ NIL NIL (-923 S) ((|constructor| (NIL "A queue is a bag where the first item inserted is the first item extracted.")) (|back| ((|#1| $) "\\spad{back(q)} returns the element at the back of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|front| ((|#1| $) "\\spad{front(q)} returns the element at the front of the queue. The queue \\spad{q} is unchanged by this operation. Error: if \\spad{q} is empty.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(q)} returns the number of elements in the queue. Note: \\axiom{length(\\spad{q}) = \\spad{#q}}.")) (|rotate!| (($ $) "\\spad{rotate! q} rotates queue \\spad{q} so that the element at the front of the queue goes to the back of the queue. Note: rotate! \\spad{q} is equivalent to enqueue!(dequeue!(\\spad{q})).")) (|dequeue!| ((|#1| $) "\\spad{dequeue! s} destructively extracts the first (top) element from queue \\spad{q}. The element previously second in the queue becomes the first element. Error: if \\spad{q} is empty.")) (|enqueue!| ((|#1| |#1| $) "\\spad{enqueue!(x,{}q)} inserts \\spad{x} into the queue \\spad{q} at the back end."))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-924 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}."))) @@ -3630,7 +3630,7 @@ NIL ((|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (QUOTE (-982))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-267)))) (-925 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}."))) -((-4237 |has| |#1| (-267)) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 |has| |#1| (-267)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-926 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}."))) @@ -3638,12 +3638,12 @@ NIL NIL (-927 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.}"))) -((-4237 |has| |#1| (-267)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))))) +((-4241 |has| |#1| (-267)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-267))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))) (|HasCategory| |#1| (LIST (QUOTE -263) (|devaluate| |#1|) (|devaluate| |#1|))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-982))) (|HasCategory| |#1| (QUOTE (-508))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))))) (-928 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}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-929 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| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL @@ -3652,14 +3652,14 @@ NIL ((|constructor| (NIL "The \\spad{RadicalCategory} is a model for the rational numbers.")) (** (($ $ (|Fraction| (|Integer|))) "\\spad{x ** y} is the rational exponentiation of \\spad{x} by the power \\spad{y}.")) (|nthRoot| (($ $ (|Integer|)) "\\spad{nthRoot(x,{}n)} returns the \\spad{n}th root of \\spad{x}.")) (|sqrt| (($ $) "\\spad{sqrt(x)} returns the square root of \\spad{x}."))) NIL NIL -(-931 -2315 UP UPUP |radicnd| |n|) +(-931 -3539 UP UPUP |radicnd| |n|) ((|constructor| (NIL "Function field defined by y**n = \\spad{f}(\\spad{x})."))) -((-4237 |has| (-383 |#2|) (-339)) (-4242 |has| (-383 |#2|) (-339)) (-4236 |has| (-383 |#2|) (-339)) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3262 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3262 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3262 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3262 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) +((-4241 |has| (-383 |#2|) (-339)) (-4246 |has| (-383 |#2|) (-339)) (-4240 |has| (-383 |#2|) (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-383 |#2|) (QUOTE (-134))) (|HasCategory| (-383 |#2|) (QUOTE (-136))) (|HasCategory| (-383 |#2|) (QUOTE (-325))) (-3172 (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (|HasCategory| (-383 |#2|) (QUOTE (-339))) (|HasCategory| (-383 |#2|) (QUOTE (-344))) (-3172 (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (|HasCategory| (-383 |#2|) (QUOTE (-325)))) (-3172 (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-325))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (|HasCategory| (-383 |#2|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-383 |#2|) (QUOTE (-339)))) (-12 (|HasCategory| (-383 |#2|) (QUOTE (-211))) (|HasCategory| (-383 |#2|) (QUOTE (-339))))) (-932 |bb|) ((|constructor| (NIL "This domain allows rational numbers to be presented as repeating decimal expansions or more generally as repeating expansions in any base.")) (|fractRadix| (($ (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{fractRadix(pre,{}cyc)} creates a fractional radix expansion from a list of prefix ragits and a list of cyclic ragits. For example,{} \\spad{fractRadix([1],{}[6])} will return \\spad{0.16666666...}.")) (|wholeRadix| (($ (|List| (|Integer|))) "\\spad{wholeRadix(l)} creates an integral radix expansion from a list of ragits. For example,{} \\spad{wholeRadix([1,{}3,{}4])} will return \\spad{134}.")) (|cycleRagits| (((|List| (|Integer|)) $) "\\spad{cycleRagits(rx)} returns the cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{cycleRagits(x) = [7,{}1,{}4,{}2,{}8,{}5]}.")) (|prefixRagits| (((|List| (|Integer|)) $) "\\spad{prefixRagits(rx)} returns the non-cyclic part of the ragits of the fractional part of a radix expansion. For example,{} if \\spad{x = 3/28 = 0.10 714285 714285 ...},{} then \\spad{prefixRagits(x)=[1,{}0]}.")) (|fractRagits| (((|Stream| (|Integer|)) $) "\\spad{fractRagits(rx)} returns the ragits of the fractional part of a radix expansion.")) (|wholeRagits| (((|List| (|Integer|)) $) "\\spad{wholeRagits(rx)} returns the ragits of the integer part of a radix expansion.")) (|fractionPart| (((|Fraction| (|Integer|)) $) "\\spad{fractionPart(rx)} returns the fractional part of a radix expansion.")) (|coerce| (((|Fraction| (|Integer|)) $) "\\spad{coerce(rx)} converts a radix expansion to a rational number."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3262 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-523) (QUOTE (-840))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-1087)))) (|HasCategory| (-523) (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-136))) (|HasCategory| (-523) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-949))) (|HasCategory| (-523) (QUOTE (-759))) (-3172 (|HasCategory| (-523) (QUOTE (-759))) (|HasCategory| (-523) (QUOTE (-786)))) (|HasCategory| (-523) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-1063))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| (-523) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| (-523) (QUOTE (-211))) (|HasCategory| (-523) (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| (-523) (LIST (QUOTE -484) (QUOTE (-1087)) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -286) (QUOTE (-523)))) (|HasCategory| (-523) (LIST (QUOTE -263) (QUOTE (-523)) (QUOTE (-523)))) (|HasCategory| (-523) (QUOTE (-284))) (|HasCategory| (-523) (QUOTE (-508))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-523) (LIST (QUOTE -585) (QUOTE (-523)))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| (-523) (QUOTE (-840)))) (|HasCategory| (-523) (QUOTE (-134))))) (-933) ((|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 @@ -3679,10 +3679,10 @@ NIL (-937 A S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#2| $ |#2|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#2| $ "value" |#2|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#2|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#2| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#2| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) NIL -((|HasAttribute| |#1| (QUOTE -4245)) (|HasCategory| |#2| (QUOTE (-1016)))) +((|HasAttribute| |#1| (QUOTE -4249)) (|HasCategory| |#2| (QUOTE (-1016)))) (-938 S) ((|constructor| (NIL "A recursive aggregate over a type \\spad{S} is a model for a a directed graph containing values of type \\spad{S}. Recursively,{} a recursive aggregate is a {\\em node} consisting of a \\spadfun{value} from \\spad{S} and 0 or more \\spadfun{children} which are recursive aggregates. A node with no children is called a \\spadfun{leaf} node. A recursive aggregate may be cyclic for which some operations as noted may go into an infinite loop.")) (|setvalue!| ((|#1| $ |#1|) "\\spad{setvalue!(u,{}x)} sets the value of node \\spad{u} to \\spad{x}.")) (|setelt| ((|#1| $ "value" |#1|) "\\spad{setelt(a,{}\"value\",{}x)} (also written \\axiom{a . value \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setvalue!(a,{}\\spad{x})}")) (|setchildren!| (($ $ (|List| $)) "\\spad{setchildren!(u,{}v)} replaces the current children of node \\spad{u} with the members of \\spad{v} in left-to-right order.")) (|node?| (((|Boolean|) $ $) "\\spad{node?(u,{}v)} tests if node \\spad{u} is contained in node \\spad{v} (either as a child,{} a child of a child,{} etc.).")) (|child?| (((|Boolean|) $ $) "\\spad{child?(u,{}v)} tests if node \\spad{u} is a child of node \\spad{v}.")) (|distance| (((|Integer|) $ $) "\\spad{distance(u,{}v)} returns the path length (an integer) from node \\spad{u} to \\spad{v}.")) (|leaves| (((|List| |#1|) $) "\\spad{leaves(t)} returns the list of values in obtained by visiting the nodes of tree \\axiom{\\spad{t}} in left-to-right order.")) (|cyclic?| (((|Boolean|) $) "\\spad{cyclic?(u)} tests if \\spad{u} has a cycle.")) (|elt| ((|#1| $ "value") "\\spad{elt(u,{}\"value\")} (also written: \\axiom{a. value}) is equivalent to \\axiom{value(a)}.")) (|value| ((|#1| $) "\\spad{value(u)} returns the value of the node \\spad{u}.")) (|leaf?| (((|Boolean|) $) "\\spad{leaf?(u)} tests if \\spad{u} is a terminal node.")) (|nodes| (((|List| $) $) "\\spad{nodes(u)} returns a list of all of the nodes of aggregate \\spad{u}.")) (|children| (((|List| $) $) "\\spad{children(u)} returns a list of the children of aggregate \\spad{u}."))) -((-3656 . T)) +((-4069 . T)) NIL (-939 S) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) @@ -3690,21 +3690,21 @@ NIL NIL (-940) ((|constructor| (NIL "\\axiomType{RealClosedField} provides common acces functions for all real closed fields.")) (|approximate| (((|Fraction| (|Integer|)) $ $) "\\axiom{approximate(\\spad{n},{}\\spad{p})} gives an approximation of \\axiom{\\spad{n}} that has precision \\axiom{\\spad{p}}")) (|rename| (($ $ (|OutputForm|)) "\\axiom{rename(\\spad{x},{}name)} gives a new number that prints as name")) (|rename!| (($ $ (|OutputForm|)) "\\axiom{rename!(\\spad{x},{}name)} changes the way \\axiom{\\spad{x}} is printed")) (|sqrt| (($ (|Integer|)) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ (|Fraction| (|Integer|))) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $) "\\axiom{sqrt(\\spad{x})} is \\axiom{\\spad{x} \\spad{**} (1/2)}") (($ $ (|NonNegativeInteger|)) "\\axiom{sqrt(\\spad{x},{}\\spad{n})} is \\axiom{\\spad{x} \\spad{**} (1/n)}")) (|allRootsOf| (((|List| $) (|Polynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|Polynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Integer|))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| (|Fraction| (|Integer|)))) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely") (((|List| $) (|SparseUnivariatePolynomial| $)) "\\axiom{allRootsOf(pol)} creates all the roots of \\axiom{pol} naming each uniquely")) (|rootOf| (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|)) "\\axiom{rootOf(pol,{}\\spad{n})} creates the \\spad{n}th root for the order of \\axiom{pol} and gives it unique name") (((|Union| $ "failed") (|SparseUnivariatePolynomial| $) (|PositiveInteger|) (|OutputForm|)) "\\axiom{rootOf(pol,{}\\spad{n},{}name)} creates the \\spad{n}th root for the order of \\axiom{pol} and names it \\axiom{name}")) (|mainValue| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainValue(\\spad{x})} is the expression of \\axiom{\\spad{x}} in terms of \\axiom{SparseUnivariatePolynomial(\\$)}")) (|mainDefiningPolynomial| (((|Union| (|SparseUnivariatePolynomial| $) "failed") $) "\\axiom{mainDefiningPolynomial(\\spad{x})} is the defining polynomial for the main algebraic quantity of \\axiom{\\spad{x}}")) (|mainForm| (((|Union| (|OutputForm|) "failed") $) "\\axiom{mainForm(\\spad{x})} is the main algebraic quantity name of \\axiom{\\spad{x}}"))) -((-4237 . T) (-4242 . T) (-4236 . T) (-4239 . T) (-4238 . T) ((-4246 "*") . T) (-4241 . T)) +((-4241 . T) (-4246 . T) (-4240 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4245 . T)) NIL -(-941 R -2315) +(-941 R -3539) ((|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 -(-942 R -2315) +(-942 R -3539) ((|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 -(-943 -2315 UP) +(-943 -3539 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 -(-944 -2315 UP) +(-944 -3539 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 @@ -3734,9 +3734,9 @@ NIL NIL (-951 |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"))) -((-4237 . T) (-4242 . T) (-4236 . T) (-4239 . T) (-4238 . T) ((-4246 "*") . T) (-4241 . T)) -((-3262 (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523))))) -(-952 -2315 L) +((-4241 . T) (-4246 . T) (-4240 . T) (-4243 . T) (-4242 . T) ((-4250 "*") . T) (-4245 . T)) +((-3172 (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-383 (-523)) (LIST (QUOTE -964) (QUOTE (-523))))) +(-952 -3539 L) ((|constructor| (NIL "\\spadtype{ReductionOfOrder} provides functions for reducing the order of linear ordinary differential equations once some solutions are known.")) (|ReduceOrder| (((|Record| (|:| |eq| |#2|) (|:| |op| (|List| |#1|))) |#2| (|List| |#1|)) "\\spad{ReduceOrder(op,{} [f1,{}...,{}fk])} returns \\spad{[op1,{}[g1,{}...,{}gk]]} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = gk \\int(g_{k-1} \\int(... \\int(g1 \\int z)...)} is a solution of \\spad{op y = 0}. Each \\spad{\\spad{fi}} must satisfy \\spad{op \\spad{fi} = 0}.") ((|#2| |#2| |#1|) "\\spad{ReduceOrder(op,{} s)} returns \\spad{op1} such that for any solution \\spad{z} of \\spad{op1 z = 0},{} \\spad{y = s \\int z} is a solution of \\spad{op y = 0}. \\spad{s} must satisfy \\spad{op s = 0}."))) NIL NIL @@ -3746,12 +3746,12 @@ NIL ((|HasCategory| |#1| (QUOTE (-1016)))) (-954 R E V P) ((|constructor| (NIL "This domain provides an implementation of regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}. Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#4| (LIST (QUOTE -286) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#4| (LIST (QUOTE -563) (QUOTE (-794))))) (-955 R) ((|constructor| (NIL "RepresentationPackage1 provides functions for representation theory for finite groups and algebras. The package creates permutation representations and uses tensor products and its symmetric and antisymmetric components to create new representations of larger degree from given ones. Note: instead of having parameters from \\spadtype{Permutation} this package allows list notation of permutations as well: \\spadignore{e.g.} \\spad{[1,{}4,{}3,{}2]} denotes permutes 2 and 4 and fixes 1 and 3.")) (|permutationRepresentation| (((|List| (|Matrix| (|Integer|))) (|List| (|List| (|Integer|)))) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} if the permutations {\\em pi1},{}...,{}{\\em pik} are in list notation and are permuting {\\em {1,{}2,{}...,{}n}}.") (((|List| (|Matrix| (|Integer|))) (|List| (|Permutation| (|Integer|))) (|Integer|)) "\\spad{permutationRepresentation([pi1,{}...,{}pik],{}n)} returns the list of matrices {\\em [(deltai,{}pi1(i)),{}...,{}(deltai,{}pik(i))]} (Kronecker delta) for the permutations {\\em pi1,{}...,{}pik} of {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|List| (|Integer|))) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) if the permutation {\\em \\spad{pi}} is in list notation and permutes {\\em {1,{}2,{}...,{}n}}.") (((|Matrix| (|Integer|)) (|Permutation| (|Integer|)) (|Integer|)) "\\spad{permutationRepresentation(\\spad{pi},{}n)} returns the matrix {\\em (deltai,{}\\spad{pi}(i))} (Kronecker delta) for a permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}}.")) (|tensorProduct| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...ak])} calculates the list of Kronecker products of each matrix {\\em \\spad{ai}} with itself for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If the list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the representation with itself.") (((|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a)} calculates the Kronecker product of the matrix {\\em a} with itself.") (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{tensorProduct([a1,{}...,{}ak],{}[b1,{}...,{}bk])} calculates the list of Kronecker products of the matrices {\\em \\spad{ai}} and {\\em \\spad{bi}} for {1 \\spad{<=} \\spad{i} \\spad{<=} \\spad{k}}. Note: If each list of matrices corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.") (((|Matrix| |#1|) (|Matrix| |#1|) (|Matrix| |#1|)) "\\spad{tensorProduct(a,{}b)} calculates the Kronecker product of the matrices {\\em a} and \\spad{b}. Note: if each matrix corresponds to a group representation (repr. of generators) of one group,{} then these matrices correspond to the tensor product of the two representations.")) (|symmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{symmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if the matrices in {\\em la} are not square matrices. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{symmetricTensors(a,{}n)} applies to the \\spad{m}-by-\\spad{m} square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (n,{}0,{}...,{}0)} of \\spad{n}. Error: if {\\em a} is not a square matrix. Note: this corresponds to the symmetrization of the representation with the trivial representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the symmetric tensors of the \\spad{n}-fold tensor product.")) (|createGenericMatrix| (((|Matrix| (|Polynomial| |#1|)) (|NonNegativeInteger|)) "\\spad{createGenericMatrix(m)} creates a square matrix of dimension \\spad{k} whose entry at the \\spad{i}-th row and \\spad{j}-th column is the indeterminate {\\em x[i,{}j]} (double subscripted).")) (|antisymmetricTensors| (((|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{antisymmetricTensors(la,{}n)} applies to each \\spad{m}-by-\\spad{m} square matrix in the list {\\em la} the irreducible,{} polynomial representation of the general linear group {\\em GLm} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product.") (((|Matrix| |#1|) (|Matrix| |#1|) (|PositiveInteger|)) "\\spad{antisymmetricTensors(a,{}n)} applies to the square matrix {\\em a} the irreducible,{} polynomial representation of the general linear group {\\em GLm},{} where \\spad{m} is the number of rows of {\\em a},{} which corresponds to the partition {\\em (1,{}1,{}...,{}1,{}0,{}0,{}...,{}0)} of \\spad{n}. Error: if \\spad{n} is greater than \\spad{m}. Note: this corresponds to the symmetrization of the representation with the sign representation of the symmetric group {\\em Sn}. The carrier spaces of the representation are the antisymmetric tensors of the \\spad{n}-fold tensor product."))) NIL -((|HasAttribute| |#1| (QUOTE (-4246 "*")))) +((|HasAttribute| |#1| (QUOTE (-4250 "*")))) (-956 R) ((|constructor| (NIL "RepresentationPackage2 provides functions for working with modular representations of finite groups and algebra. The routines in this package are created,{} using ideas of \\spad{R}. Parker,{} (the meat-Axe) to get smaller representations from bigger ones,{} \\spadignore{i.e.} finding sub- and factormodules,{} or to show,{} that such the representations are irreducible. Note: most functions are randomized functions of Las Vegas type \\spadignore{i.e.} every answer is correct,{} but with small probability the algorithm fails to get an answer.")) (|scanOneDimSubspaces| (((|Vector| |#1|) (|List| (|Vector| |#1|)) (|Integer|)) "\\spad{scanOneDimSubspaces(basis,{}n)} gives a canonical representative of the {\\em n}\\spad{-}th one-dimensional subspace of the vector space generated by the elements of {\\em basis},{} all from {\\em R**n}. The coefficients of the representative are of shape {\\em (0,{}...,{}0,{}1,{}*,{}...,{}*)},{} {\\em *} in \\spad{R}. If the size of \\spad{R} is \\spad{q},{} then there are {\\em (q**n-1)/(q-1)} of them. We first reduce \\spad{n} modulo this number,{} then find the largest \\spad{i} such that {\\em +/[q**i for i in 0..i-1] <= n}. Subtracting this sum of powers from \\spad{n} results in an \\spad{i}-digit number to \\spad{basis} \\spad{q}. This fills the positions of the stars.")) (|meatAxe| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|PositiveInteger|)) "\\spad{meatAxe(aG,{} numberOfTries)} calls {\\em meatAxe(aG,{}true,{}numberOfTries,{}7)}. Notes: 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|)) "\\spad{meatAxe(aG,{} randomElements)} calls {\\em meatAxe(aG,{}false,{}6,{}7)},{} only using Parker\\spad{'s} fingerprints,{} if {\\em randomElemnts} is \\spad{false}. If it is \\spad{true},{} it calls {\\em meatAxe(aG,{}true,{}25,{}7)},{} only using random elements. Note: the choice of 25 was rather arbitrary. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|))) "\\spad{meatAxe(aG)} calls {\\em meatAxe(aG,{}false,{}25,{}7)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG}) creates at most 25 random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most 7 elements of its kernel to generate a proper submodule. If successful a list which contains first the list of the representations of the submodule,{} then a list of the representations of the factor module is returned. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. Notes: the first 6 tries use Parker\\spad{'s} fingerprints. Also,{} 7 covers the case of three-dimensional kernels over the field with 2 elements.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|) (|Integer|)) "\\spad{meatAxe(aG,{}randomElements,{}numberOfTries,{} maxTests)} returns a 2-list of representations as follows. All matrices of argument \\spad{aG} are assumed to be square and of equal size. Then \\spad{aG} generates a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an A-module in the usual way. meatAxe(\\spad{aG},{}\\spad{numberOfTries},{} maxTests) creates at most {\\em numberOfTries} random elements of the algebra,{} tests them for singularity. If singular,{} it tries at most {\\em maxTests} elements of its kernel to generate a proper submodule. If successful,{} a 2-list is returned: first,{} a list containing first the list of the representations of the submodule,{} then a list of the representations of the factor module. Otherwise,{} if we know that all the kernel is already scanned,{} Norton\\spad{'s} irreducibility test can be used either to prove irreducibility or to find the splitting. If {\\em randomElements} is {\\em false},{} the first 6 tries use Parker\\spad{'s} fingerprints.")) (|split| (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| (|Vector| |#1|))) "\\spad{split(aG,{}submodule)} uses a proper \\spad{submodule} of {\\em R**n} to create the representations of the \\spad{submodule} and of the factor module.") (((|List| (|List| (|Matrix| |#1|))) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{split(aG,{} vector)} returns a subalgebra \\spad{A} of all square matrix of dimension \\spad{n} as a list of list of matrices,{} generated by the list of matrices \\spad{aG},{} where \\spad{n} denotes both the size of vector as well as the dimension of each of the square matrices. {\\em V R} is an A-module in the natural way. split(\\spad{aG},{} vector) then checks whether the cyclic submodule generated by {\\em vector} is a proper submodule of {\\em V R}. If successful,{} it returns a two-element list,{} which contains first the list of the representations of the submodule,{} then the list of the representations of the factor module. If the vector generates the whole module,{} a one-element list of the old representation is given. Note: a later version this should call the other split.")) (|isAbsolutelyIrreducible?| (((|Boolean|) (|List| (|Matrix| |#1|))) "\\spad{isAbsolutelyIrreducible?(aG)} calls {\\em isAbsolutelyIrreducible?(aG,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Boolean|) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{isAbsolutelyIrreducible?(aG,{} numberOfTries)} uses Norton\\spad{'s} irreducibility test to check for absolute irreduciblity,{} assuming if a one-dimensional kernel is found. As no field extension changes create \"new\" elements in a one-dimensional space,{} the criterium stays \\spad{true} for every extension. The method looks for one-dimensionals only by creating random elements (no fingerprints) since a run of {\\em meatAxe} would have proved absolute irreducibility anyway.")) (|areEquivalent?| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}numberOfTries)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|))) "\\spad{areEquivalent?(aG0,{}aG1)} calls {\\em areEquivalent?(aG0,{}aG1,{}true,{}25)}. Note: the choice of 25 was rather arbitrary.") (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|List| (|Matrix| |#1|)) (|Boolean|) (|Integer|)) "\\spad{areEquivalent?(aG0,{}aG1,{}randomelements,{}numberOfTries)} tests whether the two lists of matrices,{} all assumed of same square shape,{} can be simultaneously conjugated by a non-singular matrix. If these matrices represent the same group generators,{} the representations are equivalent. The algorithm tries {\\em numberOfTries} times to create elements in the generated algebras in the same fashion. If their ranks differ,{} they are not equivalent. If an isomorphism is assumed,{} then the kernel of an element of the first algebra is mapped to the kernel of the corresponding element in the second algebra. Now consider the one-dimensional ones. If they generate the whole space (\\spadignore{e.g.} irreducibility !) we use {\\em standardBasisOfCyclicSubmodule} to create the only possible transition matrix. The method checks whether the matrix conjugates all corresponding matrices from {\\em aGi}. The way to choose the singular matrices is as in {\\em meatAxe}. If the two representations are equivalent,{} this routine returns the transformation matrix {\\em TM} with {\\em aG0.i * TM = TM * aG1.i} for all \\spad{i}. If the representations are not equivalent,{} a small 0-matrix is returned. Note: the case with different sets of group generators cannot be handled.")) (|standardBasisOfCyclicSubmodule| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{standardBasisOfCyclicSubmodule(lm,{}v)} returns a matrix as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. standardBasisOfCyclicSubmodule(\\spad{lm},{}\\spad{v}) calculates a matrix whose non-zero column vectors are the \\spad{R}-Basis of {\\em Av} achieved in the way as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to {\\em cyclicSubmodule},{} the result is not in echelon form.")) (|cyclicSubmodule| (((|Vector| (|Vector| |#1|)) (|List| (|Matrix| |#1|)) (|Vector| |#1|)) "\\spad{cyclicSubmodule(lm,{}v)} generates a basis as follows. It is assumed that the size \\spad{n} of the vector equals the number of rows and columns of the matrices. Then the matrices generate a subalgebra,{} say \\spad{A},{} of the algebra of all square matrices of dimension \\spad{n}. {\\em V R} is an \\spad{A}-module in the natural way. cyclicSubmodule(\\spad{lm},{}\\spad{v}) generates the \\spad{R}-Basis of {\\em Av} as described in section 6 of \\spad{R}. A. Parker\\spad{'s} \"The Meat-Axe\". Note: in contrast to the description in \"The Meat-Axe\" and to {\\em standardBasisOfCyclicSubmodule} the result is in echelon form.")) (|createRandomElement| (((|Matrix| |#1|) (|List| (|Matrix| |#1|)) (|Matrix| |#1|)) "\\spad{createRandomElement(aG,{}x)} creates a random element of the group algebra generated by {\\em aG}.")) (|completeEchelonBasis| (((|Matrix| |#1|) (|Vector| (|Vector| |#1|))) "\\spad{completeEchelonBasis(lv)} completes the basis {\\em lv} assumed to be in echelon form of a subspace of {\\em R**n} (\\spad{n} the length of all the vectors in {\\em lv}) with unit vectors to a basis of {\\em R**n}. It is assumed that the argument is not an empty vector and that it is not the basis of the 0-subspace. Note: the rows of the result correspond to the vectors of the basis."))) NIL @@ -3772,14 +3772,14 @@ NIL ((|constructor| (NIL "This package provides coercions for the special types \\spadtype{Exit} and \\spadtype{Void}.")) (|coerce| ((|#1| (|Exit|)) "\\spad{coerce(e)} is never really evaluated. This coercion is used for formal type correctness when a function will not return directly to its caller.") (((|Void|) |#1|) "\\spad{coerce(s)} throws all information about \\spad{s} away. This coercion allows values of any type to appear in contexts where they will not be used. For example,{} it allows the resolution of different types in the \\spad{then} and \\spad{else} branches when an \\spad{if} is in a context where the resulting value is not used."))) NIL NIL -(-961 -2315 |Expon| |VarSet| |FPol| |LFPol|) +(-961 -3539 |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"))) -(((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-962) ((|constructor| (NIL "A domain used to return the results from a call to the NAG Library. It prints as a list of names and types,{} though the user may choose to display values automatically if he or she wishes.")) (|showArrayValues| (((|Boolean|) (|Boolean|)) "\\spad{showArrayValues(true)} forces the values of array components to be \\indented{1}{displayed rather than just their types.}")) (|showScalarValues| (((|Boolean|) (|Boolean|)) "\\spad{showScalarValues(true)} forces the values of scalar components to be \\indented{1}{displayed rather than just their types.}"))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2433) (QUOTE (-51))))))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2482) (QUOTE (-51))))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) (-963 A S) ((|constructor| (NIL "A is retractable to \\spad{B} means that some elementsif A can be converted into elements of \\spad{B} and any element of \\spad{B} can be converted into an element of A.")) (|retract| ((|#2| $) "\\spad{retract(a)} transforms a into an element of \\spad{S} if possible. Error: if a cannot be made into an element of \\spad{S}.")) (|retractIfCan| (((|Union| |#2| "failed") $) "\\spad{retractIfCan(a)} transforms a into an element of \\spad{S} if possible. Returns \"failed\" if a cannot be made into an element of \\spad{S}.")) (|coerce| (($ |#2|) "\\spad{coerce(a)} transforms a into an element of \\%."))) NIL @@ -3810,7 +3810,7 @@ NIL NIL (-970 R |ls|) ((|constructor| (NIL "A domain for regular chains (\\spadignore{i.e.} regular triangular sets) over a \\spad{Gcd}-Domain and with a fix list of variables. This is just a front-end for the \\spadtype{RegularTriangularSet} domain constructor.")) (|zeroSetSplit| (((|List| $) (|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) (|Boolean|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?,{}info?)} returns a list \\spad{lts} of regular chains such that the union of the closures of their regular zero sets equals the affine variety associated with \\spad{lp}. Moreover,{} if \\spad{clos?} is \\spad{false} then the union of the regular zero set of the \\spad{ts} (for \\spad{ts} in \\spad{lts}) equals this variety. If \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSet}."))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| (-719 |#1| (-796 |#2|)) (QUOTE (-1016))) (|HasCategory| (-719 |#1| (-796 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -719) (|devaluate| |#1|) (LIST (QUOTE -796) (|devaluate| |#2|)))))) (|HasCategory| (-719 |#1| (-796 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-719 |#1| (-796 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| (-796 |#2|) (QUOTE (-344))) (|HasCategory| (-719 |#1| (-796 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-971) ((|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"))) @@ -3822,9 +3822,9 @@ NIL NIL (-973) ((|constructor| (NIL "The category of rings with unity,{} always associative,{} but not necessarily commutative.")) (|unitsKnown| ((|attribute|) "recip truly yields reciprocal or \"failed\" if not a unit. Note: \\spad{recip(0) = \"failed\"}.")) (|coerce| (($ (|Integer|)) "\\spad{coerce(i)} converts the integer \\spad{i} to a member of the given domain.")) (|characteristic| (((|NonNegativeInteger|)) "\\spad{characteristic()} returns the characteristic of the ring this is the smallest positive integer \\spad{n} such that \\spad{n*x=0} for all \\spad{x} in the ring,{} or zero if no such \\spad{n} exists."))) -((-4241 . T)) +((-4245 . T)) NIL -(-974 |xx| -2315) +(-974 |xx| -3539) ((|constructor| (NIL "This package exports rational interpolation algorithms"))) NIL NIL @@ -3834,12 +3834,12 @@ NIL ((|HasCategory| |#4| (QUOTE (-284))) (|HasCategory| |#4| (QUOTE (-339))) (|HasCategory| |#4| (QUOTE (-515))) (|HasCategory| |#4| (QUOTE (-158)))) (-976 |m| |n| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{RectangularMatrixCategory} is a category of matrices of fixed dimensions. The dimensions of the matrix will be parameters of the domain. Domains in this category will be \\spad{R}-modules and will be non-mutable.")) (|nullSpace| (((|List| |#5|) $) "\\spad{nullSpace(m)}+ returns a basis for the null space of the matrix \\spad{m}.")) (|nullity| (((|NonNegativeInteger|) $) "\\spad{nullity(m)} returns the nullity of the matrix \\spad{m}. This is the dimension of the null space of the matrix \\spad{m}.")) (|rank| (((|NonNegativeInteger|) $) "\\spad{rank(m)} returns the rank of the matrix \\spad{m}.")) (|rowEchelon| (($ $) "\\spad{rowEchelon(m)} returns the row echelon form of the matrix \\spad{m}.")) (/ (($ $ |#3|) "\\spad{m/r} divides the elements of \\spad{m} by \\spad{r}. Error: if \\spad{r = 0}.")) (|exquo| (((|Union| $ "failed") $ |#3|) "\\spad{exquo(m,{}r)} computes the exact quotient of the elements of \\spad{m} by \\spad{r},{} returning \\axiom{\"failed\"} if this is not possible.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(f,{}a,{}b)} returns \\spad{c},{} where \\spad{c} is such that \\spad{c(i,{}j) = f(a(i,{}j),{}b(i,{}j))} for all \\spad{i},{} \\spad{j}.") (($ (|Mapping| |#3| |#3|) $) "\\spad{map(f,{}a)} returns \\spad{b},{} where \\spad{b(i,{}j) = a(i,{}j)} for all \\spad{i},{} \\spad{j}.")) (|column| ((|#5| $ (|Integer|)) "\\spad{column(m,{}j)} returns the \\spad{j}th column of the matrix \\spad{m}. Error: if the index outside the proper range.")) (|row| ((|#4| $ (|Integer|)) "\\spad{row(m,{}i)} returns the \\spad{i}th row of the matrix \\spad{m}. Error: if the index is outside the proper range.")) (|qelt| ((|#3| $ (|Integer|) (|Integer|)) "\\spad{qelt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Note: there is NO error check to determine if indices are in the proper ranges.")) (|elt| ((|#3| $ (|Integer|) (|Integer|) |#3|) "\\spad{elt(m,{}i,{}j,{}r)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m},{} if \\spad{m} has an \\spad{i}th row and a \\spad{j}th column,{} and returns \\spad{r} otherwise.") ((|#3| $ (|Integer|) (|Integer|)) "\\spad{elt(m,{}i,{}j)} returns the element in the \\spad{i}th row and \\spad{j}th column of the matrix \\spad{m}. Error: if indices are outside the proper ranges.")) (|listOfLists| (((|List| (|List| |#3|)) $) "\\spad{listOfLists(m)} returns the rows of the matrix \\spad{m} as a list of lists.")) (|ncols| (((|NonNegativeInteger|) $) "\\spad{ncols(m)} returns the number of columns in the matrix \\spad{m}.")) (|nrows| (((|NonNegativeInteger|) $) "\\spad{nrows(m)} returns the number of rows in the matrix \\spad{m}.")) (|maxColIndex| (((|Integer|) $) "\\spad{maxColIndex(m)} returns the index of the 'last' column of the matrix \\spad{m}.")) (|minColIndex| (((|Integer|) $) "\\spad{minColIndex(m)} returns the index of the 'first' column of the matrix \\spad{m}.")) (|maxRowIndex| (((|Integer|) $) "\\spad{maxRowIndex(m)} returns the index of the 'last' row of the matrix \\spad{m}.")) (|minRowIndex| (((|Integer|) $) "\\spad{minRowIndex(m)} returns the index of the 'first' row of the matrix \\spad{m}.")) (|antisymmetric?| (((|Boolean|) $) "\\spad{antisymmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and antisymmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = -m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|symmetric?| (((|Boolean|) $) "\\spad{symmetric?(m)} returns \\spad{true} if the matrix \\spad{m} is square and symmetric (\\spadignore{i.e.} \\spad{m[i,{}j] = m[j,{}i]} for all \\spad{i} and \\spad{j}) and \\spad{false} otherwise.")) (|diagonal?| (((|Boolean|) $) "\\spad{diagonal?(m)} returns \\spad{true} if the matrix \\spad{m} is square and diagonal (\\spadignore{i.e.} all entries of \\spad{m} not on the diagonal are zero) and \\spad{false} otherwise.")) (|square?| (((|Boolean|) $) "\\spad{square?(m)} returns \\spad{true} if \\spad{m} is a square matrix (\\spadignore{i.e.} if \\spad{m} has the same number of rows as columns) and \\spad{false} otherwise.")) (|matrix| (($ (|List| (|List| |#3|))) "\\spad{matrix(l)} converts the list of lists \\spad{l} to a matrix,{} where the list of lists is viewed as a list of the rows of the matrix.")) (|finiteAggregate| ((|attribute|) "matrices are finite"))) -((-4244 . T) (-3656 . T) (-4239 . T) (-4238 . T)) +((-4248 . T) (-4069 . T) (-4243 . T) (-4242 . T)) NIL (-977 |m| |n| R) ((|constructor| (NIL "\\spadtype{RectangularMatrix} is a matrix domain where the number of rows and the number of columns are parameters of the domain.")) (|coerce| (((|Matrix| |#3|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{RectangularMatrix} to a matrix of type \\spad{Matrix}.")) (|rectangularMatrix| (($ (|Matrix| |#3|)) "\\spad{rectangularMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spad{RectangularMatrix}."))) -((-4244 . T) (-4239 . T) (-4238 . T)) -((-3262 (-12 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-339)))) (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-284))) (|HasCategory| |#3| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) +((-4248 . T) (-4243 . T) (-4242 . T)) +((-3172 (-12 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) (|HasCategory| |#3| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (QUOTE (-339)))) (|HasCategory| |#3| (QUOTE (-339))) (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (QUOTE (-284))) (|HasCategory| |#3| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-158))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|))))) (-978 |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 @@ -3858,7 +3858,7 @@ NIL NIL (-982) ((|constructor| (NIL "The real number system category is intended as a model for the real numbers. The real numbers form an ordered normed field. Note that we have purposely not included \\spadtype{DifferentialRing} or the elementary functions (see \\spadtype{TranscendentalFunctionCategory}) in the definition.")) (|abs| (($ $) "\\spad{abs x} returns the absolute value of \\spad{x}.")) (|round| (($ $) "\\spad{round x} computes the integer closest to \\spad{x}.")) (|truncate| (($ $) "\\spad{truncate x} returns the integer between \\spad{x} and 0 closest to \\spad{x}.")) (|fractionPart| (($ $) "\\spad{fractionPart x} returns the fractional part of \\spad{x}.")) (|wholePart| (((|Integer|) $) "\\spad{wholePart x} returns the integer part of \\spad{x}.")) (|floor| (($ $) "\\spad{floor x} returns the largest integer \\spad{<= x}.")) (|ceiling| (($ $) "\\spad{ceiling x} returns the small integer \\spad{>= x}.")) (|norm| (($ $) "\\spad{norm x} returns the same as absolute value."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-983 |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| $) "\\axiom{left(rootChar)} is the left bound of the isolating interval"))) @@ -3866,19 +3866,19 @@ NIL NIL (-984) ((|constructor| (NIL "\\spadtype{RomanNumeral} provides functions for converting \\indented{1}{integers to roman numerals.}")) (|roman| (($ (|Integer|)) "\\spad{roman(n)} creates a roman numeral for \\spad{n}.") (($ (|Symbol|)) "\\spad{roman(n)} creates a roman numeral for symbol \\spad{n}.")) (|convert| (($ (|Symbol|)) "\\spad{convert(n)} creates a roman numeral for symbol \\spad{n}.")) (|noetherian| ((|attribute|) "ascending chain condition on ideals.")) (|canonicalsClosed| ((|attribute|) "two positives multiply to give positive.")) (|canonical| ((|attribute|) "mathematical equality is data structure equality."))) -((-4232 . T) (-4236 . T) (-4231 . T) (-4242 . T) (-4243 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4236 . T) (-4240 . T) (-4235 . T) (-4246 . T) (-4247 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-985) ((|constructor| (NIL "\\axiomType{RoutinesTable} implements a database and associated tuning mechanisms for a set of known NAG routines")) (|recoverAfterFail| (((|Union| (|String|) "failed") $ (|String|) (|Integer|)) "\\spad{recoverAfterFail(routs,{}routineName,{}ifailValue)} acts on the instructions given by the ifail list")) (|showTheRoutinesTable| (($) "\\spad{showTheRoutinesTable()} returns the current table of NAG routines.")) (|deleteRoutine!| (($ $ (|Symbol|)) "\\spad{deleteRoutine!(R,{}s)} destructively deletes the given routine from the current database of NAG routines")) (|getExplanations| (((|List| (|String|)) $ (|String|)) "\\spad{getExplanations(R,{}s)} gets the explanations of the output parameters for the given NAG routine.")) (|getMeasure| (((|Float|) $ (|Symbol|)) "\\spad{getMeasure(R,{}s)} gets the current value of the maximum measure for the given NAG routine.")) (|changeMeasure| (($ $ (|Symbol|) (|Float|)) "\\spad{changeMeasure(R,{}s,{}newValue)} changes the maximum value for a measure of the given NAG routine.")) (|changeThreshhold| (($ $ (|Symbol|) (|Float|)) "\\spad{changeThreshhold(R,{}s,{}newValue)} changes the value below which,{} given a NAG routine generating a higher measure,{} the routines will make no attempt to generate a measure.")) (|selectMultiDimensionalRoutines| (($ $) "\\spad{selectMultiDimensionalRoutines(R)} chooses only those routines from the database which are designed for use with multi-dimensional expressions")) (|selectNonFiniteRoutines| (($ $) "\\spad{selectNonFiniteRoutines(R)} chooses only those routines from the database which are designed for use with non-finite expressions.")) (|selectSumOfSquaresRoutines| (($ $) "\\spad{selectSumOfSquaresRoutines(R)} chooses only those routines from the database which are designed for use with sums of squares")) (|selectFiniteRoutines| (($ $) "\\spad{selectFiniteRoutines(R)} chooses only those routines from the database which are designed for use with finite expressions")) (|selectODEIVPRoutines| (($ $) "\\spad{selectODEIVPRoutines(R)} chooses only those routines from the database which are for the solution of ODE\\spad{'s}")) (|selectPDERoutines| (($ $) "\\spad{selectPDERoutines(R)} chooses only those routines from the database which are for the solution of PDE\\spad{'s}")) (|selectOptimizationRoutines| (($ $) "\\spad{selectOptimizationRoutines(R)} chooses only those routines from the database which are for integration")) (|selectIntegrationRoutines| (($ $) "\\spad{selectIntegrationRoutines(R)} chooses only those routines from the database which are for integration")) (|routines| (($) "\\spad{routines()} initialises a database of known NAG routines")) (|concat| (($ $ $) "\\spad{concat(x,{}y)} merges two tables \\spad{x} and \\spad{y}"))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2433) (QUOTE (-51))))))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1087))) (LIST (QUOTE |:|) (QUOTE -2482) (QUOTE (-51))))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-51) (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| (-51) (QUOTE (-1016))) (|HasCategory| (-51) (LIST (QUOTE -286) (QUOTE (-51))))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (QUOTE (-1016))) (|HasCategory| (-1087) (QUOTE (-786))) (|HasCategory| (-51) (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-51) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (LIST (QUOTE -563) (QUOTE (-794))))) (-986 S R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#2| |#2| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#2|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#2|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#2|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#2|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#2|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#4|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#4|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#4|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#4|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#4|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#4|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#4|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#4| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) NIL ((|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-508))) (|HasCategory| |#2| (LIST (QUOTE -37) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -921) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-1087))))) (-987 R E V) ((|constructor| (NIL "A category for general multi-variate polynomials with coefficients in a ring,{} variables in an ordered set,{} and exponents from an ordered abelian monoid,{} with a \\axiomOp{sup} operation. When not constant,{} such a polynomial is viewed as a univariate polynomial in its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in the ordered set,{} so that some operations usually defined for univariate polynomials make sense here.")) (|mainSquareFreePart| (($ $) "\\axiom{mainSquareFreePart(\\spad{p})} returns the square free part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainPrimitivePart| (($ $) "\\axiom{mainPrimitivePart(\\spad{p})} returns the primitive part of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|mainContent| (($ $) "\\axiom{mainContent(\\spad{p})} returns the content of \\axiom{\\spad{p}} viewed as a univariate polynomial in its main variable and with coefficients in the polynomial ring generated by its other variables over \\axiom{\\spad{R}}.")) (|primitivePart!| (($ $) "\\axiom{primitivePart!(\\spad{p})} replaces \\axiom{\\spad{p}} by its primitive part.")) (|gcd| ((|#1| |#1| $) "\\axiom{\\spad{gcd}(\\spad{r},{}\\spad{p})} returns the \\spad{gcd} of \\axiom{\\spad{r}} and the content of \\axiom{\\spad{p}}.")) (|nextsubResultant2| (($ $ $ $ $) "\\axiom{nextsubResultant2(\\spad{p},{}\\spad{q},{}\\spad{z},{}\\spad{s})} is the multivariate version of the operation \\axiomOpFrom{next_sousResultant2}{PseudoRemainderSequence} from the \\axiomType{PseudoRemainderSequence} constructor.")) (|LazardQuotient2| (($ $ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient2(\\spad{p},{}a,{}\\spad{b},{}\\spad{n})} returns \\axiom{(a**(\\spad{n}-1) * \\spad{p}) exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|LazardQuotient| (($ $ $ (|NonNegativeInteger|)) "\\axiom{LazardQuotient(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a**n exquo \\spad{b**}(\\spad{n}-1)} assuming that this quotient does not fail.")) (|lastSubResultant| (($ $ $) "\\axiom{lastSubResultant(a,{}\\spad{b})} returns the last non-zero subresultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|subResultantChain| (((|List| $) $ $) "\\axiom{subResultantChain(a,{}\\spad{b})},{} where \\axiom{a} and \\axiom{\\spad{b}} are not contant polynomials with the same main variable,{} returns the subresultant chain of \\axiom{a} and \\axiom{\\spad{b}}.")) (|resultant| (($ $ $) "\\axiom{resultant(a,{}\\spad{b})} computes the resultant of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}}.")) (|halfExtendedSubResultantGcd2| (((|Record| (|:| |gcd| $) (|:| |coef2| $)) $ $) "\\axiom{halfExtendedSubResultantGcd2(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}\\spad{cb}]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|halfExtendedSubResultantGcd1| (((|Record| (|:| |gcd| $) (|:| |coef1| $)) $ $) "\\axiom{halfExtendedSubResultantGcd1(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca]} if \\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[\\spad{g},{}ca,{}\\spad{cb}]} otherwise produces an error.")) (|extendedSubResultantGcd| (((|Record| (|:| |gcd| $) (|:| |coef1| $) (|:| |coef2| $)) $ $) "\\axiom{extendedSubResultantGcd(a,{}\\spad{b})} returns \\axiom{[ca,{}\\spad{cb},{}\\spad{r}]} such that \\axiom{\\spad{r}} is \\axiom{subResultantGcd(a,{}\\spad{b})} and we have \\axiom{ca * a + \\spad{cb} * \\spad{cb} = \\spad{r}} .")) (|subResultantGcd| (($ $ $) "\\axiom{subResultantGcd(a,{}\\spad{b})} computes a \\spad{gcd} of \\axiom{a} and \\axiom{\\spad{b}} where \\axiom{a} and \\axiom{\\spad{b}} are assumed to have the same main variable \\axiom{\\spad{v}} and are viewed as univariate polynomials in \\axiom{\\spad{v}} with coefficients in the fraction field of the polynomial ring generated by their other variables over \\axiom{\\spad{R}}.")) (|exactQuotient!| (($ $ $) "\\axiom{exactQuotient!(a,{}\\spad{b})} replaces \\axiom{a} by \\axiom{exactQuotient(a,{}\\spad{b})}") (($ $ |#1|) "\\axiom{exactQuotient!(\\spad{p},{}\\spad{r})} replaces \\axiom{\\spad{p}} by \\axiom{exactQuotient(\\spad{p},{}\\spad{r})}.")) (|exactQuotient| (($ $ $) "\\axiom{exactQuotient(a,{}\\spad{b})} computes the exact quotient of \\axiom{a} by \\axiom{\\spad{b}},{} which is assumed to be a divisor of \\axiom{a}. No error is returned if this exact quotient fails!") (($ $ |#1|) "\\axiom{exactQuotient(\\spad{p},{}\\spad{r})} computes the exact quotient of \\axiom{\\spad{p}} by \\axiom{\\spad{r}},{} which is assumed to be a divisor of \\axiom{\\spad{p}}. No error is returned if this exact quotient fails!")) (|primPartElseUnitCanonical!| (($ $) "\\axiom{primPartElseUnitCanonical!(\\spad{p})} replaces \\axiom{\\spad{p}} by \\axiom{primPartElseUnitCanonical(\\spad{p})}.")) (|primPartElseUnitCanonical| (($ $) "\\axiom{primPartElseUnitCanonical(\\spad{p})} returns \\axiom{primitivePart(\\spad{p})} if \\axiom{\\spad{R}} is a \\spad{gcd}-domain,{} otherwise \\axiom{unitCanonical(\\spad{p})}.")) (|convert| (($ (|Polynomial| |#1|)) "\\axiom{convert(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}},{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.") (($ (|Polynomial| (|Integer|))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{convert(\\spad{p})} returns the same as \\axiom{retract(\\spad{p})}.")) (|retract| (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| |#1|)) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Integer|))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.") (($ (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retract(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if \\axiom{retractIfCan(\\spad{p})} does not return \"failed\",{} otherwise an error is produced.")) (|retractIfCan| (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| |#1|)) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Integer|))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.") (((|Union| $ "failed") (|Polynomial| (|Fraction| (|Integer|)))) "\\axiom{retractIfCan(\\spad{p})} returns \\axiom{\\spad{p}} as an element of the current domain if all its variables belong to \\axiom{\\spad{V}}.")) (|initiallyReduce| (($ $ $) "\\axiom{initiallyReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|headReduce| (($ $ $) "\\axiom{headReduce(a,{}\\spad{b})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduced?(\\spad{r},{}\\spad{b})} holds and there exists an integer \\axiom{\\spad{e}} such that \\axiom{init(\\spad{b})^e a - \\spad{r}} is zero modulo \\axiom{\\spad{b}}.")) (|lazyResidueClass| (((|Record| (|:| |polnum| $) (|:| |polden| $) (|:| |power| (|NonNegativeInteger|))) $ $) "\\axiom{lazyResidueClass(a,{}\\spad{b})} returns \\axiom{[\\spad{p},{}\\spad{q},{}\\spad{n}]} where \\axiom{\\spad{p} / q**n} represents the residue class of \\axiom{a} modulo \\axiom{\\spad{b}} and \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and \\axiom{\\spad{q}} is \\axiom{init(\\spad{b})}.")) (|monicModulo| (($ $ $) "\\axiom{monicModulo(a,{}\\spad{b})} computes \\axiom{a mod \\spad{b}},{} if \\axiom{\\spad{b}} is monic as univariate polynomial in its main variable.")) (|pseudoDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{pseudoDivide(a,{}\\spad{b})} computes \\axiom{[pquo(a,{}\\spad{b}),{}prem(a,{}\\spad{b})]},{} both polynomials viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}},{} if \\axiom{\\spad{b}} is not a constant polynomial.")) (|lazyPseudoDivide| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})},{} \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]} such that \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}] = lazyPremWithDefault(a,{}\\spad{b})} and \\axiom{\\spad{q}} is the pseudo-quotient computed in this lazy pseudo-division.")) (|lazyPremWithDefault| (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $ |#3|) "\\axiom{lazyPremWithDefault(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b},{}\\spad{v})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b},{}\\spad{v})}.") (((|Record| (|:| |coef| $) (|:| |gap| (|NonNegativeInteger|)) (|:| |remainder| $)) $ $) "\\axiom{lazyPremWithDefault(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{r}]} such that \\axiom{\\spad{r} = lazyPrem(a,{}\\spad{b})} and \\axiom{(c**g)\\spad{*r} = prem(a,{}\\spad{b})}.")) (|lazyPquo| (($ $ $ |#3|) "\\axiom{lazyPquo(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b},{}\\spad{v})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.") (($ $ $) "\\axiom{lazyPquo(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{q}} such that \\axiom{lazyPseudoDivide(a,{}\\spad{b})} returns \\axiom{[\\spad{c},{}\\spad{g},{}\\spad{q},{}\\spad{r}]}.")) (|lazyPrem| (($ $ $ |#3|) "\\axiom{lazyPrem(a,{}\\spad{b},{}\\spad{v})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} viewed as univariate polynomials in the variable \\axiom{\\spad{v}} such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.") (($ $ $) "\\axiom{lazyPrem(a,{}\\spad{b})} returns the polynomial \\axiom{\\spad{r}} reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{b}} and such that \\axiom{\\spad{b}} divides \\axiom{init(\\spad{b})^e a - \\spad{r}} where \\axiom{\\spad{e}} is the number of steps of this pseudo-division.")) (|pquo| (($ $ $ |#3|) "\\axiom{pquo(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{pquo(a,{}\\spad{b})} computes the pseudo-quotient of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|prem| (($ $ $ |#3|) "\\axiom{prem(a,{}\\spad{b},{}\\spad{v})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in \\axiom{\\spad{v}}.") (($ $ $) "\\axiom{prem(a,{}\\spad{b})} computes the pseudo-remainder of \\axiom{a} by \\axiom{\\spad{b}},{} both viewed as univariate polynomials in the main variable of \\axiom{\\spad{b}}.")) (|normalized?| (((|Boolean|) $ (|List| $)) "\\axiom{normalized?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{normalized?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{normalized?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{a} and its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variable of \\axiom{\\spad{b}}")) (|initiallyReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{initiallyReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{initiallyReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{initiallyReduced?(a,{}\\spad{b})} returns \\spad{false} iff there exists an iterated initial of \\axiom{a} which is not reduced \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{b}}.")) (|headReduced?| (((|Boolean|) $ (|List| $)) "\\axiom{headReduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{headReduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{headReduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(head(a),{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|reduced?| (((|Boolean|) $ (|List| $)) "\\axiom{reduced?(\\spad{q},{}\\spad{lp})} returns \\spad{true} iff \\axiom{reduced?(\\spad{q},{}\\spad{p})} holds for every \\axiom{\\spad{p}} in \\axiom{\\spad{lp}}.") (((|Boolean|) $ $) "\\axiom{reduced?(a,{}\\spad{b})} returns \\spad{true} iff \\axiom{degree(a,{}mvar(\\spad{b})) < mdeg(\\spad{b})}.")) (|supRittWu?| (((|Boolean|) $ $) "\\axiom{supRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is greater than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(a,{}\\spad{b})} returns \\spad{true} if \\axiom{a} is less than \\axiom{\\spad{b}} \\spad{w}.\\spad{r}.\\spad{t}. the Ritt and Wu Wen Tsun ordering using the refinement of Lazard.")) (|RittWuCompare| (((|Union| (|Boolean|) "failed") $ $) "\\axiom{RittWuCompare(a,{}\\spad{b})} returns \\axiom{\"failed\"} if \\axiom{a} and \\axiom{\\spad{b}} have same rank \\spad{w}.\\spad{r}.\\spad{t}. Ritt and Wu Wen Tsun ordering using the refinement of Lazard,{} otherwise returns \\axiom{infRittWu?(a,{}\\spad{b})}.")) (|mainMonomials| (((|List| $) $) "\\axiom{mainMonomials(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [1],{} otherwise returns the list of the monomials of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainCoefficients| (((|List| $) $) "\\axiom{mainCoefficients(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns [\\spad{p}],{} otherwise returns the list of the coefficients of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|leastMonomial| (($ $) "\\axiom{leastMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} the monomial of \\axiom{\\spad{p}} with lowest degree,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mainMonomial| (($ $) "\\axiom{mainMonomial(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{\\spad{O}},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{1},{} otherwise,{} \\axiom{mvar(\\spad{p})} raised to the power \\axiom{mdeg(\\spad{p})}.")) (|quasiMonic?| (((|Boolean|) $) "\\axiom{quasiMonic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff the initial of \\axiom{\\spad{p}} lies in the base ring \\axiom{\\spad{R}}.")) (|monic?| (((|Boolean|) $) "\\axiom{monic?(\\spad{p})} returns \\spad{false} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns \\spad{true} iff \\axiom{\\spad{p}} is monic as a univariate polynomial in its main variable.")) (|reductum| (($ $ |#3|) "\\axiom{reductum(\\spad{p},{}\\spad{v})} returns the reductum of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in \\axiom{\\spad{v}}.")) (|leadingCoefficient| (($ $ |#3|) "\\axiom{leadingCoefficient(\\spad{p},{}\\spad{v})} returns the leading coefficient of \\axiom{\\spad{p}},{} where \\axiom{\\spad{p}} is viewed as A univariate polynomial in \\axiom{\\spad{v}}.")) (|deepestInitial| (($ $) "\\axiom{deepestInitial(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the last term of \\axiom{iteratedInitials(\\spad{p})}.")) (|iteratedInitials| (((|List| $) $) "\\axiom{iteratedInitials(\\spad{p})} returns \\axiom{[]} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns the list of the iterated initials of \\axiom{\\spad{p}}.")) (|deepestTail| (($ $) "\\axiom{deepestTail(\\spad{p})} returns \\axiom{0} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns tail(\\spad{p}),{} if \\axiom{tail(\\spad{p})} belongs to \\axiom{\\spad{R}} or \\axiom{mvar(tail(\\spad{p})) < mvar(\\spad{p})},{} otherwise returns \\axiom{deepestTail(tail(\\spad{p}))}.")) (|tail| (($ $) "\\axiom{tail(\\spad{p})} returns its reductum,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|head| (($ $) "\\axiom{head(\\spad{p})} returns \\axiom{\\spad{p}} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading term (monomial in the AXIOM sense),{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|init| (($ $) "\\axiom{init(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its leading coefficient,{} where \\axiom{\\spad{p}} is viewed as a univariate polynomial in its main variable.")) (|mdeg| (((|NonNegativeInteger|) $) "\\axiom{mdeg(\\spad{p})} returns an error if \\axiom{\\spad{p}} is \\axiom{0},{} otherwise,{} if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}} returns \\axiom{0},{} otherwise,{} returns the degree of \\axiom{\\spad{p}} in its main variable.")) (|mvar| ((|#3| $) "\\axiom{mvar(\\spad{p})} returns an error if \\axiom{\\spad{p}} belongs to \\axiom{\\spad{R}},{} otherwise returns its main variable \\spad{w}. \\spad{r}. \\spad{t}. to the total ordering on the elements in \\axiom{\\spad{V}}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL (-988 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}"))) @@ -3898,7 +3898,7 @@ NIL NIL (-992 R E V P) ((|constructor| (NIL "The category of regular triangular sets,{} introduced under the name regular chains in [1] (and other papers). In [3] it is proved that regular triangular sets and towers of simple extensions of a field are equivalent notions. In the following definitions,{} all polynomials and ideals are taken from the polynomial ring \\spad{k[x1,{}...,{}xn]} where \\spad{k} is the fraction field of \\spad{R}. The triangular set \\spad{[t1,{}...,{}tm]} is regular iff for every \\spad{i} the initial of \\spad{ti+1} is invertible in the tower of simple extensions associated with \\spad{[t1,{}...,{}\\spad{ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given ideal \\spad{I} iff the radical of \\spad{I} is equal to the intersection of the radical ideals generated by the saturated ideals of the \\spad{[T1,{}...,{}\\spad{Ti}]}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Kalkbrener of a given triangular set \\spad{T} iff it is a split of Kalkbrener of the saturated ideal of \\spad{T}. Let \\spad{K} be an algebraic closure of \\spad{k}. Assume that \\spad{V} is finite with cardinality \\spad{n} and let \\spad{A} be the affine space \\spad{K^n}. For a regular triangular set \\spad{T} let denote by \\spad{W(T)} the set of regular zeros of \\spad{T}. A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given subset \\spad{S} of \\spad{A} iff the union of the \\spad{W(\\spad{Ti})} contains \\spad{S} and is contained in the closure of \\spad{S} (\\spad{w}.\\spad{r}.\\spad{t}. Zariski topology). A family \\spad{[T1,{}...,{}Ts]} of regular triangular sets is a split of Lazard of a given triangular set \\spad{T} if it is a split of Lazard of \\spad{W(T)}. Note that if \\spad{[T1,{}...,{}Ts]} is a split of Lazard of \\spad{T} then it is also a split of Kalkbrener of \\spad{T}. The converse is \\spad{false}. This category provides operations related to both kinds of splits,{} the former being related to ideals decomposition whereas the latter deals with varieties decomposition. See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets. \\newline References : \\indented{1}{[1] \\spad{M}. KALKBRENER \"Three contributions to elimination theory\"} \\indented{5}{\\spad{Phd} Thesis,{} University of Linz,{} Austria,{} 1991.} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Journal of Symbol. Comp. 1998} \\indented{1}{[3] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)} \\indented{1}{[4] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|)) "\\spad{zeroSetSplit(lp,{}clos?)} returns \\spad{lts} a split of Kalkbrener of the radical ideal associated with \\spad{lp}. If \\spad{clos?} is \\spad{false},{} it is also a decomposition of the variety associated with \\spad{lp} into the regular zero set of the \\spad{ts} in \\spad{lts} (or,{} in other words,{} a split of Lazard of this variety). See the example illustrating the \\spadtype{RegularTriangularSet} constructor for more explanations about decompositions by means of regular triangular sets.")) (|extend| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{extend(lp,{}lts)} returns the same as \\spad{concat([extend(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{extend(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp} \\spad{extend(p,{}ts)} if \\spad{lp = [p]} else \\spad{extend(first lp,{} extend(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{extend(p,{}lts)} returns the same as \\spad{concat([extend(p,{}ts) for ts in lts])|}") (((|List| $) |#4| $) "\\spad{extend(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is not a regular triangular set.")) (|internalAugment| (($ (|List| |#4|) $) "\\spad{internalAugment(lp,{}ts)} returns \\spad{ts} if \\spad{lp} is empty otherwise returns \\spad{internalAugment(rest lp,{} internalAugment(first lp,{} ts))}") (($ |#4| $) "\\spad{internalAugment(p,{}ts)} assumes that \\spad{augment(p,{}ts)} returns a singleton and returns it.")) (|augment| (((|List| $) (|List| |#4|) (|List| $)) "\\spad{augment(lp,{}lts)} returns the same as \\spad{concat([augment(lp,{}ts) for ts in lts])}") (((|List| $) (|List| |#4|) $) "\\spad{augment(lp,{}ts)} returns \\spad{ts} if \\spad{empty? lp},{} \\spad{augment(p,{}ts)} if \\spad{lp = [p]},{} otherwise \\spad{augment(first lp,{} augment(rest lp,{} ts))}") (((|List| $) |#4| (|List| $)) "\\spad{augment(p,{}lts)} returns the same as \\spad{concat([augment(p,{}ts) for ts in lts])}") (((|List| $) |#4| $) "\\spad{augment(p,{}ts)} assumes that \\spad{p} is a non-constant polynomial whose main variable is greater than any variable of \\spad{ts}. This operation assumes also that if \\spad{p} is added to \\spad{ts} the resulting set,{} say \\spad{ts+p},{} is a regular triangular set. Then it returns a split of Kalkbrener of \\spad{ts+p}. This may not be \\spad{ts+p} itself,{} if for instance \\spad{ts+p} is required to be square-free.")) (|intersect| (((|List| $) |#4| (|List| $)) "\\spad{intersect(p,{}lts)} returns the same as \\spad{intersect([p],{}lts)}") (((|List| $) (|List| |#4|) (|List| $)) "\\spad{intersect(lp,{}lts)} returns the same as \\spad{concat([intersect(lp,{}ts) for ts in lts])|}") (((|List| $) (|List| |#4|) $) "\\spad{intersect(lp,{}ts)} returns \\spad{lts} a split of Lazard of the intersection of the affine variety associated with \\spad{lp} and the regular zero set of \\spad{ts}.") (((|List| $) |#4| $) "\\spad{intersect(p,{}ts)} returns the same as \\spad{intersect([p],{}ts)}")) (|squareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| $) "\\spad{squareFreePart(p,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a square-free polynomial \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} this polynomial being associated with \\spad{p} modulo \\spad{lpwt.i.tower},{} for every \\spad{i}. Moreover,{} the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. WARNING: This assumes that \\spad{p} is a non-constant polynomial such that if \\spad{p} is added to \\spad{ts},{} then the resulting set is a regular triangular set.")) (|lastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| $))) |#4| |#4| $) "\\spad{lastSubResultant(p1,{}p2,{}ts)} returns \\spad{lpwt} such that \\spad{lpwt.i.val} is a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower},{} for every \\spad{i},{} and such that the list of the \\spad{lpwt.i.tower} is a split of Kalkbrener of \\spad{ts}. Moreover,{} if \\spad{p1} and \\spad{p2} do not have a non-trivial \\spad{gcd} \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower} then \\spad{lpwt.i.val} is the resultant of these polynomials \\spad{w}.\\spad{r}.\\spad{t}. \\spad{lpwt.i.tower}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|lastSubResultantElseSplit| (((|Union| |#4| (|List| $)) |#4| |#4| $) "\\spad{lastSubResultantElseSplit(p1,{}p2,{}ts)} returns either \\spad{g} a quasi-monic \\spad{gcd} of \\spad{p1} and \\spad{p2} \\spad{w}.\\spad{r}.\\spad{t}. the \\spad{ts} or a split of Kalkbrener of \\spad{ts}. This assumes that \\spad{p1} and \\spad{p2} have the same maim variable and that this variable is greater that any variable occurring in \\spad{ts}.")) (|invertibleSet| (((|List| $) |#4| $) "\\spad{invertibleSet(p,{}ts)} returns a split of Kalkbrener of the quotient ideal of the ideal \\axiom{\\spad{I}} by \\spad{p} where \\spad{I} is the radical of saturated of \\spad{ts}.")) (|invertible?| (((|Boolean|) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{true} iff \\spad{p} is invertible in the tower associated with \\spad{ts}.") (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| $))) |#4| $) "\\spad{invertible?(p,{}ts)} returns \\spad{lbwt} where \\spad{lbwt.i} is the result of \\spad{invertibleElseSplit?(p,{}lbwt.i.tower)} and the list of the \\spad{(lqrwt.i).tower} is a split of Kalkbrener of \\spad{ts}.")) (|invertibleElseSplit?| (((|Union| (|Boolean|) (|List| $)) |#4| $) "\\spad{invertibleElseSplit?(p,{}ts)} returns \\spad{true} (resp. \\spad{false}) if \\spad{p} is invertible in the tower associated with \\spad{ts} or returns a split of Kalkbrener of \\spad{ts}.")) (|purelyAlgebraicLeadingMonomial?| (((|Boolean|) |#4| $) "\\spad{purelyAlgebraicLeadingMonomial?(p,{}ts)} returns \\spad{true} iff the main variable of any non-constant iterarted initial of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|algebraicCoefficients?| (((|Boolean|) |#4| $) "\\spad{algebraicCoefficients?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} which is not the main one of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}.")) (|purelyTranscendental?| (((|Boolean|) |#4| $) "\\spad{purelyTranscendental?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is not algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}")) (|purelyAlgebraic?| (((|Boolean|) $) "\\spad{purelyAlgebraic?(ts)} returns \\spad{true} iff for every algebraic variable \\spad{v} of \\spad{ts} we have \\spad{algebraicCoefficients?(t_v,{}ts_v_-)} where \\spad{ts_v} is \\axiomOpFrom{select}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}) and \\spad{ts_v_-} is \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\spad{v}).") (((|Boolean|) |#4| $) "\\spad{purelyAlgebraic?(p,{}ts)} returns \\spad{true} iff every variable of \\spad{p} is algebraic \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ts}."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-993 R E V P TS) ((|constructor| (NIL "An internal package for computing gcds and resultants of univariate polynomials with coefficients in a tower of simple extensions of a field.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA and \\spad{R}. RIOBOO \"Computations of \\spad{gcd} over} \\indented{5}{algebraic towers of simple extensions\" In proceedings of AAECC11} \\indented{5}{Paris,{} 1995.} \\indented{1}{[2] \\spad{M}. MORENO MAZA \"Calculs de pgcd au-dessus des tours} \\indented{5}{d'extensions simples et resolution des systemes d'equations} \\indented{5}{algebriques\" These,{} Universite \\spad{P}.etM. Curie,{} Paris,{} 1997.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}")) (|toseSquareFreePart| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseSquareFreePart(\\spad{p},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{squareFreePart}{RegularTriangularSetCategory}.")) (|toseInvertibleSet| (((|List| |#5|) |#4| |#5|) "\\axiom{toseInvertibleSet(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertibleSet}{RegularTriangularSetCategory}.")) (|toseInvertible?| (((|List| (|Record| (|:| |val| (|Boolean|)) (|:| |tower| |#5|))) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.") (((|Boolean|) |#4| |#5|) "\\axiom{toseInvertible?(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{invertible?}{RegularTriangularSetCategory}.")) (|toseLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{toseLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} has the same specifications as \\axiomOpFrom{lastSubResultant}{RegularTriangularSetCategory}.")) (|integralLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{integralLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|internalLastSubResultant| (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) (|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#3| (|Boolean|)) "\\axiom{internalLastSubResultant(lpwt,{}\\spad{v},{}flag)} is an internal subroutine,{} exported only for developement.") (((|List| (|Record| (|:| |val| |#4|) (|:| |tower| |#5|))) |#4| |#4| |#5| (|Boolean|) (|Boolean|)) "\\axiom{internalLastSubResultant(\\spad{p1},{}\\spad{p2},{}\\spad{ts},{}inv?,{}break?)} is an internal subroutine,{} exported only for developement.")) (|prepareSubResAlgo| (((|List| (|Record| (|:| |val| (|List| |#4|)) (|:| |tower| |#5|))) |#4| |#4| |#5|) "\\axiom{prepareSubResAlgo(\\spad{p1},{}\\spad{p2},{}\\spad{ts})} is an internal subroutine,{} exported only for developement.")) (|stopTableInvSet!| (((|Void|)) "\\axiom{stopTableInvSet!()} is an internal subroutine,{} exported only for developement.")) (|startTableInvSet!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableInvSet!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement.")) (|stopTableGcd!| (((|Void|)) "\\axiom{stopTableGcd!()} is an internal subroutine,{} exported only for developement.")) (|startTableGcd!| (((|Void|) (|String|) (|String|) (|String|)) "\\axiom{startTableGcd!(\\spad{s1},{}\\spad{s2},{}\\spad{s3})} is an internal subroutine,{} exported only for developement."))) @@ -3908,11 +3908,11 @@ NIL ((|constructor| (NIL "This domain implements named rules")) (|name| (((|Symbol|) $) "\\spad{name(x)} returns the symbol"))) NIL NIL -(-995 |Base| R -2315) +(-995 |Base| R -3539) ((|constructor| (NIL "\\indented{1}{Rules for the pattern matcher} Author: Manuel Bronstein Date Created: 24 Oct 1988 Date Last Updated: 26 October 1993 Keywords: pattern,{} matching,{} rule.")) (|quotedOperators| (((|List| (|Symbol|)) $) "\\spad{quotedOperators(r)} returns the list of operators on the right hand side of \\spad{r} that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.")) (|elt| ((|#3| $ |#3| (|PositiveInteger|)) "\\spad{elt(r,{}f,{}n)} or \\spad{r}(\\spad{f},{} \\spad{n}) applies the rule \\spad{r} to \\spad{f} at most \\spad{n} times.")) (|rhs| ((|#3| $) "\\spad{rhs(r)} returns the right hand side of the rule \\spad{r}.")) (|lhs| ((|#3| $) "\\spad{lhs(r)} returns the left hand side of the rule \\spad{r}.")) (|pattern| (((|Pattern| |#1|) $) "\\spad{pattern(r)} returns the pattern corresponding to the left hand side of the rule \\spad{r}.")) (|suchThat| (($ $ (|List| (|Symbol|)) (|Mapping| (|Boolean|) (|List| |#3|))) "\\spad{suchThat(r,{} [a1,{}...,{}an],{} f)} returns the rewrite rule \\spad{r} with the predicate \\spad{f(a1,{}...,{}an)} attached to it.")) (|rule| (($ |#3| |#3| (|List| (|Symbol|))) "\\spad{rule(f,{} g,{} [f1,{}...,{}fn])} creates the rewrite rule \\spad{f == eval(eval(g,{} g is f),{} [f1,{}...,{}fn])},{} that is a rule with left-hand side \\spad{f} and right-hand side \\spad{g}; The symbols \\spad{f1},{}...,{}\\spad{fn} are the operators that are considered quoted,{} that is they are not evaluated during any rewrite,{} but just applied formally to their arguments.") (($ |#3| |#3|) "\\spad{rule(f,{} g)} creates the rewrite rule: \\spad{f == eval(g,{} g is f)},{} with left-hand side \\spad{f} and right-hand side \\spad{g}."))) NIL NIL -(-996 |Base| R -2315) +(-996 |Base| R -3539) ((|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 @@ -3926,8 +3926,8 @@ NIL NIL (-999 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."))) -((-4237 |has| |#1| (-339)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-325)))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339)))) (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339))))) +((-4241 |has| |#1| (-339)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-325))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-325)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-344))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339)))) (|HasCategory| |#1| (QUOTE (-325)))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-12 (|HasCategory| |#1| (QUOTE (-325))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087))))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339)))) (-12 (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (QUOTE (-339))))) (-1000 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 @@ -3950,8 +3950,8 @@ NIL NIL (-1005 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"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1006 (-1087)) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-211))) (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-1006 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 @@ -3970,7 +3970,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-1016)))) (-1010 S) ((|constructor| (NIL "This category provides operations on ranges,{} or {\\em segments} as they are called.")) (|convert| (($ |#1|) "\\spad{convert(i)} creates the segment \\spad{i..i}.")) (|segment| (($ |#1| |#1|) "\\spad{segment(i,{}j)} is an alternate way to create the segment \\spad{i..j}.")) (|incr| (((|Integer|) $) "\\spad{incr(s)} returns \\spad{n},{} where \\spad{s} is a segment in which every \\spad{n}\\spad{-}th element is used. Note: \\spad{incr(l..h by n) = n}.")) (|high| ((|#1| $) "\\spad{high(s)} returns the second endpoint of \\spad{s}. Note: \\spad{high(l..h) = h}.")) (|low| ((|#1| $) "\\spad{low(s)} returns the first endpoint of \\spad{s}. Note: \\spad{low(l..h) = l}.")) (|hi| ((|#1| $) "\\spad{\\spad{hi}(s)} returns the second endpoint of \\spad{s}. Note: \\spad{\\spad{hi}(l..h) = h}.")) (|lo| ((|#1| $) "\\spad{lo(s)} returns the first endpoint of \\spad{s}. Note: \\spad{lo(l..h) = l}.")) (BY (($ $ (|Integer|)) "\\spad{s by n} creates a new segment in which only every \\spad{n}\\spad{-}th element is used.")) (SEGMENT (($ |#1| |#1|) "\\spad{l..h} creates a segment with \\spad{l} and \\spad{h} as the endpoints."))) -((-3656 . T)) +((-4069 . T)) NIL (-1011 S) ((|constructor| (NIL "This type is used to specify a range of values from type \\spad{S}."))) @@ -3978,7 +3978,7 @@ NIL ((|HasCategory| |#1| (QUOTE (-784))) (|HasCategory| |#1| (QUOTE (-1016)))) (-1012 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| $)) "\\spad{expand(l)} creates a new value of type \\spad{L} in which each segment \\spad{l..h by k} is replaced with \\spad{l,{} l+k,{} ... lN},{} where \\spad{lN <= h < lN+k}. For example,{} \\spad{expand [1..4,{} 7..9] = [1,{}2,{}3,{}4,{}7,{}8,{}9]}."))) -((-3656 . T)) +((-4069 . T)) NIL (-1013 A S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#2| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#2|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#2|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#2|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#2|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) @@ -3986,7 +3986,7 @@ NIL NIL (-1014 S) ((|constructor| (NIL "A set category lists a collection of set-theoretic operations useful for both finite sets and multisets. Note however that finite sets are distinct from multisets. Although the operations defined for set categories are common to both,{} the relationship between the two cannot be described by inclusion or inheritance.")) (|union| (($ |#1| $) "\\spad{union(x,{}u)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{x},{}\\spad{u})} returns a copy of \\spad{u}.") (($ $ |#1|) "\\spad{union(u,{}x)} returns the set aggregate \\spad{u} with the element \\spad{x} added. If \\spad{u} already contains \\spad{x},{} \\axiom{union(\\spad{u},{}\\spad{x})} returns a copy of \\spad{u}.") (($ $ $) "\\spad{union(u,{}v)} returns the set aggregate of elements which are members of either set aggregate \\spad{u} or \\spad{v}.")) (|subset?| (((|Boolean|) $ $) "\\spad{subset?(u,{}v)} tests if \\spad{u} is a subset of \\spad{v}. Note: equivalent to \\axiom{reduce(and,{}{member?(\\spad{x},{}\\spad{v}) for \\spad{x} in \\spad{u}},{}\\spad{true},{}\\spad{false})}.")) (|symmetricDifference| (($ $ $) "\\spad{symmetricDifference(u,{}v)} returns the set aggregate of elements \\spad{x} which are members of set aggregate \\spad{u} or set aggregate \\spad{v} but not both. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{symmetricDifference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: \\axiom{symmetricDifference(\\spad{u},{}\\spad{v}) = union(difference(\\spad{u},{}\\spad{v}),{}difference(\\spad{v},{}\\spad{u}))}")) (|difference| (($ $ |#1|) "\\spad{difference(u,{}x)} returns the set aggregate \\spad{u} with element \\spad{x} removed. If \\spad{u} does not contain \\spad{x},{} a copy of \\spad{u} is returned. Note: \\axiom{difference(\\spad{s},{} \\spad{x}) = difference(\\spad{s},{} {\\spad{x}})}.") (($ $ $) "\\spad{difference(u,{}v)} returns the set aggregate \\spad{w} consisting of elements in set aggregate \\spad{u} but not in set aggregate \\spad{v}. If \\spad{u} and \\spad{v} have no elements in common,{} \\axiom{difference(\\spad{u},{}\\spad{v})} returns a copy of \\spad{u}. Note: equivalent to the notation (not currently supported) \\axiom{{\\spad{x} for \\spad{x} in \\spad{u} | not member?(\\spad{x},{}\\spad{v})}}.")) (|intersect| (($ $ $) "\\spad{intersect(u,{}v)} returns the set aggregate \\spad{w} consisting of elements common to both set aggregates \\spad{u} and \\spad{v}. Note: equivalent to the notation (not currently supported) {\\spad{x} for \\spad{x} in \\spad{u} | member?(\\spad{x},{}\\spad{v})}.")) (|set| (($ (|List| |#1|)) "\\spad{set([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}.") (($) "\\spad{set()}\\$\\spad{D} creates an empty set aggregate of type \\spad{D}.")) (|brace| (($ (|List| |#1|)) "\\spad{brace([x,{}y,{}...,{}z])} creates a set aggregate containing items \\spad{x},{}\\spad{y},{}...,{}\\spad{z}. This form is considered obsolete. Use \\axiomFun{set} instead.") (($) "\\spad{brace()}\\$\\spad{D} (otherwise written {}\\$\\spad{D}) creates an empty set aggregate of type \\spad{D}. This form is considered obsolete. Use \\axiomFun{set} instead.")) (< (((|Boolean|) $ $) "\\spad{s < t} returns \\spad{true} if all elements of set aggregate \\spad{s} are also elements of set aggregate \\spad{t}."))) -((-4234 . T) (-3656 . T)) +((-4238 . T) (-4069 . T)) NIL (-1015 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}."))) @@ -4002,8 +4002,8 @@ NIL NIL (-1018 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)}}"))) -((-4244 . T) (-4234 . T) (-4245 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4238 . T) (-4249 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#1| (QUOTE (-344))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1019 |Str| |Sym| |Int| |Flt| |Expr|) ((|constructor| (NIL "This category allows the manipulation of Lisp values while keeping the grunge fairly localized.")) (|elt| (($ $ (|List| (|Integer|))) "\\spad{elt((a1,{}...,{}an),{} [i1,{}...,{}im])} returns \\spad{(a_i1,{}...,{}a_im)}.") (($ $ (|Integer|)) "\\spad{elt((a1,{}...,{}an),{} i)} returns \\spad{\\spad{ai}}.")) (|#| (((|Integer|) $) "\\spad{\\#((a1,{}...,{}an))} returns \\spad{n}.")) (|cdr| (($ $) "\\spad{cdr((a1,{}...,{}an))} returns \\spad{(a2,{}...,{}an)}.")) (|car| (($ $) "\\spad{car((a1,{}...,{}an))} returns a1.")) (|convert| (($ |#5|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#4|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#3|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#2|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ |#1|) "\\spad{convert(x)} returns the Lisp atom \\spad{x}.") (($ (|List| $)) "\\spad{convert([a1,{}...,{}an])} returns the \\spad{S}-expression \\spad{(a1,{}...,{}an)}.")) (|expr| ((|#5| $) "\\spad{expr(s)} returns \\spad{s} as an element of Expr; Error: if \\spad{s} is not an atom that also belongs to Expr.")) (|float| ((|#4| $) "\\spad{float(s)} returns \\spad{s} as an element of \\spad{Flt}; Error: if \\spad{s} is not an atom that also belongs to \\spad{Flt}.")) (|integer| ((|#3| $) "\\spad{integer(s)} returns \\spad{s} as an element of Int. Error: if \\spad{s} is not an atom that also belongs to Int.")) (|symbol| ((|#2| $) "\\spad{symbol(s)} returns \\spad{s} as an element of \\spad{Sym}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Sym}.")) (|string| ((|#1| $) "\\spad{string(s)} returns \\spad{s} as an element of \\spad{Str}. Error: if \\spad{s} is not an atom that also belongs to \\spad{Str}.")) (|destruct| (((|List| $) $) "\\spad{destruct((a1,{}...,{}an))} returns the list [a1,{}...,{}an].")) (|float?| (((|Boolean|) $) "\\spad{float?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Flt}.")) (|integer?| (((|Boolean|) $) "\\spad{integer?(s)} is \\spad{true} if \\spad{s} is an atom and belong to Int.")) (|symbol?| (((|Boolean|) $) "\\spad{symbol?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Sym}.")) (|string?| (((|Boolean|) $) "\\spad{string?(s)} is \\spad{true} if \\spad{s} is an atom and belong to \\spad{Str}.")) (|list?| (((|Boolean|) $) "\\spad{list?(s)} is \\spad{true} if \\spad{s} is a Lisp list,{} possibly ().")) (|pair?| (((|Boolean|) $) "\\spad{pair?(s)} is \\spad{true} if \\spad{s} has is a non-null Lisp list.")) (|atom?| (((|Boolean|) $) "\\spad{atom?(s)} is \\spad{true} if \\spad{s} is a Lisp atom.")) (|null?| (((|Boolean|) $) "\\spad{null?(s)} is \\spad{true} if \\spad{s} is the \\spad{S}-expression ().")) (|eq| (((|Boolean|) $ $) "\\spad{eq(s,{} t)} is \\spad{true} if EQ(\\spad{s},{}\\spad{t}) is \\spad{true} in Lisp."))) NIL @@ -4030,7 +4030,7 @@ NIL NIL (-1025 R E V P) ((|constructor| (NIL "The category of square-free regular triangular sets. A regular triangular set \\spad{ts} is square-free if the \\spad{gcd} of any polynomial \\spad{p} in \\spad{ts} and \\spad{differentiate(p,{}mvar(p))} \\spad{w}.\\spad{r}.\\spad{t}. \\axiomOpFrom{collectUnder}{TriangularSetCategory}(\\spad{ts},{}\\axiomOpFrom{mvar}{RecursivePolynomialCategory}(\\spad{p})) has degree zero \\spad{w}.\\spad{r}.\\spad{t}. \\spad{mvar(p)}. Thus any square-free regular set defines a tower of square-free simple extensions.\\newline References : \\indented{1}{[1] \\spad{D}. LAZARD \"A new method for solving algebraic systems of} \\indented{5}{positive dimension\" Discr. App. Math. 33:147-160,{}1991} \\indented{1}{[2] \\spad{M}. KALKBRENER \"Algorithmic properties of polynomial rings\"} \\indented{5}{Habilitation Thesis,{} ETZH,{} Zurich,{} 1995.} \\indented{1}{[3] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-1026) ((|constructor| (NIL "SymmetricGroupCombinatoricFunctions contains combinatoric functions concerning symmetric groups and representation theory: list young tableaus,{} improper partitions,{} subsets bijection of Coleman.")) (|unrankImproperPartitions1| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions1(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in at most \\spad{m} nonnegative parts ordered as follows: first,{} in reverse lexicographically according to their non-zero parts,{} then according to their positions (\\spadignore{i.e.} lexicographical order using {\\em subSet}: {\\em [3,{}0,{}0] < [0,{}3,{}0] < [0,{}0,{}3] < [2,{}1,{}0] < [2,{}0,{}1] < [0,{}2,{}1] < [1,{}2,{}0] < [1,{}0,{}2] < [0,{}1,{}2] < [1,{}1,{}1]}). Note: counting of subtrees is done by {\\em numberOfImproperPartitionsInternal}.")) (|unrankImproperPartitions0| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{unrankImproperPartitions0(n,{}m,{}k)} computes the {\\em k}\\spad{-}th improper partition of nonnegative \\spad{n} in \\spad{m} nonnegative parts in reverse lexicographical order. Example: {\\em [0,{}0,{}3] < [0,{}1,{}2] < [0,{}2,{}1] < [0,{}3,{}0] < [1,{}0,{}2] < [1,{}1,{}1] < [1,{}2,{}0] < [2,{}0,{}1] < [2,{}1,{}0] < [3,{}0,{}0]}. Error: if \\spad{k} is negative or too big. Note: counting of subtrees is done by \\spadfunFrom{numberOfImproperPartitions}{SymmetricGroupCombinatoricFunctions}.")) (|subSet| (((|List| (|Integer|)) (|Integer|) (|Integer|) (|Integer|)) "\\spad{subSet(n,{}m,{}k)} calculates the {\\em k}\\spad{-}th {\\em m}-subset of the set {\\em 0,{}1,{}...,{}(n-1)} in the lexicographic order considered as a decreasing map from {\\em 0,{}...,{}(m-1)} into {\\em 0,{}...,{}(n-1)}. See \\spad{S}.\\spad{G}. Williamson: Theorem 1.60. Error: if not {\\em (0 <= m <= n and 0 < = k < (n choose m))}.")) (|numberOfImproperPartitions| (((|Integer|) (|Integer|) (|Integer|)) "\\spad{numberOfImproperPartitions(n,{}m)} computes the number of partitions of the nonnegative integer \\spad{n} in \\spad{m} nonnegative parts with regarding the order (improper partitions). Example: {\\em numberOfImproperPartitions (3,{}3)} is 10,{} since {\\em [0,{}0,{}3],{} [0,{}1,{}2],{} [0,{}2,{}1],{} [0,{}3,{}0],{} [1,{}0,{}2],{} [1,{}1,{}1],{} [1,{}2,{}0],{} [2,{}0,{}1],{} [2,{}1,{}0],{} [3,{}0,{}0]} are the possibilities. Note: this operation has a recursive implementation.")) (|nextPartition| (((|Vector| (|Integer|)) (|List| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. the first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.") (((|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Vector| (|Integer|)) (|Integer|)) "\\spad{nextPartition(gamma,{}part,{}number)} generates the partition of {\\em number} which follows {\\em part} according to the right-to-left lexicographical order. The partition has the property that its components do not exceed the corresponding components of {\\em gamma}. The first partition is achieved by {\\em part=[]}. Also,{} {\\em []} indicates that {\\em part} is the last partition.")) (|nextLatticePermutation| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Boolean|)) "\\spad{nextLatticePermutation(lambda,{}lattP,{}constructNotFirst)} generates the lattice permutation according to the proper partition {\\em lambda} succeeding the lattice permutation {\\em lattP} in lexicographical order as long as {\\em constructNotFirst} is \\spad{true}. If {\\em constructNotFirst} is \\spad{false},{} the first lattice permutation is returned. The result {\\em nil} indicates that {\\em lattP} has no successor.")) (|nextColeman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{nextColeman(alpha,{}beta,{}C)} generates the next Coleman matrix of column sums {\\em alpha} and row sums {\\em beta} according to the lexicographical order from bottom-to-top. The first Coleman matrix is achieved by {\\em C=new(1,{}1,{}0)}. Also,{} {\\em new(1,{}1,{}0)} indicates that \\spad{C} is the last Coleman matrix.")) (|makeYoungTableau| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{makeYoungTableau(lambda,{}gitter)} computes for a given lattice permutation {\\em gitter} and for an improper partition {\\em lambda} the corresponding standard tableau of shape {\\em lambda}. Notes: see {\\em listYoungTableaus}. The entries are from {\\em 0,{}...,{}n-1}.")) (|listYoungTableaus| (((|List| (|Matrix| (|Integer|))) (|List| (|Integer|))) "\\spad{listYoungTableaus(lambda)} where {\\em lambda} is a proper partition generates the list of all standard tableaus of shape {\\em lambda} by means of lattice permutations. The numbers of the lattice permutation are interpreted as column labels. Hence the contents of these lattice permutations are the conjugate of {\\em lambda}. Notes: the functions {\\em nextLatticePermutation} and {\\em makeYoungTableau} are used. The entries are from {\\em 0,{}...,{}n-1}.")) (|inverseColeman| (((|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|Matrix| (|Integer|))) "\\spad{inverseColeman(alpha,{}beta,{}C)}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For such a matrix \\spad{C},{} inverseColeman(\\spad{alpha},{}\\spad{beta},{}\\spad{C}) calculates the lexicographical smallest {\\em \\spad{pi}} in the corresponding double coset. Note: the resulting permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} is given in list form. Notes: the inverse of this map is {\\em coleman}. For details,{} see James/Kerber.")) (|coleman| (((|Matrix| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|)) (|List| (|Integer|))) "\\spad{coleman(alpha,{}beta,{}\\spad{pi})}: there is a bijection from the set of matrices having nonnegative entries and row sums {\\em alpha},{} column sums {\\em beta} to the set of {\\em Salpha - Sbeta} double cosets of the symmetric group {\\em Sn}. ({\\em Salpha} is the Young subgroup corresponding to the improper partition {\\em alpha}). For a representing element {\\em \\spad{pi}} of such a double coset,{} coleman(\\spad{alpha},{}\\spad{beta},{}\\spad{pi}) generates the Coleman-matrix corresponding to {\\em alpha,{} beta,{} \\spad{pi}}. Note: The permutation {\\em \\spad{pi}} of {\\em {1,{}2,{}...,{}n}} has to be given in list form. Note: the inverse of this map is {\\em inverseColeman} (if {\\em \\spad{pi}} is the lexicographical smallest permutation in the coset). For details see James/Kerber."))) @@ -4046,13 +4046,13 @@ NIL NIL (-1029 |dimtot| |dim1| S) ((|constructor| (NIL "\\indented{2}{This type represents the finite direct or cartesian product of an} underlying ordered component type. The vectors are ordered as if they were split into two blocks. The dim1 parameter specifies the length of the first block. The ordering is lexicographic between the blocks but acts like \\spadtype{HomogeneousDirectProduct} within each block. This type is a suitable third argument for \\spadtype{GeneralDistributedMultivariatePolynomial}."))) -((-4238 |has| |#3| (-973)) (-4239 |has| |#3| (-973)) (-4241 |has| |#3| (-6 -4241)) ((-4246 "*") |has| |#3| (-158)) (-4244 . 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(-523)))))) (|HasCategory| (-523) (QUOTE (-786))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#3| (QUOTE (-211))) (|HasCategory| |#3| (QUOTE (-973)))) (-12 (|HasCategory| |#3| (QUOTE (-973))) (|HasCategory| |#3| (LIST (QUOTE -831) (QUOTE (-1087))))) (|HasCategory| |#3| (QUOTE (-666))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523))))) (-3172 (|HasCategory| |#3| (QUOTE (-973))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -964) (QUOTE (-523)))))) (-12 (|HasCategory| |#3| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#3| (QUOTE (-1016)))) (|HasAttribute| |#3| (QUOTE -4245)) (|HasCategory| |#3| (QUOTE (-124))) (|HasCategory| |#3| (QUOTE (-25))) (-12 (|HasCategory| |#3| (QUOTE (-1016))) (|HasCategory| |#3| (LIST (QUOTE -286) (|devaluate| |#3|)))) (|HasCategory| |#3| (LIST (QUOTE -563) (QUOTE (-794))))) (-1030 R |x|) ((|constructor| (NIL "This package produces functions for counting etc. real roots of univariate polynomials in \\spad{x} over \\spad{R},{} which must be an OrderedIntegralDomain")) (|countRealRootsMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRootsMultiple(p)} says how many real roots \\spad{p} has,{} counted with multiplicity")) (|SturmHabichtMultiple| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtMultiple(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|countRealRoots| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{countRealRoots(p)} says how many real roots \\spad{p} has")) (|SturmHabicht| (((|Integer|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabicht(p1,{}p2)} computes \\spad{c_}{+}\\spad{-c_}{-} where \\spad{c_}{+} is the number of real roots of \\spad{p1} with p2>0 and \\spad{c_}{-} is the number of real roots of \\spad{p1} with p2<0. If p2=1 what you get is the number of real roots of \\spad{p1}.")) (|SturmHabichtCoefficients| (((|List| |#1|) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtCoefficients(p1,{}p2)} computes the principal Sturm-Habicht coefficients of \\spad{p1} and \\spad{p2}")) (|SturmHabichtSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{SturmHabichtSequence(p1,{}p2)} computes the Sturm-Habicht sequence of \\spad{p1} and \\spad{p2}")) (|subresultantSequence| (((|List| (|UnivariatePolynomial| |#2| |#1|)) (|UnivariatePolynomial| |#2| |#1|) (|UnivariatePolynomial| |#2| |#1|)) "\\spad{subresultantSequence(p1,{}p2)} computes the (standard) subresultant sequence of \\spad{p1} and \\spad{p2}"))) NIL ((|HasCategory| |#1| (QUOTE (-427)))) -(-1031 R -2315) +(-1031 R -3539) ((|constructor| (NIL "This package provides functions to determine the sign of an elementary function around a point or infinity.")) (|sign| (((|Union| (|Integer|) "failed") |#2| (|Symbol|) |#2| (|String|)) "\\spad{sign(f,{} x,{} a,{} s)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a} from below if \\spad{s} is \"left\",{} or above if \\spad{s} is \"right\".") (((|Union| (|Integer|) "failed") |#2| (|Symbol|) (|OrderedCompletion| |#2|)) "\\spad{sign(f,{} x,{} a)} returns the sign of \\spad{f} as \\spad{x} nears \\spad{a},{} from both sides if \\spad{a} is finite.") (((|Union| (|Integer|) "failed") |#2|) "\\spad{sign(f)} returns the sign of \\spad{f} if it is constant everywhere."))) NIL NIL @@ -4066,19 +4066,19 @@ NIL NIL (-1034) ((|constructor| (NIL "SingleInteger is intended to support machine integer arithmetic.")) (|Or| (($ $ $) "\\spad{Or(n,{}m)} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|And| (($ $ $) "\\spad{And(n,{}m)} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (|Not| (($ $) "\\spad{Not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|xor| (($ $ $) "\\spad{xor(n,{}m)} returns the bit-by-bit logical {\\em xor} of the single integers \\spad{n} and \\spad{m}.")) (|\\/| (($ $ $) "\\spad{n} \\spad{\\/} \\spad{m} returns the bit-by-bit logical {\\em or} of the single integers \\spad{n} and \\spad{m}.")) (|/\\| (($ $ $) "\\spad{n} \\spad{/\\} \\spad{m} returns the bit-by-bit logical {\\em and} of the single integers \\spad{n} and \\spad{m}.")) (~ (($ $) "\\spad{~ n} returns the bit-by-bit logical {\\em not } of the single integer \\spad{n}.")) (|not| (($ $) "\\spad{not(n)} returns the bit-by-bit logical {\\em not} of the single integer \\spad{n}.")) (|min| (($) "\\spad{min()} returns the smallest single integer.")) (|max| (($) "\\spad{max()} returns the largest single integer.")) (|noetherian| ((|attribute|) "\\spad{noetherian} all ideals are finitely generated (in fact principal).")) (|canonicalsClosed| ((|attribute|) "\\spad{canonicalClosed} means two positives multiply to give positive.")) (|canonical| ((|attribute|) "\\spad{canonical} means that mathematical equality is implied by data structure equality."))) -((-4232 . T) (-4236 . T) (-4231 . T) (-4242 . T) (-4243 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4236 . T) (-4240 . T) (-4235 . T) (-4246 . T) (-4247 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-1035 S) ((|constructor| (NIL "A stack is a bag where the last item inserted is the first item extracted.")) (|depth| (((|NonNegativeInteger|) $) "\\spad{depth(s)} returns the number of elements of stack \\spad{s}. Note: \\axiom{depth(\\spad{s}) = \\spad{#s}}.")) (|top| ((|#1| $) "\\spad{top(s)} returns the top element \\spad{x} from \\spad{s}; \\spad{s} remains unchanged. Note: Use \\axiom{pop!(\\spad{s})} to obtain \\spad{x} and remove it from \\spad{s}.")) (|pop!| ((|#1| $) "\\spad{pop!(s)} returns the top element \\spad{x},{} destructively removing \\spad{x} from \\spad{s}. Note: Use \\axiom{top(\\spad{s})} to obtain \\spad{x} without removing it from \\spad{s}. Error: if \\spad{s} is empty.")) (|push!| ((|#1| |#1| $) "\\spad{push!(x,{}s)} pushes \\spad{x} onto stack \\spad{s},{} \\spadignore{i.e.} destructively changing \\spad{s} so as to have a new first (top) element \\spad{x}. Afterwards,{} pop!(\\spad{s}) produces \\spad{x} and pop!(\\spad{s}) produces the original \\spad{s}."))) -((-4244 . T) (-4245 . T) (-3656 . T)) +((-4248 . T) (-4249 . T) (-4069 . T)) NIL (-1036 S |ndim| R |Row| |Col|) ((|constructor| (NIL "\\spadtype{SquareMatrixCategory} is a general square matrix category which allows different representations and indexing schemes. Rows and columns may be extracted with rows returned as objects of type Row and colums returned as objects of type Col.")) (** (($ $ (|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}\\spad{'s} on the diagonal and zeroes elsewhere."))) NIL -((|HasCategory| |#3| (QUOTE (-339))) (|HasAttribute| |#3| (QUOTE (-4246 "*"))) (|HasCategory| |#3| (QUOTE (-158)))) +((|HasCategory| |#3| (QUOTE (-339))) (|HasAttribute| |#3| (QUOTE (-4250 "*"))) (|HasCategory| |#3| (QUOTE (-158)))) (-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}\\spad{'s} on the diagonal and zeroes elsewhere."))) -((-3656 . T) (-4244 . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4069 . T) (-4248 . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL (-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}."))) @@ -4086,17 +4086,17 @@ NIL NIL (-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."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-840))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-840))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (|HasCategory| |#1| (QUOTE (-427))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246)) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-840)))) (|HasCategory| |#1| (QUOTE (-134))))) (-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 \\spad{SMP}. The \\spad{n}th element of the stream is a form of degree \\spad{n}. SMTS is an internal domain.")) (|fintegrate| (($ (|Mapping| $) |#2| |#1|) "\\spad{fintegrate(f,{}v,{}c)} is the integral of \\spad{f()} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.} \\indented{1}{The evaluation of \\spad{f()} is delayed.}")) (|integrate| (($ $ |#2| |#1|) "\\spad{integrate(s,{}v,{}c)} is the integral of \\spad{s} with respect \\indented{1}{to \\spad{v} and having \\spad{c} as the constant of integration.}")) (|csubst| (((|Mapping| (|Stream| |#3|) |#3|) (|List| |#2|) (|List| (|Stream| |#3|))) "\\spad{csubst(a,{}b)} is for internal use only")) (* (($ |#3| $) "\\spad{smp*ts} multiplies a TaylorSeries by a monomial \\spad{SMP}.")) (|coerce| (($ |#3|) "\\spad{coerce(poly)} regroups the terms by total degree and forms a series.") (($ |#2|) "\\spad{coerce(var)} converts a variable to a Taylor series")) (|coefficient| ((|#3| $ (|NonNegativeInteger|)) "\\spad{coefficient(s,{} n)} gives the terms of total degree \\spad{n}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) (-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}"))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL -(-1042 UP -2315) +(-1042 UP -3539) ((|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 @@ -4142,19 +4142,19 @@ NIL NIL (-1053 V C) ((|constructor| (NIL "This domain exports a modest implementation of splitting trees. Spliiting trees are needed when the evaluation of some quantity under some hypothesis requires to split the hypothesis into sub-cases. For instance by adding some new hypothesis on one hand and its negation on another hand. The computations are terminated is a splitting tree \\axiom{a} when \\axiom{status(value(a))} is \\axiom{\\spad{true}}. Thus,{} if for the splitting tree \\axiom{a} the flag \\axiom{status(value(a))} is \\axiom{\\spad{true}},{} then \\axiom{status(value(\\spad{d}))} is \\axiom{\\spad{true}} for any subtree \\axiom{\\spad{d}} of \\axiom{a}. This property of splitting trees is called the termination condition. If no vertex in a splitting tree \\axiom{a} is equal to another,{} \\axiom{a} is said to satisfy the no-duplicates condition. The splitting tree \\axiom{a} will satisfy this condition if nodes are added to \\axiom{a} by mean of \\axiom{splitNodeOf!} and if \\axiom{construct} is only used to create the root of \\axiom{a} with no children.")) (|splitNodeOf!| (($ $ $ (|List| (|SplittingNode| |#1| |#2|)) (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls},{}sub?)} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not subNodeOf?(\\spad{s},{}a,{}sub?)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.") (($ $ $ (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{splitNodeOf!(\\spad{l},{}a,{}\\spad{ls})} returns \\axiom{a} where the children list of \\axiom{\\spad{l}} has been set to \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls} | not nodeOf?(\\spad{s},{}a)]}. Thus,{} if \\axiom{\\spad{l}} is not a node of \\axiom{a},{} this latter splitting tree is unchanged.")) (|remove!| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove!(\\spad{s},{}a)} replaces a by remove(\\spad{s},{}a)")) (|remove| (($ (|SplittingNode| |#1| |#2|) $) "\\axiom{remove(\\spad{s},{}a)} returns the splitting tree obtained from a by removing every sub-tree \\axiom{\\spad{b}} such that \\axiom{value(\\spad{b})} and \\axiom{\\spad{s}} have the same value,{} condition and status.")) (|subNodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $ (|Mapping| (|Boolean|) |#2| |#2|)) "\\axiom{subNodeOf?(\\spad{s},{}a,{}sub?)} returns \\spad{true} iff for some node \\axiom{\\spad{n}} in \\axiom{a} we have \\axiom{\\spad{s} = \\spad{n}} or \\axiom{status(\\spad{n})} and \\axiom{subNode?(\\spad{s},{}\\spad{n},{}sub?)}.")) (|nodeOf?| (((|Boolean|) (|SplittingNode| |#1| |#2|) $) "\\axiom{nodeOf?(\\spad{s},{}a)} returns \\spad{true} iff some node of \\axiom{a} is equal to \\axiom{\\spad{s}}")) (|result| (((|List| (|Record| (|:| |val| |#1|) (|:| |tower| |#2|))) $) "\\axiom{result(a)} where \\axiom{\\spad{ls}} is the leaves list of \\axiom{a} returns \\axiom{[[value(\\spad{s}),{}condition(\\spad{s})]\\$\\spad{VT} for \\spad{s} in \\spad{ls}]} if the computations are terminated in \\axiom{a} else an error is produced.")) (|conditions| (((|List| |#2|) $) "\\axiom{conditions(a)} returns the list of the conditions of the leaves of a")) (|construct| (($ |#1| |#2| |#1| (|List| |#2|)) "\\axiom{construct(\\spad{v1},{}\\spad{t},{}\\spad{v2},{}\\spad{lt})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[[\\spad{v},{}\\spad{t}]\\$\\spad{S}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| (|SplittingNode| |#1| |#2|))) "\\axiom{construct(\\spad{v},{}\\spad{t},{}\\spad{ls})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with children list given by \\axiom{[[\\spad{s}]\\$\\% for \\spad{s} in \\spad{ls}]}.") (($ |#1| |#2| (|List| $)) "\\axiom{construct(\\spad{v},{}\\spad{t},{}la)} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{[\\spad{v},{}\\spad{t}]\\$\\spad{S}} and with \\axiom{la} as children list.") (($ (|SplittingNode| |#1| |#2|)) "\\axiom{construct(\\spad{s})} creates a splitting tree with value (\\spadignore{i.e.} root vertex) given by \\axiom{\\spad{s}} and no children. Thus,{} if the status of \\axiom{\\spad{s}} is \\spad{false},{} \\axiom{[\\spad{s}]} represents the starting point of the evaluation \\axiom{value(\\spad{s})} under the hypothesis \\axiom{condition(\\spad{s})}.")) (|updateStatus!| (($ $) "\\axiom{updateStatus!(a)} returns a where the status of the vertices are updated to satisfy the \"termination condition\".")) (|extractSplittingLeaf| (((|Union| $ "failed") $) "\\axiom{extractSplittingLeaf(a)} returns the left most leaf (as a tree) whose status is \\spad{false} if any,{} else \"failed\" is returned."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))) (-3262 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))))) (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))) (-3172 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794)))) (-12 (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -286) (LIST (QUOTE -1052) (|devaluate| |#1|) (|devaluate| |#2|)))) (|HasCategory| (-1052 |#1| |#2|) (QUOTE (-1016))))) (|HasCategory| (-1052 |#1| |#2|) (LIST (QUOTE -563) (QUOTE (-794))))) (-1054 |ndim| R) ((|constructor| (NIL "\\spadtype{SquareMatrix} is a matrix domain of square matrices,{} where the number of rows (= number of columns) is a parameter of the type.")) (|unitsKnown| ((|attribute|) "the invertible matrices are simply the matrices whose determinants are units in the Ring \\spad{R}.")) (|central| ((|attribute|) "the elements of the Ring \\spad{R},{} viewed as diagonal matrices,{} commute with all matrices and,{} indeed,{} are the only matrices which commute with all matrices.")) (|coerce| (((|Matrix| |#2|) $) "\\spad{coerce(m)} converts a matrix of type \\spadtype{SquareMatrix} to a matrix of type \\spadtype{Matrix}.")) (|squareMatrix| (($ (|Matrix| |#2|)) "\\spad{squareMatrix(m)} converts a matrix of type \\spadtype{Matrix} to a matrix of type \\spadtype{SquareMatrix}.")) (|transpose| (($ $) "\\spad{transpose(m)} returns the transpose of the matrix \\spad{m}."))) -((-4241 . T) (-4233 |has| |#2| (-6 (-4246 "*"))) (-4244 . T) (-4238 . T) (-4239 . T)) -((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4246 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3262 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (-3262 (|HasAttribute| |#2| (QUOTE (-4246 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) +((-4245 . T) (-4237 |has| |#2| (-6 (-4250 "*"))) (-4248 . T) (-4242 . T) (-4243 . T)) +((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (-3172 (-12 (|HasCategory| |#2| (QUOTE (-211))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523))))) (-12 (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (QUOTE (-284))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-339))) (-3172 (|HasAttribute| |#2| (QUOTE (-4250 "*"))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasCategory| |#2| (QUOTE (-211)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-158)))) (-1055 S) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) NIL NIL (-1056) ((|constructor| (NIL "A string aggregate is a category for strings,{} that is,{} one dimensional arrays of characters.")) (|elt| (($ $ $) "\\spad{elt(s,{}t)} returns the concatenation of \\spad{s} and \\spad{t}. It is provided to allow juxtaposition of strings to work as concatenation. For example,{} \\axiom{\"smoo\" \"shed\"} returns \\axiom{\"smooshed\"}.")) (|rightTrim| (($ $ (|CharacterClass|)) "\\spad{rightTrim(s,{}cc)} returns \\spad{s} with all trailing occurences of characters in \\spad{cc} deleted. For example,{} \\axiom{rightTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"(abc\"}.") (($ $ (|Character|)) "\\spad{rightTrim(s,{}c)} returns \\spad{s} with all trailing occurrences of \\spad{c} deleted. For example,{} \\axiom{rightTrim(\" abc \",{} char \" \")} returns \\axiom{\" abc\"}.")) (|leftTrim| (($ $ (|CharacterClass|)) "\\spad{leftTrim(s,{}cc)} returns \\spad{s} with all leading characters in \\spad{cc} deleted. For example,{} \\axiom{leftTrim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc)\"}.") (($ $ (|Character|)) "\\spad{leftTrim(s,{}c)} returns \\spad{s} with all leading characters \\spad{c} deleted. For example,{} \\axiom{leftTrim(\" abc \",{} char \" \")} returns \\axiom{\"abc \"}.")) (|trim| (($ $ (|CharacterClass|)) "\\spad{trim(s,{}cc)} returns \\spad{s} with all characters in \\spad{cc} deleted from right and left ends. For example,{} \\axiom{trim(\"(abc)\",{} charClass \"()\")} returns \\axiom{\"abc\"}.") (($ $ (|Character|)) "\\spad{trim(s,{}c)} returns \\spad{s} with all characters \\spad{c} deleted from right and left ends. For example,{} \\axiom{trim(\" abc \",{} char \" \")} returns \\axiom{\"abc\"}.")) (|split| (((|List| $) $ (|CharacterClass|)) "\\spad{split(s,{}cc)} returns a list of substrings delimited by characters in \\spad{cc}.") (((|List| $) $ (|Character|)) "\\spad{split(s,{}c)} returns a list of substrings delimited by character \\spad{c}.")) (|coerce| (($ (|Character|)) "\\spad{coerce(c)} returns \\spad{c} as a string \\spad{s} with the character \\spad{c}.")) (|position| (((|Integer|) (|CharacterClass|) $ (|Integer|)) "\\spad{position(cc,{}t,{}i)} returns the position \\axiom{\\spad{j} \\spad{>=} \\spad{i}} in \\spad{t} of the first character belonging to \\spad{cc}.") (((|Integer|) $ $ (|Integer|)) "\\spad{position(s,{}t,{}i)} returns the position \\spad{j} of the substring \\spad{s} in string \\spad{t},{} where \\axiom{\\spad{j} \\spad{>=} \\spad{i}} is required.")) (|replace| (($ $ (|UniversalSegment| (|Integer|)) $) "\\spad{replace(s,{}i..j,{}t)} replaces the substring \\axiom{\\spad{s}(\\spad{i}..\\spad{j})} of \\spad{s} by string \\spad{t}.")) (|match?| (((|Boolean|) $ $ (|Character|)) "\\spad{match?(s,{}t,{}c)} tests if \\spad{s} matches \\spad{t} except perhaps for multiple and consecutive occurrences of character \\spad{c}. Typically \\spad{c} is the blank character.")) (|match| (((|NonNegativeInteger|) $ $ (|Character|)) "\\spad{match(p,{}s,{}wc)} tests if pattern \\axiom{\\spad{p}} matches subject \\axiom{\\spad{s}} where \\axiom{\\spad{wc}} is a wild card character. If no match occurs,{} the index \\axiom{0} is returned; otheriwse,{} the value returned is the first index of the first character in the subject matching the subject (excluding that matched by an initial wild-card). For example,{} \\axiom{match(\"*to*\",{}\"yorktown\",{}\\spad{\"*\"})} returns \\axiom{5} indicating a successful match starting at index \\axiom{5} of \\axiom{\"yorktown\"}.")) (|substring?| (((|Boolean|) $ $ (|Integer|)) "\\spad{substring?(s,{}t,{}i)} tests if \\spad{s} is a substring of \\spad{t} beginning at index \\spad{i}. Note: \\axiom{substring?(\\spad{s},{}\\spad{t},{}0) = prefix?(\\spad{s},{}\\spad{t})}.")) (|suffix?| (((|Boolean|) $ $) "\\spad{suffix?(s,{}t)} tests if the string \\spad{s} is the final substring of \\spad{t}. Note: \\axiom{suffix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.(\\spad{n} - \\spad{m} + \\spad{i}) for \\spad{i} in 0..maxIndex \\spad{s}])} where \\spad{m} and \\spad{n} denote the maxIndex of \\spad{s} and \\spad{t} respectively.")) (|prefix?| (((|Boolean|) $ $) "\\spad{prefix?(s,{}t)} tests if the string \\spad{s} is the initial substring of \\spad{t}. Note: \\axiom{prefix?(\\spad{s},{}\\spad{t}) \\spad{==} reduce(and,{}[\\spad{s}.\\spad{i} = \\spad{t}.\\spad{i} for \\spad{i} in 0..maxIndex \\spad{s}])}.")) (|upperCase!| (($ $) "\\spad{upperCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by upper case characters.")) (|upperCase| (($ $) "\\spad{upperCase(s)} returns the string with all characters in upper case.")) (|lowerCase!| (($ $) "\\spad{lowerCase!(s)} destructively replaces the alphabetic characters in \\spad{s} by lower case.")) (|lowerCase| (($ $) "\\spad{lowerCase(s)} returns the string with all characters in lower case."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-1057 R E V P TS) ((|constructor| (NIL "A package providing a new algorithm for solving polynomial systems by means of regular chains. Two ways of solving are provided: in the sense of Zariski closure (like in Kalkbrener\\spad{'s} algorithm) or in the sense of the regular zeros (like in Wu,{} Wang or Lazard- Moreno methods). This algorithm is valid for nay type of regular set. It does not care about the way a polynomial is added in an regular set,{} or how two quasi-components are compared (by an inclusion-test),{} or how the invertibility test is made in the tower of simple extensions associated with a regular set. These operations are realized respectively by the domain \\spad{TS} and the packages \\spad{QCMPPK(R,{}E,{}V,{}P,{}TS)} and \\spad{RSETGCD(R,{}E,{}V,{}P,{}TS)}. The same way it does not care about the way univariate polynomial gcds (with coefficients in the tower of simple extensions associated with a regular set) are computed. The only requirement is that these gcds need to have invertible initials (normalized or not). WARNING. There is no need for a user to call diectly any operation of this package since they can be accessed by the domain \\axiomType{\\spad{TS}}. Thus,{} the operations of this package are not documented.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.}"))) @@ -4162,24 +4162,24 @@ NIL NIL (-1058 R E V P) ((|constructor| (NIL "This domain provides an implementation of square-free regular chains. Moreover,{} the operation \\axiomOpFrom{zeroSetSplit}{SquareFreeRegularTriangularSetCategory} is an implementation of a new algorithm for solving polynomial systems by means of regular chains.\\newline References : \\indented{1}{[1] \\spad{M}. MORENO MAZA \"A new algorithm for computing triangular} \\indented{5}{decomposition of algebraic varieties\" NAG Tech. Rep. 4/98.} \\indented{2}{Version: 2}")) (|preprocess| (((|Record| (|:| |val| (|List| |#4|)) (|:| |towers| (|List| $))) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{pre_process(\\spad{lp},{}\\spad{b1},{}\\spad{b2})} is an internal subroutine,{} exported only for developement.")) (|internalZeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalZeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3})} is an internal subroutine,{} exported only for developement.")) (|zeroSetSplit| (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}\\spad{b1},{}\\spad{b2}.\\spad{b3},{}\\spad{b4})} is an internal subroutine,{} exported only for developement.") (((|List| $) (|List| |#4|) (|Boolean|) (|Boolean|)) "\\axiom{zeroSetSplit(\\spad{lp},{}clos?,{}info?)} has the same specifications as \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory} from \\spadtype{RegularTriangularSetCategory} Moreover,{} if \\axiom{clos?} then solves in the sense of the Zariski closure else solves in the sense of the regular zeros. If \\axiom{info?} then do print messages during the computations.")) (|internalAugment| (((|List| $) |#4| $ (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|) (|Boolean|)) "\\axiom{internalAugment(\\spad{p},{}\\spad{ts},{}\\spad{b1},{}\\spad{b2},{}\\spad{b3},{}\\spad{b4},{}\\spad{b5})} is an internal subroutine,{} exported only for developement."))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#4| (LIST (QUOTE -286) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#4| (LIST (QUOTE -563) (QUOTE (-794))))) (-1059 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}."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1060 A S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) NIL NIL (-1061 S) ((|constructor| (NIL "A stream aggregate is a linear aggregate which possibly has an infinite number of elements. A basic domain constructor which builds stream aggregates is \\spadtype{Stream}. From streams,{} a number of infinite structures such power series can be built. A stream aggregate may also be infinite since it may be cyclic. For example,{} see \\spadtype{DecimalExpansion}.")) (|possiblyInfinite?| (((|Boolean|) $) "\\spad{possiblyInfinite?(s)} tests if the stream \\spad{s} could possibly have an infinite number of elements. Note: for many datatypes,{} \\axiom{possiblyInfinite?(\\spad{s}) = not explictlyFinite?(\\spad{s})}.")) (|explicitlyFinite?| (((|Boolean|) $) "\\spad{explicitlyFinite?(s)} tests if the stream has a finite number of elements,{} and \\spad{false} otherwise. Note: for many datatypes,{} \\axiom{explicitlyFinite?(\\spad{s}) = not possiblyInfinite?(\\spad{s})}."))) -((-3656 . T)) +((-4069 . T)) NIL (-1062 |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."))) -((-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| |#1| (QUOTE (-786))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-1063) ((|constructor| (NIL "A class of objects which can be 'stepped through'. Repeated applications of \\spadfun{nextItem} is guaranteed never to return duplicate items and only return \"failed\" after exhausting all elements of the domain. This assumes that the sequence starts with \\spad{init()}. For infinite domains,{} repeated application of \\spadfun{nextItem} is not required to reach all possible domain elements starting from any initial element. \\blankline Conditional attributes: \\indented{2}{infinite\\tab{15}repeated \\spad{nextItem}\\spad{'s} are never \"failed\".}")) (|nextItem| (((|Union| $ "failed") $) "\\spad{nextItem(x)} returns the next item,{} or \"failed\" if domain is exhausted.")) (|init| (($) "\\spad{init()} chooses an initial object for stepping."))) NIL @@ -4202,20 +4202,20 @@ NIL NIL (-1068 S) ((|constructor| (NIL "A stream is an implementation of an infinite sequence using a list of terms that have been computed and a function closure to compute additional terms when needed.")) (|filterUntil| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterUntil(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = true}.")) (|filterWhile| (($ (|Mapping| (|Boolean|) |#1|) $) "\\spad{filterWhile(p,{}s)} returns \\spad{[x0,{}x1,{}...,{}x(n-1)]} where \\spad{s = [x0,{}x1,{}x2,{}..]} and \\spad{n} is the smallest index such that \\spad{p(xn) = false}.")) (|generate| (($ (|Mapping| |#1| |#1|) |#1|) "\\spad{generate(f,{}x)} creates an infinite stream whose first element is \\spad{x} and whose \\spad{n}th element (\\spad{n > 1}) is \\spad{f} applied to the previous element. Note: \\spad{generate(f,{}x) = [x,{}f(x),{}f(f(x)),{}...]}.") (($ (|Mapping| |#1|)) "\\spad{generate(f)} creates an infinite stream all of whose elements are equal to \\spad{f()}. Note: \\spad{generate(f) = [f(),{}f(),{}f(),{}...]}.")) (|setrest!| (($ $ (|Integer|) $) "\\spad{setrest!(x,{}n,{}y)} sets rest(\\spad{x},{}\\spad{n}) to \\spad{y}. The function will expand cycles if necessary.")) (|showAll?| (((|Boolean|)) "\\spad{showAll?()} returns \\spad{true} if all computed entries of streams will be displayed.")) (|showAllElements| (((|OutputForm|) $) "\\spad{showAllElements(s)} creates an output form which displays all computed elements.")) (|output| (((|Void|) (|Integer|) $) "\\spad{output(n,{}st)} computes and displays the first \\spad{n} entries of \\spad{st}.")) (|cons| (($ |#1| $) "\\spad{cons(a,{}s)} returns a stream whose \\spad{first} is \\spad{a} and whose \\spad{rest} is \\spad{s}. Note: \\spad{cons(a,{}s) = concat(a,{}s)}.")) (|delay| (($ (|Mapping| $)) "\\spad{delay(f)} creates a stream with a lazy evaluation defined by function \\spad{f}. Caution: This function can only be called in compiled code.")) (|findCycle| (((|Record| (|:| |cycle?| (|Boolean|)) (|:| |prefix| (|NonNegativeInteger|)) (|:| |period| (|NonNegativeInteger|))) (|NonNegativeInteger|) $) "\\spad{findCycle(n,{}st)} determines if \\spad{st} is periodic within \\spad{n}.")) (|repeating?| (((|Boolean|) (|List| |#1|) $) "\\spad{repeating?(l,{}s)} returns \\spad{true} if a stream \\spad{s} is periodic with period \\spad{l},{} and \\spad{false} otherwise.")) (|repeating| (($ (|List| |#1|)) "\\spad{repeating(l)} is a repeating stream whose period is the list \\spad{l}.")) (|coerce| (($ (|List| |#1|)) "\\spad{coerce(l)} converts a list \\spad{l} to a stream.")) (|shallowlyMutable| ((|attribute|) "one may destructively alter a stream by assigning new values to its entries."))) -((-4245 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1069) ((|constructor| (NIL "A category for string-like objects")) (|string| (($ (|Integer|)) "\\spad{string(i)} returns the decimal representation of \\spad{i} in a string"))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL (-1070) NIL -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133)))))) (|HasCategory| (-133) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| (-133) (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| (-133) (QUOTE (-1016))) (-12 (|HasCategory| (-133) (QUOTE (-1016))) (|HasCategory| (-133) (LIST (QUOTE -286) (QUOTE (-133))))) (|HasCategory| (-133) (LIST (QUOTE -563) (QUOTE (-794))))) (-1071 |Entry|) ((|constructor| (NIL "This domain provides tables where the keys are strings. A specialized hash function for strings is used."))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#1|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (QUOTE (-1070))) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#1|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (QUOTE (-1016))) (|HasCategory| (-1070) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (LIST (QUOTE -563) (QUOTE (-794))))) (-1072 A) ((|constructor| (NIL "StreamTaylorSeriesOperations implements Taylor series arithmetic,{} where a Taylor series is represented by a stream of its coefficients.")) (|power| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{power(a,{}f)} returns the power series \\spad{f} raised to the power \\spad{a}.")) (|lazyGintegrate| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyGintegrate(f,{}r,{}g)} is used for fixed point computations.")) (|mapdiv| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapdiv([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0/b0,{}a1/b1,{}..]}.")) (|powern| (((|Stream| |#1|) (|Fraction| (|Integer|)) (|Stream| |#1|)) "\\spad{powern(r,{}f)} raises power series \\spad{f} to the power \\spad{r}.")) (|nlde| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{nlde(u)} solves a first order non-linear differential equation described by \\spad{u} of the form \\spad{[[b<0,{}0>,{}b<0,{}1>,{}...],{}[b<1,{}0>,{}b<1,{}1>,{}.],{}...]}. the differential equation has the form \\spad{y' = sum(i=0 to infinity,{}j=0 to infinity,{}b<i,{}j>*(x**i)*(y**j))}.")) (|lazyIntegrate| (((|Stream| |#1|) |#1| (|Mapping| (|Stream| |#1|))) "\\spad{lazyIntegrate(r,{}f)} is a local function used for fixed point computations.")) (|integrate| (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{integrate(r,{}a)} returns the integral of the power series \\spad{a} with respect to the power series variableintegration where \\spad{r} denotes the constant of integration. Thus \\spad{integrate(a,{}[a0,{}a1,{}a2,{}...]) = [a,{}a0,{}a1/2,{}a2/3,{}...]}.")) (|invmultisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{invmultisect(a,{}b,{}st)} substitutes \\spad{x**((a+b)*n)} for \\spad{x**n} and multiplies by \\spad{x**b}.")) (|multisect| (((|Stream| |#1|) (|Integer|) (|Integer|) (|Stream| |#1|)) "\\spad{multisect(a,{}b,{}st)} selects the coefficients of \\spad{x**((a+b)*n+a)},{} and changes them to \\spad{x**n}.")) (|generalLambert| (((|Stream| |#1|) (|Stream| |#1|) (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x**a) + f(x**(a + d)) + f(x**(a + 2 d)) + ...}. \\spad{f(x)} should have zero constant coefficient and \\spad{a} and \\spad{d} should be positive.")) (|evenlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{evenlambert(st)} computes \\spad{f(x**2) + f(x**4) + f(x**6) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1,{} then \\spad{prod(f(x**(2*n)),{}n=1..infinity) = exp(evenlambert(log(f(x))))}.")) (|oddlambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{oddlambert(st)} computes \\spad{f(x) + f(x**3) + f(x**5) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f}(\\spad{x}) is a power series with constant coefficient 1 then \\spad{prod(f(x**(2*n-1)),{}n=1..infinity) = exp(oddlambert(log(f(x))))}.")) (|lambert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lambert(st)} computes \\spad{f(x) + f(x**2) + f(x**3) + ...} if \\spad{st} is a stream representing \\spad{f(x)}. This function is used for computing infinite products. If \\spad{f(x)} is a power series with constant coefficient 1 then \\spad{prod(f(x**n),{}n = 1..infinity) = exp(lambert(log(f(x))))}.")) (|addiag| (((|Stream| |#1|) (|Stream| (|Stream| |#1|))) "\\spad{addiag(x)} performs diagonal addition of a stream of streams. if \\spad{x} = \\spad{[[a<0,{}0>,{}a<0,{}1>,{}..],{}[a<1,{}0>,{}a<1,{}1>,{}..],{}[a<2,{}0>,{}a<2,{}1>,{}..],{}..]} and \\spad{addiag(x) = [b<0,{}b<1>,{}...],{} then b<k> = sum(i+j=k,{}a<i,{}j>)}.")) (|revert| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{revert(a)} computes the inverse of a power series \\spad{a} with respect to composition. the series should have constant coefficient 0 and first order coefficient 1.")) (|lagrange| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{lagrange(g)} produces the power series for \\spad{f} where \\spad{f} is implicitly defined as \\spad{f(z) = z*g(f(z))}.")) (|compose| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{compose(a,{}b)} composes the power series \\spad{a} with the power series \\spad{b}.")) (|eval| (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{eval(a,{}r)} returns a stream of partial sums of the power series \\spad{a} evaluated at the power series variable equal to \\spad{r}.")) (|coerce| (((|Stream| |#1|) |#1|) "\\spad{coerce(r)} converts a ring element \\spad{r} to a stream with one element.")) (|gderiv| (((|Stream| |#1|) (|Mapping| |#1| (|Integer|)) (|Stream| |#1|)) "\\spad{gderiv(f,{}[a0,{}a1,{}a2,{}..])} returns \\spad{[f(0)*a0,{}f(1)*a1,{}f(2)*a2,{}..]}.")) (|deriv| (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{deriv(a)} returns the derivative of the power series with respect to the power series variable. Thus \\spad{deriv([a0,{}a1,{}a2,{}...])} returns \\spad{[a1,{}2 a2,{}3 a3,{}...]}.")) (|mapmult| (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{mapmult([a0,{}a1,{}..],{}[b0,{}b1,{}..])} returns \\spad{[a0*b0,{}a1*b1,{}..]}.")) (|int| (((|Stream| |#1|) |#1|) "\\spad{int(r)} returns [\\spad{r},{}\\spad{r+1},{}\\spad{r+2},{}...],{} where \\spad{r} is a ring element.")) (|oddintegers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{oddintegers(n)} returns \\spad{[n,{}n+2,{}n+4,{}...]}.")) (|integers| (((|Stream| (|Integer|)) (|Integer|)) "\\spad{integers(n)} returns \\spad{[n,{}n+1,{}n+2,{}...]}.")) (|monom| (((|Stream| |#1|) |#1| (|Integer|)) "\\spad{monom(deg,{}coef)} is a monomial of degree \\spad{deg} with coefficient \\spad{coef}.")) (|recip| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|)) "\\spad{recip(a)} returns the power series reciprocal of \\spad{a},{} or \"failed\" if not possible.")) (/ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a / b} returns the power series quotient of \\spad{a} by \\spad{b}. An error message is returned if \\spad{b} is not invertible. This function is used in fixed point computations.")) (|exquo| (((|Union| (|Stream| |#1|) "failed") (|Stream| |#1|) (|Stream| |#1|)) "\\spad{exquo(a,{}b)} returns the power series quotient of \\spad{a} by \\spad{b},{} if the quotient exists,{} and \"failed\" otherwise")) (* (((|Stream| |#1|) (|Stream| |#1|) |#1|) "\\spad{a * r} returns the power series scalar multiplication of \\spad{a} by \\spad{r:} \\spad{[a0,{}a1,{}...] * r = [a0 * r,{}a1 * r,{}...]}") (((|Stream| |#1|) |#1| (|Stream| |#1|)) "\\spad{r * a} returns the power series scalar multiplication of \\spad{r} by \\spad{a}: \\spad{r * [a0,{}a1,{}...] = [r * a0,{}r * a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a * b} returns the power series (Cauchy) product of \\spad{a} and \\spad{b:} \\spad{[a0,{}a1,{}...] * [b0,{}b1,{}...] = [c0,{}c1,{}...]} where \\spad{ck = sum(i + j = k,{}\\spad{ai} * bk)}.")) (- (((|Stream| |#1|) (|Stream| |#1|)) "\\spad{- a} returns the power series negative of \\spad{a}: \\spad{- [a0,{}a1,{}...] = [- a0,{}- a1,{}...]}") (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a - b} returns the power series difference of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] - [b0,{}b1,{}..] = [a0 - b0,{}a1 - b1,{}..]}")) (+ (((|Stream| |#1|) (|Stream| |#1|) (|Stream| |#1|)) "\\spad{a + b} returns the power series sum of \\spad{a} and \\spad{b}: \\spad{[a0,{}a1,{}..] + [b0,{}b1,{}..] = [a0 + b0,{}a1 + b1,{}..]}"))) NIL @@ -4242,9 +4242,9 @@ NIL NIL (-1078 |Coef| |var| |cen|) ((|constructor| (NIL "Sparse Laurent series in one variable \\indented{2}{\\spadtype{SparseUnivariateLaurentSeries} is a domain representing Laurent} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{SparseUnivariateLaurentSeries(Integer,{}x,{}3)} represents Laurent} \\indented{2}{series in \\spad{(x - 3)} with integer coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. 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T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -1458) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1957) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) (-1086) ((|constructor| (NIL "This domain builds representations of boolean expressions for use with the \\axiomType{FortranCode} domain.")) (NOT (($ $) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.") (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{NOT(x)} returns the \\axiomType{Switch} expression representing \\spad{\\~~x}.")) (AND (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{AND(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x and y}.")) (EQ (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{EQ(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x = y}.")) (OR (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{OR(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x or y}.")) (GE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>=y}.")) (LE (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LE(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<=y}.")) (GT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{GT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x>y}.")) (LT (($ (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $)) (|Union| (|:| I (|Expression| (|Integer|))) (|:| F (|Expression| (|Float|))) (|:| CF (|Expression| (|Complex| (|Float|)))) (|:| |switch| $))) "\\spad{LT(x,{}y)} returns the \\axiomType{Switch} expression representing \\spad{x<y}.")) (|coerce| (($ (|Symbol|)) "\\spad{coerce(s)} \\undocumented{}"))) NIL @@ -4286,8 +4286,8 @@ NIL NIL (-1089 R) ((|constructor| (NIL "This domain implements symmetric polynomial"))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-6 -4242)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| (-900) (QUOTE (-124))) (|HasCategory| |#1| (QUOTE (-515)))) (-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4242))) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-6 -4246)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-427))) (-12 (|HasCategory| (-900) (QUOTE (-124))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasAttribute| |#1| (QUOTE -4246))) (-1090) ((|constructor| (NIL "Creates and manipulates one global symbol table for FORTRAN code generation,{} containing details of types,{} dimensions,{} and argument lists.")) (|symbolTableOf| (((|SymbolTable|) (|Symbol|) $) "\\spad{symbolTableOf(f,{}tab)} returns the symbol table of \\spad{f}")) (|argumentListOf| (((|List| (|Symbol|)) (|Symbol|) $) "\\spad{argumentListOf(f,{}tab)} returns the argument list of \\spad{f}")) (|returnTypeOf| (((|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) (|Symbol|) $) "\\spad{returnTypeOf(f,{}tab)} returns the type of the object returned by \\spad{f}")) (|empty| (($) "\\spad{empty()} creates a new,{} empty symbol table.")) (|printTypes| (((|Void|) (|Symbol|)) "\\spad{printTypes(tab)} produces FORTRAN type declarations from \\spad{tab},{} on the current FORTRAN output stream")) (|printHeader| (((|Void|)) "\\spad{printHeader()} produces the FORTRAN header for the current subprogram in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|)) "\\spad{printHeader(f)} produces the FORTRAN header for subprogram \\spad{f} in the global symbol table on the current FORTRAN output stream.") (((|Void|) (|Symbol|) $) "\\spad{printHeader(f,{}tab)} produces the FORTRAN header for subprogram \\spad{f} in symbol table \\spad{tab} on the current FORTRAN output stream.")) (|returnType!| (((|Void|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(t)} declares that the return type of he current subprogram in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void"))) "\\spad{returnType!(f,{}t)} declares that the return type of subprogram \\spad{f} in the global symbol table is \\spad{t}.") (((|Void|) (|Symbol|) (|Union| (|:| |fst| (|FortranScalarType|)) (|:| |void| "void")) $) "\\spad{returnType!(f,{}t,{}tab)} declares that the return type of subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{t}.")) (|argumentList!| (((|Void|) (|List| (|Symbol|))) "\\spad{argumentList!(l)} declares that the argument list for the current subprogram in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|))) "\\spad{argumentList!(f,{}l)} declares that the argument list for subprogram \\spad{f} in the global symbol table is \\spad{l}.") (((|Void|) (|Symbol|) (|List| (|Symbol|)) $) "\\spad{argumentList!(f,{}l,{}tab)} declares that the argument list for subprogram \\spad{f} in symbol table \\spad{tab} is \\spad{l}.")) (|endSubProgram| (((|Symbol|)) "\\spad{endSubProgram()} asserts that we are no longer processing the current subprogram.")) (|currentSubProgram| (((|Symbol|)) "\\spad{currentSubProgram()} returns the name of the current subprogram being processed")) (|newSubProgram| (((|Void|) (|Symbol|)) "\\spad{newSubProgram(f)} asserts that from now on type declarations are part of subprogram \\spad{f}.")) (|declare!| (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|)) "\\spad{declare!(u,{}t,{}asp)} declares the parameter \\spad{u} to have type \\spad{t} in \\spad{asp}.") (((|FortranType|) (|Symbol|) (|FortranType|)) "\\spad{declare!(u,{}t)} declares the parameter \\spad{u} to have type \\spad{t} in the current level of the symbol table.") (((|FortranType|) (|List| (|Symbol|)) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameters \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.") (((|FortranType|) (|Symbol|) (|FortranType|) (|Symbol|) $) "\\spad{declare!(u,{}t,{}asp,{}tab)} declares the parameter \\spad{u} of subprogram \\spad{asp} to have type \\spad{t} in symbol table \\spad{tab}.")) (|clearTheSymbolTable| (((|Void|) (|Symbol|)) "\\spad{clearTheSymbolTable(x)} removes the symbol \\spad{x} from the table") (((|Void|)) "\\spad{clearTheSymbolTable()} clears the current symbol table.")) (|showTheSymbolTable| (($) "\\spad{showTheSymbolTable()} returns the current symbol table."))) NIL @@ -4304,409 +4304,413 @@ NIL ((|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 -(-1094 S) -((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) +(-1094) +((|constructor| (NIL "The package \\spadtype{System} provides information about the runtime system and its characteristics.")) (|loadNativeModule| (((|Void|) (|String|)) "\\spad{loadNativeModule(path)} loads the native modile designated by \\spadvar{\\spad{path}}.")) (|nativeModuleExtension| (((|String|)) "\\spad{nativeModuleExtension()} returns a string representation of a filename extension for native modules.")) (|hostPlatform| (((|String|)) "\\spad{hostPlatform()} returns a string `triplet' description of the platform hosting the running OpenAxiom system.")) (|rootDirectory| (((|String|)) "\\spad{rootDirectory()} returns the pathname of the root directory for the running OpenAxiom system."))) NIL NIL (-1095 S) +((|constructor| (NIL "TableauBumpers implements the Schenstead-Knuth correspondence between sequences and pairs of Young tableaux. The 2 Young tableaux are represented as a single tableau with pairs as components.")) (|mr| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| (|List| (|List| |#1|)))) "\\spad{mr(t)} is an auxiliary function which finds the position of the maximum element of a tableau \\spad{t} which is in the lowest row,{} producing a record of results")) (|maxrow| (((|Record| (|:| |f1| (|List| |#1|)) (|:| |f2| (|List| (|List| (|List| |#1|)))) (|:| |f3| (|List| (|List| |#1|))) (|:| |f4| (|List| (|List| (|List| |#1|))))) (|List| |#1|) (|List| (|List| (|List| |#1|))) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|))) (|List| (|List| (|List| |#1|)))) "\\spad{maxrow(a,{}b,{}c,{}d,{}e)} is an auxiliary function for \\spad{mr}")) (|inverse| (((|List| |#1|) (|List| |#1|)) "\\spad{inverse(ls)} forms the inverse of a sequence \\spad{ls}")) (|slex| (((|List| (|List| |#1|)) (|List| |#1|)) "\\spad{slex(ls)} sorts the argument sequence \\spad{ls},{} then zips (see \\spadfunFrom{map}{ListFunctions3}) the original argument sequence with the sorted result to a list of pairs")) (|lex| (((|List| (|List| |#1|)) (|List| (|List| |#1|))) "\\spad{lex(ls)} sorts a list of pairs to lexicographic order")) (|tab| (((|Tableau| (|List| |#1|)) (|List| |#1|)) "\\spad{tab(ls)} creates a tableau from \\spad{ls} by first creating a list of pairs using \\spadfunFrom{slex}{TableauBumpers},{} then creating a tableau using \\spadfunFrom{tab1}{TableauBumpers}.")) (|tab1| (((|List| (|List| (|List| |#1|))) (|List| (|List| |#1|))) "\\spad{tab1(lp)} creates a tableau from a list of pairs \\spad{lp}")) (|bat| (((|List| (|List| |#1|)) (|Tableau| (|List| |#1|))) "\\spad{bat(ls)} unbumps a tableau \\spad{ls}")) (|bat1| (((|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{bat1(llp)} unbumps a tableau \\spad{llp}. Operation bat1 is the inverse of tab1.")) (|untab| (((|List| (|List| |#1|)) (|List| (|List| |#1|)) (|List| (|List| (|List| |#1|)))) "\\spad{untab(lp,{}llp)} is an auxiliary function which unbumps a tableau \\spad{llp},{} using \\spad{lp} to accumulate pairs")) (|bumptab1| (((|List| (|List| (|List| |#1|))) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab1(pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spadfun{<},{} returning a new tableau")) (|bumptab| (((|List| (|List| (|List| |#1|))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| (|List| |#1|)))) "\\spad{bumptab(cf,{}pr,{}t)} bumps a tableau \\spad{t} with a pair \\spad{pr} using comparison function \\spad{cf},{} returning a new tableau")) (|bumprow| (((|Record| (|:| |fs| (|Boolean|)) (|:| |sd| (|List| |#1|)) (|:| |td| (|List| (|List| |#1|)))) (|Mapping| (|Boolean|) |#1| |#1|) (|List| |#1|) (|List| (|List| |#1|))) "\\spad{bumprow(cf,{}pr,{}r)} is an auxiliary function which bumps a row \\spad{r} with a pair \\spad{pr} using comparison function \\spad{cf},{} and returns a record"))) +NIL +NIL +(-1096 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 -(-1096 |Key| |Entry|) +(-1097 |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}"))) -((-4244 . T) (-4245 . T)) -((-12 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -1853) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2433) (|devaluate| |#2|)))))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3262 (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) -(-1097 R) +((-4248 . T) (-4249 . T)) +((-12 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -286) (LIST (QUOTE -2) (LIST (QUOTE |:|) (QUOTE -3772) (|devaluate| |#1|)) (LIST (QUOTE |:|) (QUOTE -2482) (|devaluate| |#2|)))))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#2| (QUOTE (-1016)))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -564) (QUOTE (-499)))) (-12 (|HasCategory| |#2| (QUOTE (-1016))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#2| (QUOTE (-1016))) (-3172 (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#2| (LIST (QUOTE -563) (QUOTE (-794)))) (|HasCategory| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (LIST (QUOTE -563) (QUOTE (-794))))) +(-1098 R) ((|constructor| (NIL "Expands tangents of sums and scalar products.")) (|tanNa| ((|#1| |#1| (|Integer|)) "\\spad{tanNa(a,{} n)} returns \\spad{f(a)} such that if \\spad{a = tan(u)} then \\spad{f(a) = tan(n * u)}.")) (|tanAn| (((|SparseUnivariatePolynomial| |#1|) |#1| (|PositiveInteger|)) "\\spad{tanAn(a,{} n)} returns \\spad{P(x)} such that if \\spad{a = tan(u)} then \\spad{P(tan(u/n)) = 0}.")) (|tanSum| ((|#1| (|List| |#1|)) "\\spad{tanSum([a1,{}...,{}an])} returns \\spad{f(a1,{}...,{}an)} such that if \\spad{\\spad{ai} = tan(\\spad{ui})} then \\spad{f(a1,{}...,{}an) = tan(u1 + ... + un)}."))) NIL NIL -(-1098 S |Key| |Entry|) +(-1099 S |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#3| |#3| |#3|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#2|) (|:| |entry| |#3|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#3| $ |#2| |#3|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) NIL NIL -(-1099 |Key| |Entry|) +(-1100 |Key| |Entry|) ((|constructor| (NIL "A table aggregate is a model of a table,{} \\spadignore{i.e.} a discrete many-to-one mapping from keys to entries.")) (|map| (($ (|Mapping| |#2| |#2| |#2|) $ $) "\\spad{map(fn,{}t1,{}t2)} creates a new table \\spad{t} from given tables \\spad{t1} and \\spad{t2} with elements \\spad{fn}(\\spad{x},{}\\spad{y}) where \\spad{x} and \\spad{y} are corresponding elements from \\spad{t1} and \\spad{t2} respectively.")) (|table| (($ (|List| (|Record| (|:| |key| |#1|) (|:| |entry| |#2|)))) "\\spad{table([x,{}y,{}...,{}z])} creates a table consisting of entries \\axiom{\\spad{x},{}\\spad{y},{}...,{}\\spad{z}}.") (($) "\\spad{table()}\\$\\spad{T} creates an empty table of type \\spad{T}.")) (|setelt| ((|#2| $ |#1| |#2|) "\\spad{setelt(t,{}k,{}e)} (also written \\axiom{\\spad{t}.\\spad{k} \\spad{:=} \\spad{e}}) is equivalent to \\axiom{(insert([\\spad{k},{}\\spad{e}],{}\\spad{t}); \\spad{e})}."))) -((-4245 . T) (-3656 . T)) +((-4249 . T) (-4069 . T)) NIL -(-1100 |Key| |Entry|) +(-1101 |Key| |Entry|) ((|constructor| (NIL "\\axiom{TabulatedComputationPackage(Key ,{}Entry)} provides some modest support for dealing with operations with type \\axiom{Key \\spad{->} Entry}. The result of such operations can be stored and retrieved with this package by using a hash-table. The user does not need to worry about the management of this hash-table. However,{} onnly one hash-table is built by calling \\axiom{TabulatedComputationPackage(Key ,{}Entry)}.")) (|insert!| (((|Void|) |#1| |#2|) "\\axiom{insert!(\\spad{x},{}\\spad{y})} stores the item whose key is \\axiom{\\spad{x}} and whose entry is \\axiom{\\spad{y}}.")) (|extractIfCan| (((|Union| |#2| "failed") |#1|) "\\axiom{extractIfCan(\\spad{x})} searches the item whose key is \\axiom{\\spad{x}}.")) (|makingStats?| (((|Boolean|)) "\\axiom{makingStats?()} returns \\spad{true} iff the statisitics process is running.")) (|printingInfo?| (((|Boolean|)) "\\axiom{printingInfo?()} returns \\spad{true} iff messages are printed when manipulating items from the hash-table.")) (|usingTable?| (((|Boolean|)) "\\axiom{usingTable?()} returns \\spad{true} iff the hash-table is used")) (|clearTable!| (((|Void|)) "\\axiom{clearTable!()} clears the hash-table and assumes that it will no longer be used.")) (|printStats!| (((|Void|)) "\\axiom{printStats!()} prints the statistics.")) (|startStats!| (((|Void|) (|String|)) "\\axiom{startStats!(\\spad{x})} initializes the statisitics process and sets the comments to display when statistics are printed")) (|printInfo!| (((|Void|) (|String|) (|String|)) "\\axiom{printInfo!(\\spad{x},{}\\spad{y})} initializes the mesages to be printed when manipulating items from the hash-table. If a key is retrieved then \\axiom{\\spad{x}} is displayed. If an item is stored then \\axiom{\\spad{y}} is displayed.")) (|initTable!| (((|Void|)) "\\axiom{initTable!()} initializes the hash-table."))) NIL NIL -(-1101) +(-1102) ((|constructor| (NIL "This package provides functions for template manipulation")) (|stripCommentsAndBlanks| (((|String|) (|String|)) "\\spad{stripCommentsAndBlanks(s)} treats \\spad{s} as a piece of AXIOM input,{} and removes comments,{} and leading and trailing blanks.")) (|interpretString| (((|Any|) (|String|)) "\\spad{interpretString(s)} treats a string as a piece of AXIOM input,{} by parsing and interpreting it."))) NIL NIL -(-1102 S) +(-1103 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 -(-1103) +(-1104) ((|constructor| (NIL "\\spadtype{TexFormat} provides a coercion from \\spadtype{OutputForm} to \\TeX{} format. The particular dialect of \\TeX{} used is \\LaTeX{}. The basic object consists of three parts: a prologue,{} a tex part and an epilogue. The functions \\spadfun{prologue},{} \\spadfun{tex} and \\spadfun{epilogue} extract these parts,{} respectively. The main guts of the expression go into the tex part. The other parts can be set (\\spadfun{setPrologue!},{} \\spadfun{setEpilogue!}) so that contain the appropriate tags for printing. For example,{} the prologue and epilogue might simply contain \\spad{``}\\verb+\\spad{\\[}+\\spad{''} and \\spad{``}\\verb+\\spad{\\]}+\\spad{''},{} respectively,{} so that the TeX section will be printed in LaTeX display math mode.")) (|setPrologue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setPrologue!(t,{}strings)} sets the prologue section of a TeX form \\spad{t} to \\spad{strings}.")) (|setTex!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setTex!(t,{}strings)} sets the TeX section of a TeX form \\spad{t} to \\spad{strings}.")) (|setEpilogue!| (((|List| (|String|)) $ (|List| (|String|))) "\\spad{setEpilogue!(t,{}strings)} sets the epilogue section of a TeX form \\spad{t} to \\spad{strings}.")) (|prologue| (((|List| (|String|)) $) "\\spad{prologue(t)} extracts the prologue section of a TeX form \\spad{t}.")) (|new| (($) "\\spad{new()} create a new,{} empty object. Use \\spadfun{setPrologue!},{} \\spadfun{setTex!} and \\spadfun{setEpilogue!} to set the various components of this object.")) (|tex| (((|List| (|String|)) $) "\\spad{tex(t)} extracts the TeX section of a TeX form \\spad{t}.")) (|epilogue| (((|List| (|String|)) $) "\\spad{epilogue(t)} extracts the epilogue section of a TeX form \\spad{t}.")) (|display| (((|Void|) $) "\\spad{display(t)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to the value set by the system command \\spadsyscom{set output length}.") (((|Void|) $ (|Integer|)) "\\spad{display(t,{}width)} outputs the TeX formatted code \\spad{t} so that each line has length less than or equal to \\spadvar{\\spad{width}}.")) (|convert| (($ (|OutputForm|) (|Integer|) (|OutputForm|)) "\\spad{convert(o,{}step,{}type)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number and \\spad{type}. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.") (($ (|OutputForm|) (|Integer|)) "\\spad{convert(o,{}step)} changes \\spad{o} in standard output format to TeX format and also adds the given \\spad{step} number. This is useful if you want to create equations with given numbers or have the equation numbers correspond to the interpreter \\spad{step} numbers.")) (|coerce| (($ (|OutputForm|)) "\\spad{coerce(o)} changes \\spad{o} in the standard output format to TeX format."))) NIL NIL -(-1104) +(-1105) ((|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 -(-1105 R) +(-1106 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 -(-1106) +(-1107) ((|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 -(-1107 S) +(-1108 S) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1108) +(-1109) ((|constructor| (NIL "Category for the transcendental elementary functions.")) (|pi| (($) "\\spad{\\spad{pi}()} returns the constant \\spad{pi}."))) NIL NIL -(-1109 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}."))) -((-4245 . T) (-4244 . T)) -((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (-1110 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| $)) "\\spad{tree(nd,{}ls)} creates a tree with value \\spad{nd},{} and children \\spad{ls}."))) +((-4249 . T) (-4248 . T)) +((-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (QUOTE (-1016))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-1111 S) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1111) +(-1112) ((|constructor| (NIL "Category for the trigonometric functions.")) (|tan| (($ $) "\\spad{tan(x)} returns the tangent of \\spad{x}.")) (|sin| (($ $) "\\spad{sin(x)} returns the sine of \\spad{x}.")) (|sec| (($ $) "\\spad{sec(x)} returns the secant of \\spad{x}.")) (|csc| (($ $) "\\spad{csc(x)} returns the cosecant of \\spad{x}.")) (|cot| (($ $) "\\spad{cot(x)} returns the cotangent of \\spad{x}.")) (|cos| (($ $) "\\spad{cos(x)} returns the cosine of \\spad{x}."))) NIL NIL -(-1112 R -2315) +(-1113 R -3539) ((|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 -(-1113 R |Row| |Col| M) +(-1114 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 -(-1114 R -2315) +(-1115 R -3539) ((|constructor| (NIL "TranscendentalManipulations provides functions to simplify and expand expressions involving transcendental operators.")) (|expandTrigProducts| ((|#2| |#2|) "\\spad{expandTrigProducts(e)} replaces \\axiom{sin(\\spad{x})*sin(\\spad{y})} by \\spad{(cos(x-y)-cos(x+y))/2},{} \\axiom{cos(\\spad{x})*cos(\\spad{y})} by \\spad{(cos(x-y)+cos(x+y))/2},{} and \\axiom{sin(\\spad{x})*cos(\\spad{y})} by \\spad{(sin(x-y)+sin(x+y))/2}. Note that this operation uses the pattern matcher and so is relatively expensive. To avoid getting into an infinite loop the transformations are applied at most ten times.")) (|removeSinhSq| ((|#2| |#2|) "\\spad{removeSinhSq(f)} converts every \\spad{sinh(u)**2} appearing in \\spad{f} into \\spad{1 - cosh(x)**2},{} and also reduces higher powers of \\spad{sinh(u)} with that formula.")) (|removeCoshSq| ((|#2| |#2|) "\\spad{removeCoshSq(f)} converts every \\spad{cosh(u)**2} appearing in \\spad{f} into \\spad{1 - sinh(x)**2},{} and also reduces higher powers of \\spad{cosh(u)} with that formula.")) (|removeSinSq| ((|#2| |#2|) "\\spad{removeSinSq(f)} converts every \\spad{sin(u)**2} appearing in \\spad{f} into \\spad{1 - cos(x)**2},{} and also reduces higher powers of \\spad{sin(u)} with that formula.")) (|removeCosSq| ((|#2| |#2|) "\\spad{removeCosSq(f)} converts every \\spad{cos(u)**2} appearing in \\spad{f} into \\spad{1 - sin(x)**2},{} and also reduces higher powers of \\spad{cos(u)} with that formula.")) (|coth2tanh| ((|#2| |#2|) "\\spad{coth2tanh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{1/tanh(u)}.")) (|cot2tan| ((|#2| |#2|) "\\spad{cot2tan(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{1/tan(u)}.")) (|tanh2coth| ((|#2| |#2|) "\\spad{tanh2coth(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{1/coth(u)}.")) (|tan2cot| ((|#2| |#2|) "\\spad{tan2cot(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{1/cot(u)}.")) (|tanh2trigh| ((|#2| |#2|) "\\spad{tanh2trigh(f)} converts every \\spad{tanh(u)} appearing in \\spad{f} into \\spad{sinh(u)/cosh(u)}.")) (|tan2trig| ((|#2| |#2|) "\\spad{tan2trig(f)} converts every \\spad{tan(u)} appearing in \\spad{f} into \\spad{sin(u)/cos(u)}.")) (|sinh2csch| ((|#2| |#2|) "\\spad{sinh2csch(f)} converts every \\spad{sinh(u)} appearing in \\spad{f} into \\spad{1/csch(u)}.")) (|sin2csc| ((|#2| |#2|) "\\spad{sin2csc(f)} converts every \\spad{sin(u)} appearing in \\spad{f} into \\spad{1/csc(u)}.")) (|sech2cosh| ((|#2| |#2|) "\\spad{sech2cosh(f)} converts every \\spad{sech(u)} appearing in \\spad{f} into \\spad{1/cosh(u)}.")) (|sec2cos| ((|#2| |#2|) "\\spad{sec2cos(f)} converts every \\spad{sec(u)} appearing in \\spad{f} into \\spad{1/cos(u)}.")) (|csch2sinh| ((|#2| |#2|) "\\spad{csch2sinh(f)} converts every \\spad{csch(u)} appearing in \\spad{f} into \\spad{1/sinh(u)}.")) (|csc2sin| ((|#2| |#2|) "\\spad{csc2sin(f)} converts every \\spad{csc(u)} appearing in \\spad{f} into \\spad{1/sin(u)}.")) (|coth2trigh| ((|#2| |#2|) "\\spad{coth2trigh(f)} converts every \\spad{coth(u)} appearing in \\spad{f} into \\spad{cosh(u)/sinh(u)}.")) (|cot2trig| ((|#2| |#2|) "\\spad{cot2trig(f)} converts every \\spad{cot(u)} appearing in \\spad{f} into \\spad{cos(u)/sin(u)}.")) (|cosh2sech| ((|#2| |#2|) "\\spad{cosh2sech(f)} converts every \\spad{cosh(u)} appearing in \\spad{f} into \\spad{1/sech(u)}.")) (|cos2sec| ((|#2| |#2|) "\\spad{cos2sec(f)} converts every \\spad{cos(u)} appearing in \\spad{f} into \\spad{1/sec(u)}.")) (|expandLog| ((|#2| |#2|) "\\spad{expandLog(f)} converts every \\spad{log(a/b)} appearing in \\spad{f} into \\spad{log(a) - log(b)},{} and every \\spad{log(a*b)} into \\spad{log(a) + log(b)}..")) (|expandPower| ((|#2| |#2|) "\\spad{expandPower(f)} converts every power \\spad{(a/b)**c} appearing in \\spad{f} into \\spad{a**c * b**(-c)}.")) (|simplifyLog| ((|#2| |#2|) "\\spad{simplifyLog(f)} converts every \\spad{log(a) - log(b)} appearing in \\spad{f} into \\spad{log(a/b)},{} every \\spad{log(a) + log(b)} into \\spad{log(a*b)} and every \\spad{n*log(a)} into \\spad{log(a^n)}.")) (|simplifyExp| ((|#2| |#2|) "\\spad{simplifyExp(f)} converts every product \\spad{exp(a)*exp(b)} appearing in \\spad{f} into \\spad{exp(a+b)}.")) (|htrigs| ((|#2| |#2|) "\\spad{htrigs(f)} converts all the exponentials in \\spad{f} into hyperbolic sines and cosines.")) (|simplify| ((|#2| |#2|) "\\spad{simplify(f)} performs the following simplifications on \\spad{f:}\\begin{items} \\item 1. rewrites trigs and hyperbolic trigs in terms of \\spad{sin} ,{}\\spad{cos},{} \\spad{sinh},{} \\spad{cosh}. \\item 2. rewrites \\spad{sin**2} and \\spad{sinh**2} in terms of \\spad{cos} and \\spad{cosh},{} \\item 3. rewrites \\spad{exp(a)*exp(b)} as \\spad{exp(a+b)}. \\item 4. rewrites \\spad{(a**(1/n))**m * (a**(1/s))**t} as a single power of a single radical of \\spad{a}. \\end{items}")) (|expand| ((|#2| |#2|) "\\spad{expand(f)} performs the following expansions on \\spad{f:}\\begin{items} \\item 1. logs of products are expanded into sums of logs,{} \\item 2. trigonometric and hyperbolic trigonometric functions of sums are expanded into sums of products of trigonometric and hyperbolic trigonometric functions. \\item 3. formal powers of the form \\spad{(a/b)**c} are expanded into \\spad{a**c * b**(-c)}. \\end{items}"))) NIL ((-12 (|HasCategory| |#1| (LIST (QUOTE -564) (LIST (QUOTE -823) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -817) (|devaluate| |#1|))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (|devaluate| |#1|)))) (|HasCategory| |#2| (LIST (QUOTE -817) (|devaluate| |#1|))))) -(-1115 S R E V P) +(-1116 S R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#5|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#5|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#5| "failed") $ |#4|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#4| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#4|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#5| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#5| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#5|)))) (|List| |#5|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#5|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#5| |#5| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#5| |#5| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#5| |#5| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#5| |#5| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#5| |#5| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#5|) (|List| |#5|) $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#5| |#5| $ (|Mapping| |#5| |#5| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#5| (|List| |#5|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#5| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#5| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#5| $ (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#5| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#5|)) (|:| |open| (|List| |#5|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#5|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#5|))) "failed") (|List| |#5|) (|Mapping| (|Boolean|) |#5| |#5|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) NIL ((|HasCategory| |#4| (QUOTE (-344)))) -(-1116 R E V P) +(-1117 R E V P) ((|constructor| (NIL "The category of triangular sets of multivariate polynomials with coefficients in an integral domain. Let \\axiom{\\spad{R}} be an integral domain and \\axiom{\\spad{V}} a finite ordered set of variables,{} say \\axiom{\\spad{X1} < \\spad{X2} < ... < \\spad{Xn}}. A set \\axiom{\\spad{S}} of polynomials in \\axiom{\\spad{R}[\\spad{X1},{}\\spad{X2},{}...,{}\\spad{Xn}]} is triangular if no elements of \\axiom{\\spad{S}} lies in \\axiom{\\spad{R}},{} and if two distinct elements of \\axiom{\\spad{S}} have distinct main variables. Note that the empty set is a triangular set. A triangular set is not necessarily a (lexicographical) Groebner basis and the notion of reduction related to triangular sets is based on the recursive view of polynomials. We recall this notion here and refer to [1] for more details. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a non-constant polynomial \\axiom{\\spad{Q}} if the degree of \\axiom{\\spad{P}} in the main variable of \\axiom{\\spad{Q}} is less than the main degree of \\axiom{\\spad{Q}}. A polynomial \\axiom{\\spad{P}} is reduced \\spad{w}.\\spad{r}.\\spad{t} a triangular set \\axiom{\\spad{T}} if it is reduced \\spad{w}.\\spad{r}.\\spad{t}. every polynomial of \\axiom{\\spad{T}}. \\newline References : \\indented{1}{[1] \\spad{P}. AUBRY,{} \\spad{D}. LAZARD and \\spad{M}. MORENO MAZA \"On the Theories} \\indented{5}{of Triangular Sets\" Journal of Symbol. Comp. (to appear)}")) (|coHeight| (((|NonNegativeInteger|) $) "\\axiom{coHeight(\\spad{ts})} returns \\axiom{size()\\spad{\\$}\\spad{V}} minus \\axiom{\\spad{\\#}\\spad{ts}}.")) (|extend| (($ $ |#4|) "\\axiom{extend(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current category If the required properties do not hold an error is returned.")) (|extendIfCan| (((|Union| $ "failed") $ |#4|) "\\axiom{extendIfCan(\\spad{ts},{}\\spad{p})} returns a triangular set which encodes the simple extension by \\axiom{\\spad{p}} of the extension of the base field defined by \\axiom{\\spad{ts}},{} according to the properties of triangular sets of the current domain. If the required properties do not hold then \"failed\" is returned. This operation encodes in some sense the properties of the triangular sets of the current category. Is is used to implement the \\axiom{construct} operation to guarantee that every triangular set build from a list of polynomials has the required properties.")) (|select| (((|Union| |#4| "failed") $ |#3|) "\\axiom{select(\\spad{ts},{}\\spad{v})} returns the polynomial of \\axiom{\\spad{ts}} with \\axiom{\\spad{v}} as main variable,{} if any.")) (|algebraic?| (((|Boolean|) |#3| $) "\\axiom{algebraic?(\\spad{v},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{v}} is the main variable of some polynomial in \\axiom{\\spad{ts}}.")) (|algebraicVariables| (((|List| |#3|) $) "\\axiom{algebraicVariables(\\spad{ts})} returns the decreasingly sorted list of the main variables of the polynomials of \\axiom{\\spad{ts}}.")) (|rest| (((|Union| $ "failed") $) "\\axiom{rest(\\spad{ts})} returns the polynomials of \\axiom{\\spad{ts}} with smaller main variable than \\axiom{mvar(\\spad{ts})} if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \"failed\"")) (|last| (((|Union| |#4| "failed") $) "\\axiom{last(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with smallest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|first| (((|Union| |#4| "failed") $) "\\axiom{first(\\spad{ts})} returns the polynomial of \\axiom{\\spad{ts}} with greatest main variable if \\axiom{\\spad{ts}} is not empty,{} otherwise returns \\axiom{\"failed\"}.")) (|zeroSetSplitIntoTriangularSystems| (((|List| (|Record| (|:| |close| $) (|:| |open| (|List| |#4|)))) (|List| |#4|)) "\\axiom{zeroSetSplitIntoTriangularSystems(\\spad{lp})} returns a list of triangular systems \\axiom{[[\\spad{ts1},{}\\spad{qs1}],{}...,{}[\\spad{tsn},{}\\spad{qsn}]]} such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the \\axiom{W_i} where \\axiom{W_i} consists of the zeros of \\axiom{\\spad{ts}} which do not cancel any polynomial in \\axiom{qsi}.")) (|zeroSetSplit| (((|List| $) (|List| |#4|)) "\\axiom{zeroSetSplit(\\spad{lp})} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{lp}} is the union of the closures of the regular zero sets of the members of \\axiom{\\spad{lts}}.")) (|reduceByQuasiMonic| ((|#4| |#4| $) "\\axiom{reduceByQuasiMonic(\\spad{p},{}\\spad{ts})} returns the same as \\axiom{remainder(\\spad{p},{}collectQuasiMonic(\\spad{ts})).polnum}.")) (|collectQuasiMonic| (($ $) "\\axiom{collectQuasiMonic(\\spad{ts})} returns the subset of \\axiom{\\spad{ts}} consisting of the polynomials with initial in \\axiom{\\spad{R}}.")) (|removeZero| ((|#4| |#4| $) "\\axiom{removeZero(\\spad{p},{}\\spad{ts})} returns \\axiom{0} if \\axiom{\\spad{p}} reduces to \\axiom{0} by pseudo-division \\spad{w}.\\spad{r}.\\spad{t} \\axiom{\\spad{ts}} otherwise returns a polynomial \\axiom{\\spad{q}} computed from \\axiom{\\spad{p}} by removing any coefficient in \\axiom{\\spad{p}} reducing to \\axiom{0}.")) (|initiallyReduce| ((|#4| |#4| $) "\\axiom{initiallyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{initiallyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|headReduce| ((|#4| |#4| $) "\\axiom{headReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{headReduce?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|stronglyReduce| ((|#4| |#4| $) "\\axiom{stronglyReduce(\\spad{p},{}\\spad{ts})} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{stronglyReduced?(\\spad{r},{}\\spad{ts})} holds and there exists some product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}.")) (|rewriteSetWithReduction| (((|List| |#4|) (|List| |#4|) $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{rewriteSetWithReduction(\\spad{lp},{}\\spad{ts},{}redOp,{}redOp?)} returns a list \\axiom{\\spad{lq}} of polynomials such that \\axiom{[reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?) for \\spad{p} in \\spad{lp}]} and \\axiom{\\spad{lp}} have the same zeros inside the regular zero set of \\axiom{\\spad{ts}}. Moreover,{} for every polynomial \\axiom{\\spad{q}} in \\axiom{\\spad{lq}} and every polynomial \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{q},{}\\spad{t})} holds and there exists a polynomial \\axiom{\\spad{p}} in the ideal generated by \\axiom{\\spad{lp}} and a product \\axiom{\\spad{h}} of \\axiom{initials(\\spad{ts})} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|reduce| ((|#4| |#4| $ (|Mapping| |#4| |#4| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduce(\\spad{p},{}\\spad{ts},{}redOp,{}redOp?)} returns a polynomial \\axiom{\\spad{r}} such that \\axiom{redOp?(\\spad{r},{}\\spad{p})} holds for every \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} and there exists some product \\axiom{\\spad{h}} of the initials of the members of \\axiom{\\spad{ts}} such that \\axiom{\\spad{h*p} - \\spad{r}} lies in the ideal generated by \\axiom{\\spad{ts}}. The operation \\axiom{redOp} must satisfy the following conditions. For every \\axiom{\\spad{p}} and \\axiom{\\spad{q}} we have \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|autoReduced?| (((|Boolean|) $ (|Mapping| (|Boolean|) |#4| (|List| |#4|))) "\\axiom{autoReduced?(\\spad{ts},{}redOp?)} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to every other in the sense of \\axiom{redOp?}")) (|initiallyReduced?| (((|Boolean|) $) "\\spad{initiallyReduced?(ts)} returns \\spad{true} iff for every element \\axiom{\\spad{p}} of \\axiom{\\spad{ts}} \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the other elements of \\axiom{\\spad{ts}} with the same main variable.") (((|Boolean|) |#4| $) "\\axiom{initiallyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials are reduced \\spad{w}.\\spad{r}.\\spad{t}. to the elements of \\axiom{\\spad{ts}} with the same main variable.")) (|headReduced?| (((|Boolean|) $) "\\spad{headReduced?(ts)} returns \\spad{true} iff the head of every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{headReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff the head of \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|stronglyReduced?| (((|Boolean|) $) "\\axiom{stronglyReduced?(\\spad{ts})} returns \\spad{true} iff every element of \\axiom{\\spad{ts}} is reduced \\spad{w}.\\spad{r}.\\spad{t} to any other element of \\axiom{\\spad{ts}}.") (((|Boolean|) |#4| $) "\\axiom{stronglyReduced?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. \\axiom{\\spad{ts}}.")) (|reduced?| (((|Boolean|) |#4| $ (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{reduced?(\\spad{p},{}\\spad{ts},{}redOp?)} returns \\spad{true} iff \\axiom{\\spad{p}} is reduced \\spad{w}.\\spad{r}.\\spad{t}. in the sense of the operation \\axiom{redOp?},{} that is if for every \\axiom{\\spad{t}} in \\axiom{\\spad{ts}} \\axiom{redOp?(\\spad{p},{}\\spad{t})} holds.")) (|normalized?| (((|Boolean|) $) "\\axiom{normalized?(\\spad{ts})} returns \\spad{true} iff for every axiom{\\spad{p}} in axiom{\\spad{ts}} we have \\axiom{normalized?(\\spad{p},{}us)} where \\axiom{us} is \\axiom{collectUnder(\\spad{ts},{}mvar(\\spad{p}))}.") (((|Boolean|) |#4| $) "\\axiom{normalized?(\\spad{p},{}\\spad{ts})} returns \\spad{true} iff \\axiom{\\spad{p}} and all its iterated initials have degree zero \\spad{w}.\\spad{r}.\\spad{t}. the main variables of the polynomials of \\axiom{\\spad{ts}}")) (|quasiComponent| (((|Record| (|:| |close| (|List| |#4|)) (|:| |open| (|List| |#4|))) $) "\\axiom{quasiComponent(\\spad{ts})} returns \\axiom{[\\spad{lp},{}\\spad{lq}]} where \\axiom{\\spad{lp}} is the list of the members of \\axiom{\\spad{ts}} and \\axiom{\\spad{lq}}is \\axiom{initials(\\spad{ts})}.")) (|degree| (((|NonNegativeInteger|) $) "\\axiom{degree(\\spad{ts})} returns the product of main degrees of the members of \\axiom{\\spad{ts}}.")) (|initials| (((|List| |#4|) $) "\\axiom{initials(\\spad{ts})} returns the list of the non-constant initials of the members of \\axiom{\\spad{ts}}.")) (|basicSet| (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}pred?,{}redOp?)} returns the same as \\axiom{basicSet(\\spad{qs},{}redOp?)} where \\axiom{\\spad{qs}} consists of the polynomials of \\axiom{\\spad{ps}} satisfying property \\axiom{pred?}.") (((|Union| (|Record| (|:| |bas| $) (|:| |top| (|List| |#4|))) "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|)) "\\axiom{basicSet(\\spad{ps},{}redOp?)} returns \\axiom{[\\spad{bs},{}\\spad{ts}]} where \\axiom{concat(\\spad{bs},{}\\spad{ts})} is \\axiom{\\spad{ps}} and \\axiom{\\spad{bs}} is a basic set in Wu Wen Tsun sense of \\axiom{\\spad{ps}} \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?},{} if no non-zero constant polynomial lie in \\axiom{\\spad{ps}},{} otherwise \\axiom{\"failed\"} is returned.")) (|infRittWu?| (((|Boolean|) $ $) "\\axiom{infRittWu?(\\spad{ts1},{}\\spad{ts2})} returns \\spad{true} iff \\axiom{\\spad{ts2}} has higher rank than \\axiom{\\spad{ts1}} in Wu Wen Tsun sense."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL -(-1117 |Coef|) +(-1118 |Coef|) ((|constructor| (NIL "\\spadtype{TaylorSeries} is a general multivariate Taylor series domain over the ring Coef and with variables of type Symbol.")) (|fintegrate| (($ (|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}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) -(-1118 |Curve|) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-136))) (|HasCategory| |#1| (QUOTE (-134))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-339)))) +(-1119 |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 -(-1119) +(-1120) ((|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 -(-1120 S) +(-1121 S) ((|constructor| (NIL "\\indented{1}{This domain is used to interface with the interpreter\\spad{'s} notion} of comma-delimited sequences of values.")) (|length| (((|NonNegativeInteger|) $) "\\spad{length(x)} returns the number of elements in tuple \\spad{x}")) (|select| ((|#1| $ (|NonNegativeInteger|)) "\\spad{select(x,{}n)} returns the \\spad{n}-th element of tuple \\spad{x}. tuples are 0-based")) (|coerce| (($ (|PrimitiveArray| |#1|)) "\\spad{coerce(a)} makes a tuple from primitive array a"))) NIL ((|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-1121 -2315) +(-1122 -3539) ((|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 -(-1122) +(-1123) ((|constructor| (NIL "The fundamental Type."))) -((-3656 . T)) +((-4069 . T)) NIL -(-1123 S) +(-1124 S) ((|constructor| (NIL "Provides functions to force a partial ordering on any set.")) (|more?| (((|Boolean|) |#1| |#1|) "\\spad{more?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and uses the ordering on \\spad{S} if \\spad{a} and \\spad{b} are not comparable in the partial ordering.")) (|userOrdered?| (((|Boolean|)) "\\spad{userOrdered?()} tests if the partial ordering induced by \\spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.")) (|largest| ((|#1| (|List| |#1|)) "\\spad{largest l} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by the ordering on \\spad{S}.") ((|#1| (|List| |#1|) (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{largest(l,{} fn)} returns the largest element of \\spad{l} where the partial ordering induced by setOrder is completed into a total one by \\spad{fn}.")) (|less?| (((|Boolean|) |#1| |#1| (|Mapping| (|Boolean|) |#1| |#1|)) "\\spad{less?(a,{} b,{} fn)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder,{} and returns \\spad{fn(a,{} b)} if \\spad{a} and \\spad{b} are not comparable in that ordering.") (((|Union| (|Boolean|) "failed") |#1| |#1|) "\\spad{less?(a,{} b)} compares \\spad{a} and \\spad{b} in the partial ordering induced by setOrder.")) (|getOrder| (((|Record| (|:| |low| (|List| |#1|)) (|:| |high| (|List| |#1|)))) "\\spad{getOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the partial ordering on \\spad{S} was given by \\spad{setOrder([b1,{}...,{}bm],{}[a1,{}...,{}an])}.")) (|setOrder| (((|Void|) (|List| |#1|) (|List| |#1|)) "\\spad{setOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{bj < c < \\spad{ai}}\\space{2}for \\spad{c} not among the \\spad{ai}\\spad{'s} and \\spad{bj}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(c,{}d)} if neither is among the \\spad{ai}\\spad{'s},{}\\spad{bj}\\spad{'s}.}") (((|Void|) (|List| |#1|)) "\\spad{setOrder([a1,{}...,{}an])} defines a partial ordering on \\spad{S} given \\spad{by:} \\indented{3}{(1)\\space{2}\\spad{a1 < a2 < ... < an}.} \\indented{3}{(2)\\space{2}\\spad{b < \\spad{ai}\\space{3}for i = 1..n} and \\spad{b} not among the \\spad{ai}\\spad{'s}.} \\indented{3}{(3)\\space{2}undefined on \\spad{(b,{} c)} if neither is among the \\spad{ai}\\spad{'s}.}"))) NIL ((|HasCategory| |#1| (QUOTE (-786)))) -(-1124) +(-1125) ((|constructor| (NIL "This packages provides functions to allow the user to select the ordering on the variables and operators for displaying polynomials,{} fractions and expressions. The ordering affects the display only and not the computations.")) (|resetVariableOrder| (((|Void|)) "\\spad{resetVariableOrder()} cancels any previous use of setVariableOrder and returns to the default system ordering.")) (|getVariableOrder| (((|Record| (|:| |high| (|List| (|Symbol|))) (|:| |low| (|List| (|Symbol|))))) "\\spad{getVariableOrder()} returns \\spad{[[b1,{}...,{}bm],{} [a1,{}...,{}an]]} such that the ordering on the variables was given by \\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])}.")) (|setVariableOrder| (((|Void|) (|List| (|Symbol|)) (|List| (|Symbol|))) "\\spad{setVariableOrder([b1,{}...,{}bm],{} [a1,{}...,{}an])} defines an ordering on the variables given by \\spad{b1 > b2 > ... > bm >} other variables \\spad{> a1 > a2 > ... > an}.") (((|Void|) (|List| (|Symbol|))) "\\spad{setVariableOrder([a1,{}...,{}an])} defines an ordering on the variables given by \\spad{a1 > a2 > ... > an > other variables}."))) NIL NIL -(-1125 S) +(-1126 S) ((|constructor| (NIL "A constructive unique factorization domain,{} \\spadignore{i.e.} where we can constructively factor members into a product of a finite number of irreducible elements.")) (|factor| (((|Factored| $) $) "\\spad{factor(x)} returns the factorization of \\spad{x} into irreducibles.")) (|squareFreePart| (($ $) "\\spad{squareFreePart(x)} returns a product of prime factors of \\spad{x} each taken with multiplicity one.")) (|squareFree| (((|Factored| $) $) "\\spad{squareFree(x)} returns the square-free factorization of \\spad{x} \\spadignore{i.e.} such that the factors are pairwise relatively prime and each has multiple prime factors.")) (|prime?| (((|Boolean|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) NIL NIL -(-1126) +(-1127) ((|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|) $) "\\spad{prime?(x)} tests if \\spad{x} can never be written as the product of two non-units of the ring,{} \\spadignore{i.e.} \\spad{x} is an irreducible element."))) -((-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1127 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1128 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Laurent series \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Laurent series.}")) (|map| (((|UnivariateLaurentSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariateLaurentSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Laurent series \\spad{g(x)}."))) NIL NIL -(-1128 |Coef|) +(-1129 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateLaurentSeriesCategory} is the category of Laurent series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 1. We may integrate a series when we can divide coefficients by integers.")) (|rationalFunction| (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|) (|Integer|)) "\\spad{rationalFunction(f,{}k1,{}k2)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Fraction| (|Polynomial| |#1|)) $ (|Integer|)) "\\spad{rationalFunction(f,{}k)} returns a rational function consisting of the sum of all terms of \\spad{f} of degree \\spad{<=} \\spad{k}.")) (|multiplyCoefficients| (($ (|Mapping| |#1| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = n0..infinity,{}a[n] * x**n)) = sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Puiseux series are represented by a Laurent series and an exponent.")) (|series| (($ (|Stream| (|Record| (|:| |k| (|Integer|)) (|:| |c| |#1|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1129 S |Coef| UTS) +(-1130 S |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#3| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#3| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#3| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#3|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) NIL ((|HasCategory| |#2| (QUOTE (-339)))) -(-1130 |Coef| UTS) +(-1131 |Coef| UTS) ((|constructor| (NIL "This is a category of univariate Laurent series constructed from univariate Taylor series. A Laurent series is represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}.")) (|taylorIfCan| (((|Union| |#2| "failed") $) "\\spad{taylorIfCan(f(x))} converts the Laurent series \\spad{f(x)} to a Taylor series,{} if possible. If this is not possible,{} \"failed\" is returned.")) (|taylor| ((|#2| $) "\\spad{taylor(f(x))} converts the Laurent series \\spad{f}(\\spad{x}) to a Taylor series,{} if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Taylor series \\spad{f(x)} to a Laurent series.")) (|removeZeroes| (($ (|Integer|) $) "\\spad{removeZeroes(n,{}f(x))} removes up to \\spad{n} leading zeroes from the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable.") (($ $) "\\spad{removeZeroes(f(x))} removes leading zeroes from the representation of the Laurent series \\spad{f(x)}. A Laurent series is represented by (1) an exponent and (2) a Taylor series which may have leading zero coefficients. When the Taylor series has a leading zero coefficient,{} the 'leading zero' is removed from the Laurent series as follows: the series is rewritten by increasing the exponent by 1 and dividing the Taylor series by its variable. Note: \\spad{removeZeroes(f)} removes all leading zeroes from \\spad{f}")) (|taylorRep| ((|#2| $) "\\spad{taylorRep(f(x))} returns \\spad{g(x)},{} where \\spad{f = x**n * g(x)} is represented by \\spad{[n,{}g(x)]}.")) (|degree| (((|Integer|) $) "\\spad{degree(f(x))} returns the degree of the lowest order term of \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurent| (($ (|Integer|) |#2|) "\\spad{laurent(n,{}f(x))} returns \\spad{x**n * f(x)}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-3656 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4069 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1131 |Coef| UTS) +(-1132 |Coef| UTS) ((|constructor| (NIL "This package enables one to construct a univariate Laurent series domain from a univariate Taylor series domain. Univariate Laurent series are represented by a pair \\spad{[n,{}f(x)]},{} where \\spad{n} is an arbitrary integer and \\spad{f(x)} is a Taylor series. This pair represents the Laurent series \\spad{x**n * f(x)}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) -((-3262 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -263) (|devaluate| |#2|) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -484) (QUOTE (-1087)) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-759)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-786)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-840)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-949)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-1063)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -286) (|devaluate| |#2|)))) (-12 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#2| (LIST (QUOTE -964) 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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 -(-1134 R S) +(-1135 R S) ((|constructor| (NIL "This package provides operations for mapping functions onto segments.")) (|map| (((|Stream| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}s)} expands the segment \\spad{s},{} applying \\spad{f} to each value.") (((|UniversalSegment| |#2|) (|Mapping| |#2| |#1|) (|UniversalSegment| |#1|)) "\\spad{map(f,{}seg)} returns the new segment obtained by applying \\spad{f} to the endpoints of \\spad{seg}."))) NIL ((|HasCategory| |#1| (QUOTE (-784)))) -(-1135 S) +(-1136 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 (-784))) (|HasCategory| |#1| (QUOTE (-1016)))) -(-1136 |x| R |y| S) +(-1137 |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 -(-1137 R Q UP) +(-1138 R Q UP) ((|constructor| (NIL "UnivariatePolynomialCommonDenominator provides functions to compute the common denominator of the coefficients of univariate polynomials over the quotient field of a \\spad{gcd} domain.")) (|splitDenominator| (((|Record| (|:| |num| |#3|) (|:| |den| |#1|)) |#3|) "\\spad{splitDenominator(q)} returns \\spad{[p,{} d]} such that \\spad{q = p/d} and \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|clearDenominator| ((|#3| |#3|) "\\spad{clearDenominator(q)} returns \\spad{p} such that \\spad{q = p/d} where \\spad{d} is a common denominator for the coefficients of \\spad{q}.")) (|commonDenominator| ((|#1| |#3|) "\\spad{commonDenominator(q)} returns a common denominator \\spad{d} for the coefficients of \\spad{q}."))) NIL NIL -(-1138 R UP) +(-1139 R UP) ((|constructor| (NIL "UnivariatePolynomialDecompositionPackage implements functional decomposition of univariate polynomial with coefficients in an \\spad{IntegralDomain} of \\spad{CharacteristicZero}.")) (|monicCompleteDecompose| (((|List| |#2|) |#2|) "\\spad{monicCompleteDecompose(f)} returns a list of factors of \\spad{f} for the functional decomposition ([ \\spad{f1},{} ...,{} \\spad{fn} ] means \\spad{f} = \\spad{f1} \\spad{o} ... \\spad{o} \\spad{fn}).")) (|monicDecomposeIfCan| (((|Union| (|Record| (|:| |left| |#2|) (|:| |right| |#2|)) "failed") |#2|) "\\spad{monicDecomposeIfCan(f)} returns a functional decomposition of the monic polynomial \\spad{f} of \"failed\" if it has not found any.")) (|leftFactorIfCan| (((|Union| |#2| "failed") |#2| |#2|) "\\spad{leftFactorIfCan(f,{}h)} returns the left factor (\\spad{g} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of the functional decomposition of the polynomial \\spad{f} with given \\spad{h} or \\spad{\"failed\"} if \\spad{g} does not exist.")) (|rightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|) |#1|) "\\spad{rightFactorIfCan(f,{}d,{}c)} returns a candidate to be the right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} with leading coefficient \\spad{c} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate.")) (|monicRightFactorIfCan| (((|Union| |#2| "failed") |#2| (|NonNegativeInteger|)) "\\spad{monicRightFactorIfCan(f,{}d)} returns a candidate to be the monic right factor (\\spad{h} in \\spad{f} = \\spad{g} \\spad{o} \\spad{h}) of degree \\spad{d} of a functional decomposition of the polynomial \\spad{f} or \\spad{\"failed\"} if no such candidate."))) NIL NIL -(-1139 R UP) +(-1140 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 -(-1140 R U) +(-1141 R U) ((|constructor| (NIL "This package implements Karatsuba\\spad{'s} trick for multiplying (large) univariate polynomials. It could be improved with a version doing the work on place and also with a special case for squares. We've done this in Basicmath,{} but we believe that this out of the scope of AXIOM.")) (|karatsuba| ((|#2| |#2| |#2| (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{karatsuba(a,{}b,{}l,{}k)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick provided that both \\spad{a} and \\spad{b} have at least \\spad{l} terms and \\spad{k > 0} holds and by calling \\spad{noKaratsuba} otherwise. The other multiplications are performed by recursive calls with the same third argument and \\spad{k-1} as fourth argument.")) (|karatsubaOnce| ((|#2| |#2| |#2|) "\\spad{karatsuba(a,{}b)} returns \\spad{a*b} by applying Karatsuba\\spad{'s} trick once. The other multiplications are performed by calling \\spad{*} from \\spad{U}.")) (|noKaratsuba| ((|#2| |#2| |#2|) "\\spad{noKaratsuba(a,{}b)} returns \\spad{a*b} without using Karatsuba\\spad{'s} trick at all."))) NIL NIL -(-1141 |x| R) +(-1142 |x| R) ((|constructor| (NIL "This domain represents univariate polynomials in some symbol over arbitrary (not necessarily commutative) coefficient rings. The representation is sparse in the sense that only non-zero terms are represented.")) 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T)) -((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3262 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3262 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3262 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE -4242)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3262 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) -(-1142 R PR S PS) +(((-4250 "*") |has| |#2| (-158)) (-4241 |has| |#2| (-515)) (-4244 |has| |#2| (-339)) (-4246 |has| |#2| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#2| (QUOTE (-840))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-515)))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-355)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-355))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -817) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -817) (QUOTE (-523))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-355)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -564) (LIST (QUOTE -823) (QUOTE (-523)))))) (-12 (|HasCategory| (-1001) (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#2| (LIST (QUOTE -564) (QUOTE (-499))))) (|HasCategory| |#2| (QUOTE (-786))) (|HasCategory| |#2| (LIST (QUOTE -585) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-136))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (-3172 (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-1063))) (|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (-3172 (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| |#2| (QUOTE (-211))) (|HasAttribute| |#2| (QUOTE -4246)) (|HasCategory| |#2| (QUOTE (-427))) (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (-3172 (-12 (|HasCategory| $ (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-840)))) (|HasCategory| |#2| (QUOTE (-134))))) +(-1143 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 -(-1143 S R) +(-1144 S R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#2|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#2| (|Fraction| $) |#2|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#2| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#2| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#2| |#2|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#2|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#2|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#2|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) NIL ((|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339))) (|HasCategory| |#2| (QUOTE (-427))) (|HasCategory| |#2| (QUOTE (-515))) (|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (QUOTE (-1063)))) -(-1144 R) +(-1145 R) ((|constructor| (NIL "The category of univariate polynomials over a ring \\spad{R}. No particular model is assumed - implementations can be either sparse or dense.")) (|integrate| (($ $) "\\spad{integrate(p)} integrates the univariate polynomial \\spad{p} with respect to its distinguished variable.")) (|additiveValuation| ((|attribute|) "euclideanSize(a*b) = euclideanSize(a) + euclideanSize(\\spad{b})")) (|separate| (((|Record| (|:| |primePart| $) (|:| |commonPart| $)) $ $) "\\spad{separate(p,{} q)} returns \\spad{[a,{} b]} such that polynomial \\spad{p = a b} and \\spad{a} is relatively prime to \\spad{q}.")) (|pseudoDivide| (((|Record| (|:| |coef| |#1|) (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{pseudoDivide(p,{}q)} returns \\spad{[c,{} q,{} r]},{} when \\spad{p' := p*lc(q)**(deg p - deg q + 1) = c * p} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|pseudoQuotient| (($ $ $) "\\spad{pseudoQuotient(p,{}q)} returns \\spad{r},{} the quotient when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|composite| (((|Union| (|Fraction| $) "failed") (|Fraction| $) $) "\\spad{composite(f,{} q)} returns \\spad{h} if \\spad{f} = \\spad{h}(\\spad{q}),{} and \"failed\" is no such \\spad{h} exists.") (((|Union| $ "failed") $ $) "\\spad{composite(p,{} q)} returns \\spad{h} if \\spad{p = h(q)},{} and \"failed\" no such \\spad{h} exists.")) (|subResultantGcd| (($ $ $) "\\spad{subResultantGcd(p,{}q)} computes the \\spad{gcd} of the polynomials \\spad{p} and \\spad{q} using the SubResultant \\spad{GCD} algorithm.")) (|order| (((|NonNegativeInteger|) $ $) "\\spad{order(p,{} q)} returns the largest \\spad{n} such that \\spad{q**n} divides polynomial \\spad{p} \\spadignore{i.e.} the order of \\spad{p(x)} at \\spad{q(x)=0}.")) (|elt| ((|#1| (|Fraction| $) |#1|) "\\spad{elt(a,{}r)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by the constant \\spad{r}.") (((|Fraction| $) (|Fraction| $) (|Fraction| $)) "\\spad{elt(a,{}b)} evaluates the fraction of univariate polynomials \\spad{a} with the distinguished variable replaced by \\spad{b}.")) (|resultant| ((|#1| $ $) "\\spad{resultant(p,{}q)} returns the resultant of the polynomials \\spad{p} and \\spad{q}.")) (|discriminant| ((|#1| $) "\\spad{discriminant(p)} returns the discriminant of the polynomial \\spad{p}.")) (|differentiate| (($ $ (|Mapping| |#1| |#1|) $) "\\spad{differentiate(p,{} d,{} x')} extends the \\spad{R}-derivation \\spad{d} to an extension \\spad{D} in \\spad{R[x]} where \\spad{Dx} is given by \\spad{x'},{} and returns \\spad{Dp}.")) (|pseudoRemainder| (($ $ $) "\\spad{pseudoRemainder(p,{}q)} = \\spad{r},{} for polynomials \\spad{p} and \\spad{q},{} returns the remainder when \\spad{p' := p*lc(q)**(deg p - deg q + 1)} is pseudo right-divided by \\spad{q},{} \\spadignore{i.e.} \\spad{p' = s q + r}.")) (|shiftLeft| (($ $ (|NonNegativeInteger|)) "\\spad{shiftLeft(p,{}n)} returns \\spad{p * monomial(1,{}n)}")) (|shiftRight| (($ $ (|NonNegativeInteger|)) "\\spad{shiftRight(p,{}n)} returns \\spad{monicDivide(p,{}monomial(1,{}n)).quotient}")) (|karatsubaDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ (|NonNegativeInteger|)) "\\spad{karatsubaDivide(p,{}n)} returns the same as \\spad{monicDivide(p,{}monomial(1,{}n))}")) (|monicDivide| (((|Record| (|:| |quotient| $) (|:| |remainder| $)) $ $) "\\spad{monicDivide(p,{}q)} divide the polynomial \\spad{p} by the monic polynomial \\spad{q},{} returning the pair \\spad{[quotient,{} remainder]}. Error: if \\spad{q} isn\\spad{'t} monic.")) (|divideExponents| (((|Union| $ "failed") $ (|NonNegativeInteger|)) "\\spad{divideExponents(p,{}n)} returns a new polynomial resulting from dividing all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n},{} or \"failed\" if some exponent is not exactly divisible by \\spad{n}.")) (|multiplyExponents| (($ $ (|NonNegativeInteger|)) "\\spad{multiplyExponents(p,{}n)} returns a new polynomial resulting from multiplying all exponents of the polynomial \\spad{p} by the non negative integer \\spad{n}.")) (|unmakeSUP| (($ (|SparseUnivariatePolynomial| |#1|)) "\\spad{unmakeSUP(sup)} converts \\spad{sup} of type \\spadtype{SparseUnivariatePolynomial(R)} to be a member of the given type. Note: converse of makeSUP.")) (|makeSUP| (((|SparseUnivariatePolynomial| |#1|) $) "\\spad{makeSUP(p)} converts the polynomial \\spad{p} to be of type SparseUnivariatePolynomial over the same coefficients.")) (|vectorise| (((|Vector| |#1|) $ (|NonNegativeInteger|)) "\\spad{vectorise(p,{} n)} returns \\spad{[a0,{}...,{}a(n-1)]} where \\spad{p = a0 + a1*x + ... + a(n-1)*x**(n-1)} + higher order terms. The degree of polynomial \\spad{p} can be different from \\spad{n-1}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4240 |has| |#1| (-339)) (-4242 |has| |#1| (-6 -4242)) (-4239 . T) (-4238 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4244 |has| |#1| (-339)) (-4246 |has| |#1| (-6 -4246)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL -(-1145 S |Coef| |Expon|) +(-1146 S |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#2|) $ |#2|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#3|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#2| $ |#3|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#3| |#3|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#3|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#3| $ |#3|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#3| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#2| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#2| $ |#3|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#3|) (|:| |c| |#2|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1028))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1458) (LIST (|devaluate| |#2|) (QUOTE (-1087)))))) -(-1146 |Coef| |Expon|) +((|HasCategory| |#2| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#2| (LIST (QUOTE *) (LIST (|devaluate| |#2|) (|devaluate| |#3|) (|devaluate| |#2|)))) (|HasCategory| |#3| (QUOTE (-1028))) (|HasSignature| |#2| (LIST (QUOTE **) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (|devaluate| |#3|)))) (|HasSignature| |#2| (LIST (QUOTE -1691) (LIST (|devaluate| |#2|) (QUOTE (-1087)))))) +(-1147 |Coef| |Expon|) ((|constructor| (NIL "\\spadtype{UnivariatePowerSeriesCategory} is the most general univariate power series category with exponents in an ordered abelian monoid. Note: this category exports a substitution function if it is possible to multiply exponents. Note: this category exports a derivative operation if it is possible to multiply coefficients by exponents.")) (|eval| (((|Stream| |#1|) $ |#1|) "\\spad{eval(f,{}a)} evaluates a power series at a value in the ground ring by returning a stream of partial sums.")) (|extend| (($ $ |#2|) "\\spad{extend(f,{}n)} causes all terms of \\spad{f} of degree \\spad{<=} \\spad{n} to be computed.")) (|approximate| ((|#1| $ |#2|) "\\spad{approximate(f)} returns a truncated power series with the series variable viewed as an element of the coefficient domain.")) (|truncate| (($ $ |#2| |#2|) "\\spad{truncate(f,{}k1,{}k2)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (($ $ |#2|) "\\spad{truncate(f,{}k)} returns a (finite) power series consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|order| ((|#2| $ |#2|) "\\spad{order(f,{}n) = min(m,{}n)},{} where \\spad{m} is the degree of the lowest order non-zero term in \\spad{f}.") ((|#2| $) "\\spad{order(f)} is the degree of the lowest order non-zero term in \\spad{f}. This will result in an infinite loop if \\spad{f} has no non-zero terms.")) (|multiplyExponents| (($ $ (|PositiveInteger|)) "\\spad{multiplyExponents(f,{}n)} multiplies all exponents of the power series \\spad{f} by the positive integer \\spad{n}.")) (|center| ((|#1| $) "\\spad{center(f)} returns the point about which the series \\spad{f} is expanded.")) (|variable| (((|Symbol|) $) "\\spad{variable(f)} returns the (unique) power series variable of the power series \\spad{f}.")) (|elt| ((|#1| $ |#2|) "\\spad{elt(f(x),{}r)} returns the coefficient of the term of degree \\spad{r} in \\spad{f(x)}. This is the same as the function \\spadfun{coefficient}.")) (|terms| (((|Stream| (|Record| (|:| |k| |#2|) (|:| |c| |#1|))) $) "\\spad{terms(f(x))} returns a stream of non-zero terms,{} where a a term is an exponent-coefficient pair. The terms in the stream are ordered by increasing order of exponents."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1147 RC P) +(-1148 RC P) ((|constructor| (NIL "This package provides for square-free decomposition of univariate polynomials over arbitrary rings,{} \\spadignore{i.e.} a partial factorization such that each factor is a product of irreducibles with multiplicity one and the factors are pairwise relatively prime. If the ring has characteristic zero,{} the result is guaranteed to satisfy this condition. If the ring is an infinite ring of finite characteristic,{} then it may not be possible to decide when polynomials contain factors which are \\spad{p}th powers. In this case,{} the flag associated with that polynomial is set to \"nil\" (meaning that that polynomials are not guaranteed to be square-free).")) (|BumInSepFFE| (((|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|))) (|Record| (|:| |flg| (|Union| "nil" "sqfr" "irred" "prime")) (|:| |fctr| |#2|) (|:| |xpnt| (|Integer|)))) "\\spad{BumInSepFFE(f)} is a local function,{} exported only because it has multiple conditional definitions.")) (|squareFreePart| ((|#2| |#2|) "\\spad{squareFreePart(p)} returns a polynomial which has the same irreducible factors as the univariate polynomial \\spad{p},{} but each factor has multiplicity one.")) (|squareFree| (((|Factored| |#2|) |#2|) "\\spad{squareFree(p)} computes the square-free factorization of the univariate polynomial \\spad{p}. Each factor has no repeated roots,{} and the factors are pairwise relatively prime.")) (|gcd| (($ $ $) "\\spad{gcd(p,{}q)} computes the greatest-common-divisor of \\spad{p} and \\spad{q}."))) NIL NIL -(-1148 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) +(-1149 |Coef1| |Coef2| |var1| |var2| |cen1| |cen2|) ((|constructor| (NIL "Mapping package for univariate Puiseux series. This package allows one to apply a function to the coefficients of a univariate Puiseux series.")) (|map| (((|UnivariatePuiseuxSeries| |#2| |#4| |#6|) (|Mapping| |#2| |#1|) (|UnivariatePuiseuxSeries| |#1| |#3| |#5|)) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of the Puiseux series \\spad{g(x)}."))) NIL NIL -(-1149 |Coef|) +(-1150 |Coef|) ((|constructor| (NIL "\\spadtype{UnivariatePuiseuxSeriesCategory} is the category of Puiseux series in one variable.")) (|integrate| (($ $ (|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."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1150 S |Coef| ULS) +(-1151 S |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#3| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#3| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#3|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#3| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#3|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) NIL NIL -(-1151 |Coef| ULS) +(-1152 |Coef| ULS) ((|constructor| (NIL "This is a category of univariate Puiseux series constructed from univariate Laurent series. A Puiseux series is represented by a pair \\spad{[r,{}f(x)]},{} where \\spad{r} is a positive rational number and \\spad{f(x)} is a Laurent series. This pair represents the Puiseux series \\spad{f(x^r)}.")) (|laurentIfCan| (((|Union| |#2| "failed") $) "\\spad{laurentIfCan(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. If this is not possible,{} \"failed\" is returned.")) (|laurent| ((|#2| $) "\\spad{laurent(f(x))} converts the Puiseux series \\spad{f(x)} to a Laurent series if possible. Error: if this is not possible.")) (|coerce| (($ |#2|) "\\spad{coerce(f(x))} converts the Laurent series \\spad{f(x)} to a Puiseux series.")) (|degree| (((|Fraction| (|Integer|)) $) "\\spad{degree(f(x))} returns the degree of the leading term of the Puiseux series \\spad{f(x)},{} which may have zero as a coefficient.")) (|laurentRep| ((|#2| $) "\\spad{laurentRep(f(x))} returns \\spad{g(x)} where the Puiseux series \\spad{f(x) = g(x^r)} is represented by \\spad{[r,{}g(x)]}.")) (|rationalPower| (((|Fraction| (|Integer|)) $) "\\spad{rationalPower(f(x))} returns \\spad{r} where the Puiseux series \\spad{f(x) = g(x^r)}.")) (|puiseux| (($ (|Fraction| (|Integer|)) |#2|) "\\spad{puiseux(r,{}f(x))} returns \\spad{f(x^r)}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1152 |Coef| ULS) +(-1153 |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)}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1458) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3262 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1957) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) -(-1153 |Coef| |var| |cen|) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|)))))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) +(-1154 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Puiseux series in one variable \\indented{2}{\\spadtype{UnivariatePuiseuxSeries} is a domain representing Puiseux} \\indented{2}{series in one variable with coefficients in an arbitrary ring.\\space{2}The} \\indented{2}{parameters of the type specify the coefficient ring,{} the power series} \\indented{2}{variable,{} and the center of the power series expansion.\\space{2}For example,{}} \\indented{2}{\\spad{UnivariatePuiseuxSeries(Integer,{}x,{}3)} represents Puiseux series in} \\indented{2}{\\spad{(x - 3)} with \\spadtype{Integer} coefficients.}")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} returns the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a Puiseux series."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4242 |has| |#1| (-339)) (-4236 |has| |#1| (-339)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3262 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1458) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3262 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1957) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) -(-1154 R FE |var| |cen|) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4246 |has| |#1| (-339)) (-4240 |has| |#1| (-339)) (-4242 . 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T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#1| (QUOTE (-158))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523))) (|devaluate| |#1|)))) (|HasCategory| (-383 (-523)) (QUOTE (-1028))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-3172 (|HasCategory| |#1| (QUOTE (-339))) (|HasCategory| |#1| (QUOTE (-515)))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (LIST (QUOTE -383) (QUOTE (-523)))))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +(-1155 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))}."))) -(((-4246 "*") |has| (-1153 |#2| |#3| |#4|) (-158)) (-4237 |has| (-1153 |#2| |#3| |#4|) (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| (-1153 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1153 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1153 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1153 |#2| |#3| |#4|) (QUOTE (-158))) (|HasCategory| (-1153 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1153 |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-1153 |#2| |#3| |#4|) (QUOTE (-339))) (|HasCategory| (-1153 |#2| |#3| |#4|) (QUOTE (-427))) (-3262 (|HasCategory| (-1153 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1153 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| (-1153 |#2| |#3| |#4|) (QUOTE (-515)))) -(-1155 A S) +(((-4250 "*") |has| (-1154 |#2| |#3| |#4|) (-158)) (-4241 |has| (-1154 |#2| |#3| |#4|) (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-134))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-136))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-158))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (QUOTE (-523)))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-339))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-427))) (-3172 (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (LIST (QUOTE -964) (LIST (QUOTE -383) (QUOTE (-523)))))) (|HasCategory| (-1154 |#2| |#3| |#4|) (QUOTE (-515)))) +(-1156 A S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#2| $ |#2|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#2| $ "last" |#2|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#2| $ "first" |#2|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#2| $ |#2|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#2|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#2| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#2| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#2| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#2| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#2| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#2| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#2| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) NIL -((|HasAttribute| |#1| (QUOTE -4245))) -(-1156 S) +((|HasAttribute| |#1| (QUOTE -4249))) +(-1157 S) ((|constructor| (NIL "A unary-recursive aggregate is a one where nodes may have either 0 or 1 children. This aggregate models,{} though not precisely,{} a linked list possibly with a single cycle. A node with one children models a non-empty list,{} with the \\spadfun{value} of the list designating the head,{} or \\spadfun{first},{} of the list,{} and the child designating the tail,{} or \\spadfun{rest},{} of the list. A node with no child then designates the empty list. Since these aggregates are recursive aggregates,{} they may be cyclic.")) (|split!| (($ $ (|Integer|)) "\\spad{split!(u,{}n)} splits \\spad{u} into two aggregates: \\axiom{\\spad{v} = rest(\\spad{u},{}\\spad{n})} and \\axiom{\\spad{w} = first(\\spad{u},{}\\spad{n})},{} returning \\axiom{\\spad{v}}. Note: afterwards \\axiom{rest(\\spad{u},{}\\spad{n})} returns \\axiom{empty()}.")) (|setlast!| ((|#1| $ |#1|) "\\spad{setlast!(u,{}x)} destructively changes the last element of \\spad{u} to \\spad{x}.")) (|setrest!| (($ $ $) "\\spad{setrest!(u,{}v)} destructively changes the rest of \\spad{u} to \\spad{v}.")) (|setelt| ((|#1| $ "last" |#1|) "\\spad{setelt(u,{}\"last\",{}x)} (also written: \\axiom{\\spad{u}.last \\spad{:=} \\spad{b}}) is equivalent to \\axiom{setlast!(\\spad{u},{}\\spad{v})}.") (($ $ "rest" $) "\\spad{setelt(u,{}\"rest\",{}v)} (also written: \\axiom{\\spad{u}.rest \\spad{:=} \\spad{v}}) is equivalent to \\axiom{setrest!(\\spad{u},{}\\spad{v})}.") ((|#1| $ "first" |#1|) "\\spad{setelt(u,{}\"first\",{}x)} (also written: \\axiom{\\spad{u}.first \\spad{:=} \\spad{x}}) is equivalent to \\axiom{setfirst!(\\spad{u},{}\\spad{x})}.")) (|setfirst!| ((|#1| $ |#1|) "\\spad{setfirst!(u,{}x)} destructively changes the first element of a to \\spad{x}.")) (|cycleSplit!| (($ $) "\\spad{cycleSplit!(u)} splits the aggregate by dropping off the cycle. The value returned is the cycle entry,{} or nil if none exists. For example,{} if \\axiom{\\spad{w} = concat(\\spad{u},{}\\spad{v})} is the cyclic list where \\spad{v} is the head of the cycle,{} \\axiom{cycleSplit!(\\spad{w})} will drop \\spad{v} off \\spad{w} thus destructively changing \\spad{w} to \\spad{u},{} and returning \\spad{v}.")) (|concat!| (($ $ |#1|) "\\spad{concat!(u,{}x)} destructively adds element \\spad{x} to the end of \\spad{u}. Note: \\axiom{concat!(a,{}\\spad{x}) = setlast!(a,{}[\\spad{x}])}.") (($ $ $) "\\spad{concat!(u,{}v)} destructively concatenates \\spad{v} to the end of \\spad{u}. Note: \\axiom{concat!(\\spad{u},{}\\spad{v}) = setlast_!(\\spad{u},{}\\spad{v})}.")) (|cycleTail| (($ $) "\\spad{cycleTail(u)} returns the last node in the cycle,{} or empty if none exists.")) (|cycleLength| (((|NonNegativeInteger|) $) "\\spad{cycleLength(u)} returns the length of a top-level cycle contained in aggregate \\spad{u},{} or 0 is \\spad{u} has no such cycle.")) (|cycleEntry| (($ $) "\\spad{cycleEntry(u)} returns the head of a top-level cycle contained in aggregate \\spad{u},{} or \\axiom{empty()} if none exists.")) (|third| ((|#1| $) "\\spad{third(u)} returns the third element of \\spad{u}. Note: \\axiom{third(\\spad{u}) = first(rest(rest(\\spad{u})))}.")) (|second| ((|#1| $) "\\spad{second(u)} returns the second element of \\spad{u}. Note: \\axiom{second(\\spad{u}) = first(rest(\\spad{u}))}.")) (|tail| (($ $) "\\spad{tail(u)} returns the last node of \\spad{u}. Note: if \\spad{u} is \\axiom{shallowlyMutable},{} \\axiom{setrest(tail(\\spad{u}),{}\\spad{v}) = concat(\\spad{u},{}\\spad{v})}.")) (|last| (($ $ (|NonNegativeInteger|)) "\\spad{last(u,{}n)} returns a copy of the last \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) nodes of \\spad{u}. Note: \\axiom{last(\\spad{u},{}\\spad{n})} is a list of \\spad{n} elements.") ((|#1| $) "\\spad{last(u)} resturn the last element of \\spad{u}. Note: for lists,{} \\axiom{last(\\spad{u}) = \\spad{u} . (maxIndex \\spad{u}) = \\spad{u} . (\\# \\spad{u} - 1)}.")) (|rest| (($ $ (|NonNegativeInteger|)) "\\spad{rest(u,{}n)} returns the \\axiom{\\spad{n}}th (\\spad{n} \\spad{>=} 0) node of \\spad{u}. Note: \\axiom{rest(\\spad{u},{}0) = \\spad{u}}.") (($ $) "\\spad{rest(u)} returns an aggregate consisting of all but the first element of \\spad{u} (equivalently,{} the next node of \\spad{u}).")) (|elt| ((|#1| $ "last") "\\spad{elt(u,{}\"last\")} (also written: \\axiom{\\spad{u} . last}) is equivalent to last \\spad{u}.") (($ $ "rest") "\\spad{elt(\\%,{}\"rest\")} (also written: \\axiom{\\spad{u}.rest}) is equivalent to \\axiom{rest \\spad{u}}.") ((|#1| $ "first") "\\spad{elt(u,{}\"first\")} (also written: \\axiom{\\spad{u} . first}) is equivalent to first \\spad{u}.")) (|first| (($ $ (|NonNegativeInteger|)) "\\spad{first(u,{}n)} returns a copy of the first \\spad{n} (\\axiom{\\spad{n} \\spad{>=} 0}) elements of \\spad{u}.") ((|#1| $) "\\spad{first(u)} returns the first element of \\spad{u} (equivalently,{} the value at the current node).")) (|concat| (($ |#1| $) "\\spad{concat(x,{}u)} returns aggregate consisting of \\spad{x} followed by the elements of \\spad{u}. Note: if \\axiom{\\spad{v} = concat(\\spad{x},{}\\spad{u})} then \\axiom{\\spad{x} = first \\spad{v}} and \\axiom{\\spad{u} = rest \\spad{v}}.") (($ $ $) "\\spad{concat(u,{}v)} returns an aggregate \\spad{w} consisting of the elements of \\spad{u} followed by the elements of \\spad{v}. Note: \\axiom{\\spad{v} = rest(\\spad{w},{}\\#a)}."))) -((-3656 . T)) +((-4069 . T)) NIL -(-1157 |Coef1| |Coef2| UTS1 UTS2) +(-1158 |Coef1| |Coef2| UTS1 UTS2) ((|constructor| (NIL "Mapping package for univariate Taylor series. \\indented{2}{This package allows one to apply a function to the coefficients of} \\indented{2}{a univariate Taylor series.}")) (|map| ((|#4| (|Mapping| |#2| |#1|) |#3|) "\\spad{map(f,{}g(x))} applies the map \\spad{f} to the coefficients of \\indented{1}{the Taylor series \\spad{g(x)}.}"))) NIL NIL -(-1158 S |Coef|) +(-1159 S |Coef|) ((|constructor| (NIL "\\spadtype{UnivariateTaylorSeriesCategory} is the category of Taylor series in one variable.")) (|integrate| (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $ (|Symbol|)) "\\spad{integrate(f(x),{}y)} returns an anti-derivative of the power series \\spad{f(x)} with respect to the variable \\spad{y}.") (($ $) "\\spad{integrate(f(x))} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (** (($ $ |#2|) "\\spad{f(x) ** a} computes a power of a power series. When the coefficient ring is a field,{} we may raise a series to an exponent from the coefficient ring provided that the constant coefficient of the series is 1.")) (|polynomial| (((|Polynomial| |#2|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k1,{}k2)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{d} with \\spad{k1 <= d <= k2}.") (((|Polynomial| |#2|) $ (|NonNegativeInteger|)) "\\spad{polynomial(f,{}k)} returns a polynomial consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.")) (|multiplyCoefficients| (($ (|Mapping| |#2| (|Integer|)) $) "\\spad{multiplyCoefficients(f,{}sum(n = 0..infinity,{}a[n] * x**n))} returns \\spad{sum(n = 0..infinity,{}f(n) * a[n] * x**n)}. This function is used when Laurent series are represented by a Taylor series and an order.")) (|quoByVar| (($ $) "\\spad{quoByVar(a0 + a1 x + a2 x**2 + ...)} returns \\spad{a1 + a2 x + a3 x**2 + ...} Thus,{} this function substracts the constant term and divides by the series variable. This function is used when Laurent series are represented by a Taylor series and an order.")) (|coefficients| (((|Stream| |#2|) $) "\\spad{coefficients(a0 + a1 x + a2 x**2 + ...)} returns a stream of coefficients: \\spad{[a0,{}a1,{}a2,{}...]}. The entries of the stream may be zero.")) (|series| (($ (|Stream| |#2|)) "\\spad{series([a0,{}a1,{}a2,{}...])} is the Taylor series \\spad{a0 + a1 x + a2 x**2 + ...}.") (($ (|Stream| (|Record| (|:| |k| (|NonNegativeInteger|)) (|:| |c| |#2|)))) "\\spad{series(st)} creates a series from a stream of non-zero terms,{} where a term is an exponent-coefficient pair. The terms in the stream should be ordered by increasing order of exponents."))) NIL -((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-889))) (|HasCategory| |#2| (QUOTE (-1108))) (|HasSignature| |#2| (LIST (QUOTE -1957) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -3417) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1087))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339)))) -(-1159 |Coef|) +((|HasCategory| |#2| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#2| (QUOTE (-889))) (|HasCategory| |#2| (QUOTE (-1109))) (|HasSignature| |#2| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#2|)))) (|HasSignature| |#2| (LIST (QUOTE -2814) (LIST (|devaluate| |#2|) (|devaluate| |#2|) (QUOTE (-1087))))) (|HasCategory| |#2| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#2| (QUOTE (-339)))) +(-1160 |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."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1160 |Coef| |var| |cen|) +(-1161 |Coef| |var| |cen|) ((|constructor| (NIL "Dense Taylor series in one variable \\spadtype{UnivariateTaylorSeries} is a domain representing Taylor series in one variable with coefficients in an arbitrary ring. The parameters of the type specify the coefficient ring,{} the power series variable,{} and the center of the power series expansion. For example,{} \\spadtype{UnivariateTaylorSeries}(Integer,{}\\spad{x},{}3) represents Taylor series in \\spad{(x - 3)} with \\spadtype{Integer} coefficients.")) (|integrate| (($ $ (|Variable| |#2|)) "\\spad{integrate(f(x),{}x)} returns an anti-derivative of the power series \\spad{f(x)} with constant coefficient 0. We may integrate a series when we can divide coefficients by integers.")) (|invmultisect| (($ (|Integer|) (|Integer|) $) "\\spad{invmultisect(a,{}b,{}f(x))} substitutes \\spad{x^((a+b)*n)} \\indented{1}{for \\spad{x^n} and multiples by \\spad{x^b}.}")) (|multisect| (($ (|Integer|) (|Integer|) $) "\\spad{multisect(a,{}b,{}f(x))} selects the coefficients of \\indented{1}{\\spad{x^((a+b)*n+a)},{} and changes this monomial to \\spad{x^n}.}")) (|revert| (($ $) "\\spad{revert(f(x))} returns a Taylor series \\spad{g(x)} such that \\spad{f(g(x)) = g(f(x)) = x}. Series \\spad{f(x)} should have constant coefficient 0 and 1st order coefficient 1.")) (|generalLambert| (($ $ (|Integer|) (|Integer|)) "\\spad{generalLambert(f(x),{}a,{}d)} returns \\spad{f(x^a) + f(x^(a + d)) + \\indented{1}{f(x^(a + 2 d)) + ... }. \\spad{f(x)} should have zero constant} \\indented{1}{coefficient and \\spad{a} and \\spad{d} should be positive.}")) (|evenlambert| (($ $) "\\spad{evenlambert(f(x))} returns \\spad{f(x^2) + f(x^4) + f(x^6) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n))) = exp(log(evenlambert(f(x))))}.}")) (|oddlambert| (($ $) "\\spad{oddlambert(f(x))} returns \\spad{f(x) + f(x^3) + f(x^5) + ...}. \\indented{1}{\\spad{f(x)} should have a zero constant coefficient.} \\indented{1}{This function is used for computing infinite products.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n=1..infinity,{}f(x^(2*n-1)))=exp(log(oddlambert(f(x))))}.}")) (|lambert| (($ $) "\\spad{lambert(f(x))} returns \\spad{f(x) + f(x^2) + f(x^3) + ...}. \\indented{1}{This function is used for computing infinite products.} \\indented{1}{\\spad{f(x)} should have zero constant coefficient.} \\indented{1}{If \\spad{f(x)} is a Taylor series with constant term 1,{} then} \\indented{1}{\\spad{product(n = 1..infinity,{}f(x^n)) = exp(log(lambert(f(x))))}.}")) (|lagrange| (($ $) "\\spad{lagrange(g(x))} produces the Taylor series for \\spad{f(x)} \\indented{1}{where \\spad{f(x)} is implicitly defined as \\spad{f(x) = x*g(f(x))}.}")) (|differentiate| (($ $ (|Variable| |#2|)) "\\spad{differentiate(f(x),{}x)} computes the derivative of \\spad{f(x)} with respect to \\spad{x}.")) (|univariatePolynomial| (((|UnivariatePolynomial| |#2| |#1|) $ (|NonNegativeInteger|)) "\\spad{univariatePolynomial(f,{}k)} returns a univariate polynomial \\indented{1}{consisting of the sum of all terms of \\spad{f} of degree \\spad{<= k}.}")) (|coerce| (($ (|Variable| |#2|)) "\\spad{coerce(var)} converts the series variable \\spad{var} into a \\indented{1}{Taylor series.}") (($ (|UnivariatePolynomial| |#2| |#1|)) "\\spad{coerce(p)} converts a univariate polynomial \\spad{p} in the variable \\spad{var} to a univariate Taylor series in \\spad{var}."))) -(((-4246 "*") |has| |#1| (-158)) (-4237 |has| |#1| (-515)) (-4238 . T) (-4239 . T) (-4241 . T)) -((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3262 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -1458) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3262 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1108))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -3417) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1957) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) -(-1161 |Coef| UTS) +(((-4250 "*") |has| |#1| (-158)) (-4241 |has| |#1| (-515)) (-4242 . T) (-4243 . T) (-4245 . T)) +((|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasCategory| |#1| (QUOTE (-515))) (-3172 (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-515)))) (|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-134))) (|HasCategory| |#1| (QUOTE (-136))) (-12 (|HasCategory| |#1| (LIST (QUOTE -831) (QUOTE (-1087)))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|))))) (|HasSignature| |#1| (LIST (QUOTE *) (LIST (|devaluate| |#1|) (QUOTE (-710)) (|devaluate| |#1|)))) (|HasCategory| (-710) (QUOTE (-1028))) (-12 (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasSignature| |#1| (LIST (QUOTE -1691) (LIST (|devaluate| |#1|) (QUOTE (-1087)))))) (|HasSignature| |#1| (LIST (QUOTE **) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-710))))) (|HasCategory| |#1| (QUOTE (-339))) (-3172 (-12 (|HasCategory| |#1| (LIST (QUOTE -29) (QUOTE (-523)))) (|HasCategory| |#1| (QUOTE (-889))) (|HasCategory| |#1| (QUOTE (-1109))) (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523)))))) (-12 (|HasCategory| |#1| (LIST (QUOTE -37) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasSignature| |#1| (LIST (QUOTE -2814) (LIST (|devaluate| |#1|) (|devaluate| |#1|) (QUOTE (-1087))))) (|HasSignature| |#1| (LIST (QUOTE -1292) (LIST (LIST (QUOTE -589) (QUOTE (-1087))) (|devaluate| |#1|))))))) +(-1162 |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 -(-1162 -2315 UP L UTS) +(-1163 -3539 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 (-515)))) -(-1163) +(-1164) ((|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."))) -((-3656 . T)) +((-4069 . T)) NIL -(-1164 |sym|) +(-1165 |sym|) ((|constructor| (NIL "This domain implements variables")) (|variable| (((|Symbol|)) "\\spad{variable()} returns the symbol")) (|coerce| (((|Symbol|) $) "\\spad{coerce(x)} returns the symbol"))) NIL NIL -(-1165 S R) +(-1166 S R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#2| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#2| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#2|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#2| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#2|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#2| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) NIL ((|HasCategory| |#2| (QUOTE (-930))) (|HasCategory| |#2| (QUOTE (-973))) (|HasCategory| |#2| (QUOTE (-666))) (|HasCategory| |#2| (QUOTE (-21))) (|HasCategory| |#2| (QUOTE (-23))) (|HasCategory| |#2| (QUOTE (-25)))) -(-1166 R) +(-1167 R) ((|constructor| (NIL "\\spadtype{VectorCategory} represents the type of vector like objects,{} \\spadignore{i.e.} finite sequences indexed by some finite segment of the integers. The operations available on vectors depend on the structure of the underlying components. Many operations from the component domain are defined for vectors componentwise. It can by assumed that extraction or updating components can be done in constant time.")) (|magnitude| ((|#1| $) "\\spad{magnitude(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the length")) (|length| ((|#1| $) "\\spad{length(v)} computes the sqrt(dot(\\spad{v},{}\\spad{v})),{} \\spadignore{i.e.} the magnitude")) (|cross| (($ $ $) "vectorProduct(\\spad{u},{}\\spad{v}) constructs the cross product of \\spad{u} and \\spad{v}. Error: if \\spad{u} and \\spad{v} are not of length 3.")) (|outerProduct| (((|Matrix| |#1|) $ $) "\\spad{outerProduct(u,{}v)} constructs the matrix whose (\\spad{i},{}\\spad{j})\\spad{'}th element is \\spad{u}(\\spad{i})\\spad{*v}(\\spad{j}).")) (|dot| ((|#1| $ $) "\\spad{dot(x,{}y)} computes the inner product of the two vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.")) (* (($ $ |#1|) "\\spad{y * r} multiplies each component of the vector \\spad{y} by the element \\spad{r}.") (($ |#1| $) "\\spad{r * y} multiplies the element \\spad{r} times each component of the vector \\spad{y}.") (($ (|Integer|) $) "\\spad{n * y} multiplies each component of the vector \\spad{y} by the integer \\spad{n}.")) (- (($ $ $) "\\spad{x - y} returns the component-wise difference of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length.") (($ $) "\\spad{-x} negates all components of the vector \\spad{x}.")) (|zero| (($ (|NonNegativeInteger|)) "\\spad{zero(n)} creates a zero vector of length \\spad{n}.")) (+ (($ $ $) "\\spad{x + y} returns the component-wise sum of the vectors \\spad{x} and \\spad{y}. Error: if \\spad{x} and \\spad{y} are not of the same length."))) -((-4245 . T) (-4244 . T) (-3656 . T)) +((-4249 . T) (-4248 . T) (-4069 . T)) NIL -(-1167 A B) +(-1168 A B) ((|constructor| (NIL "\\indented{2}{This package provides operations which all take as arguments} vectors of elements of some type \\spad{A} and functions from \\spad{A} to another of type \\spad{B}. The operations all iterate over their vector argument and either return a value of type \\spad{B} or a vector over \\spad{B}.")) (|map| (((|Union| (|Vector| |#2|) "failed") (|Mapping| (|Union| |#2| "failed") |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values or \\spad{\"failed\"}.") (((|Vector| |#2|) (|Mapping| |#2| |#1|) (|Vector| |#1|)) "\\spad{map(f,{} v)} applies the function \\spad{f} to every element of the vector \\spad{v} producing a new vector containing the values.")) (|reduce| ((|#2| (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{reduce(func,{}vec,{}ident)} combines the elements in \\spad{vec} using the binary function \\spad{func}. Argument \\spad{ident} is returned if \\spad{vec} is empty.")) (|scan| (((|Vector| |#2|) (|Mapping| |#2| |#1| |#2|) (|Vector| |#1|) |#2|) "\\spad{scan(func,{}vec,{}ident)} creates a new vector whose elements are the result of applying reduce to the binary function \\spad{func},{} increasing initial subsequences of the vector \\spad{vec},{} and the element \\spad{ident}."))) NIL NIL -(-1168 R) +(-1169 R) ((|constructor| (NIL "This type represents vector like objects with varying lengths and indexed by a finite segment of integers starting at 1.")) (|vector| (($ (|List| |#1|)) "\\spad{vector(l)} converts the list \\spad{l} to a vector."))) -((-4245 . T) (-4244 . T)) -((-3262 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3262 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3262 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) -(-1169) +((-4249 . T) (-4248 . T)) +((-3172 (-12 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|))))) (-3172 (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) (|HasCategory| |#1| (LIST (QUOTE -564) (QUOTE (-499)))) (-3172 (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016)))) (|HasCategory| |#1| (QUOTE (-786))) (|HasCategory| (-523) (QUOTE (-786))) (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-25))) (|HasCategory| |#1| (QUOTE (-23))) (|HasCategory| |#1| (QUOTE (-21))) (|HasCategory| |#1| (QUOTE (-666))) (|HasCategory| |#1| (QUOTE (-973))) (-12 (|HasCategory| |#1| (QUOTE (-930))) (|HasCategory| |#1| (QUOTE (-973)))) (-12 (|HasCategory| |#1| (QUOTE (-1016))) (|HasCategory| |#1| (LIST (QUOTE -286) (|devaluate| |#1|)))) (|HasCategory| |#1| (LIST (QUOTE -563) (QUOTE (-794))))) +(-1170) ((|constructor| (NIL "TwoDimensionalViewport creates viewports to display graphs.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} returns the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport} as output of the domain \\spadtype{OutputForm}.")) (|key| (((|Integer|) $) "\\spad{key(v)} returns the process ID number of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|reset| (((|Void|) $) "\\spad{reset(v)} sets the current state of the graph characteristics of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} back to their initial settings.")) (|write| (((|String|) $ (|String|) (|List| (|String|))) "\\spad{write(v,{}s,{}lf)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and the optional file types indicated by the list \\spad{lf}.") (((|String|) $ (|String|) (|String|)) "\\spad{write(v,{}s,{}f)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v} and an optional file type \\spad{f}.") (((|String|) $ (|String|)) "\\spad{write(v,{}s)} takes the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and creates a directory indicated by \\spad{s},{} which contains the graph data files for \\spad{v}.")) (|resize| (((|Void|) $ (|PositiveInteger|) (|PositiveInteger|)) "\\spad{resize(v,{}w,{}h)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with a width of \\spad{w} and a height of \\spad{h},{} keeping the upper left-hand corner position unchanged.")) (|update| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{update(v,{}gr,{}n)} drops the graph \\spad{gr} in slot \\spad{n} of viewport \\spad{v}. The graph \\spad{gr} must have been transmitted already and acquired an integer key.")) (|move| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|)) "\\spad{move(v,{}x,{}y)} displays the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the upper left-hand corner of the viewport window at the screen coordinate position \\spad{x},{} \\spad{y}.")) (|show| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{show(v,{}n,{}s)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the graph if \\spad{s} is \"off\".")) (|translate| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{translate(v,{}n,{}dx,{}dy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} translated by \\spad{dx} in the \\spad{x}-coordinate direction from the center of the viewport,{} and by \\spad{dy} in the \\spad{y}-coordinate direction from the center. Setting \\spad{dx} and \\spad{dy} to \\spad{0} places the center of the graph at the center of the viewport.")) (|scale| (((|Void|) $ (|PositiveInteger|) (|Float|) (|Float|)) "\\spad{scale(v,{}n,{}sx,{}sy)} displays the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} scaled by the factor \\spad{sx} in the \\spad{x}-coordinate direction and by the factor \\spad{sy} in the \\spad{y}-coordinate direction.")) (|dimensions| (((|Void|) $ (|NonNegativeInteger|) (|NonNegativeInteger|) (|PositiveInteger|) (|PositiveInteger|)) "\\spad{dimensions(v,{}x,{}y,{}width,{}height)} sets the position of the upper left-hand corner of the two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to the window coordinate \\spad{x},{} \\spad{y},{} and sets the dimensions of the window to that of \\spad{width},{} \\spad{height}. The new dimensions are not displayed until the function \\spadfun{makeViewport2D} is executed again for \\spad{v}.")) (|close| (((|Void|) $) "\\spad{close(v)} closes the viewport window of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} and terminates the corresponding process ID.")) (|controlPanel| (((|Void|) $ (|String|)) "\\spad{controlPanel(v,{}s)} displays the control panel of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or hides the control panel if \\spad{s} is \"off\".")) (|connect| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{connect(v,{}n,{}s)} displays the lines connecting the graph points in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the lines if \\spad{s} is \"off\".")) (|region| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{region(v,{}n,{}s)} displays the bounding box of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the bounding box if \\spad{s} is \"off\".")) (|points| (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{points(v,{}n,{}s)} displays the points of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the points if \\spad{s} is \"off\".")) (|units| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{units(v,{}n,{}c)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the units color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{units(v,{}n,{}s)} displays the units of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the units if \\spad{s} is \"off\".")) (|axes| (((|Void|) $ (|PositiveInteger|) (|Palette|)) "\\spad{axes(v,{}n,{}c)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} with the axes color set to the given palette color \\spad{c}.") (((|Void|) $ (|PositiveInteger|) (|String|)) "\\spad{axes(v,{}n,{}s)} displays the axes of the graph in field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} if \\spad{s} is \"on\",{} or does not display the axes if \\spad{s} is \"off\".")) (|getGraph| (((|GraphImage|) $ (|PositiveInteger|)) "\\spad{getGraph(v,{}n)} returns the graph which is of the domain \\spadtype{GraphImage} which is located in graph field \\spad{n} of the given two-dimensional viewport,{} \\spad{v},{} which is of the domain \\spadtype{TwoDimensionalViewport}.")) (|putGraph| (((|Void|) $ (|GraphImage|) (|PositiveInteger|)) "\\spad{putGraph(v,{}\\spad{gi},{}n)} sets the graph field indicated by \\spad{n},{} of the indicated two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport},{} to be the graph,{} \\spad{\\spad{gi}} of domain \\spadtype{GraphImage}. The contents of viewport,{} \\spad{v},{} will contain \\spad{\\spad{gi}} when the function \\spadfun{makeViewport2D} is called to create the an updated viewport \\spad{v}.")) (|title| (((|Void|) $ (|String|)) "\\spad{title(v,{}s)} changes the title which is shown in the two-dimensional viewport window,{} \\spad{v} of domain \\spadtype{TwoDimensionalViewport}.")) (|graphs| (((|Vector| (|Union| (|GraphImage|) "undefined")) $) "\\spad{graphs(v)} returns a vector,{} or list,{} which is a union of all the graphs,{} of the domain \\spadtype{GraphImage},{} which are allocated for the two-dimensional viewport,{} \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport}. Those graphs which have no data are labeled \"undefined\",{} otherwise their contents are shown.")) (|graphStates| (((|Vector| (|Record| (|:| |scaleX| (|DoubleFloat|)) (|:| |scaleY| (|DoubleFloat|)) (|:| |deltaX| (|DoubleFloat|)) (|:| |deltaY| (|DoubleFloat|)) (|:| |points| (|Integer|)) (|:| |connect| (|Integer|)) (|:| |spline| (|Integer|)) (|:| |axes| (|Integer|)) (|:| |axesColor| (|Palette|)) (|:| |units| (|Integer|)) (|:| |unitsColor| (|Palette|)) (|:| |showing| (|Integer|)))) $) "\\spad{graphStates(v)} returns and shows a listing of a record containing the current state of the characteristics of each of the ten graph records in the given two-dimensional viewport,{} \\spad{v},{} which is of domain \\spadtype{TwoDimensionalViewport}.")) (|graphState| (((|Void|) $ (|PositiveInteger|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|DoubleFloat|) (|Integer|) (|Integer|) (|Integer|) (|Integer|) (|Palette|) (|Integer|) (|Palette|) (|Integer|)) "\\spad{graphState(v,{}num,{}sX,{}sY,{}dX,{}dY,{}pts,{}lns,{}box,{}axes,{}axesC,{}un,{}unC,{}cP)} sets the state of the characteristics for the graph indicated by \\spad{num} in the given two-dimensional viewport \\spad{v},{} of domain \\spadtype{TwoDimensionalViewport},{} to the values given as parameters. The scaling of the graph in the \\spad{x} and \\spad{y} component directions is set to be \\spad{sX} and \\spad{sY}; the window translation in the \\spad{x} and \\spad{y} component directions is set to be \\spad{dX} and \\spad{dY}; The graph points,{} lines,{} bounding \\spad{box},{} \\spad{axes},{} or units will be shown in the viewport if their given parameters \\spad{pts},{} \\spad{lns},{} \\spad{box},{} \\spad{axes} or \\spad{un} are set to be \\spad{1},{} but will not be shown if they are set to \\spad{0}. The color of the \\spad{axes} and the color of the units are indicated by the palette colors \\spad{axesC} and \\spad{unC} respectively. To display the control panel when the viewport window is displayed,{} set \\spad{cP} to \\spad{1},{} otherwise set it to \\spad{0}.")) (|options| (($ $ (|List| (|DrawOption|))) "\\spad{options(v,{}lopt)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns \\spad{v} with it\\spad{'s} draw options modified to be those which are indicated in the given list,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (((|List| (|DrawOption|)) $) "\\spad{options(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and returns a list containing the draw options from the domain \\spadtype{DrawOption} for \\spad{v}.")) (|makeViewport2D| (($ (|GraphImage|) (|List| (|DrawOption|))) "\\spad{makeViewport2D(\\spad{gi},{}lopt)} creates and displays a viewport window of the domain \\spadtype{TwoDimensionalViewport} whose graph field is assigned to be the given graph,{} \\spad{\\spad{gi}},{} of domain \\spadtype{GraphImage},{} and whose options field is set to be the list of options,{} \\spad{lopt} of domain \\spadtype{DrawOption}.") (($ $) "\\spad{makeViewport2D(v)} takes the given two-dimensional viewport,{} \\spad{v},{} of the domain \\spadtype{TwoDimensionalViewport} and displays a viewport window on the screen which contains the contents of \\spad{v}.")) (|viewport2D| (($) "\\spad{viewport2D()} returns an undefined two-dimensional viewport of the domain \\spadtype{TwoDimensionalViewport} whose contents are empty.")) (|getPickedPoints| (((|List| (|Point| (|DoubleFloat|))) $) "\\spad{getPickedPoints(x)} returns a list of small floats for the points the user interactively picked on the viewport for full integration into the system,{} some design issues need to be addressed: \\spadignore{e.g.} how to go through the GraphImage interface,{} how to default to graphs,{} etc."))) NIL NIL -(-1170) +(-1171) ((|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 -(-1171) +(-1172) ((|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 -(-1172) +(-1173) ((|constructor| (NIL "ViewportPackage provides functions for creating GraphImages and TwoDimensionalViewports from lists of lists of points.")) (|coerce| (((|TwoDimensionalViewport|) (|GraphImage|)) "\\spad{coerce(\\spad{gi})} converts the indicated \\spadtype{GraphImage},{} \\spad{gi},{} into the \\spadtype{TwoDimensionalViewport} form.")) (|drawCurves| (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|TwoDimensionalViewport|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{drawCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{TwoDimensionalViewport} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The point color is specified by \\spad{ptColor},{} the line color is specified by \\spad{lineColor},{} and the point size is specified by \\spad{ptSize}.")) (|graphCurves| (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|))))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]])} creates a \\spadtype{GraphImage} from the list of lists of points indicated by \\spad{p0} through \\spad{pn}.") (((|GraphImage|) (|List| (|List| (|Point| (|DoubleFloat|)))) (|Palette|) (|Palette|) (|PositiveInteger|) (|List| (|DrawOption|))) "\\spad{graphCurves([[p0],{}[p1],{}...,{}[pn]],{}ptColor,{}lineColor,{}ptSize,{}[options])} creates a \\spadtype{GraphImage} from the list of lists of points,{} \\spad{p0} throught \\spad{pn},{} using the options specified in the list \\spad{options}. The graph point color is specified by \\spad{ptColor},{} the graph line color is specified by \\spad{lineColor},{} and the size of the points is specified by \\spad{ptSize}."))) NIL NIL -(-1173) +(-1174) ((|constructor| (NIL "This type is used when no value is needed,{} \\spadignore{e.g.} in the \\spad{then} part of a one armed \\spad{if}. All values can be coerced to type Void. Once a value has been coerced to Void,{} it cannot be recovered.")) (|coerce| (((|OutputForm|) $) "\\spad{coerce(v)} coerces void object to outputForm.")) (|void| (($) "\\spad{void()} produces a void object."))) NIL NIL -(-1174 A S) +(-1175 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 -(-1175 S) +(-1176 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}."))) -((-4239 . T) (-4238 . T)) +((-4243 . T) (-4242 . T)) NIL -(-1176 R) +(-1177 R) ((|constructor| (NIL "This package implements the Weierstrass preparation theorem \\spad{f} or multivariate power series. weierstrass(\\spad{v},{}\\spad{p}) where \\spad{v} is a variable,{} and \\spad{p} is a TaylorSeries(\\spad{R}) in which the terms of lowest degree \\spad{s} must include c*v**s where \\spad{c} is a constant,{}\\spad{s>0},{} is a list of TaylorSeries coefficients A[\\spad{i}] of the equivalent polynomial A = A[0] + A[1]\\spad{*v} + A[2]*v**2 + ... + A[\\spad{s}-1]*v**(\\spad{s}-1) + v**s such that p=A*B ,{} \\spad{B} being a TaylorSeries of minimum degree 0")) (|qqq| (((|Mapping| (|Stream| (|TaylorSeries| |#1|)) (|Stream| (|TaylorSeries| |#1|))) (|NonNegativeInteger|) (|TaylorSeries| |#1|) (|Stream| (|TaylorSeries| |#1|))) "\\spad{qqq(n,{}s,{}st)} is used internally.")) (|weierstrass| (((|List| (|TaylorSeries| |#1|)) (|Symbol|) (|TaylorSeries| |#1|)) "\\spad{weierstrass(v,{}ts)} where \\spad{v} is a variable and \\spad{ts} is \\indented{1}{a TaylorSeries,{} impements the Weierstrass Preparation} \\indented{1}{Theorem. The result is a list of TaylorSeries that} \\indented{1}{are the coefficients of the equivalent series.}")) (|clikeUniv| (((|Mapping| (|SparseUnivariatePolynomial| (|Polynomial| |#1|)) (|Polynomial| |#1|)) (|Symbol|)) "\\spad{clikeUniv(v)} is used internally.")) (|sts2stst| (((|Stream| (|Stream| (|Polynomial| |#1|))) (|Symbol|) (|Stream| (|Polynomial| |#1|))) "\\spad{sts2stst(v,{}s)} is used internally.")) (|cfirst| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{cfirst n} is used internally.")) (|crest| (((|Mapping| (|Stream| (|Polynomial| |#1|)) (|Stream| (|Polynomial| |#1|))) (|NonNegativeInteger|)) "\\spad{crest n} is used internally."))) NIL NIL -(-1177 K R UP -2315) +(-1178 K R UP -3539) ((|constructor| (NIL "In this package \\spad{K} is a finite field,{} \\spad{R} is a ring of univariate polynomials over \\spad{K},{} and \\spad{F} is a framed algebra over \\spad{R}. The package provides a function to compute the integral closure of \\spad{R} in the quotient field of \\spad{F} as well as a function to compute a \"local integral basis\" at a specific prime.")) (|localIntegralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|))) |#2|) "\\spad{integralBasis(p)} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the local integral closure of \\spad{R} at the prime \\spad{p} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the local integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}.")) (|integralBasis| (((|Record| (|:| |basis| (|Matrix| |#2|)) (|:| |basisDen| |#2|) (|:| |basisInv| (|Matrix| |#2|)))) "\\spad{integralBasis()} returns a record \\spad{[basis,{}basisDen,{}basisInv]} containing information regarding the integral closure of \\spad{R} in the quotient field of \\spad{F},{} where \\spad{F} is a framed algebra with \\spad{R}-module basis \\spad{w1,{}w2,{}...,{}wn}. If \\spad{basis} is the matrix \\spad{(aij,{} i = 1..n,{} j = 1..n)},{} then the \\spad{i}th element of the integral basis is \\spad{\\spad{vi} = (1/basisDen) * sum(aij * wj,{} j = 1..n)},{} \\spadignore{i.e.} the \\spad{i}th row of \\spad{basis} contains the coordinates of the \\spad{i}th basis vector. Similarly,{} the \\spad{i}th row of the matrix \\spad{basisInv} contains the coordinates of \\spad{\\spad{wi}} with respect to the basis \\spad{v1,{}...,{}vn}: if \\spad{basisInv} is the matrix \\spad{(bij,{} i = 1..n,{} j = 1..n)},{} then \\spad{\\spad{wi} = sum(bij * vj,{} j = 1..n)}."))) NIL NIL -(-1178 R |VarSet| E P |vl| |wl| |wtlevel|) +(-1179 R |VarSet| E P |vl| |wl| |wtlevel|) ((|constructor| (NIL "This domain represents truncated weighted polynomials over a general (not necessarily commutative) polynomial type. The variables must be specified,{} as must the weights. The representation is sparse in the sense that only non-zero terms are represented.")) (|changeWeightLevel| (((|Void|) (|NonNegativeInteger|)) "\\spad{changeWeightLevel(n)} changes the weight level to the new value given: \\spad{NB:} previously calculated terms are not affected")) (/ (((|Union| $ "failed") $ $) "\\spad{x/y} division (only works if minimum weight of divisor is zero,{} and if \\spad{R} is a Field)")) (|coerce| (($ |#4|) "\\spad{coerce(p)} coerces \\spad{p} into Weighted form,{} applying weights and ignoring terms") ((|#4| $) "convert back into a \\spad{\"P\"},{} ignoring weights"))) -((-4239 |has| |#1| (-158)) (-4238 |has| |#1| (-158)) (-4241 . T)) +((-4243 |has| |#1| (-158)) (-4242 |has| |#1| (-158)) (-4245 . T)) ((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339)))) -(-1179 R E V P) +(-1180 R E V P) ((|constructor| (NIL "A domain constructor of the category \\axiomType{GeneralTriangularSet}. The only requirement for a list of polynomials to be a member of such a domain is the following: no polynomial is constant and two distinct polynomials have distinct main variables. Such a triangular set may not be auto-reduced or consistent. The \\axiomOpFrom{construct}{WuWenTsunTriangularSet} operation does not check the previous requirement. Triangular sets are stored as sorted lists \\spad{w}.\\spad{r}.\\spad{t}. the main variables of their members. Furthermore,{} this domain exports operations dealing with the characteristic set method of Wu Wen Tsun and some optimizations mainly proposed by Dong Ming Wang.\\newline References : \\indented{1}{[1] \\spad{W}. \\spad{T}. WU \"A Zero Structure Theorem for polynomial equations solving\"} \\indented{6}{\\spad{MM} Research Preprints,{} 1987.} \\indented{1}{[2] \\spad{D}. \\spad{M}. WANG \"An implementation of the characteristic set method in Maple\"} \\indented{6}{Proc. DISCO'92. Bath,{} England.}")) (|characteristicSerie| (((|List| $) (|List| |#4|)) "\\axiom{characteristicSerie(\\spad{ps})} returns the same as \\axiom{characteristicSerie(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|List| $) (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSerie(\\spad{ps},{}redOp?,{}redOp)} returns a list \\axiom{\\spad{lts}} of triangular sets such that the zero set of \\axiom{\\spad{ps}} is the union of the regular zero sets of the members of \\axiom{\\spad{lts}}. This is made by the Ritt and Wu Wen Tsun process applying the operation \\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} to compute characteristic sets in Wu Wen Tsun sense.")) (|characteristicSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{characteristicSet(\\spad{ps})} returns the same as \\axiom{characteristicSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{characteristicSet(\\spad{ps},{}redOp?,{}redOp)} returns a non-contradictory characteristic set of \\axiom{\\spad{ps}} in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?} (using \\axiom{redOp} to reduce polynomials \\spad{w}.\\spad{r}.\\spad{t} a \\axiom{redOp?} basic set),{} if no non-zero constant polynomial appear during those reductions,{} else \\axiom{\"failed\"} is returned. The operations \\axiom{redOp} and \\axiom{redOp?} must satisfy the following conditions: \\axiom{redOp?(redOp(\\spad{p},{}\\spad{q}),{}\\spad{q})} holds for every polynomials \\axiom{\\spad{p},{}\\spad{q}} and there exists an integer \\axiom{\\spad{e}} and a polynomial \\axiom{\\spad{f}} such that we have \\axiom{init(\\spad{q})^e*p = \\spad{f*q} + redOp(\\spad{p},{}\\spad{q})}.")) (|medialSet| (((|Union| $ "failed") (|List| |#4|)) "\\axiom{medial(\\spad{ps})} returns the same as \\axiom{medialSet(\\spad{ps},{}initiallyReduced?,{}initiallyReduce)}.") (((|Union| $ "failed") (|List| |#4|) (|Mapping| (|Boolean|) |#4| |#4|) (|Mapping| |#4| |#4| |#4|)) "\\axiom{medialSet(\\spad{ps},{}redOp?,{}redOp)} returns \\axiom{\\spad{bs}} a basic set (in Wu Wen Tsun sense \\spad{w}.\\spad{r}.\\spad{t} the reduction-test \\axiom{redOp?}) of some set generating the same ideal as \\axiom{\\spad{ps}} (with rank not higher than any basic set of \\axiom{\\spad{ps}}),{} if no non-zero constant polynomials appear during the computatioms,{} else \\axiom{\"failed\"} is returned. In the former case,{} \\axiom{\\spad{bs}} has to be understood as a candidate for being a characteristic set of \\axiom{\\spad{ps}}. In the original algorithm,{} \\axiom{\\spad{bs}} is simply a basic set of \\axiom{\\spad{ps}}."))) -((-4245 . T) (-4244 . T)) +((-4249 . T) (-4248 . T)) ((-12 (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#4| (LIST (QUOTE -286) (|devaluate| |#4|)))) (|HasCategory| |#4| (LIST (QUOTE -564) (QUOTE (-499)))) (|HasCategory| |#4| (QUOTE (-1016))) (|HasCategory| |#1| (QUOTE (-515))) (|HasCategory| |#3| (QUOTE (-344))) (|HasCategory| |#4| (LIST (QUOTE -563) (QUOTE (-794))))) -(-1180 R) +(-1181 R) ((|constructor| (NIL "This is the category of algebras over non-commutative rings. It is used by constructors of non-commutative algebras such as: \\indented{4}{\\spadtype{XPolynomialRing}.} \\indented{4}{\\spadtype{XFreeAlgebra}} Author: Michel Petitot (petitot@lifl.\\spad{fr})")) (|coerce| (($ |#1|) "\\spad{coerce(r)} equals \\spad{r*1}."))) -((-4238 . T) (-4239 . T) (-4241 . T)) +((-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1181 |vl| R) +(-1182 |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."))) -((-4241 . T) (-4237 |has| |#2| (-6 -4237)) (-4239 . T) (-4238 . T)) -((|HasCategory| |#2| (QUOTE (-158))) (|HasAttribute| |#2| (QUOTE -4237))) -(-1182 R |VarSet| XPOLY) +((-4245 . T) (-4241 |has| |#2| (-6 -4241)) (-4243 . T) (-4242 . T)) +((|HasCategory| |#2| (QUOTE (-158))) (|HasAttribute| |#2| (QUOTE -4241))) +(-1183 R |VarSet| XPOLY) ((|constructor| (NIL "This package provides computations of logarithms and exponentials for polynomials in non-commutative variables. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|Hausdorff| ((|#3| |#3| |#3| (|NonNegativeInteger|)) "\\axiom{Hausdorff(a,{}\\spad{b},{}\\spad{n})} returns log(exp(a)*exp(\\spad{b})) truncated at order \\axiom{\\spad{n}}.")) (|log| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{} \\spad{n})} returns the logarithm of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}.")) (|exp| ((|#3| |#3| (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{} \\spad{n})} returns the exponential of \\axiom{\\spad{p}} truncated at order \\axiom{\\spad{n}}."))) NIL NIL -(-1183 |vl| R) +(-1184 |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| $) "\\spad{v * x} returns the product of a variable \\spad{x} by \\spad{x}."))) -((-4237 |has| |#2| (-6 -4237)) (-4239 . T) (-4238 . T) (-4241 . T)) +((-4241 |has| |#2| (-6 -4241)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL -(-1184 S -2315) +(-1185 S -3539) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) NIL ((|HasCategory| |#2| (QUOTE (-344))) (|HasCategory| |#2| (QUOTE (-134))) (|HasCategory| |#2| (QUOTE (-136)))) -(-1185 -2315) +(-1186 -3539) ((|constructor| (NIL "ExtensionField {\\em F} is the category of fields which extend the field \\spad{F}")) (|Frobenius| (($ $ (|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|) $) "\\spad{algebraic?(a)} tests whether an element \\spad{a} is algebraic with respect to the ground field \\spad{F}."))) -((-4236 . T) (-4242 . T) (-4237 . T) ((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +((-4240 . T) (-4246 . T) (-4241 . T) ((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL -(-1186 |VarSet| R) +(-1187 |VarSet| R) ((|constructor| (NIL "This domain constructor implements polynomials in non-commutative variables written in the Poincare-Birkhoff-Witt basis from the Lyndon basis. These polynomials can be used to compute Baker-Campbell-Hausdorff relations. \\newline Author: Michel Petitot (petitot@lifl.\\spad{fr}).")) (|log| (($ $ (|NonNegativeInteger|)) "\\axiom{log(\\spad{p},{}\\spad{n})} returns the logarithm of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|exp| (($ $ (|NonNegativeInteger|)) "\\axiom{exp(\\spad{p},{}\\spad{n})} returns the exponential of \\axiom{\\spad{p}} (truncated up to order \\axiom{\\spad{n}}).")) (|product| (($ $ $ (|NonNegativeInteger|)) "\\axiom{product(a,{}\\spad{b},{}\\spad{n})} returns \\axiom{a*b} (truncated up to order \\axiom{\\spad{n}}).")) (|LiePolyIfCan| (((|Union| (|LiePolynomial| |#1| |#2|) "failed") $) "\\axiom{LiePolyIfCan(\\spad{p})} return \\axiom{\\spad{p}} if \\axiom{\\spad{p}} is a Lie polynomial.")) (|coerce| (((|XRecursivePolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a recursive polynomial.") (((|XDistributedPolynomial| |#1| |#2|) $) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}} as a distributed polynomial.") (($ (|LiePolynomial| |#1| |#2|)) "\\axiom{coerce(\\spad{p})} returns \\axiom{\\spad{p}}."))) -((-4237 |has| |#2| (-6 -4237)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (LIST (QUOTE -657) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasAttribute| |#2| (QUOTE -4237))) -(-1187 |vl| R) +((-4241 |has| |#2| (-6 -4241)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#2| (QUOTE (-158))) (|HasCategory| |#2| (LIST (QUOTE -657) (LIST (QUOTE -383) (QUOTE (-523))))) (|HasAttribute| |#2| (QUOTE -4241))) +(-1188 |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|) $) "\\spad{maxdeg(p)} returns the greatest leading word in the support of \\spad{p}."))) -((-4237 |has| |#2| (-6 -4237)) (-4239 . T) (-4238 . T) (-4241 . T)) +((-4241 |has| |#2| (-6 -4241)) (-4243 . T) (-4242 . T) (-4245 . T)) NIL -(-1188 R) +(-1189 R) ((|constructor| (NIL "\\indented{2}{This type supports multivariate polynomials} whose set of variables is \\spadtype{Symbol}. The representation is recursive. The coefficient ring may be non-commutative and the variables do not commute. However,{} coefficients and variables commute."))) -((-4237 |has| |#1| (-6 -4237)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#1| (QUOTE (-158))) (|HasAttribute| |#1| (QUOTE -4237))) -(-1189 R E) +((-4241 |has| |#1| (-6 -4241)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#1| (QUOTE (-158))) (|HasAttribute| |#1| (QUOTE -4241))) +(-1190 R E) ((|constructor| (NIL "This domain represents generalized polynomials with coefficients (from a not necessarily commutative ring),{} and words belonging to an arbitrary \\spadtype{OrderedMonoid}. This type is used,{} for instance,{} by the \\spadtype{XDistributedPolynomial} domain constructor where the Monoid is free.")) (|canonicalUnitNormal| ((|attribute|) "canonicalUnitNormal guarantees that the function unitCanonical returns the same representative for all associates of any particular element.")) (/ (($ $ |#1|) "\\spad{p/r} returns \\spad{p*(1/r)}.")) (|map| (($ (|Mapping| |#1| |#1|) $) "\\spad{map(fn,{}x)} returns \\spad{Sum(fn(r_i) w_i)} if \\spad{x} writes \\spad{Sum(r_i w_i)}.")) (|quasiRegular| (($ $) "\\spad{quasiRegular(x)} return \\spad{x} minus its constant term.")) (|quasiRegular?| (((|Boolean|) $) "\\spad{quasiRegular?(x)} return \\spad{true} if \\spad{constant(p)} is zero.")) (|constant| ((|#1| $) "\\spad{constant(p)} return the constant term of \\spad{p}.")) (|constant?| (((|Boolean|) $) "\\spad{constant?(p)} tests whether the polynomial \\spad{p} belongs to the coefficient ring.")) (|coef| ((|#1| $ |#2|) "\\spad{coef(p,{}e)} extracts the coefficient of the monomial \\spad{e}. Returns zero if \\spad{e} is not present.")) (|reductum| (($ $) "\\spad{reductum(p)} returns \\spad{p} minus its leading term. An error is produced if \\spad{p} is zero.")) (|mindeg| ((|#2| $) "\\spad{mindeg(p)} returns the smallest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|maxdeg| ((|#2| $) "\\spad{maxdeg(p)} returns the greatest word occurring in the polynomial \\spad{p} with a non-zero coefficient. An error is produced if \\spad{p} is zero.")) (|coerce| (($ |#2|) "\\spad{coerce(e)} returns \\spad{1*e}")) (|#| (((|NonNegativeInteger|) $) "\\spad{\\# p} returns the number of terms in \\spad{p}.")) (* (($ $ |#1|) "\\spad{p*r} returns the product of \\spad{p} by \\spad{r}."))) -((-4241 . T) (-4242 |has| |#1| (-6 -4242)) (-4237 |has| |#1| (-6 -4237)) (-4239 . T) (-4238 . T)) -((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasAttribute| |#1| (QUOTE -4241)) (|HasAttribute| |#1| (QUOTE -4242)) (|HasAttribute| |#1| (QUOTE -4237))) -(-1190 |VarSet| R) +((-4245 . T) (-4246 |has| |#1| (-6 -4246)) (-4241 |has| |#1| (-6 -4241)) (-4243 . T) (-4242 . T)) +((|HasCategory| |#1| (QUOTE (-158))) (|HasCategory| |#1| (QUOTE (-339))) (|HasAttribute| |#1| (QUOTE -4245)) (|HasAttribute| |#1| (QUOTE -4246)) (|HasAttribute| |#1| (QUOTE -4241))) +(-1191 |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."))) -((-4237 |has| |#2| (-6 -4237)) (-4239 . T) (-4238 . T) (-4241 . T)) -((|HasCategory| |#2| (QUOTE (-158))) (|HasAttribute| |#2| (QUOTE -4237))) -(-1191 A) +((-4241 |has| |#2| (-6 -4241)) (-4243 . T) (-4242 . T) (-4245 . T)) +((|HasCategory| |#2| (QUOTE (-158))) (|HasAttribute| |#2| (QUOTE -4241))) +(-1192 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 -(-1192 R |ls| |ls2|) +(-1193 R |ls| |ls2|) ((|constructor| (NIL "A package for computing symbolically the complex and real roots of zero-dimensional algebraic systems over the integer or rational numbers. Complex roots are given by means of univariate representations of irreducible regular chains. Real roots are given by means of tuples of coordinates lying in the \\spadtype{RealClosure} of the coefficient ring. This constructor takes three arguments. The first one \\spad{R} is the coefficient ring. The second one \\spad{ls} is the list of variables involved in the systems to solve. The third one must be \\spad{concat(ls,{}s)} where \\spad{s} is an additional symbol used for the univariate representations. WARNING: The third argument is not checked. All operations are based on triangular decompositions. The default is to compute these decompositions directly from the input system by using the \\spadtype{RegularChain} domain constructor. The lexTriangular algorithm can also be used for computing these decompositions (see the \\spadtype{LexTriangularPackage} package constructor). For that purpose,{} the operations \\axiomOpFrom{univariateSolve}{ZeroDimensionalSolvePackage},{} \\axiomOpFrom{realSolve}{ZeroDimensionalSolvePackage} and \\axiomOpFrom{positiveSolve}{ZeroDimensionalSolvePackage} admit an optional argument. \\newline Author: Marc Moreno Maza.")) (|convert| (((|List| (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) "\\spad{convert(st)} returns the members of \\spad{st}.") (((|SparseUnivariatePolynomial| (|RealClosure| (|Fraction| |#1|))) (|SparseUnivariatePolynomial| |#1|)) "\\spad{convert(u)} converts \\spad{u}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|))) "\\spad{convert(q)} converts \\spad{q}.") (((|Polynomial| (|RealClosure| (|Fraction| |#1|))) (|Polynomial| |#1|)) "\\spad{convert(p)} converts \\spad{p}.") (((|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#2|))) "\\spad{convert(q)} converts \\spad{q}.")) (|squareFree| (((|List| (|SquareFreeRegularTriangularSet| |#1| (|IndexedExponents| (|OrderedVariableList| |#3|)) (|OrderedVariableList| |#3|) (|NewSparseMultivariatePolynomial| |#1| (|OrderedVariableList| |#3|)))) (|RegularChain| |#1| |#2|)) "\\spad{squareFree(ts)} returns the square-free factorization of \\spad{ts}. Moreover,{} each factor is a Lazard triangular set and the decomposition is a Kalkbrener split of \\spad{ts},{} which is enough here for the matter of solving zero-dimensional algebraic systems. WARNING: \\spad{ts} is not checked to be zero-dimensional.")) (|positiveSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{positiveSolve(lp)} returns the same as \\spad{positiveSolve(lp,{}info?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{positiveSolve(lp,{}info?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are (real) strictly positive. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{positiveSolve(lp,{}info?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{positiveSolve(ts)} returns the points of the regular set of \\spad{ts} with (real) strictly positive coordinates.")) (|realSolve| (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|))) "\\spad{realSolve(lp)} returns the same as \\spad{realSolve(ts,{}false,{}false,{}false)}") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{realSolve(ts,{}info?)} returns the same as \\spad{realSolve(ts,{}info?,{}false,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?)} returns the same as \\spad{realSolve(ts,{}info?,{}check?,{}false)}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} returns the set of the points in the variety associated with \\spad{lp} whose coordinates are all real. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}. WARNING: For each set of coordinates given by \\spad{realSolve(ts,{}info?,{}check?,{}lextri?)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.") (((|List| (|List| (|RealClosure| (|Fraction| |#1|)))) (|RegularChain| |#1| |#2|)) "\\spad{realSolve(ts)} returns the set of the points in the regular zero set of \\spad{ts} whose coordinates are all real. WARNING: For each set of coordinates given by \\spad{realSolve(ts)} the ordering of the indeterminates is reversed \\spad{w}.\\spad{r}.\\spad{t}. \\spad{ls}.")) (|univariateSolve| (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|))) "\\spad{univariateSolve(lp)} returns the same as \\spad{univariateSolve(lp,{}false,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}false,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?)} returns the same as \\spad{univariateSolve(lp,{}info?,{}check?,{}false)}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|) (|Boolean|)) "\\spad{univariateSolve(lp,{}info?,{}check?,{}lextri?)} returns a univariate representation of the variety associated with \\spad{lp}. Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the decomposition into regular chains. If \\spad{check?} is \\spad{true} then the result is checked. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}.") (((|List| (|Record| (|:| |complexRoots| (|SparseUnivariatePolynomial| |#1|)) (|:| |coordinates| (|List| (|Polynomial| |#1|))))) (|RegularChain| |#1| |#2|)) "\\spad{univariateSolve(ts)} returns a univariate representation of \\spad{ts}. See \\axiomOpFrom{rur}{RationalUnivariateRepresentationPackage}(\\spad{lp},{}\\spad{true}).")) (|triangSolve| (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|))) "\\spad{triangSolve(lp)} returns the same as \\spad{triangSolve(lp,{}false,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|)) "\\spad{triangSolve(lp,{}info?)} returns the same as \\spad{triangSolve(lp,{}false)}") (((|List| (|RegularChain| |#1| |#2|)) (|List| (|Polynomial| |#1|)) (|Boolean|) (|Boolean|)) "\\spad{triangSolve(lp,{}info?,{}lextri?)} decomposes the variety associated with \\axiom{\\spad{lp}} into regular chains. Thus a point belongs to this variety iff it is a regular zero of a regular set in in the output. Note that \\axiom{\\spad{lp}} needs to generate a zero-dimensional ideal. If \\axiom{\\spad{lp}} is not zero-dimensional then the result is only a decomposition of its zero-set in the sense of the closure (\\spad{w}.\\spad{r}.\\spad{t}. Zarisky topology). Moreover,{} if \\spad{info?} is \\spad{true} then some information is displayed during the computations. See \\axiomOpFrom{zeroSetSplit}{RegularTriangularSetCategory}(\\spad{lp},{}\\spad{true},{}\\spad{info?}). If \\spad{lextri?} is \\spad{true} then the lexTriangular algorithm is called from the \\spadtype{LexTriangularPackage} constructor (see \\axiomOpFrom{zeroSetSplit}{LexTriangularPackage}(\\spad{lp},{}\\spad{false})). Otherwise,{} the triangular decomposition is computed directly from the input system by using the \\axiomOpFrom{zeroSetSplit}{RegularChain} from \\spadtype{RegularChain}."))) NIL NIL -(-1193 R) +(-1194 R) ((|constructor| (NIL "Test for linear dependence over the integers.")) (|solveLinearlyOverQ| (((|Union| (|Vector| (|Fraction| (|Integer|))) "failed") (|Vector| |#1|) |#1|) "\\spad{solveLinearlyOverQ([v1,{}...,{}vn],{} u)} returns \\spad{[c1,{}...,{}cn]} such that \\spad{c1*v1 + ... + cn*vn = u},{} \"failed\" if no such rational numbers \\spad{ci}\\spad{'s} exist.")) (|linearDependenceOverZ| (((|Union| (|Vector| (|Integer|)) "failed") (|Vector| |#1|)) "\\spad{linearlyDependenceOverZ([v1,{}...,{}vn])} returns \\spad{[c1,{}...,{}cn]} if \\spad{c1*v1 + ... + cn*vn = 0} and not all the \\spad{ci}\\spad{'s} are 0,{} \"failed\" if the \\spad{vi}\\spad{'s} are linearly independent over the integers.")) (|linearlyDependentOverZ?| (((|Boolean|) (|Vector| |#1|)) "\\spad{linearlyDependentOverZ?([v1,{}...,{}vn])} returns \\spad{true} if the \\spad{vi}\\spad{'s} are linearly dependent over the integers,{} \\spad{false} otherwise."))) NIL NIL -(-1194 |p|) +(-1195 |p|) ((|constructor| (NIL "IntegerMod(\\spad{n}) creates the ring of integers reduced modulo the integer \\spad{n}."))) -(((-4246 "*") . T) (-4238 . T) (-4239 . T) (-4241 . T)) +(((-4250 "*") . T) (-4242 . T) (-4243 . T) (-4245 . T)) NIL NIL NIL @@ -4724,4 +4728,4 @@ NIL NIL NIL NIL -((-3 NIL 2235816 2235821 2235826 2235831) (-2 NIL 2235796 2235801 2235806 2235811) (-1 NIL 2235776 2235781 2235786 2235791) (0 NIL 2235756 2235761 2235766 2235771) (-1194 "ZMOD.spad" 2235565 2235578 2235694 2235751) (-1193 "ZLINDEP.spad" 2234609 2234620 2235555 2235560) (-1192 "ZDSOLVE.spad" 2224458 2224480 2234599 2234604) (-1191 "YSTREAM.spad" 2223951 2223962 2224448 2224453) (-1190 "XRPOLY.spad" 2223171 2223191 2223807 2223876) (-1189 "XPR.spad" 2220900 2220913 2222889 2222988) (-1188 "XPOLY.spad" 2220455 2220466 2220756 2220825) (-1187 "XPOLYC.spad" 2219772 2219788 2220381 2220450) (-1186 "XPBWPOLY.spad" 2218209 2218229 2219552 2219621) (-1185 "XF.spad" 2216670 2216685 2218111 2218204) (-1184 "XF.spad" 2215111 2215128 2216554 2216559) (-1183 "XFALG.spad" 2212135 2212151 2215037 2215106) (-1182 "XEXPPKG.spad" 2211386 2211412 2212125 2212130) (-1181 "XDPOLY.spad" 2211000 2211016 2211242 2211311) (-1180 "XALG.spad" 2210598 2210609 2210956 2210995) (-1179 "WUTSET.spad" 2206437 2206454 2210244 2210271) (-1178 "WP.spad" 2205451 2205495 2206295 2206362) (-1177 "WFFINTBS.spad" 2203014 2203036 2205441 2205446) (-1176 "WEIER.spad" 2201228 2201239 2203004 2203009) (-1175 "VSPACE.spad" 2200901 2200912 2201196 2201223) (-1174 "VSPACE.spad" 2200594 2200607 2200891 2200896) (-1173 "VOID.spad" 2200184 2200193 2200584 2200589) (-1172 "VIEW.spad" 2197806 2197815 2200174 2200179) (-1171 "VIEWDEF.spad" 2193003 2193012 2197796 2197801) (-1170 "VIEW3D.spad" 2176838 2176847 2192993 2192998) (-1169 "VIEW2D.spad" 2164575 2164584 2176828 2176833) (-1168 "VECTOR.spad" 2163252 2163263 2163503 2163530) (-1167 "VECTOR2.spad" 2161879 2161892 2163242 2163247) (-1166 "VECTCAT.spad" 2159767 2159778 2161835 2161874) (-1165 "VECTCAT.spad" 2157476 2157489 2159546 2159551) (-1164 "VARIABLE.spad" 2157256 2157271 2157466 2157471) (-1163 "UTYPE.spad" 2156890 2156899 2157236 2157251) (-1162 "UTSODETL.spad" 2156183 2156207 2156846 2156851) (-1161 "UTSODE.spad" 2154371 2154391 2156173 2156178) (-1160 "UTS.spad" 2149160 2149188 2152838 2152935) (-1159 "UTSCAT.spad" 2146611 2146627 2149058 2149155) (-1158 "UTSCAT.spad" 2143706 2143724 2146155 2146160) (-1157 "UTS2.spad" 2143299 2143334 2143696 2143701) (-1156 "URAGG.spad" 2137921 2137932 2143279 2143294) (-1155 "URAGG.spad" 2132517 2132530 2137877 2137882) (-1154 "UPXSSING.spad" 2130163 2130189 2131601 2131734) (-1153 "UPXS.spad" 2127190 2127218 2128295 2128444) (-1152 "UPXSCONS.spad" 2124947 2124967 2125322 2125471) (-1151 "UPXSCCA.spad" 2123405 2123425 2124793 2124942) (-1150 "UPXSCCA.spad" 2122005 2122027 2123395 2123400) (-1149 "UPXSCAT.spad" 2120586 2120602 2121851 2122000) (-1148 "UPXS2.spad" 2120127 2120180 2120576 2120581) (-1147 "UPSQFREE.spad" 2118539 2118553 2120117 2120122) (-1146 "UPSCAT.spad" 2116132 2116156 2118437 2118534) (-1145 "UPSCAT.spad" 2113431 2113457 2115738 2115743) (-1144 "UPOLYC.spad" 2108409 2108420 2113273 2113426) (-1143 "UPOLYC.spad" 2103279 2103292 2108145 2108150) (-1142 "UPOLYC2.spad" 2102748 2102767 2103269 2103274) (-1141 "UP.spad" 2099793 2099808 2100301 2100454) (-1140 "UPMP.spad" 2098683 2098696 2099783 2099788) (-1139 "UPDIVP.spad" 2098246 2098260 2098673 2098678) (-1138 "UPDECOMP.spad" 2096483 2096497 2098236 2098241) (-1137 "UPCDEN.spad" 2095690 2095706 2096473 2096478) (-1136 "UP2.spad" 2095052 2095073 2095680 2095685) (-1135 "UNISEG.spad" 2094405 2094416 2094971 2094976) (-1134 "UNISEG2.spad" 2093898 2093911 2094361 2094366) (-1133 "UNIFACT.spad" 2092999 2093011 2093888 2093893) (-1132 "ULS.spad" 2083558 2083586 2084651 2085080) (-1131 "ULSCONS.spad" 2077601 2077621 2077973 2078122) (-1130 "ULSCCAT.spad" 2075198 2075218 2077421 2077596) (-1129 "ULSCCAT.spad" 2072929 2072951 2075154 2075159) (-1128 "ULSCAT.spad" 2071145 2071161 2072775 2072924) (-1127 "ULS2.spad" 2070657 2070710 2071135 2071140) (-1126 "UFD.spad" 2069722 2069731 2070583 2070652) (-1125 "UFD.spad" 2068849 2068860 2069712 2069717) (-1124 "UDVO.spad" 2067696 2067705 2068839 2068844) (-1123 "UDPO.spad" 2065123 2065134 2067652 2067657) (-1122 "TYPE.spad" 2065045 2065054 2065103 2065118) (-1121 "TWOFACT.spad" 2063695 2063710 2065035 2065040) (-1120 "TUPLE.spad" 2063081 2063092 2063594 2063599) (-1119 "TUBETOOL.spad" 2059918 2059927 2063071 2063076) (-1118 "TUBE.spad" 2058559 2058576 2059908 2059913) (-1117 "TS.spad" 2057148 2057164 2058124 2058221) (-1116 "TSETCAT.spad" 2044263 2044280 2057104 2057143) (-1115 "TSETCAT.spad" 2031376 2031395 2044219 2044224) (-1114 "TRMANIP.spad" 2025742 2025759 2031082 2031087) (-1113 "TRIMAT.spad" 2024701 2024726 2025732 2025737) (-1112 "TRIGMNIP.spad" 2023218 2023235 2024691 2024696) (-1111 "TRIGCAT.spad" 2022730 2022739 2023208 2023213) (-1110 "TRIGCAT.spad" 2022240 2022251 2022720 2022725) (-1109 "TREE.spad" 2020811 2020822 2021847 2021874) (-1108 "TRANFUN.spad" 2020642 2020651 2020801 2020806) (-1107 "TRANFUN.spad" 2020471 2020482 2020632 2020637) (-1106 "TOPSP.spad" 2020145 2020154 2020461 2020466) (-1105 "TOOLSIGN.spad" 2019808 2019819 2020135 2020140) (-1104 "TEXTFILE.spad" 2018365 2018374 2019798 2019803) (-1103 "TEX.spad" 2015382 2015391 2018355 2018360) (-1102 "TEX1.spad" 2014938 2014949 2015372 2015377) (-1101 "TEMUTL.spad" 2014493 2014502 2014928 2014933) (-1100 "TBCMPPK.spad" 2012586 2012609 2014483 2014488) (-1099 "TBAGG.spad" 2011610 2011633 2012554 2012581) (-1098 "TBAGG.spad" 2010654 2010679 2011600 2011605) (-1097 "TANEXP.spad" 2010030 2010041 2010644 2010649) (-1096 "TABLE.spad" 2008441 2008464 2008711 2008738) (-1095 "TABLEAU.spad" 2007922 2007933 2008431 2008436) (-1094 "TABLBUMP.spad" 2004705 2004716 2007912 2007917) (-1093 "SYSSOLP.spad" 2002178 2002189 2004695 2004700) (-1092 "SYNTAX.spad" 1998370 1998379 2002168 2002173) (-1091 "SYMTAB.spad" 1996426 1996435 1998360 1998365) (-1090 "SYMS.spad" 1992411 1992420 1996416 1996421) (-1089 "SYMPOLY.spad" 1991421 1991432 1991503 1991630) (-1088 "SYMFUNC.spad" 1990896 1990907 1991411 1991416) (-1087 "SYMBOL.spad" 1988232 1988241 1990886 1990891) (-1086 "SWITCH.spad" 1984989 1984998 1988222 1988227) (-1085 "SUTS.spad" 1981888 1981916 1983456 1983553) (-1084 "SUPXS.spad" 1978902 1978930 1980020 1980169) (-1083 "SUP.spad" 1975674 1975685 1976455 1976608) (-1082 "SUPFRACF.spad" 1974779 1974797 1975664 1975669) (-1081 "SUP2.spad" 1974169 1974182 1974769 1974774) (-1080 "SUMRF.spad" 1973135 1973146 1974159 1974164) (-1079 "SUMFS.spad" 1972768 1972785 1973125 1973130) (-1078 "SULS.spad" 1963314 1963342 1964420 1964849) (-1077 "SUCH.spad" 1962994 1963009 1963304 1963309) (-1076 "SUBSPACE.spad" 1955001 1955016 1962984 1962989) (-1075 "SUBRESP.spad" 1954161 1954175 1954957 1954962) (-1074 "STTF.spad" 1950260 1950276 1954151 1954156) (-1073 "STTFNC.spad" 1946728 1946744 1950250 1950255) (-1072 "STTAYLOR.spad" 1939126 1939137 1946609 1946614) (-1071 "STRTBL.spad" 1937631 1937648 1937780 1937807) (-1070 "STRING.spad" 1937040 1937049 1937054 1937081) (-1069 "STRICAT.spad" 1936816 1936825 1936996 1937035) (-1068 "STREAM.spad" 1933584 1933595 1936341 1936356) (-1067 "STREAM3.spad" 1933129 1933144 1933574 1933579) (-1066 "STREAM2.spad" 1932197 1932210 1933119 1933124) (-1065 "STREAM1.spad" 1931901 1931912 1932187 1932192) (-1064 "STINPROD.spad" 1930807 1930823 1931891 1931896) (-1063 "STEP.spad" 1930008 1930017 1930797 1930802) (-1062 "STBL.spad" 1928534 1928562 1928701 1928716) (-1061 "STAGG.spad" 1927599 1927610 1928514 1928529) (-1060 "STAGG.spad" 1926672 1926685 1927589 1927594) (-1059 "STACK.spad" 1926023 1926034 1926279 1926306) (-1058 "SREGSET.spad" 1923727 1923744 1925669 1925696) (-1057 "SRDCMPK.spad" 1922272 1922292 1923717 1923722) (-1056 "SRAGG.spad" 1917357 1917366 1922228 1922267) (-1055 "SRAGG.spad" 1912474 1912485 1917347 1917352) (-1054 "SQMATRIX.spad" 1910100 1910118 1911008 1911095) (-1053 "SPLTREE.spad" 1904652 1904665 1909536 1909563) (-1052 "SPLNODE.spad" 1901240 1901253 1904642 1904647) (-1051 "SPFCAT.spad" 1900017 1900026 1901230 1901235) (-1050 "SPECOUT.spad" 1898567 1898576 1900007 1900012) (-1049 "spad-parser.spad" 1898032 1898041 1898557 1898562) (-1048 "SPACEC.spad" 1882045 1882056 1898022 1898027) (-1047 "SPACE3.spad" 1881821 1881832 1882035 1882040) (-1046 "SORTPAK.spad" 1881366 1881379 1881777 1881782) (-1045 "SOLVETRA.spad" 1879123 1879134 1881356 1881361) (-1044 "SOLVESER.spad" 1877643 1877654 1879113 1879118) (-1043 "SOLVERAD.spad" 1873653 1873664 1877633 1877638) (-1042 "SOLVEFOR.spad" 1872073 1872091 1873643 1873648) (-1041 "SNTSCAT.spad" 1871661 1871678 1872029 1872068) (-1040 "SMTS.spad" 1869921 1869947 1871226 1871323) (-1039 "SMP.spad" 1867363 1867383 1867753 1867880) (-1038 "SMITH.spad" 1866206 1866231 1867353 1867358) (-1037 "SMATCAT.spad" 1864304 1864334 1866138 1866201) (-1036 "SMATCAT.spad" 1862346 1862378 1864182 1864187) (-1035 "SKAGG.spad" 1861295 1861306 1862302 1862341) (-1034 "SINT.spad" 1859603 1859612 1861161 1861290) (-1033 "SIMPAN.spad" 1859331 1859340 1859593 1859598) (-1032 "SIGNRF.spad" 1858439 1858450 1859321 1859326) (-1031 "SIGNEF.spad" 1857708 1857725 1858429 1858434) (-1030 "SHP.spad" 1855626 1855641 1857664 1857669) (-1029 "SHDP.spad" 1847016 1847043 1847525 1847654) (-1028 "SGROUP.spad" 1846482 1846491 1847006 1847011) (-1027 "SGROUP.spad" 1845946 1845957 1846472 1846477) (-1026 "SGCF.spad" 1838827 1838836 1845936 1845941) (-1025 "SFRTCAT.spad" 1837743 1837760 1838783 1838822) (-1024 "SFRGCD.spad" 1836806 1836826 1837733 1837738) (-1023 "SFQCMPK.spad" 1831443 1831463 1836796 1836801) (-1022 "SFORT.spad" 1830878 1830892 1831433 1831438) (-1021 "SEXOF.spad" 1830721 1830761 1830868 1830873) (-1020 "SEX.spad" 1830613 1830622 1830711 1830716) (-1019 "SEXCAT.spad" 1827717 1827757 1830603 1830608) (-1018 "SET.spad" 1826017 1826028 1827138 1827177) (-1017 "SETMN.spad" 1824451 1824468 1826007 1826012) (-1016 "SETCAT.spad" 1823936 1823945 1824441 1824446) (-1015 "SETCAT.spad" 1823419 1823430 1823926 1823931) (-1014 "SETAGG.spad" 1819942 1819953 1823387 1823414) (-1013 "SETAGG.spad" 1816485 1816498 1819932 1819937) (-1012 "SEGXCAT.spad" 1815597 1815610 1816465 1816480) (-1011 "SEG.spad" 1815410 1815421 1815516 1815521) (-1010 "SEGCAT.spad" 1814229 1814240 1815390 1815405) (-1009 "SEGBIND.spad" 1813301 1813312 1814184 1814189) (-1008 "SEGBIND2.spad" 1812997 1813010 1813291 1813296) (-1007 "SEG2.spad" 1812422 1812435 1812953 1812958) (-1006 "SDVAR.spad" 1811698 1811709 1812412 1812417) (-1005 "SDPOL.spad" 1809091 1809102 1809382 1809509) (-1004 "SCPKG.spad" 1807170 1807181 1809081 1809086) (-1003 "SCOPE.spad" 1806315 1806324 1807160 1807165) (-1002 "SCACHE.spad" 1804997 1805008 1806305 1806310) (-1001 "SAOS.spad" 1804869 1804878 1804987 1804992) (-1000 "SAERFFC.spad" 1804582 1804602 1804859 1804864) (-999 "SAE.spad" 1802761 1802776 1803371 1803506) (-998 "SAEFACT.spad" 1802463 1802482 1802751 1802756) (-997 "RURPK.spad" 1800105 1800120 1802453 1802458) (-996 "RULESET.spad" 1799547 1799570 1800095 1800100) (-995 "RULE.spad" 1797752 1797775 1799537 1799542) (-994 "RULECOLD.spad" 1797605 1797617 1797742 1797747) (-993 "RSETGCD.spad" 1793984 1794003 1797595 1797600) (-992 "RSETCAT.spad" 1783757 1783773 1793940 1793979) (-991 "RSETCAT.spad" 1773562 1773580 1783747 1783752) (-990 "RSDCMPK.spad" 1772015 1772034 1773552 1773557) (-989 "RRCC.spad" 1770400 1770429 1772005 1772010) (-988 "RRCC.spad" 1768783 1768814 1770390 1770395) (-987 "RPOLCAT.spad" 1748144 1748158 1768651 1768778) (-986 "RPOLCAT.spad" 1727220 1727236 1747729 1747734) (-985 "ROUTINE.spad" 1723084 1723092 1725867 1725894) (-984 "ROMAN.spad" 1722317 1722325 1722950 1723079) (-983 "ROIRC.spad" 1721398 1721429 1722307 1722312) (-982 "RNS.spad" 1720302 1720310 1721300 1721393) (-981 "RNS.spad" 1719292 1719302 1720292 1720297) (-980 "RNG.spad" 1719028 1719036 1719282 1719287) (-979 "RMODULE.spad" 1718667 1718677 1719018 1719023) (-978 "RMCAT2.spad" 1718076 1718132 1718657 1718662) (-977 "RMATRIX.spad" 1716756 1716774 1717243 1717282) (-976 "RMATCAT.spad" 1712278 1712308 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1542898 1542903) (-881 "POLYCATQ.spad" 1540271 1540293 1542159 1542164) (-880 "POLYCAT.spad" 1533677 1533698 1540139 1540266) (-879 "POLYCAT.spad" 1526385 1526408 1532849 1532854) (-878 "POLY2UP.spad" 1525833 1525847 1526375 1526380) (-877 "POLY2.spad" 1525428 1525440 1525823 1525828) (-876 "POLUTIL.spad" 1524369 1524398 1525384 1525389) (-875 "POLTOPOL.spad" 1523117 1523132 1524359 1524364) (-874 "POINT.spad" 1521958 1521968 1522045 1522072) (-873 "PNTHEORY.spad" 1518624 1518632 1521948 1521953) (-872 "PMTOOLS.spad" 1517381 1517395 1518614 1518619) (-871 "PMSYM.spad" 1516926 1516936 1517371 1517376) (-870 "PMQFCAT.spad" 1516513 1516527 1516916 1516921) (-869 "PMPRED.spad" 1515982 1515996 1516503 1516508) (-868 "PMPREDFS.spad" 1515426 1515448 1515972 1515977) (-867 "PMPLCAT.spad" 1514496 1514514 1515358 1515363) (-866 "PMLSAGG.spad" 1514077 1514091 1514486 1514491) (-865 "PMKERNEL.spad" 1513644 1513656 1514067 1514072) (-864 "PMINS.spad" 1513220 1513230 1513634 1513639) (-863 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(-825 "PCOMP.spad" 1432377 1432390 1432516 1432521) (-824 "PBWLB.spad" 1430959 1430976 1432367 1432372) (-823 "PATTERN.spad" 1425390 1425400 1430949 1430954) (-822 "PATTERN2.spad" 1425126 1425138 1425380 1425385) (-821 "PATTERN1.spad" 1423428 1423444 1425116 1425121) (-820 "PATRES.spad" 1420975 1420987 1423418 1423423) (-819 "PATRES2.spad" 1420637 1420651 1420965 1420970) (-818 "PATMATCH.spad" 1418799 1418830 1420350 1420355) (-817 "PATMAB.spad" 1418224 1418234 1418789 1418794) (-816 "PATLRES.spad" 1417308 1417322 1418214 1418219) (-815 "PATAB.spad" 1417072 1417082 1417298 1417303) (-814 "PARTPERM.spad" 1414434 1414442 1417062 1417067) (-813 "PARSURF.spad" 1413862 1413890 1414424 1414429) (-812 "PARSU2.spad" 1413657 1413673 1413852 1413857) (-811 "script-parser.spad" 1413177 1413185 1413647 1413652) (-810 "PARSCURV.spad" 1412605 1412633 1413167 1413172) (-809 "PARSC2.spad" 1412394 1412410 1412595 1412600) (-808 "PARPCURV.spad" 1411852 1411880 1412384 1412389) (-807 "PARPC2.spad" 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1124682) (-675 "MRING.spad" 1121491 1121503 1124228 1124295) (-674 "MRF2.spad" 1121059 1121073 1121481 1121486) (-673 "MRATFAC.spad" 1120605 1120622 1121049 1121054) (-672 "MPRFF.spad" 1118635 1118654 1120595 1120600) (-671 "MPOLY.spad" 1116073 1116088 1116432 1116559) (-670 "MPCPF.spad" 1115337 1115356 1116063 1116068) (-669 "MPC3.spad" 1115152 1115192 1115327 1115332) (-668 "MPC2.spad" 1114794 1114827 1115142 1115147) (-667 "MONOTOOL.spad" 1113129 1113146 1114784 1114789) (-666 "MONOID.spad" 1112303 1112311 1113119 1113124) (-665 "MONOID.spad" 1111475 1111485 1112293 1112298) (-664 "MONOGEN.spad" 1110221 1110234 1111335 1111470) (-663 "MONOGEN.spad" 1108989 1109004 1110105 1110110) (-662 "MONADWU.spad" 1107003 1107011 1108979 1108984) (-661 "MONADWU.spad" 1105015 1105025 1106993 1106998) (-660 "MONAD.spad" 1104159 1104167 1105005 1105010) (-659 "MONAD.spad" 1103301 1103311 1104149 1104154) (-658 "MOEBIUS.spad" 1101987 1102001 1103281 1103296) (-657 "MODULE.spad" 1101857 1101867 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1084049 1084057 1085494 1085599) (-637 "MFINFACT.spad" 1083449 1083471 1084039 1084044) (-636 "MESH.spad" 1081181 1081189 1083439 1083444) (-635 "MDDFACT.spad" 1079374 1079384 1081171 1081176) (-634 "MDAGG.spad" 1078649 1078659 1079342 1079369) (-633 "MCMPLX.spad" 1074629 1074637 1075243 1075444) (-632 "MCDEN.spad" 1073837 1073849 1074619 1074624) (-631 "MCALCFN.spad" 1070939 1070965 1073827 1073832) (-630 "MATSTOR.spad" 1068215 1068225 1070929 1070934) (-629 "MATRIX.spad" 1066919 1066929 1067403 1067430) (-628 "MATLIN.spad" 1064245 1064269 1066803 1066808) (-627 "MATCAT.spad" 1055818 1055840 1064201 1064240) (-626 "MATCAT.spad" 1047275 1047299 1055660 1055665) (-625 "MATCAT2.spad" 1046543 1046591 1047265 1047270) (-624 "MAPPKG3.spad" 1045442 1045456 1046533 1046538) (-623 "MAPPKG2.spad" 1044776 1044788 1045432 1045437) (-622 "MAPPKG1.spad" 1043594 1043604 1044766 1044771) (-621 "MAPHACK3.spad" 1043402 1043416 1043584 1043589) (-620 "MAPHACK2.spad" 1043167 1043179 1043392 1043397) (-619 "MAPHACK1.spad" 1042797 1042807 1043157 1043162) (-618 "MAGMA.spad" 1040587 1040604 1042787 1042792) (-617 "M3D.spad" 1038285 1038295 1039967 1039972) (-616 "LZSTAGG.spad" 1035503 1035513 1038265 1038280) (-615 "LZSTAGG.spad" 1032729 1032741 1035493 1035498) (-614 "LWORD.spad" 1029434 1029451 1032719 1032724) (-613 "LSQM.spad" 1027662 1027676 1028060 1028111) (-612 "LSPP.spad" 1027195 1027212 1027652 1027657) (-611 "LSMP.spad" 1026035 1026063 1027185 1027190) (-610 "LSMP1.spad" 1023839 1023853 1026025 1026030) (-609 "LSAGG.spad" 1023496 1023506 1023795 1023834) (-608 "LSAGG.spad" 1023185 1023197 1023486 1023491) (-607 "LPOLY.spad" 1022139 1022158 1023041 1023110) (-606 "LPEFRAC.spad" 1021396 1021406 1022129 1022134) (-605 "LO.spad" 1020797 1020811 1021330 1021357) (-604 "LOGIC.spad" 1020399 1020407 1020787 1020792) (-603 "LOGIC.spad" 1019999 1020009 1020389 1020394) (-602 "LODOOPS.spad" 1018917 1018929 1019989 1019994) (-601 "LODO.spad" 1018303 1018319 1018599 1018638) (-600 "LODOF.spad" 1017347 1017364 1018260 1018265) (-599 "LODOCAT.spad" 1016005 1016015 1017303 1017342) (-598 "LODOCAT.spad" 1014661 1014673 1015961 1015966) (-597 "LODO2.spad" 1013936 1013948 1014343 1014382) (-596 "LODO1.spad" 1013338 1013348 1013618 1013657) (-595 "LODEEF.spad" 1012110 1012128 1013328 1013333) (-594 "LNAGG.spad" 1007902 1007912 1012090 1012105) (-593 "LNAGG.spad" 1003668 1003680 1007858 1007863) (-592 "LMOPS.spad" 1000404 1000421 1003658 1003663) (-591 "LMODULE.spad" 1000046 1000056 1000394 1000399) (-590 "LMDICT.spad" 999329 999339 999597 999624) (-589 "LIST.spad" 997047 997057 998476 998503) (-588 "LIST3.spad" 996338 996352 997037 997042) (-587 "LIST2.spad" 994978 994990 996328 996333) (-586 "LIST2MAP.spad" 991855 991867 994968 994973) (-585 "LINEXP.spad" 991287 991297 991835 991850) (-584 "LINDEP.spad" 990064 990076 991199 991204) (-583 "LIMITRF.spad" 987978 987988 990054 990059) (-582 "LIMITPS.spad" 986861 986874 987968 987973) (-581 "LIE.spad" 984875 984887 986151 986296) (-580 "LIECAT.spad" 984351 984361 984801 984870) (-579 "LIECAT.spad" 983855 983867 984307 984312) (-578 "LIB.spad" 981903 981911 982514 982529) (-577 "LGROBP.spad" 979256 979275 981893 981898) (-576 "LF.spad" 978175 978191 979246 979251) (-575 "LFCAT.spad" 977194 977202 978165 978170) (-574 "LEXTRIPK.spad" 972697 972712 977184 977189) (-573 "LEXP.spad" 970700 970727 972677 972692) (-572 "LEADCDET.spad" 969084 969101 970690 970695) (-571 "LAZM3PK.spad" 967788 967810 969074 969079) (-570 "LAUPOL.spad" 966479 966492 967383 967452) (-569 "LAPLACE.spad" 966052 966068 966469 966474) (-568 "LA.spad" 965492 965506 965974 966013) (-567 "LALG.spad" 965268 965278 965472 965487) (-566 "LALG.spad" 965052 965064 965258 965263) (-565 "KOVACIC.spad" 963765 963782 965042 965047) (-564 "KONVERT.spad" 963487 963497 963755 963760) (-563 "KOERCE.spad" 963224 963234 963477 963482) (-562 "KERNEL.spad" 961759 961769 963008 963013) (-561 "KERNEL2.spad" 961462 961474 961749 961754) (-560 "KDAGG.spad" 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930164) (-539 "IR2.spad" 927091 927107 928061 928066) (-538 "IR2F.spad" 926291 926307 927081 927086) (-537 "IPRNTPK.spad" 926051 926059 926281 926286) (-536 "IPF.spad" 925616 925628 925856 925949) (-535 "IPADIC.spad" 925377 925403 925542 925611) (-534 "INVLAPLA.spad" 925022 925038 925367 925372) (-533 "INTTR.spad" 918268 918285 925012 925017) (-532 "INTTOOLS.spad" 915980 915996 917843 917848) (-531 "INTSLPE.spad" 915286 915294 915970 915975) (-530 "INTRVL.spad" 914852 914862 915200 915281) (-529 "INTRF.spad" 913216 913230 914842 914847) (-528 "INTRET.spad" 912648 912658 913206 913211) (-527 "INTRAT.spad" 911323 911340 912638 912643) (-526 "INTPM.spad" 909686 909702 910966 910971) (-525 "INTPAF.spad" 907454 907472 909618 909623) (-524 "INTPACK.spad" 897764 897772 907444 907449) (-523 "INT.spad" 897125 897133 897618 897759) (-522 "INTHERTR.spad" 896391 896408 897115 897120) (-521 "INTHERAL.spad" 896057 896081 896381 896386) (-520 "INTHEORY.spad" 892470 892478 896047 896052) (-519 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(-417 "GALFACT.spad" 715786 715797 725643 725648) (-416 "FVFUN.spad" 712799 712807 715766 715781) (-415 "FVC.spad" 711841 711849 712779 712794) (-414 "FUNCTION.spad" 711690 711702 711831 711836) (-413 "FT.spad" 709902 709910 711680 711685) (-412 "FTEM.spad" 709065 709073 709892 709897) (-411 "FSUPFACT.spad" 707966 707985 709002 709007) (-410 "FST.spad" 706052 706060 707956 707961) (-409 "FSRED.spad" 705530 705546 706042 706047) (-408 "FSPRMELT.spad" 704354 704370 705487 705492) (-407 "FSPECF.spad" 702431 702447 704344 704349) (-406 "FS.spad" 696482 696492 702195 702426) (-405 "FS.spad" 690324 690336 696039 696044) (-404 "FSINT.spad" 689982 689998 690314 690319) (-403 "FSERIES.spad" 689169 689181 689802 689901) (-402 "FSCINT.spad" 688482 688498 689159 689164) (-401 "FSAGG.spad" 687587 687597 688426 688477) (-400 "FSAGG.spad" 686666 686678 687507 687512) (-399 "FSAGG2.spad" 685365 685381 686656 686661) (-398 "FS2UPS.spad" 679754 679788 685355 685360) (-397 "FS2.spad" 679399 679415 679744 679749) (-396 "FS2EXPXP.spad" 678522 678545 679389 679394) (-395 "FRUTIL.spad" 677464 677474 678512 678517) (-394 "FR.spad" 671161 671171 676491 676560) (-393 "FRNAALG.spad" 666248 666258 671103 671156) (-392 "FRNAALG.spad" 661347 661359 666204 666209) (-391 "FRNAAF2.spad" 660801 660819 661337 661342) (-390 "FRMOD.spad" 660196 660226 660733 660738) (-389 "FRIDEAL.spad" 659391 659412 660176 660191) (-388 "FRIDEAL2.spad" 658993 659025 659381 659386) (-387 "FRETRCT.spad" 658504 658514 658983 658988) (-386 "FRETRCT.spad" 657883 657895 658364 658369) (-385 "FRAMALG.spad" 656211 656224 657839 657878) (-384 "FRAMALG.spad" 654571 654586 656201 656206) (-383 "FRAC.spad" 651674 651684 652077 652250) (-382 "FRAC2.spad" 651277 651289 651664 651669) (-381 "FR2.spad" 650611 650623 651267 651272) (-380 "FPS.spad" 647420 647428 650501 650606) (-379 "FPS.spad" 644257 644267 647340 647345) (-378 "FPC.spad" 643299 643307 644159 644252) (-377 "FPC.spad" 642427 642437 643289 643294) (-376 "FPATMAB.spad" 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"FLOAT.spad" 608780 608788 615482 615611) (-354 "FLOATCP.spad" 606197 606211 608770 608775) (-353 "FLINEXP.spad" 605909 605919 606177 606192) (-352 "FLINEXP.spad" 605575 605587 605845 605850) (-351 "FLASORT.spad" 604895 604907 605565 605570) (-350 "FLALG.spad" 602541 602560 604821 604890) (-349 "FLAGG.spad" 599547 599557 602509 602536) (-348 "FLAGG.spad" 596466 596478 599430 599435) (-347 "FLAGG2.spad" 595147 595163 596456 596461) (-346 "FINRALG.spad" 593176 593189 595103 595142) (-345 "FINRALG.spad" 591131 591146 593060 593065) (-344 "FINITE.spad" 590283 590291 591121 591126) (-343 "FINAALG.spad" 579264 579274 590225 590278) (-342 "FINAALG.spad" 568257 568269 579220 579225) (-341 "FILE.spad" 567840 567850 568247 568252) (-340 "FILECAT.spad" 566358 566375 567830 567835) (-339 "FIELD.spad" 565764 565772 566260 566353) (-338 "FIELD.spad" 565256 565266 565754 565759) (-337 "FGROUP.spad" 563865 563875 565236 565251) (-336 "FGLMICPK.spad" 562652 562667 563855 563860) (-335 "FFX.spad" 562027 562042 562368 562461) (-334 "FFSLPE.spad" 561516 561537 562017 562022) (-333 "FFPOLY.spad" 552768 552779 561506 561511) (-332 "FFPOLY2.spad" 551828 551845 552758 552763) (-331 "FFP.spad" 551225 551245 551544 551637) (-330 "FF.spad" 550673 550689 550906 550999) (-329 "FFNBX.spad" 549185 549205 550389 550482) (-328 "FFNBP.spad" 547698 547715 548901 548994) (-327 "FFNB.spad" 546163 546184 547379 547472) (-326 "FFINTBAS.spad" 543577 543596 546153 546158) (-325 "FFIELDC.spad" 541152 541160 543479 543572) (-324 "FFIELDC.spad" 538813 538823 541142 541147) (-323 "FFHOM.spad" 537561 537578 538803 538808) (-322 "FFF.spad" 534996 535007 537551 537556) (-321 "FFCGX.spad" 533843 533863 534712 534805) (-320 "FFCGP.spad" 532732 532752 533559 533652) (-319 "FFCG.spad" 531524 531545 532413 532506) (-318 "FFCAT.spad" 524425 524447 531363 531519) (-317 "FFCAT.spad" 517405 517429 524345 524350) (-316 "FFCAT2.spad" 517150 517190 517395 517400) (-315 "FEXPR.spad" 508863 508909 516910 516949) (-314 "FEVALAB.spad" 508569 508579 508853 508858) (-313 "FEVALAB.spad" 508060 508072 508346 508351) (-312 "FDIV.spad" 507502 507526 508050 508055) (-311 "FDIVCAT.spad" 505544 505568 507492 507497) (-310 "FDIVCAT.spad" 503584 503610 505534 505539) (-309 "FDIV2.spad" 503238 503278 503574 503579) (-308 "FCPAK1.spad" 501791 501799 503228 503233) (-307 "FCOMP.spad" 501170 501180 501781 501786) (-306 "FC.spad" 490995 491003 501160 501165) (-305 "FAXF.spad" 483930 483944 490897 490990) (-304 "FAXF.spad" 476917 476933 483886 483891) (-303 "FARRAY.spad" 475063 475073 476100 476127) (-302 "FAMR.spad" 473183 473195 474961 475058) (-301 "FAMR.spad" 471287 471301 473067 473072) (-300 "FAMONOID.spad" 470937 470947 471241 471246) (-299 "FAMONC.spad" 469159 469171 470927 470932) (-298 "FAGROUP.spad" 468765 468775 469055 469082) (-297 "FACUTIL.spad" 466961 466978 468755 468760) (-296 "FACTFUNC.spad" 466137 466147 466951 466956) (-295 "EXPUPXS.spad" 462970 462993 464269 464418) (-294 "EXPRTUBE.spad" 460198 460206 462960 462965) (-293 "EXPRODE.spad" 457070 457086 460188 460193) (-292 "EXPR.spad" 452372 452382 453086 453489) (-291 "EXPR2UPS.spad" 448464 448477 452362 452367) (-290 "EXPR2.spad" 448167 448179 448454 448459) (-289 "EXPEXPAN.spad" 445108 445133 445742 445835) (-288 "EXIT.spad" 444779 444787 445098 445103) (-287 "EVALCYC.spad" 444237 444251 444769 444774) (-286 "EVALAB.spad" 443801 443811 444227 444232) (-285 "EVALAB.spad" 443363 443375 443791 443796) (-284 "EUCDOM.spad" 440905 440913 443289 443358) (-283 "EUCDOM.spad" 438509 438519 440895 440900) (-282 "ESTOOLS.spad" 430349 430357 438499 438504) (-281 "ESTOOLS2.spad" 429950 429964 430339 430344) (-280 "ESTOOLS1.spad" 429635 429646 429940 429945) (-279 "ES.spad" 422182 422190 429625 429630) (-278 "ES.spad" 414637 414647 422082 422087) (-277 "ESCONT.spad" 411410 411418 414627 414632) (-276 "ESCONT1.spad" 411159 411171 411400 411405) (-275 "ES2.spad" 410654 410670 411149 411154) (-274 "ES1.spad" 410220 410236 410644 410649) (-273 "ERROR.spad" 407541 407549 410210 410215) (-272 "EQTBL.spad" 406013 406035 406222 406249) (-271 "EQ.spad" 400897 400907 403696 403805) (-270 "EQ2.spad" 400613 400625 400887 400892) (-269 "EP.spad" 396927 396937 400603 400608) (-268 "ENV.spad" 395629 395637 396917 396922) (-267 "ENTIRER.spad" 395297 395305 395573 395624) (-266 "EMR.spad" 394498 394539 395223 395292) (-265 "ELTAGG.spad" 392738 392757 394488 394493) (-264 "ELTAGG.spad" 390942 390963 392694 392699) (-263 "ELTAB.spad" 390389 390407 390932 390937) (-262 "ELFUTS.spad" 389768 389787 390379 390384) (-261 "ELEMFUN.spad" 389457 389465 389758 389763) (-260 "ELEMFUN.spad" 389144 389154 389447 389452) (-259 "ELAGG.spad" 387075 387085 389112 389139) (-258 "ELAGG.spad" 384955 384967 386994 386999) (-257 "ELABEXPR.spad" 383886 383894 384945 384950) (-256 "EFUPXS.spad" 380662 380692 383842 383847) (-255 "EFULS.spad" 377498 377521 380618 380623) (-254 "EFSTRUC.spad" 375453 375469 377488 377493) (-253 "EF.spad" 370219 370235 375443 375448) (-252 "EAB.spad" 368495 368503 370209 370214) (-251 "E04UCFA.spad" 368031 368039 368485 368490) (-250 "E04NAFA.spad" 367608 367616 368021 368026) (-249 "E04MBFA.spad" 367188 367196 367598 367603) (-248 "E04JAFA.spad" 366724 366732 367178 367183) (-247 "E04GCFA.spad" 366260 366268 366714 366719) (-246 "E04FDFA.spad" 365796 365804 366250 366255) (-245 "E04DGFA.spad" 365332 365340 365786 365791) (-244 "E04AGNT.spad" 361174 361182 365322 365327) (-243 "DVARCAT.spad" 357859 357869 361164 361169) (-242 "DVARCAT.spad" 354542 354554 357849 357854) (-241 "DSMP.spad" 351976 351990 352281 352408) (-240 "DROPT.spad" 345921 345929 351966 351971) (-239 "DROPT1.spad" 345584 345594 345911 345916) (-238 "DROPT0.spad" 340411 340419 345574 345579) (-237 "DRAWPT.spad" 338566 338574 340401 340406) (-236 "DRAW.spad" 331166 331179 338556 338561) (-235 "DRAWHACK.spad" 330474 330484 331156 331161) (-234 "DRAWCX.spad" 327916 327924 330464 330469) (-233 "DRAWCURV.spad" 327453 327468 327906 327911) (-232 "DRAWCFUN.spad" 316625 316633 327443 327448) (-231 "DQAGG.spad" 314781 314791 316581 316620) (-230 "DPOLCAT.spad" 310122 310138 314649 314776) (-229 "DPOLCAT.spad" 305549 305567 310078 310083) (-228 "DPMO.spad" 299536 299552 299674 299970) (-227 "DPMM.spad" 293536 293554 293661 293957) (-226 "DOMAIN.spad" 292807 292815 293526 293531) (-225 "DMP.spad" 290032 290047 290604 290731) (-224 "DLP.spad" 289380 289390 290022 290027) (-223 "DLIST.spad" 287792 287802 288563 288590) (-222 "DLAGG.spad" 286193 286203 287772 287787) (-221 "DIVRING.spad" 285640 285648 286137 286188) (-220 "DIVRING.spad" 285131 285141 285630 285635) (-219 "DISPLAY.spad" 283311 283319 285121 285126) (-218 "DIRPROD.spad" 274570 274586 275210 275339) (-217 "DIRPROD2.spad" 273378 273396 274560 274565) (-216 "DIRPCAT.spad" 272310 272326 273232 273373) (-215 "DIRPCAT.spad" 270982 271000 271906 271911) (-214 "DIOSP.spad" 269807 269815 270972 270977) (-213 "DIOPS.spad" 268779 268789 269775 269802) (-212 "DIOPS.spad" 267737 267749 268735 268740) (-211 "DIFRING.spad" 267029 267037 267717 267732) (-210 "DIFRING.spad" 266329 266339 267019 267024) (-209 "DIFEXT.spad" 265488 265498 266309 266324) (-208 "DIFEXT.spad" 264564 264576 265387 265392) (-207 "DIAGG.spad" 264182 264192 264532 264559) (-206 "DIAGG.spad" 263820 263832 264172 264177) (-205 "DHMATRIX.spad" 262124 262134 263277 263304) (-204 "DFSFUN.spad" 255532 255540 262114 262119) (-203 "DFLOAT.spad" 252055 252063 255422 255527) (-202 "DFINTTLS.spad" 250264 250280 252045 252050) (-201 "DERHAM.spad" 248174 248206 250244 250259) (-200 "DEQUEUE.spad" 247492 247502 247781 247808) (-199 "DEGRED.spad" 247107 247121 247482 247487) (-198 "DEFINTRF.spad" 244632 244642 247097 247102) (-197 "DEFINTEF.spad" 243128 243144 244622 244627) (-196 "DECIMAL.spad" 241012 241020 241598 241691) (-195 "DDFACT.spad" 238811 238828 241002 241007) (-194 "DBLRESP.spad" 238409 238433 238801 238806) (-193 "DBASE.spad" 236981 236991 238399 238404) (-192 "D03FAFA.spad" 236809 236817 236971 236976) (-191 "D03EEFA.spad" 236629 236637 236799 236804) (-190 "D03AGNT.spad" 235709 235717 236619 236624) (-189 "D02EJFA.spad" 235171 235179 235699 235704) (-188 "D02CJFA.spad" 234649 234657 235161 235166) (-187 "D02BHFA.spad" 234139 234147 234639 234644) (-186 "D02BBFA.spad" 233629 233637 234129 234134) (-185 "D02AGNT.spad" 228433 228441 233619 233624) (-184 "D01WGTS.spad" 226752 226760 228423 228428) (-183 "D01TRNS.spad" 226729 226737 226742 226747) (-182 "D01GBFA.spad" 226251 226259 226719 226724) (-181 "D01FCFA.spad" 225773 225781 226241 226246) (-180 "D01ASFA.spad" 225241 225249 225763 225768) (-179 "D01AQFA.spad" 224687 224695 225231 225236) (-178 "D01APFA.spad" 224111 224119 224677 224682) (-177 "D01ANFA.spad" 223605 223613 224101 224106) (-176 "D01AMFA.spad" 223115 223123 223595 223600) (-175 "D01ALFA.spad" 222655 222663 223105 223110) (-174 "D01AKFA.spad" 222181 222189 222645 222650) (-173 "D01AJFA.spad" 221704 221712 222171 222176) (-172 "D01AGNT.spad" 217763 217771 221694 221699) (-171 "CYCLOTOM.spad" 217269 217277 217753 217758) (-170 "CYCLES.spad" 214101 214109 217259 217264) (-169 "CVMP.spad" 213518 213528 214091 214096) (-168 "CTRIGMNP.spad" 212008 212024 213508 213513) (-167 "CTORCALL.spad" 211596 211604 211998 212003) (-166 "CSTTOOLS.spad" 210839 210852 211586 211591) (-165 "CRFP.spad" 204543 204556 210829 210834) (-164 "CRAPACK.spad" 203586 203596 204533 204538) (-163 "CPMATCH.spad" 203086 203101 203511 203516) (-162 "CPIMA.spad" 202791 202810 203076 203081) (-161 "COORDSYS.spad" 197684 197694 202781 202786) (-160 "CONTOUR.spad" 197086 197094 197674 197679) (-159 "CONTFRAC.spad" 192698 192708 196988 197081) (-158 "COMRING.spad" 192372 192380 192636 192693) (-157 "COMPPROP.spad" 191886 191894 192362 192367) (-156 "COMPLPAT.spad" 191653 191668 191876 191881) (-155 "COMPLEX.spad" 185686 185696 185930 186191) (-154 "COMPLEX2.spad" 185399 185411 185676 185681) (-153 "COMPFACT.spad" 185001 185015 185389 185394) (-152 "COMPCAT.spad" 183057 183067 184723 184996) (-151 "COMPCAT.spad" 180820 180832 182488 182493) (-150 "COMMUPC.spad" 180566 180584 180810 180815) (-149 "COMMONOP.spad" 180099 180107 180556 180561) (-148 "COMM.spad" 179908 179916 180089 180094) (-147 "COMBOPC.spad" 178813 178821 179898 179903) (-146 "COMBINAT.spad" 177558 177568 178803 178808) (-145 "COMBF.spad" 174926 174942 177548 177553) (-144 "COLOR.spad" 173763 173771 174916 174921) (-143 "CMPLXRT.spad" 173472 173489 173753 173758) (-142 "CLIP.spad" 169564 169572 173462 173467) (-141 "CLIF.spad" 168203 168219 169520 169559) (-140 "CLAGG.spad" 164678 164688 168183 168198) (-139 "CLAGG.spad" 161034 161046 164541 164546) (-138 "CINTSLPE.spad" 160359 160372 161024 161029) (-137 "CHVAR.spad" 158437 158459 160349 160354) (-136 "CHARZ.spad" 158352 158360 158417 158432) (-135 "CHARPOL.spad" 157860 157870 158342 158347) (-134 "CHARNZ.spad" 157613 157621 157840 157855) (-133 "CHAR.spad" 155481 155489 157603 157608) (-132 "CFCAT.spad" 154797 154805 155471 155476) (-131 "CDEN.spad" 153955 153969 154787 154792) (-130 "CCLASS.spad" 152104 152112 153366 153405) (-129 "CATEGORY.spad" 151883 151891 152094 152099) (-128 "CARTEN.spad" 146986 147010 151873 151878) (-127 "CARTEN2.spad" 146372 146399 146976 146981) (-126 "CARD.spad" 143661 143669 146346 146367) (-125 "CACHSET.spad" 143283 143291 143651 143656) (-124 "CABMON.spad" 142836 142844 143273 143278) (-123 "BTREE.spad" 141905 141915 142443 142470) (-122 "BTOURN.spad" 140908 140918 141512 141539) (-121 "BTCAT.spad" 140284 140294 140864 140903) (-120 "BTCAT.spad" 139692 139704 140274 140279) (-119 "BTAGG.spad" 138708 138716 139648 139687) (-118 "BTAGG.spad" 137756 137766 138698 138703) (-117 "BSTREE.spad" 136491 136501 137363 137390) (-116 "BRILL.spad" 134686 134697 136481 136486) (-115 "BRAGG.spad" 133600 133610 134666 134681) (-114 "BRAGG.spad" 132488 132500 133556 133561) (-113 "BPADICRT.spad" 130472 130484 130727 130820) (-112 "BPADIC.spad" 130136 130148 130398 130467) (-111 "BOUNDZRO.spad" 129792 129809 130126 130131) (-110 "BOP.spad" 125256 125264 129782 129787) (-109 "BOP1.spad" 122642 122652 125212 125217) (-108 "BOOLEAN.spad" 121895 121903 122632 122637) (-107 "BMODULE.spad" 121607 121619 121863 121890) (-106 "BITS.spad" 121026 121034 121243 121270) (-105 "BINFILE.spad" 120369 120377 121016 121021) (-104 "BINDING.spad" 119788 119796 120359 120364) (-103 "BINARY.spad" 117681 117689 118258 118351) (-102 "BGAGG.spad" 116866 116876 117649 117676) (-101 "BGAGG.spad" 116071 116083 116856 116861) (-100 "BFUNCT.spad" 115635 115643 116051 116066) (-99 "BEZOUT.spad" 114770 114796 115585 115590) (-98 "BBTREE.spad" 111590 111599 114377 114404) (-97 "BASTYPE.spad" 111263 111270 111580 111585) (-96 "BASTYPE.spad" 110934 110943 111253 111258) (-95 "BALFACT.spad" 110374 110386 110924 110929) (-94 "AUTOMOR.spad" 109821 109830 110354 110369) (-93 "ATTREG.spad" 106540 106547 109573 109816) (-92 "ATTRBUT.spad" 102563 102570 106520 106535) (-91 "ATRIG.spad" 102033 102040 102553 102558) (-90 "ATRIG.spad" 101501 101510 102023 102028) (-89 "ASTACK.spad" 100834 100843 101108 101135) (-88 "ASSOCEQ.spad" 99634 99645 100790 100795) (-87 "ASP9.spad" 98715 98728 99624 99629) (-86 "ASP8.spad" 97758 97771 98705 98710) (-85 "ASP80.spad" 97080 97093 97748 97753) (-84 "ASP7.spad" 96240 96253 97070 97075) (-83 "ASP78.spad" 95691 95704 96230 96235) (-82 "ASP77.spad" 95060 95073 95681 95686) (-81 "ASP74.spad" 94152 94165 95050 95055) (-80 "ASP73.spad" 93423 93436 94142 94147) (-79 "ASP6.spad" 92055 92068 93413 93418) (-78 "ASP55.spad" 90564 90577 92045 92050) (-77 "ASP50.spad" 88381 88394 90554 90559) (-76 "ASP4.spad" 87676 87689 88371 88376) (-75 "ASP49.spad" 86675 86688 87666 87671) (-74 "ASP42.spad" 85082 85121 86665 86670) (-73 "ASP41.spad" 83661 83700 85072 85077) (-72 "ASP35.spad" 82649 82662 83651 83656) (-71 "ASP34.spad" 81950 81963 82639 82644) (-70 "ASP33.spad" 81510 81523 81940 81945) (-69 "ASP31.spad" 80650 80663 81500 81505) (-68 "ASP30.spad" 79542 79555 80640 80645) (-67 "ASP29.spad" 79008 79021 79532 79537) (-66 "ASP28.spad" 70281 70294 78998 79003) (-65 "ASP27.spad" 69178 69191 70271 70276) (-64 "ASP24.spad" 68265 68278 69168 69173) (-63 "ASP20.spad" 67481 67494 68255 68260) (-62 "ASP1.spad" 66862 66875 67471 67476) (-61 "ASP19.spad" 61548 61561 66852 66857) (-60 "ASP12.spad" 60962 60975 61538 61543) (-59 "ASP10.spad" 60233 60246 60952 60957) (-58 "ARRAY2.spad" 59593 59602 59840 59867) (-57 "ARRAY1.spad" 58428 58437 58776 58803) (-56 "ARRAY12.spad" 57097 57108 58418 58423) (-55 "ARR2CAT.spad" 52747 52768 57053 57092) (-54 "ARR2CAT.spad" 48429 48452 52737 52742) (-53 "APPRULE.spad" 47673 47695 48419 48424) (-52 "APPLYORE.spad" 47288 47301 47663 47668) (-51 "ANY.spad" 45630 45637 47278 47283) (-50 "ANY1.spad" 44701 44710 45620 45625) (-49 "ANTISYM.spad" 43140 43156 44681 44696) (-48 "ANON.spad" 42837 42844 43130 43135) (-47 "AN.spad" 41140 41147 42655 42748) (-46 "AMR.spad" 39319 39330 41038 41135) (-45 "AMR.spad" 37335 37348 39056 39061) (-44 "ALIST.spad" 34747 34768 35097 35124) (-43 "ALGSC.spad" 33870 33896 34619 34672) (-42 "ALGPKG.spad" 29579 29590 33826 33831) (-41 "ALGMFACT.spad" 28768 28782 29569 29574) (-40 "ALGMANIP.spad" 26189 26204 28566 28571) (-39 "ALGFF.spad" 24507 24534 24724 24880) (-38 "ALGFACT.spad" 23628 23638 24497 24502) (-37 "ALGEBRA.spad" 23359 23368 23584 23623) (-36 "ALGEBRA.spad" 23122 23133 23349 23354) (-35 "ALAGG.spad" 22620 22641 23078 23117) (-34 "AHYP.spad" 22001 22008 22610 22615) (-33 "AGG.spad" 20300 20307 21981 21996) (-32 "AGG.spad" 18573 18582 20256 20261) (-31 "AF.spad" 16999 17014 18509 18514) (-30 "ACPLOT.spad" 15570 15577 16989 16994) (-29 "ACFS.spad" 13309 13318 15460 15565) (-28 "ACFS.spad" 11146 11157 13299 13304) (-27 "ACF.spad" 7748 7755 11048 11141) (-26 "ACF.spad" 4436 4445 7738 7743) (-25 "ABELSG.spad" 3977 3984 4426 4431) (-24 "ABELSG.spad" 3516 3525 3967 3972) (-23 "ABELMON.spad" 3059 3066 3506 3511) (-22 "ABELMON.spad" 2600 2609 3049 3054) (-21 "ABELGRP.spad" 2172 2179 2590 2595) (-20 "ABELGRP.spad" 1742 1751 2162 2167) (-19 "A1AGG.spad" 870 879 1698 1737) (-18 "A1AGG.spad" 30 41 860 865))
\ No newline at end of file +((-3 NIL 2236542 2236547 2236552 2236557) (-2 NIL 2236522 2236527 2236532 2236537) (-1 NIL 2236502 2236507 2236512 2236517) (0 NIL 2236482 2236487 2236492 2236497) (-1195 "ZMOD.spad" 2236291 2236304 2236420 2236477) (-1194 "ZLINDEP.spad" 2235335 2235346 2236281 2236286) (-1193 "ZDSOLVE.spad" 2225184 2225206 2235325 2235330) (-1192 "YSTREAM.spad" 2224677 2224688 2225174 2225179) (-1191 "XRPOLY.spad" 2223897 2223917 2224533 2224602) (-1190 "XPR.spad" 2221626 2221639 2223615 2223714) (-1189 "XPOLY.spad" 2221181 2221192 2221482 2221551) (-1188 "XPOLYC.spad" 2220498 2220514 2221107 2221176) (-1187 "XPBWPOLY.spad" 2218935 2218955 2220278 2220347) (-1186 "XF.spad" 2217396 2217411 2218837 2218930) (-1185 "XF.spad" 2215837 2215854 2217280 2217285) (-1184 "XFALG.spad" 2212861 2212877 2215763 2215832) (-1183 "XEXPPKG.spad" 2212112 2212138 2212851 2212856) (-1182 "XDPOLY.spad" 2211726 2211742 2211968 2212037) (-1181 "XALG.spad" 2211324 2211335 2211682 2211721) (-1180 "WUTSET.spad" 2207163 2207180 2210970 2210997) (-1179 "WP.spad" 2206177 2206221 2207021 2207088) (-1178 "WFFINTBS.spad" 2203740 2203762 2206167 2206172) (-1177 "WEIER.spad" 2201954 2201965 2203730 2203735) (-1176 "VSPACE.spad" 2201627 2201638 2201922 2201949) (-1175 "VSPACE.spad" 2201320 2201333 2201617 2201622) (-1174 "VOID.spad" 2200910 2200919 2201310 2201315) (-1173 "VIEW.spad" 2198532 2198541 2200900 2200905) (-1172 "VIEWDEF.spad" 2193729 2193738 2198522 2198527) (-1171 "VIEW3D.spad" 2177564 2177573 2193719 2193724) (-1170 "VIEW2D.spad" 2165301 2165310 2177554 2177559) (-1169 "VECTOR.spad" 2163978 2163989 2164229 2164256) (-1168 "VECTOR2.spad" 2162605 2162618 2163968 2163973) (-1167 "VECTCAT.spad" 2160493 2160504 2162561 2162600) (-1166 "VECTCAT.spad" 2158202 2158215 2160272 2160277) (-1165 "VARIABLE.spad" 2157982 2157997 2158192 2158197) (-1164 "UTYPE.spad" 2157616 2157625 2157962 2157977) (-1163 "UTSODETL.spad" 2156909 2156933 2157572 2157577) (-1162 "UTSODE.spad" 2155097 2155117 2156899 2156904) (-1161 "UTS.spad" 2149886 2149914 2153564 2153661) (-1160 "UTSCAT.spad" 2147337 2147353 2149784 2149881) (-1159 "UTSCAT.spad" 2144432 2144450 2146881 2146886) (-1158 "UTS2.spad" 2144025 2144060 2144422 2144427) (-1157 "URAGG.spad" 2138647 2138658 2144005 2144020) (-1156 "URAGG.spad" 2133243 2133256 2138603 2138608) (-1155 "UPXSSING.spad" 2130889 2130915 2132327 2132460) (-1154 "UPXS.spad" 2127916 2127944 2129021 2129170) (-1153 "UPXSCONS.spad" 2125673 2125693 2126048 2126197) (-1152 "UPXSCCA.spad" 2124131 2124151 2125519 2125668) (-1151 "UPXSCCA.spad" 2122731 2122753 2124121 2124126) (-1150 "UPXSCAT.spad" 2121312 2121328 2122577 2122726) (-1149 "UPXS2.spad" 2120853 2120906 2121302 2121307) (-1148 "UPSQFREE.spad" 2119265 2119279 2120843 2120848) (-1147 "UPSCAT.spad" 2116858 2116882 2119163 2119260) (-1146 "UPSCAT.spad" 2114157 2114183 2116464 2116469) (-1145 "UPOLYC.spad" 2109135 2109146 2113999 2114152) (-1144 "UPOLYC.spad" 2104005 2104018 2108871 2108876) (-1143 "UPOLYC2.spad" 2103474 2103493 2103995 2104000) (-1142 "UP.spad" 2100519 2100534 2101027 2101180) (-1141 "UPMP.spad" 2099409 2099422 2100509 2100514) (-1140 "UPDIVP.spad" 2098972 2098986 2099399 2099404) (-1139 "UPDECOMP.spad" 2097209 2097223 2098962 2098967) (-1138 "UPCDEN.spad" 2096416 2096432 2097199 2097204) (-1137 "UP2.spad" 2095778 2095799 2096406 2096411) (-1136 "UNISEG.spad" 2095131 2095142 2095697 2095702) (-1135 "UNISEG2.spad" 2094624 2094637 2095087 2095092) (-1134 "UNIFACT.spad" 2093725 2093737 2094614 2094619) (-1133 "ULS.spad" 2084284 2084312 2085377 2085806) (-1132 "ULSCONS.spad" 2078327 2078347 2078699 2078848) (-1131 "ULSCCAT.spad" 2075924 2075944 2078147 2078322) (-1130 "ULSCCAT.spad" 2073655 2073677 2075880 2075885) (-1129 "ULSCAT.spad" 2071871 2071887 2073501 2073650) (-1128 "ULS2.spad" 2071383 2071436 2071861 2071866) (-1127 "UFD.spad" 2070448 2070457 2071309 2071378) (-1126 "UFD.spad" 2069575 2069586 2070438 2070443) (-1125 "UDVO.spad" 2068422 2068431 2069565 2069570) (-1124 "UDPO.spad" 2065849 2065860 2068378 2068383) (-1123 "TYPE.spad" 2065771 2065780 2065829 2065844) (-1122 "TWOFACT.spad" 2064421 2064436 2065761 2065766) (-1121 "TUPLE.spad" 2063807 2063818 2064320 2064325) (-1120 "TUBETOOL.spad" 2060644 2060653 2063797 2063802) (-1119 "TUBE.spad" 2059285 2059302 2060634 2060639) (-1118 "TS.spad" 2057874 2057890 2058850 2058947) (-1117 "TSETCAT.spad" 2044989 2045006 2057830 2057869) (-1116 "TSETCAT.spad" 2032102 2032121 2044945 2044950) (-1115 "TRMANIP.spad" 2026468 2026485 2031808 2031813) (-1114 "TRIMAT.spad" 2025427 2025452 2026458 2026463) (-1113 "TRIGMNIP.spad" 2023944 2023961 2025417 2025422) (-1112 "TRIGCAT.spad" 2023456 2023465 2023934 2023939) (-1111 "TRIGCAT.spad" 2022966 2022977 2023446 2023451) (-1110 "TREE.spad" 2021537 2021548 2022573 2022600) (-1109 "TRANFUN.spad" 2021368 2021377 2021527 2021532) (-1108 "TRANFUN.spad" 2021197 2021208 2021358 2021363) (-1107 "TOPSP.spad" 2020871 2020880 2021187 2021192) (-1106 "TOOLSIGN.spad" 2020534 2020545 2020861 2020866) (-1105 "TEXTFILE.spad" 2019091 2019100 2020524 2020529) (-1104 "TEX.spad" 2016108 2016117 2019081 2019086) (-1103 "TEX1.spad" 2015664 2015675 2016098 2016103) (-1102 "TEMUTL.spad" 2015219 2015228 2015654 2015659) (-1101 "TBCMPPK.spad" 2013312 2013335 2015209 2015214) (-1100 "TBAGG.spad" 2012336 2012359 2013280 2013307) (-1099 "TBAGG.spad" 2011380 2011405 2012326 2012331) (-1098 "TANEXP.spad" 2010756 2010767 2011370 2011375) (-1097 "TABLE.spad" 2009167 2009190 2009437 2009464) (-1096 "TABLEAU.spad" 2008648 2008659 2009157 2009162) (-1095 "TABLBUMP.spad" 2005431 2005442 2008638 2008643) (-1094 "SYSTEM.spad" 2004705 2004714 2005421 2005426) (-1093 "SYSSOLP.spad" 2002178 2002189 2004695 2004700) (-1092 "SYNTAX.spad" 1998370 1998379 2002168 2002173) (-1091 "SYMTAB.spad" 1996426 1996435 1998360 1998365) (-1090 "SYMS.spad" 1992411 1992420 1996416 1996421) (-1089 "SYMPOLY.spad" 1991421 1991432 1991503 1991630) (-1088 "SYMFUNC.spad" 1990896 1990907 1991411 1991416) (-1087 "SYMBOL.spad" 1988232 1988241 1990886 1990891) (-1086 "SWITCH.spad" 1984989 1984998 1988222 1988227) (-1085 "SUTS.spad" 1981888 1981916 1983456 1983553) (-1084 "SUPXS.spad" 1978902 1978930 1980020 1980169) (-1083 "SUP.spad" 1975674 1975685 1976455 1976608) (-1082 "SUPFRACF.spad" 1974779 1974797 1975664 1975669) (-1081 "SUP2.spad" 1974169 1974182 1974769 1974774) (-1080 "SUMRF.spad" 1973135 1973146 1974159 1974164) (-1079 "SUMFS.spad" 1972768 1972785 1973125 1973130) (-1078 "SULS.spad" 1963314 1963342 1964420 1964849) (-1077 "SUCH.spad" 1962994 1963009 1963304 1963309) (-1076 "SUBSPACE.spad" 1955001 1955016 1962984 1962989) (-1075 "SUBRESP.spad" 1954161 1954175 1954957 1954962) (-1074 "STTF.spad" 1950260 1950276 1954151 1954156) (-1073 "STTFNC.spad" 1946728 1946744 1950250 1950255) (-1072 "STTAYLOR.spad" 1939126 1939137 1946609 1946614) (-1071 "STRTBL.spad" 1937631 1937648 1937780 1937807) (-1070 "STRING.spad" 1937040 1937049 1937054 1937081) (-1069 "STRICAT.spad" 1936816 1936825 1936996 1937035) (-1068 "STREAM.spad" 1933584 1933595 1936341 1936356) (-1067 "STREAM3.spad" 1933129 1933144 1933574 1933579) (-1066 "STREAM2.spad" 1932197 1932210 1933119 1933124) (-1065 "STREAM1.spad" 1931901 1931912 1932187 1932192) (-1064 "STINPROD.spad" 1930807 1930823 1931891 1931896) (-1063 "STEP.spad" 1930008 1930017 1930797 1930802) (-1062 "STBL.spad" 1928534 1928562 1928701 1928716) (-1061 "STAGG.spad" 1927599 1927610 1928514 1928529) (-1060 "STAGG.spad" 1926672 1926685 1927589 1927594) (-1059 "STACK.spad" 1926023 1926034 1926279 1926306) (-1058 "SREGSET.spad" 1923727 1923744 1925669 1925696) (-1057 "SRDCMPK.spad" 1922272 1922292 1923717 1923722) (-1056 "SRAGG.spad" 1917357 1917366 1922228 1922267) (-1055 "SRAGG.spad" 1912474 1912485 1917347 1917352) (-1054 "SQMATRIX.spad" 1910100 1910118 1911008 1911095) (-1053 "SPLTREE.spad" 1904652 1904665 1909536 1909563) (-1052 "SPLNODE.spad" 1901240 1901253 1904642 1904647) (-1051 "SPFCAT.spad" 1900017 1900026 1901230 1901235) (-1050 "SPECOUT.spad" 1898567 1898576 1900007 1900012) (-1049 "spad-parser.spad" 1898032 1898041 1898557 1898562) (-1048 "SPACEC.spad" 1882045 1882056 1898022 1898027) (-1047 "SPACE3.spad" 1881821 1881832 1882035 1882040) (-1046 "SORTPAK.spad" 1881366 1881379 1881777 1881782) (-1045 "SOLVETRA.spad" 1879123 1879134 1881356 1881361) (-1044 "SOLVESER.spad" 1877643 1877654 1879113 1879118) (-1043 "SOLVERAD.spad" 1873653 1873664 1877633 1877638) (-1042 "SOLVEFOR.spad" 1872073 1872091 1873643 1873648) (-1041 "SNTSCAT.spad" 1871661 1871678 1872029 1872068) (-1040 "SMTS.spad" 1869921 1869947 1871226 1871323) (-1039 "SMP.spad" 1867363 1867383 1867753 1867880) (-1038 "SMITH.spad" 1866206 1866231 1867353 1867358) (-1037 "SMATCAT.spad" 1864304 1864334 1866138 1866201) (-1036 "SMATCAT.spad" 1862346 1862378 1864182 1864187) (-1035 "SKAGG.spad" 1861295 1861306 1862302 1862341) (-1034 "SINT.spad" 1859603 1859612 1861161 1861290) (-1033 "SIMPAN.spad" 1859331 1859340 1859593 1859598) (-1032 "SIGNRF.spad" 1858439 1858450 1859321 1859326) (-1031 "SIGNEF.spad" 1857708 1857725 1858429 1858434) (-1030 "SHP.spad" 1855626 1855641 1857664 1857669) (-1029 "SHDP.spad" 1847016 1847043 1847525 1847654) (-1028 "SGROUP.spad" 1846482 1846491 1847006 1847011) (-1027 "SGROUP.spad" 1845946 1845957 1846472 1846477) (-1026 "SGCF.spad" 1838827 1838836 1845936 1845941) (-1025 "SFRTCAT.spad" 1837743 1837760 1838783 1838822) (-1024 "SFRGCD.spad" 1836806 1836826 1837733 1837738) (-1023 "SFQCMPK.spad" 1831443 1831463 1836796 1836801) (-1022 "SFORT.spad" 1830878 1830892 1831433 1831438) (-1021 "SEXOF.spad" 1830721 1830761 1830868 1830873) (-1020 "SEX.spad" 1830613 1830622 1830711 1830716) (-1019 "SEXCAT.spad" 1827717 1827757 1830603 1830608) (-1018 "SET.spad" 1826017 1826028 1827138 1827177) (-1017 "SETMN.spad" 1824451 1824468 1826007 1826012) (-1016 "SETCAT.spad" 1823936 1823945 1824441 1824446) (-1015 "SETCAT.spad" 1823419 1823430 1823926 1823931) (-1014 "SETAGG.spad" 1819942 1819953 1823387 1823414) (-1013 "SETAGG.spad" 1816485 1816498 1819932 1819937) (-1012 "SEGXCAT.spad" 1815597 1815610 1816465 1816480) (-1011 "SEG.spad" 1815410 1815421 1815516 1815521) (-1010 "SEGCAT.spad" 1814229 1814240 1815390 1815405) (-1009 "SEGBIND.spad" 1813301 1813312 1814184 1814189) (-1008 "SEGBIND2.spad" 1812997 1813010 1813291 1813296) (-1007 "SEG2.spad" 1812422 1812435 1812953 1812958) (-1006 "SDVAR.spad" 1811698 1811709 1812412 1812417) (-1005 "SDPOL.spad" 1809091 1809102 1809382 1809509) (-1004 "SCPKG.spad" 1807170 1807181 1809081 1809086) (-1003 "SCOPE.spad" 1806315 1806324 1807160 1807165) (-1002 "SCACHE.spad" 1804997 1805008 1806305 1806310) (-1001 "SAOS.spad" 1804869 1804878 1804987 1804992) (-1000 "SAERFFC.spad" 1804582 1804602 1804859 1804864) (-999 "SAE.spad" 1802761 1802776 1803371 1803506) (-998 "SAEFACT.spad" 1802463 1802482 1802751 1802756) (-997 "RURPK.spad" 1800105 1800120 1802453 1802458) (-996 "RULESET.spad" 1799547 1799570 1800095 1800100) (-995 "RULE.spad" 1797752 1797775 1799537 1799542) (-994 "RULECOLD.spad" 1797605 1797617 1797742 1797747) (-993 "RSETGCD.spad" 1793984 1794003 1797595 1797600) (-992 "RSETCAT.spad" 1783757 1783773 1793940 1793979) (-991 "RSETCAT.spad" 1773562 1773580 1783747 1783752) (-990 "RSDCMPK.spad" 1772015 1772034 1773552 1773557) (-989 "RRCC.spad" 1770400 1770429 1772005 1772010) (-988 "RRCC.spad" 1768783 1768814 1770390 1770395) (-987 "RPOLCAT.spad" 1748144 1748158 1768651 1768778) (-986 "RPOLCAT.spad" 1727220 1727236 1747729 1747734) (-985 "ROUTINE.spad" 1723084 1723092 1725867 1725894) (-984 "ROMAN.spad" 1722317 1722325 1722950 1723079) (-983 "ROIRC.spad" 1721398 1721429 1722307 1722312) (-982 "RNS.spad" 1720302 1720310 1721300 1721393) (-981 "RNS.spad" 1719292 1719302 1720292 1720297) (-980 "RNG.spad" 1719028 1719036 1719282 1719287) (-979 "RMODULE.spad" 1718667 1718677 1719018 1719023) (-978 "RMCAT2.spad" 1718076 1718132 1718657 1718662) (-977 "RMATRIX.spad" 1716756 1716774 1717243 1717282) (-976 "RMATCAT.spad" 1712278 1712308 1716700 1716751) (-975 "RMATCAT.spad" 1707702 1707734 1712126 1712131) (-974 "RINTERP.spad" 1707591 1707610 1707692 1707697) (-973 "RING.spad" 1706949 1706957 1707571 1707586) (-972 "RING.spad" 1706315 1706325 1706939 1706944) (-971 "RIDIST.spad" 1705700 1705708 1706305 1706310) (-970 "RGCHAIN.spad" 1704280 1704295 1705185 1705212) (-969 "RF.spad" 1701895 1701905 1704270 1704275) (-968 "RFFACTOR.spad" 1701358 1701368 1701885 1701890) (-967 "RFFACT.spad" 1701094 1701105 1701348 1701353) (-966 "RFDIST.spad" 1700083 1700091 1701084 1701089) (-965 "RETSOL.spad" 1699501 1699513 1700073 1700078) (-964 "RETRACT.spad" 1698851 1698861 1699491 1699496) (-963 "RETRACT.spad" 1698199 1698211 1698841 1698846) (-962 "RESULT.spad" 1696260 1696268 1696846 1696873) (-961 "RESRING.spad" 1695608 1695654 1696198 1696255) (-960 "RESLATC.spad" 1694933 1694943 1695598 1695603) (-959 "REPSQ.spad" 1694663 1694673 1694923 1694928) (-958 "REP.spad" 1692216 1692224 1694653 1694658) (-957 "REPDB.spad" 1691922 1691932 1692206 1692211) (-956 "REP2.spad" 1681495 1681505 1691764 1691769) (-955 "REP1.spad" 1675486 1675496 1681445 1681450) (-954 "REGSET.spad" 1673284 1673300 1675132 1675159) (-953 "REF.spad" 1672614 1672624 1673239 1673244) (-952 "REDORDER.spad" 1671791 1671807 1672604 1672609) (-951 "RECLOS.spad" 1670581 1670600 1671284 1671377) (-950 "REALSOLV.spad" 1669714 1669722 1670571 1670576) (-949 "REAL.spad" 1669587 1669595 1669704 1669709) (-948 "REAL0Q.spad" 1666870 1666884 1669577 1669582) (-947 "REAL0.spad" 1663699 1663713 1666860 1666865) (-946 "RDIV.spad" 1663351 1663375 1663689 1663694) (-945 "RDIST.spad" 1662915 1662925 1663341 1663346) (-944 "RDETRS.spad" 1661712 1661729 1662905 1662910) (-943 "RDETR.spad" 1659820 1659837 1661702 1661707) (-942 "RDEEFS.spad" 1658894 1658910 1659810 1659815) (-941 "RDEEF.spad" 1657891 1657907 1658884 1658889) (-940 "RCFIELD.spad" 1655075 1655083 1657793 1657886) (-939 "RCFIELD.spad" 1652345 1652355 1655065 1655070) (-938 "RCAGG.spad" 1650248 1650258 1652325 1652340) (-937 "RCAGG.spad" 1648088 1648100 1650167 1650172) (-936 "RATRET.spad" 1647449 1647459 1648078 1648083) (-935 "RATFACT.spad" 1647142 1647153 1647439 1647444) (-934 "RANDSRC.spad" 1646462 1646470 1647132 1647137) (-933 "RADUTIL.spad" 1646217 1646225 1646452 1646457) (-932 "RADIX.spad" 1643010 1643023 1644687 1644780) (-931 "RADFF.spad" 1641427 1641463 1641545 1641701) (-930 "RADCAT.spad" 1641021 1641029 1641417 1641422) (-929 "RADCAT.spad" 1640613 1640623 1641011 1641016) (-928 "QUEUE.spad" 1639956 1639966 1640220 1640247) (-927 "QUAT.spad" 1638542 1638552 1638884 1638949) (-926 "QUATCT2.spad" 1638161 1638179 1638532 1638537) (-925 "QUATCAT.spad" 1636326 1636336 1638091 1638156) (-924 "QUATCAT.spad" 1634243 1634255 1636010 1636015) (-923 "QUAGG.spad" 1633057 1633067 1634199 1634238) (-922 "QFORM.spad" 1632520 1632534 1633047 1633052) (-921 "QFCAT.spad" 1631211 1631221 1632410 1632515) (-920 "QFCAT.spad" 1629508 1629520 1630709 1630714) (-919 "QFCAT2.spad" 1629199 1629215 1629498 1629503) (-918 "QEQUAT.spad" 1628756 1628764 1629189 1629194) (-917 "QCMPACK.spad" 1623503 1623522 1628746 1628751) (-916 "QALGSET.spad" 1619578 1619610 1623417 1623422) (-915 "QALGSET2.spad" 1617574 1617592 1619568 1619573) (-914 "PWFFINTB.spad" 1614884 1614905 1617564 1617569) (-913 "PUSHVAR.spad" 1614213 1614232 1614874 1614879) (-912 "PTRANFN.spad" 1610339 1610349 1614203 1614208) (-911 "PTPACK.spad" 1607427 1607437 1610329 1610334) (-910 "PTFUNC2.spad" 1607248 1607262 1607417 1607422) (-909 "PTCAT.spad" 1606330 1606340 1607204 1607243) (-908 "PSQFR.spad" 1605637 1605661 1606320 1606325) (-907 "PSEUDLIN.spad" 1604495 1604505 1605627 1605632) (-906 "PSETPK.spad" 1589928 1589944 1604373 1604378) (-905 "PSETCAT.spad" 1583836 1583859 1589896 1589923) (-904 "PSETCAT.spad" 1577730 1577755 1583792 1583797) (-903 "PSCURVE.spad" 1576713 1576721 1577720 1577725) (-902 "PSCAT.spad" 1575480 1575509 1576611 1576708) (-901 "PSCAT.spad" 1574337 1574368 1575470 1575475) (-900 "PRTITION.spad" 1573180 1573188 1574327 1574332) (-899 "PRS.spad" 1562742 1562759 1573136 1573141) (-898 "PRQAGG.spad" 1562161 1562171 1562698 1562737) (-897 "PROPLOG.spad" 1561564 1561572 1562151 1562156) (-896 "PROPFRML.spad" 1559429 1559440 1561500 1561505) (-895 "PROPERTY.spad" 1558923 1558931 1559419 1559424) (-894 "PRODUCT.spad" 1556603 1556615 1556889 1556944) (-893 "PR.spad" 1554992 1555004 1555697 1555824) (-892 "PRINT.spad" 1554744 1554752 1554982 1554987) (-891 "PRIMES.spad" 1552995 1553005 1554734 1554739) (-890 "PRIMELT.spad" 1550976 1550990 1552985 1552990) (-889 "PRIMCAT.spad" 1550599 1550607 1550966 1550971) (-888 "PRIMARR.spad" 1549604 1549614 1549782 1549809) (-887 "PRIMARR2.spad" 1548327 1548339 1549594 1549599) (-886 "PREASSOC.spad" 1547699 1547711 1548317 1548322) (-885 "PPCURVE.spad" 1546836 1546844 1547689 1547694) (-884 "POLYROOT.spad" 1545608 1545630 1546792 1546797) (-883 "POLY.spad" 1542908 1542918 1543425 1543552) (-882 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(-417 "GALFACT.spad" 715786 715797 725643 725648) (-416 "FVFUN.spad" 712799 712807 715766 715781) (-415 "FVC.spad" 711841 711849 712779 712794) (-414 "FUNCTION.spad" 711690 711702 711831 711836) (-413 "FT.spad" 709902 709910 711680 711685) (-412 "FTEM.spad" 709065 709073 709892 709897) (-411 "FSUPFACT.spad" 707966 707985 709002 709007) (-410 "FST.spad" 706052 706060 707956 707961) (-409 "FSRED.spad" 705530 705546 706042 706047) (-408 "FSPRMELT.spad" 704354 704370 705487 705492) (-407 "FSPECF.spad" 702431 702447 704344 704349) (-406 "FS.spad" 696482 696492 702195 702426) (-405 "FS.spad" 690324 690336 696039 696044) (-404 "FSINT.spad" 689982 689998 690314 690319) (-403 "FSERIES.spad" 689169 689181 689802 689901) (-402 "FSCINT.spad" 688482 688498 689159 689164) (-401 "FSAGG.spad" 687587 687597 688426 688477) (-400 "FSAGG.spad" 686666 686678 687507 687512) (-399 "FSAGG2.spad" 685365 685381 686656 686661) (-398 "FS2UPS.spad" 679754 679788 685355 685360) (-397 "FS2.spad" 679399 679415 679744 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562042 562368 562461) (-334 "FFSLPE.spad" 561516 561537 562017 562022) (-333 "FFPOLY.spad" 552768 552779 561506 561511) (-332 "FFPOLY2.spad" 551828 551845 552758 552763) (-331 "FFP.spad" 551225 551245 551544 551637) (-330 "FF.spad" 550673 550689 550906 550999) (-329 "FFNBX.spad" 549185 549205 550389 550482) (-328 "FFNBP.spad" 547698 547715 548901 548994) (-327 "FFNB.spad" 546163 546184 547379 547472) (-326 "FFINTBAS.spad" 543577 543596 546153 546158) (-325 "FFIELDC.spad" 541152 541160 543479 543572) (-324 "FFIELDC.spad" 538813 538823 541142 541147) (-323 "FFHOM.spad" 537561 537578 538803 538808) (-322 "FFF.spad" 534996 535007 537551 537556) (-321 "FFCGX.spad" 533843 533863 534712 534805) (-320 "FFCGP.spad" 532732 532752 533559 533652) (-319 "FFCG.spad" 531524 531545 532413 532506) (-318 "FFCAT.spad" 524425 524447 531363 531519) (-317 "FFCAT.spad" 517405 517429 524345 524350) (-316 "FFCAT2.spad" 517150 517190 517395 517400) (-315 "FEXPR.spad" 508863 508909 516910 516949) (-314 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\ No newline at end of file diff --git a/src/share/algebra/category.daase b/src/share/algebra/category.daase index 505188a0..94f9b9eb 100644 --- a/src/share/algebra/category.daase +++ b/src/share/algebra/category.daase @@ -1,14 +1,14 @@ -(142548 . 3415311735) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) #0#) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(142548 . 3416412006) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) (((|#2| |#2|) . T)) ((((-523)) . T)) -((($ $) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2| |#2|) . T) ((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523))))) +((($ $) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2| |#2|) . T) ((#0=(-383 (-523)) #0#) |has| |#2| (-37 (-383 (-523))))) ((($) . T)) (((|#1|) . T)) ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#2|) . T)) -((($) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2|) . T) (((-383 (-523))) |has| |#2| (-37 (-383 (-523))))) +((($) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((|#2|) . T) (((-383 (-523))) |has| |#2| (-37 (-383 (-523))))) (|has| |#1| (-840)) ((((-794)) . T)) ((((-794)) . T)) @@ -23,28 +23,28 @@ ((((-203)) . T) (((-794)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1|) . T)) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-784))) -((($ $) . T) ((#0=(-383 (-523)) #0#) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) -(-3262 (|has| |#1| (-759)) (|has| |#1| (-786))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-784))) +((($ $) . T) ((#0=(-383 (-523)) #0#) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) +(-3172 (|has| |#1| (-759)) (|has| |#1| (-786))) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-784)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#2| |#3|) . T)) (((|#4|) . T)) -((($) . T) (((-383 (-523))) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) |has| |#1| (-1016))) (((|#1|) . T) ((|#2|) . T)) (((|#1|) . 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T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3262 (|has| |#4| (-732)) (|has| |#4| (-784))) -(-3262 (|has| |#4| (-732)) (|has| |#4| (-784))) -(-3262 (|has| |#3| (-732)) (|has| |#3| (-784))) -(-3262 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-1016)) @@ -132,21 +132,21 @@ ((((-523)) . T)) ((((-523)) . T)) (((|#1|) . T)) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#1| (-710)) . T)) (|has| |#2| (-732)) -(-3262 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) (|has| |#2| (-784)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) ((((-1070) |#1|) . 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T) (((-203)) . T) (((-355)) . T) (((-823 (-355))) . T)) ((((-794)) . T)) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) (((|#1|) |has| |#1| (-158))) (((|#1| $) |has| |#1| (-263 |#1| |#1|))) ((((-794)) . T)) @@ -256,13 +256,13 @@ (|has| |#1| (-786)) (|has| |#1| (-1016)) (((|#1|) . 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T)) (((|#1| (-900)) . T)) (((#0=(-801 |#1|) $) |has| #0# (-263 #0# #0#))) @@ -271,9 +271,9 @@ (((|#1|) . T)) (((|#2| |#2|) . T)) (|has| |#1| (-1063)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) -(|has| (-1154 |#1| |#2| |#3| |#4|) (-134)) -(|has| (-1154 |#1| |#2| |#3| |#4|) (-136)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +(|has| (-1155 |#1| |#2| |#3| |#4|) (-134)) +(|has| (-1155 |#1| |#2| |#3| |#4|) (-136)) (|has| |#1| (-134)) (|has| |#1| (-136)) (((|#1|) |has| |#1| (-158))) @@ -288,40 +288,40 @@ ((($) . T) ((|#1|) . T)) (((|#2|) |has| |#2| (-973))) ((((-794)) . 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T) (($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339)))) (((|#3|) |has| |#3| (-973))) -((($) -3262 (|has| |#1| (-158)) (|has| |#1| (-515))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-515))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#1| (-1016)) (((|#2| (-758 |#1|)) . T)) (((|#1|) . T)) @@ -381,37 +381,37 @@ ((((-133)) . T)) (((|#3|) |has| |#3| (-1016)) (((-523)) -12 (|has| |#3| (-964 (-523))) (|has| |#3| (-1016))) (((-383 (-523))) -12 (|has| |#3| (-964 (-383 (-523)))) (|has| |#3| (-1016)))) ((((-794)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1|) . 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T)) ((((-794)) . T)) @@ -653,22 +653,22 @@ (|has| |#1| (-1016)) (((|#2|) . T)) ((((-499)) |has| |#2| (-564 (-499))) (((-823 (-355))) |has| |#2| (-564 (-823 (-355)))) (((-823 (-523))) |has| |#2| (-564 (-823 (-523))))) -(((|#4|) -3262 (|has| |#4| (-158)) (|has| |#4| (-339)))) -(((|#3|) -3262 (|has| |#3| (-158)) (|has| |#3| (-339)))) +(((|#4|) -3172 (|has| |#4| (-158)) (|has| |#4| (-339)))) +(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)))) ((((-794)) . T)) (((|#1|) . T)) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-840))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-840))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) ((($ $) . T) ((#0=(-1087) $) |has| |#1| (-211)) ((#0# |#1|) |has| |#1| (-211)) ((#1=(-757 (-1087)) |#1|) . T) ((#1# $) . 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T)) (|has| (-383 |#2|) (-136)) (|has| (-383 |#2|) (-134)) @@ -681,21 +681,21 @@ (|has| |#1| (-515)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-794)) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) (|has| |#1| (-37 (-383 (-523)))) -((((-364) (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) +((((-364) (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#2| (-1063)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((|#1|) . T)) ((((-364) (-1070)) . T)) (|has| |#1| (-515)) ((((-112 |#1|)) . T)) ((((-523) |#1|) . T)) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#2|) . T)) ((((-794)) . T)) ((((-758 |#1|)) . T)) @@ -708,7 +708,7 @@ (((|#1|) |has| |#1| (-158))) ((((-794)) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#2|) |has| |#2| (-286 |#2|))) (((#0=(-523) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) (((|#1|) . T)) @@ -718,7 +718,7 @@ (((#0=(-523) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) ((($) . T) (((-523)) . T) (((-383 (-523))) . T)) (|has| |#2| (-344)) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) @@ -729,24 +729,24 @@ ((((-1085 |#1| |#2| |#3|) $) -12 (|has| (-1085 |#1| |#2| |#3|) (-263 (-1085 |#1| |#2| |#3|) (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339))) (($ $) . T)) ((((-794)) . T)) ((((-794)) . T)) -((($) . T) (((-383 (-523))) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((($ $) . T)) ((($ $) . T)) ((((-794)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(((#0=(-1160 |#1| |#2| |#3|) #0#) -12 (|has| (-1160 |#1| |#2| |#3|) (-286 (-1160 |#1| |#2| |#3|))) (|has| |#1| (-339))) (((-1087) #0#) -12 (|has| (-1160 |#1| |#2| |#3|) (-484 (-1087) (-1160 |#1| |#2| |#3|))) (|has| |#1| (-339)))) +(((#0=(-1161 |#1| |#2| |#3|) #0#) -12 (|has| (-1161 |#1| |#2| |#3|) (-286 (-1161 |#1| |#2| |#3|))) (|has| |#1| (-339))) (((-1087) #0#) -12 (|has| (-1161 |#1| |#2| |#3|) (-484 (-1087) (-1161 |#1| |#2| |#3|))) (|has| |#1| (-339)))) (-12 (|has| |#1| (-1016)) (|has| |#2| (-1016))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -((($) -3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((((-383 (-523))) . T) (((-523)) . T)) ((((-523) (-133)) . T)) ((((-133)) . T)) (((|#1|) . T)) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((((-108)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-108)) . T)) @@ -754,38 +754,38 @@ ((((-499)) |has| |#1| (-564 (-499))) (((-203)) . #0=(|has| |#1| (-949))) (((-355)) . #0#)) ((((-794)) . T)) (|has| |#1| (-759)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (|has| |#1| (-786)) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) (|has| |#1| (-515)) (|has| |#1| (-840)) (((|#1|) . T)) (|has| |#1| (-1016)) ((((-794)) . 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T) (((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) . T)) +((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) . T)) (|has| |#1| (-767)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) (|has| |#1| (-1016)) @@ -811,8 +811,8 @@ (((|#3|) |has| |#3| (-1016))) (|has| |#3| (-344)) (((|#1|) . T) (((-794)) . 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T)) (|has| |#1| (-515)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-515)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) @@ -856,7 +856,7 @@ (|has| |#1| (-136)) (|has| |#1| (-134)) (|has| |#4| (-784)) -(((|#2| (-218 (-2676 |#1|) (-710)) (-796 |#1|)) . T)) +(((|#2| (-218 (-2810 |#1|) (-710)) (-796 |#1|)) . T)) (|has| |#3| (-784)) (((|#1| (-495 |#3|) |#3|) . T)) (|has| |#1| (-136)) @@ -870,21 +870,21 @@ (|has| |#1| (-134)) ((((-383 (-523))) |has| |#2| (-339)) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3262 (|has| |#1| (-325)) (|has| |#1| (-344))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#1| (-325)) (|has| |#1| (-344))) ((((-1054 |#2| |#1|)) . T) ((|#1|) . T)) (|has| |#2| (-158)) (((|#1| |#2|) . T)) (-12 (|has| |#2| (-211)) (|has| |#2| (-973))) -(((|#2|) . T) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -(-3262 (|has| |#3| (-732)) (|has| |#3| (-784))) -(-3262 (|has| |#3| (-732)) (|has| |#3| (-784))) +(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) ((((-794)) . T)) (((|#1|) . T)) (((|#2|) . T) (($) . T)) (((|#1|) . T) (($) . T)) ((((-638)) . T)) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (|has| |#1| (-515)) (((|#1|) . T)) (((|#1|) . T)) @@ -906,10 +906,10 @@ (((|#1| (-383 (-523))) . T)) (((|#3|) . T) (((-562 $)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((($ $) . T) ((|#2| $) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) (((#0=(-1085 |#1| |#2| |#3|) #0#) -12 (|has| (-1085 |#1| |#2| |#3|) (-286 (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339))) (((-1087) #0#) -12 (|has| (-1085 |#1| |#2| |#3|) (-484 (-1087) (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339)))) @@ -917,8 +917,8 @@ ((((-794)) . T)) ((((-794)) . T)) (((|#1| |#1|) . T)) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) -(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) |has| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (-286 (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) +(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))))) ((((-794)) . T)) (((|#1|) . T)) (((|#3| |#3|) . T)) @@ -929,10 +929,10 @@ ((($ $) . T) ((#0=(-796 |#1|) $) . T) ((#0# |#2|) . T)) (|has| |#1| (-767)) (|has| |#1| (-1016)) -(((|#2| |#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) -(((|#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)))) -((((-523) (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T) ((|#1| |#2|) . T)) -(((|#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) +(((|#2| |#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) +(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)))) +((((-523) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#1| |#2|) . T)) +(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) ((((-710)) . T)) ((((-523)) . T)) (|has| |#1| (-515)) @@ -945,29 +945,29 @@ ((((-112 |#1|)) . T)) (((|#1|) . 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T)) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (-12 (|has| |#3| (-211)) (|has| |#3| (-973))) (|has| |#2| (-1063)) -(((#0=(-51)) . T) (((-2 (|:| -1853 (-1087)) (|:| -2433 #0#))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3772 (-1087)) (|:| -2482 #0#))) . T)) (((|#1| |#2|) . T)) -(-3262 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) (((|#1| (-523) (-1001)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| (-383 (-523)) (-1001)) . T)) -((($) -3262 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) (((-383 (-523))) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) -3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-523) |#2|) . T)) (((|#1| |#2|) . T)) (((|#1| |#2|) . T)) @@ -975,37 +975,37 @@ (-12 (|has| |#1| (-344)) (|has| |#2| (-344))) ((((-794)) . T)) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|)) ((|#1| |#1|) |has| |#1| (-286 |#1|))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (((|#1|) . 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T)) (((|#1|) |has| |#1| (-286 |#1|))) (|has| |#1| (-344)) @@ -1013,32 +1013,32 @@ (|has| |#1| (-344)) ((((-1087) $) |has| |#1| (-484 (-1087) $)) (($ $) |has| |#1| (-286 $)) ((|#1| |#1|) |has| |#1| (-286 |#1|)) (((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|))) ((((-1087)) |has| |#1| (-831 (-1087)))) -(-3262 (-12 (|has| |#1| (-211)) (|has| |#1| (-339))) (|has| |#1| (-325))) +(-3172 (-12 (|has| |#1| (-211)) (|has| |#1| (-339))) (|has| |#1| (-325))) ((((-364) (-1034)) . T)) (((|#1| |#4|) . T)) (((|#1| |#3|) . T)) ((((-364) |#1|) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-1016)) ((((-794)) . T)) ((((-794)) . T)) ((((-841 |#1|)) . T)) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) -((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) (((|#1| |#2|) . T)) ((($) . T)) (((|#1| |#1|) . T)) (((#0=(-801 |#1|)) |has| #0# (-286 #0#))) (((|#1| |#2|) . T)) -(-3262 (|has| |#2| (-732)) (|has| |#2| (-784))) -(-3262 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732))) (((|#1|) . T)) (-12 (|has| |#1| (-732)) (|has| |#2| (-732))) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#2|) . T) (($) . T)) -(((|#2|) . T) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -(|has| |#1| (-1108)) +(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +(|has| |#1| (-1109)) (((#0=(-523) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) ((((-383 (-523))) . T) (($) . T)) (((|#4|) |has| |#4| (-973))) @@ -1048,8 +1048,8 @@ (((|#1| |#1|) . T) (($ $) . T) ((#0=(-383 (-523)) #0#) . T)) (|has| |#1| (-339)) ((((-523)) . T) (((-383 (-523))) . T) (($) . T)) -((($ $) . T) ((#0=(-383 (-523)) #0#) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((($ $) . T) ((#0=(-383 (-523)) #0#) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1| |#1|) . T)) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) . T) (($) . T) (((-383 (-523))) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -1064,14 +1064,14 @@ (((|#1| |#2|) . T)) (|has| |#1| (-784)) (|has| |#1| (-784)) -((($) . T) (((-383 (-523))) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-515))) -(((#0=(-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) #0#) |has| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (-286 (-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))))) +((($) . T) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) +(((#0=(-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) #0#) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) ((($) . T)) (|has| |#2| (-786)) ((($) . T)) (((|#2|) |has| |#2| (-1016))) -((((-794)) -3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1168 |#2|)) . T)) +((((-794)) -3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1169 |#2|)) . T)) (|has| |#1| (-786)) (|has| |#1| (-786)) ((((-1070) (-51)) . T)) @@ -1079,10 +1079,10 @@ ((((-794)) . T)) ((((-523)) |has| #0=(-383 |#2|) (-585 (-523))) ((#0#) . T)) ((((-523) (-133)) . T)) -((((-523) (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T) ((|#1| |#2|) . T)) +((((-523) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#1| |#2|) . T)) ((((-383 (-523))) . T) (($) . T)) (((|#1|) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-794)) . T)) ((((-841 |#1|)) . T)) (|has| |#1| (-339)) @@ -1096,7 +1096,7 @@ (|has| |#1| (-784)) ((((-1087)) |has| |#1| (-831 (-1087)))) (((|#1| (-1087)) . T)) -(((|#1| (-1168 |#1|) (-1168 |#1|)) . T)) +(((|#1| (-1169 |#1|) (-1169 |#1|)) . T)) (((|#1| |#2|) . T)) ((($ $) . T)) (|has| |#1| (-1016)) @@ -1107,31 +1107,31 @@ ((($) . T)) (((|#2|) . T) (($) . T)) (((|#1|) |has| |#1| (-158))) -((((-523) (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T) ((|#1| |#2|) . T)) +((((-523) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#1| |#2|) . T)) (((|#1|) . T)) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#3|) . T)) (((|#1|) |has| |#1| (-158))) -((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) -((($) -3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((((-383 (-523))) |has| |#1| (-37 (-383 (-523)))) ((|#1|) |has| |#1| (-158)) (($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840)))) +((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) . T)) (((|#1|) . T)) ((((-499)) |has| |#1| (-564 (-499))) (((-823 (-355))) |has| |#1| (-564 (-823 (-355)))) (((-823 (-523))) |has| |#1| (-564 (-823 (-523))))) ((((-794)) . T)) -(((|#2|) . T) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (|has| |#2| (-784)) (-12 (|has| |#2| (-211)) (|has| |#2| (-973))) (|has| |#1| (-515)) (|has| |#1| (-1063)) ((((-1070) |#1|) . T)) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(((#0=(-383 (-523)) #0#) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($ $) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1| |#1|) . T)) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(((#0=(-383 (-523)) #0#) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1| |#1|) . T)) ((((-383 (-523))) |has| |#1| (-964 (-523))) (((-523)) |has| |#1| (-964 (-523))) (((-1087)) |has| |#1| (-964 (-1087))) ((|#1|) . T)) ((((-523) |#2|) . T)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) ((((-523)) |has| |#1| (-817 (-523))) (((-355)) |has| |#1| (-817 (-355)))) -((((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1|) . T)) +((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) ((|#1|) . T)) (((|#1|) . T)) ((((-589 |#4|)) . T) (((-794)) . T)) ((((-499)) |has| |#4| (-564 (-499)))) @@ -1144,17 +1144,17 @@ (((|#1|) . T)) (((|#2|) . T)) ((((-1087)) |has| (-383 |#2|) (-831 (-1087)))) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) #0#) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) ((($) . T)) ((($) . T)) (((|#2|) . T)) -((((-794)) -3262 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-563 (-794))) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) (((-1168 |#3|)) . T)) +((((-794)) -3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-563 (-794))) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) (((-1169 |#3|)) . T)) ((((-523) |#2|) . T)) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) -(((|#2| |#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(((|#2| |#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($ $) |has| |#2| (-158))) ((((-794)) . T)) ((((-794)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T) ((|#2|) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((|#2|) . T)) ((((-794)) . T)) ((((-794)) . T)) ((((-1070) (-1087) (-523) (-203) (-794)) . T)) @@ -1189,8 +1189,8 @@ (|has| |#1| (-37 (-383 (-523)))) ((((-794)) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -(((|#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-973))) (($) |has| |#2| (-158))) (|has| $ (-136)) ((((-383 |#2|)) . T)) ((((-383 (-523))) |has| #0=(-383 |#2|) (-964 (-383 (-523)))) (((-523)) |has| #0# (-964 (-523))) ((#0#) . T)) @@ -1201,11 +1201,11 @@ (((|#3|) |has| |#3| (-158))) (|has| |#1| (-136)) (|has| |#1| (-134)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) (((|#1|) . T)) (((|#2|) . T)) @@ -1236,7 +1236,7 @@ ((((-927 |#1|)) . T) ((|#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-383 (-523))) . T) (((-383 |#1|)) . T) ((|#1|) . T) (($) . T)) (((|#1| (-1083 |#1|)) . T)) ((((-523)) . T) (($) . T) (((-383 (-523))) . T)) @@ -1244,15 +1244,15 @@ (|has| |#1| (-786)) (((|#2|) . T)) ((((-523)) . T) (($) . T) (((-383 (-523))) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) ((((-523) |#2|) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#2|) . T)) ((((-523) |#3|) . T)) (((|#2|) . T)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -((((-1160 |#1| |#2| |#3|)) |has| |#1| (-339))) +((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) ((((-794)) . T)) @@ -1261,7 +1261,7 @@ (((|#3|) -12 (|has| |#3| (-286 |#3|)) (|has| |#3| (-1016)))) (((|#2|) . T)) (((|#1|) . T)) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) #0#) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) (((|#2| |#2|) . T)) (|has| |#2| (-339)) (((|#2|) . T) (((-523)) |has| |#2| (-964 (-523))) (((-383 (-523))) |has| |#2| (-964 (-383 (-523))))) @@ -1291,19 +1291,19 @@ (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#2|) . T)) ((((-523) (-133)) . T)) -(((#0=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) #0#) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) -((($) -3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +(((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) ((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) +((($) -3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (|has| |#1| (-786)) (((|#2| (-710) (-1001)) . T)) (((|#1| |#2|) . T)) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) (|has| |#1| (-730)) (((|#1|) |has| |#1| (-158))) (((|#4|) . T)) (((|#4|) . T)) (((|#1| |#2|) . T)) -(-3262 (|has| |#1| (-136)) (-12 (|has| |#1| (-339)) (|has| |#2| (-136)))) -(-3262 (|has| |#1| (-134)) (-12 (|has| |#1| (-339)) (|has| |#2| (-134)))) +(-3172 (|has| |#1| (-136)) (-12 (|has| |#1| (-339)) (|has| |#2| (-136)))) +(-3172 (|has| |#1| (-134)) (-12 (|has| |#1| (-339)) (|has| |#2| (-134)))) (((|#4|) . T)) (|has| |#1| (-134)) ((((-1070) |#1|) . T)) @@ -1315,11 +1315,11 @@ ((((-794)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#3|) . T)) -((((-1160 |#1| |#2| |#3|)) |has| |#1| (-339))) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016))) (((-888 |#1|)) . T)) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016))) (((-888 |#1|)) . T)) (|has| |#1| (-784)) (|has| |#1| (-784)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) @@ -1332,8 +1332,8 @@ ((($) . T)) ((((-364) (-1070)) . T)) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((((-794)) -3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1168 |#2|)) . T)) -(((#0=(-51)) . T) (((-2 (|:| -1853 (-1070)) (|:| -2433 #0#))) . T)) +((((-794)) -3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-563 (-794))) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((-1169 |#2|)) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3772 (-1070)) (|:| -2482 #0#))) . T)) (((|#1|) . T)) ((((-794)) . T)) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) @@ -1341,7 +1341,7 @@ (|has| |#2| (-134)) (|has| |#2| (-136)) (|has| |#1| (-448)) -(-3262 (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3172 (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) (|has| |#1| (-339)) ((((-794)) . T)) (|has| |#1| (-37 (-383 (-523)))) @@ -1350,8 +1350,8 @@ (|has| |#1| (-784)) (|has| |#1| (-784)) ((((-794)) . T)) -((((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3262 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1160 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) -(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3262 (|has| |#1| (-339)) (|has| |#1| (-515)))) +((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-1161 |#1| |#2| |#3|)) |has| |#1| (-339)) ((|#1|) |has| |#1| (-158))) +(((|#1|) |has| |#1| (-158)) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515)))) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1| |#2|) . T)) ((((-1087)) |has| |#1| (-831 (-1087)))) @@ -1359,7 +1359,7 @@ ((((-794)) . T)) ((((-794)) . T)) (|has| |#1| (-1016)) -(((|#2| (-456 (-2676 |#1|) (-710)) (-796 |#1|)) . T)) +(((|#2| (-456 (-2810 |#1|) (-710)) (-796 |#1|)) . T)) ((((-383 (-523))) . #0=(|has| |#2| (-339))) (($) . #0#)) (((|#1| (-495 (-1087)) (-1087)) . T)) (((|#1|) . T)) @@ -1379,22 +1379,22 @@ (|has| |#1| (-136)) (((|#1|) . T)) (((|#2|) . T)) -(((|#1|) . T) (((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -((((-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))) . T)) +(((|#1|) . T) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-1087) (-51)) . T)) ((($ $) . T)) (((|#1| (-523)) . T)) ((((-841 |#1|)) . T)) -(((|#1|) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973))) (($) -3262 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)))) +(((|#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973))) (($) -3172 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)))) (((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) |has| |#1| (-964 (-383 (-523))))) (|has| |#1| (-786)) (|has| |#1| (-786)) ((((-523) |#2|) . T)) ((((-523)) . T)) -((((-1160 |#1| |#2| |#3|)) -12 (|has| (-1160 |#1| |#2| |#3|) (-286 (-1160 |#1| |#2| |#3|))) (|has| |#1| (-339)))) +((((-1161 |#1| |#2| |#3|)) -12 (|has| (-1161 |#1| |#2| |#3|) (-286 (-1161 |#1| |#2| |#3|))) (|has| |#1| (-339)))) (|has| |#1| (-786)) ((((-629 |#2|)) . T) (((-794)) . T)) (((|#1| |#2|) . T)) @@ -1403,13 +1403,13 @@ (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) (((|#1|) |has| |#1| (-158))) (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) -(((|#3|) -3262 (|has| |#3| (-158)) (|has| |#3| (-339)))) +(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)))) (|has| |#2| (-786)) (|has| |#1| (-786)) -(-3262 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3172 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-840))) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T)) ((((-523) |#2|) . T)) -(((|#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)))) +(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)))) (|has| |#1| (-325)) (((|#3| |#3|) -12 (|has| |#3| (-286 |#3|)) (|has| |#3| (-1016)))) ((($) . T) (((-383 (-523))) . T)) @@ -1417,7 +1417,7 @@ (|has| |#1| (-759)) (|has| |#1| (-759)) (((|#1|) . T)) -(-3262 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-784)) (|has| |#1| (-784)) (|has| |#1| (-784)) @@ -1426,13 +1426,13 @@ ((((-523)) . T) (($) . T) (((-383 (-523))) . T)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-37 (-383 (-523)))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-1087)) |has| |#1| (-831 (-1087))) (((-1001)) . T)) (((|#1|) . T)) (|has| |#1| (-784)) -(((#0=(-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) #0#) |has| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (-286 (-2 (|:| -1853 (-1070)) (|:| -2433 (-51)))))) +(((#0=(-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) #0#) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (|has| |#1| (-1016)) (((|#1|) . T)) @@ -1450,7 +1450,7 @@ (((|#1|) . T)) ((((-133)) . T)) (((|#2|) |has| |#2| (-158))) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((|#1|) . T)) (|has| |#1| (-134)) (|has| |#1| (-136)) @@ -1472,32 +1472,32 @@ (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1|) . T)) (((|#1| |#2|) . T)) -(((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) ((#0=(-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) #0#) |has| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (-286 (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))))) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-840))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-840))) +(((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) ((#0=(-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) #0#) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) (((|#1|) . T) (($) . T)) (((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#1| |#2|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(((|#3|) -3262 (|has| |#3| (-158)) (|has| |#3| (-339)))) +(((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)))) (|has| |#1| (-786)) (|has| |#1| (-515)) ((((-536 |#1|)) . T)) ((($) . T)) (((|#2|) . T)) -(-3262 (-12 (|has| |#1| (-339)) (|has| |#2| (-759))) (-12 (|has| |#1| (-339)) (|has| |#2| (-786)))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (-12 (|has| |#1| (-339)) (|has| |#2| (-759))) (-12 (|has| |#1| (-339)) (|has| |#2| (-786)))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) ((((-841 |#1|)) . T)) (((|#1| (-467 |#1| |#3|) (-467 |#1| |#2|)) . T)) (((|#1| |#4| |#5|) . T)) (((|#1| (-710)) . 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T)) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) ((((-383 |#2|)) . T) (((-383 (-523))) . T) (($) . T)) ((((-614 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) @@ -1505,19 +1505,19 @@ ((((-794)) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) -((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) +((((-383 (-523))) |has| |#2| (-37 (-383 (-523)))) ((|#2|) |has| |#2| (-158)) (($) -3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840)))) ((((-794)) . T)) ((((-794)) . T)) ((((-794)) . T)) (((|#2|) . T)) -(-3262 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) -(|has| |#1| (-1108)) -(|has| |#1| (-1108)) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) -(|has| |#1| (-1108)) -(|has| |#1| (-1108)) +(|has| |#1| (-1109)) +(|has| |#1| (-1109)) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(|has| |#1| (-1109)) +(|has| |#1| (-1109)) (((|#3| |#3|) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T) ((#1=(-383 |#1|) #1#) . T) ((|#1| |#1|) . T)) @@ -1528,43 +1528,43 @@ (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) ((((-1070) (-51)) . T)) (|has| |#1| (-1016)) -(-3262 (|has| |#2| (-759)) (|has| |#2| (-786))) +(-3172 (|has| |#2| (-759)) (|has| |#2| (-786))) (((|#1|) . T)) -((($) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) (((|#1|) |has| |#1| (-158)) (($) . T)) ((($) . T)) ((((-1085 |#1| |#2| |#3|)) -12 (|has| (-1085 |#1| |#2| |#3|) (-286 (-1085 |#1| |#2| |#3|))) (|has| |#1| (-339)))) ((((-794)) . T)) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) ((($) . T)) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) (|has| |#2| (-840)) (|has| |#1| (-339)) (((|#2|) |has| |#2| (-1016))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((($) . T) ((|#2|) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) (|has| |#1| (-840)) (|has| |#1| (-840)) ((((-499)) . T) (((-383 (-1083 (-523)))) . T) (((-203)) . T) (((-355)) . T)) ((((-355)) . T) (((-203)) . T) (((-794)) . T)) (|has| |#1| (-840)) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) ((($ $) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((($ $) . T)) ((((-523) (-108)) . T)) ((($) . T)) (((|#1|) . T)) ((((-523)) . T)) ((((-108)) . T)) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-37 (-383 (-523)))) (((|#1| (-523)) . T)) ((($) . T)) @@ -1580,13 +1580,13 @@ (((|#1|) . T)) ((((-794)) . T)) (((|#1| (-523)) . T)) -(((|#1| (-1160 |#1| |#2| |#3|)) . T)) +(((|#1| (-1161 |#1| |#2| |#3|)) . T)) (((|#1|) . T)) (((|#1| (-383 (-523))) . T)) -(((|#1| (-1132 |#1| |#2| |#3|)) . T)) +(((|#1| (-1133 |#1| |#2| |#3|)) . T)) (((|#1| (-710)) . T)) (((|#1|) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-794)) . T)) (|has| |#1| (-1016)) ((((-1070) |#1|) . T)) @@ -1595,8 +1595,8 @@ (|has| |#2| (-134)) (((|#1| (-495 (-757 (-1087))) (-757 (-1087))) . T)) ((((-794)) . T)) -((((-1154 |#1| |#2| |#3| |#4|)) . T)) -((((-1154 |#1| |#2| |#3| |#4|)) . T)) +((((-1155 |#1| |#2| |#3| |#4|)) . T)) +((((-1155 |#1| |#2| |#3| |#4|)) . T)) (((|#1|) |has| |#1| (-973))) ((((-523) (-108)) . T)) ((((-794)) |has| |#1| (-1016))) @@ -1606,34 +1606,34 @@ (((|#1|) . T)) ((((-523)) . T)) ((((-794)) . T)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-325))) ((((-794)) . T)) (|has| |#1| (-136)) (((|#3|) . T)) -(-3262 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((((-794)) . T)) -((((-1153 |#2| |#3| |#4|)) . T) (((-1154 |#1| |#2| |#3| |#4|)) . T)) +((((-1154 |#2| |#3| |#4|)) . T) (((-1155 |#1| |#2| |#3| |#4|)) . T)) ((((-794)) . T)) -((((-47)) -12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (((-562 $)) . T) ((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) -3262 (-12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (|has| |#1| (-964 (-383 (-523))))) (((-383 (-883 |#1|))) |has| |#1| (-515)) (((-883 |#1|)) |has| |#1| (-973)) (((-1087)) . T)) +((((-47)) -12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (((-562 $)) . T) ((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) -3172 (-12 (|has| |#1| (-515)) (|has| |#1| (-964 (-523)))) (|has| |#1| (-964 (-383 (-523))))) (((-383 (-883 |#1|))) |has| |#1| (-515)) (((-883 |#1|)) |has| |#1| (-973)) (((-1087)) . T)) (((|#1|) . T) (($) . T)) (((|#1| (-710)) . T)) -((($) -3262 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) +((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) (((|#1|) |has| |#1| (-286 |#1|))) -((((-1154 |#1| |#2| |#3| |#4|)) . T)) +((((-1155 |#1| |#2| |#3| |#4|)) . T)) ((((-523)) |has| |#1| (-817 (-523))) (((-355)) |has| |#1| (-817 (-355)))) (((|#1|) . T)) (|has| |#1| (-515)) (((|#1|) . T)) ((((-794)) . T)) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) (((|#1|) |has| |#1| (-158))) ((($) |has| |#1| (-515)) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#1|) . T)) (((|#3|) |has| |#3| (-1016))) -(((|#2|) -3262 (|has| |#2| (-158)) (|has| |#2| (-339)))) -((((-1153 |#2| |#3| |#4|)) . T)) +(((|#2|) -3172 (|has| |#2| (-158)) (|has| |#2| (-339)))) +((((-1154 |#2| |#3| |#4|)) . T)) ((((-108)) . T)) (|has| |#1| (-759)) (|has| |#1| (-759)) @@ -1642,8 +1642,8 @@ (|has| |#1| (-784)) (|has| |#1| (-784)) (((|#1| (-523) (-1001)) . T)) -(-3262 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +(-3172 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1| (-383 (-523)) (-1001)) . T)) (((|#1| (-710) (-1001)) . T)) (|has| |#1| (-786)) @@ -1659,28 +1659,28 @@ (((|#1|) . T)) (|has| |#1| (-1016)) ((((-523)) -12 (|has| |#1| (-339)) (|has| |#2| (-585 (-523)))) ((|#2|) |has| |#1| (-339))) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) (((|#2|) |has| |#2| (-158))) (((|#1|) |has| |#1| (-158))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) ((((-794)) . T)) (|has| |#3| (-784)) ((((-794)) . T)) -((((-1153 |#2| |#3| |#4|) (-295 |#2| |#3| |#4|)) . T)) +((((-1154 |#2| |#3| |#4|) (-295 |#2| |#3| |#4|)) . T)) ((((-794)) . T)) -(((|#1| |#1|) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) +(((|#1| |#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) (((|#1|) . T)) ((((-523)) . T)) ((((-523)) . T)) -(((|#1|) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) +(((|#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-973)))) (((|#2|) |has| |#2| (-339))) ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-339))) (|has| |#1| (-786)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#2|) . T)) -((((-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))) |has| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (-286 (-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-840))) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-840))) (((|#2|) . T) (((-523)) |has| |#2| (-585 (-523)))) ((((-794)) . T)) ((((-794)) . T)) @@ -1714,18 +1714,18 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (((|#1|) . T)) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) . T) (($ $) . T)) ((((-794)) . T)) (((|#1|) . T) (((-383 (-523))) . T) (($) . T)) ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (|has| |#1| (-339)) (|has| |#1| (-339)) (|has| (-383 |#2|) (-211)) (|has| |#1| (-840)) (((|#2|) |has| |#2| (-973))) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) (|has| |#1| (-339)) (((|#1|) |has| |#1| (-158))) (((|#1| |#1|) . T)) @@ -1750,7 +1750,7 @@ (((|#1| (-383 (-523)) (-1001)) . T)) (((|#1| (-710) (-1001)) . T)) (((#0=(-383 |#2|) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) -(((|#1|) . T) (((-523)) -3262 (|has| (-383 (-523)) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) . T)) +(((|#1|) . T) (((-523)) -3172 (|has| (-383 (-523)) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) . T)) (((|#1| (-554 |#1| |#3|) (-554 |#1| |#2|)) . T)) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) @@ -1769,24 +1769,24 @@ ((((-638)) . T)) (((|#2|) |has| |#2| (-158))) (|has| |#2| (-784)) -((((-108)) |has| |#1| (-1016)) (((-794)) -3262 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016)))) +((((-108)) |has| |#1| (-1016)) (((-794)) -3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016)))) (((|#1|) . T) (($) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 (-51)))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) . T)) ((((-794)) . T)) ((((-523) |#1|) . T)) ((((-638)) . T) (((-383 (-523))) . T) (((-523)) . T)) (((|#1| |#1|) |has| |#1| (-158))) (((|#2|) . T)) -(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) ((((-355)) . T)) ((((-638)) . T)) ((((-383 (-523))) . #0=(|has| |#2| (-339))) (($) . #0#)) (((|#1|) |has| |#1| (-158))) ((((-383 (-883 |#1|))) . T)) (((|#2| |#2|) . T)) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#2|) . T)) (|has| |#2| (-786)) (((|#3|) |has| |#3| (-973))) @@ -1796,14 +1796,14 @@ (|has| |#1| (-786)) ((((-1087)) |has| |#2| (-831 (-1087)))) ((((-794)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-383 (-523))) . T) (($) . T)) (|has| |#1| (-448)) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| |#1| (-344)) (|has| |#1| (-339)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-448)) (|has| |#1| (-515)) (|has| |#1| (-973)) (|has| |#1| (-1028))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-448)) (|has| |#1| (-515)) (|has| |#1| (-973)) (|has| |#1| (-1028))) (|has| |#1| (-37 (-383 (-523)))) ((((-112 |#1|)) . T)) ((((-112 |#1|)) . T)) @@ -1824,11 +1824,11 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-786)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) (((|#1| |#2|) . T)) (|has| |#1| (-136)) (|has| |#1| (-134)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)))) ((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) ((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#2|) . T)) (((|#3|) . T)) ((((-112 |#1|)) . T)) @@ -1846,11 +1846,11 @@ ((((-499)) |has| |#1| (-564 (-499))) (((-823 (-523))) |has| |#1| (-564 (-823 (-523)))) (((-823 (-355))) |has| |#1| (-564 (-823 (-355)))) (((-355)) . #0=(|has| |#1| (-949))) (((-203)) . #0#)) (((|#1|) |has| |#1| (-339))) ((((-794)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((($ $) . T) (((-562 $) $) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -((($) . T) (((-1154 |#1| |#2| |#3| |#4|)) . T) (((-383 (-523))) . T)) -((($) -3262 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +((($) . T) (((-1155 |#1| |#2| |#3| |#4|)) . T) (((-383 (-523))) . T)) +((($) -3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-515))) (|has| |#1| (-339)) (|has| |#1| (-339)) (|has| |#1| (-339)) @@ -1861,11 +1861,11 @@ ((((-355)) . T)) (((|#3|) -12 (|has| |#3| (-286 |#3|)) (|has| |#3| (-1016)))) ((((-794)) . T)) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-840))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-840))) (((|#1|) . T)) (|has| |#1| (-786)) (|has| |#1| (-786)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) (((|#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (|has| |#1| (-1016)) @@ -1874,13 +1874,13 @@ (|has| |#1| (-134)) (|has| |#1| (-136)) ((((-523)) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -(((#0=(-1153 |#2| |#3| |#4|)) . T) (((-383 (-523))) |has| #0# (-37 (-383 (-523)))) (($) . T)) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(((#0=(-1154 |#2| |#3| |#4|)) . T) (((-383 (-523))) |has| #0# (-37 (-383 (-523)))) (($) . T)) ((((-523)) . T)) (|has| |#1| (-339)) -(-3262 (-12 (|has| (-1160 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) -(-3262 (-12 (|has| (-1160 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) +(-3172 (-12 (|has| (-1161 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) +(-3172 (-12 (|has| (-1161 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) (|has| |#1| (-339)) (|has| |#1| (-134)) (|has| |#1| (-136)) @@ -1897,18 +1897,18 @@ (((|#1| |#2|) . T)) (((|#1|) . T) (((-523)) |has| |#1| (-585 (-523)))) (((|#3|) |has| |#3| (-158))) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) ((((-523)) . T)) (((|#1| $) |has| |#1| (-263 |#1| |#1|))) ((((-383 (-523))) . T) (($) . T) (((-383 |#1|)) . T) ((|#1|) . T)) ((((-794)) . T)) (((|#3|) . T)) -(((|#1| |#1|) . T) (($ $) -3262 (|has| |#1| (-267)) (|has| |#1| (-339))) ((#0=(-383 (-523)) #0#) |has| |#1| (-339))) -((((-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))) . T)) +(((|#1| |#1|) . T) (($ $) -3172 (|has| |#1| (-267)) (|has| |#1| (-339))) ((#0=(-383 (-523)) #0#) |has| |#1| (-339))) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) ((($) . T)) ((((-523) |#1|) . T)) ((((-1087)) |has| (-383 |#2|) (-831 (-1087)))) -(((|#1|) . T) (($) -3262 (|has| |#1| (-267)) (|has| |#1| (-339))) (((-383 (-523))) |has| |#1| (-339))) +(((|#1|) . T) (($) -3172 (|has| |#1| (-267)) (|has| |#1| (-339))) (((-383 (-523))) |has| |#1| (-339))) ((((-499)) |has| |#2| (-564 (-499)))) ((((-629 |#2|)) . T) (((-794)) . T)) (((|#1|) . T)) @@ -1916,8 +1916,8 @@ (((|#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) ((((-801 |#1|)) . T)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3262 (|has| |#4| (-732)) (|has| |#4| (-784))) -(-3262 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) ((((-794)) . T)) ((((-794)) . T)) (((|#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) @@ -1933,17 +1933,17 @@ ((((-383 (-523))) . T) (($) . T)) ((((-383 (-523))) . T) (($) . T)) ((((-383 (-523))) . T) (($) . T)) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-1126))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-1127))) ((($) . T)) ((((-383 (-523))) |has| #0=(-383 |#2|) (-964 (-383 (-523)))) (((-523)) |has| #0# (-964 (-523))) ((#0#) . T)) (((|#2|) . T) (((-523)) |has| |#2| (-585 (-523)))) (((|#1| (-710)) . T)) (|has| |#1| (-786)) (((|#1|) . T) (((-523)) |has| |#1| (-585 (-523)))) -((($) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3262 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) +((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (((-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((|#1|) . T)) ((((-523)) . T)) (|has| |#1| (-37 (-383 (-523)))) -((((-2 (|:| -1853 (-1070)) (|:| -2433 (-51)))) |has| (-2 (|:| -1853 (-1070)) (|:| -2433 (-51))) (-286 (-2 (|:| -1853 (-1070)) (|:| -2433 (-51)))))) +((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))))) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (|has| |#1| (-784)) (|has| |#1| (-37 (-383 (-523)))) @@ -1968,24 +1968,24 @@ (((|#1| |#2|) . T)) ((((-133)) . T)) ((((-719 |#1| (-796 |#2|))) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -(|has| |#1| (-1108)) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +(|has| |#1| (-1109)) (((|#1|) . T)) -(-3262 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) +(-3172 (|has| |#3| (-25)) (|has| |#3| (-124)) (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-344)) (|has| |#3| (-732)) (|has| |#3| (-784)) (|has| |#3| (-973)) (|has| |#3| (-1016))) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|))) (((|#2|) . T)) -((($ $) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) -((($) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($ $) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) |has| |#1| (-37 (-383 (-523))))) +((($) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((((-841 |#1|)) . T)) ((($) . T)) ((((-383 (-883 |#1|))) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-499)) |has| |#4| (-564 (-499)))) ((((-794)) . T) (((-589 |#4|)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1|) . T)) (|has| |#1| (-784)) -(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) |has| (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|)) (-286 (-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))))) +(((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016))) (((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) |has| (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|)) (-286 (-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))))) (|has| |#1| (-1016)) (|has| |#1| (-339)) (|has| |#1| (-786)) @@ -1993,17 +1993,17 @@ (((|#1|) . T)) (((|#1|) . T)) ((($) . T) (((-383 (-523))) . T)) -((($) -3262 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) +((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#1|) |has| |#1| (-158))) (|has| |#1| (-134)) (|has| |#1| (-136)) -(-3262 (-12 (|has| (-1085 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) -(-3262 (-12 (|has| (-1085 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) +(-3172 (-12 (|has| (-1085 |#1| |#2| |#3|) (-136)) (|has| |#1| (-339))) (|has| |#1| (-136))) +(-3172 (-12 (|has| (-1085 |#1| |#2| |#3|) (-134)) (|has| |#1| (-339))) (|has| |#1| (-134))) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-136)) (|has| |#1| (-134)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -((((-1160 |#1| |#2| |#3|)) |has| |#1| (-339))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) (|has| |#1| (-784)) (((|#1| |#2|) . T)) (((|#1|) . T) (((-523)) |has| |#1| (-585 (-523)))) @@ -2025,9 +2025,9 @@ ((((-794)) . T)) ((((-794)) . T)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|)) ((|#1| |#1|) |has| |#1| (-286 |#1|))) -(((|#1|) -3262 (|has| |#1| (-158)) (|has| |#1| (-339)))) +(((|#1|) -3172 (|has| |#1| (-158)) (|has| |#1| (-339)))) ((((-292 |#1|)) . T)) (((|#2|) |has| |#2| (-339))) (((|#2|) . T)) @@ -2048,14 +2048,14 @@ (|has| |#1| (-134)) (|has| |#1| (-136)) ((($ $) . T)) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) (|has| |#1| (-515)) (((|#2|) . T)) ((((-523)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-158)) (|has| |#1| (-515)) (|has| |#1| (-973))) ((((-536 |#1|)) . T)) ((($) . T)) (((|#1| (-57 |#1|) (-57 |#1|)) . T)) @@ -2063,7 +2063,7 @@ ((($) . T)) (((|#1|) . T)) ((((-794)) . T)) -(((|#2|) |has| |#2| (-6 (-4246 "*")))) +(((|#2|) |has| |#2| (-6 (-4250 "*")))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2080,17 +2080,17 @@ (((|#1| |#2|) . T)) ((((-1087) |#1|) . T)) (((|#4|) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) ((((-1087) (-51)) . T)) -((((-1153 |#2| |#3| |#4|) (-295 |#2| |#3| |#4|)) . T)) +((((-1154 |#2| |#3| |#4|) (-295 |#2| |#3| |#4|)) . T)) ((((-383 (-523))) |has| |#1| (-964 (-383 (-523)))) (((-523)) |has| |#1| (-964 (-523))) ((|#1|) . T)) ((((-794)) . T)) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) -(((#0=(-1154 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-344)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973)) (|has| |#2| (-1016))) +(((#0=(-1155 |#1| |#2| |#3| |#4|) #0#) . T) ((#1=(-383 (-523)) #1#) . T) (($ $) . T)) (((|#1| |#1|) |has| |#1| (-158)) ((#0=(-383 (-523)) #0#) |has| |#1| (-515)) (($ $) |has| |#1| (-515))) (((|#1|) . T) (($) . T) (((-383 (-523))) . T)) (((|#1| $) |has| |#1| (-263 |#1| |#1|))) -((((-1154 |#1| |#2| |#3| |#4|)) . T) (((-383 (-523))) . T) (($) . T)) +((((-1155 |#1| |#2| |#3| |#4|)) . T) (((-383 (-523))) . T) (($) . T)) (((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-515)) (($) |has| |#1| (-515))) (|has| |#1| (-339)) (|has| |#1| (-134)) @@ -2104,29 +2104,29 @@ (((|#1|) . T)) (((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016)))) (((|#2| |#3|) . T)) -(-3262 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#2| (-339)) (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) (((|#1| (-495 |#2|)) . T)) (((|#1| (-710)) . T)) (((|#1| (-495 (-1006 (-1087)))) . T)) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) (|has| |#2| (-840)) -(-3262 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) ((((-794)) . T)) -((($ $) . T) ((#0=(-1153 |#2| |#3| |#4|) #0#) . T) ((#1=(-383 (-523)) #1#) |has| #0# (-37 (-383 (-523))))) +((($ $) . T) ((#0=(-1154 |#2| |#3| |#4|) #0#) . T) ((#1=(-383 (-523)) #1#) |has| #0# (-37 (-383 (-523))))) ((((-841 |#1|)) . T)) (-12 (|has| |#1| (-339)) (|has| |#2| (-759))) ((($) . T) (((-383 (-523))) . T)) ((($) . T)) ((($) . T)) (|has| |#1| (-339)) -(-3262 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325)) (|has| |#1| (-515))) (|has| |#1| (-339)) -((($) . T) ((#0=(-1153 |#2| |#3| |#4|)) . T) (((-383 (-523))) |has| #0# (-37 (-383 (-523))))) +((($) . T) ((#0=(-1154 |#2| |#3| |#4|)) . T) (((-383 (-523))) |has| #0# (-37 (-383 (-523))))) (((|#1| |#2|) . T)) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) -(-3262 (-12 (|has| |#1| (-284)) (|has| |#1| (-840))) (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3262 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) +(-3172 (-12 (|has| |#1| (-284)) (|has| |#1| (-840))) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-831 (-1087))) (|has| |#1| (-973))) ((((-523)) |has| |#1| (-585 (-523))) ((|#1|) . T)) (((|#1| |#2|) . T)) ((((-794)) . T)) @@ -2158,27 +2158,27 @@ (((|#1|) |has| |#1| (-158))) ((((-794)) . T)) (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) -(((|#2|) -3262 (|has| |#2| (-6 (-4246 "*"))) (|has| |#2| (-158)))) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(((|#2|) -3172 (|has| |#2| (-6 (-4250 "*"))) (|has| |#2| (-158)))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (|has| |#2| (-786)) (|has| |#2| (-840)) (|has| |#1| (-840)) (((|#2|) |has| |#2| (-158))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -((((-1160 |#1| |#2| |#3|)) |has| |#1| (-339))) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-1161 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-794)) . T)) ((((-794)) . T)) ((((-499)) . T) (((-523)) . T) (((-823 (-523))) . T) (((-355)) . T) (((-203)) . T)) (((|#1| |#2|) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 (-51)))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) . T)) (((|#1|) . T)) ((((-794)) . T)) (((|#1| |#2|) . T)) (((|#1| (-383 (-523))) . T)) (((|#1|) . T)) -(-3262 (|has| |#1| (-267)) (|has| |#1| (-339))) +(-3172 (|has| |#1| (-267)) (|has| |#1| (-339))) ((((-133)) . T)) ((((-383 |#2|)) . T) (((-383 (-523))) . T) (($) . T)) (|has| |#1| (-784)) @@ -2193,7 +2193,7 @@ ((((-383 (-523))) . T) (($) . T)) ((((-794)) . T)) ((((-794)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#2| |#2|) . T) ((|#1| |#1|) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -2204,7 +2204,7 @@ (((|#1|) . T)) ((((-589 (-133))) . T) (((-1070)) . T)) ((((-794)) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) ((((-1087) |#1|) |has| |#1| (-484 (-1087) |#1|)) ((|#1| |#1|) |has| |#1| (-286 |#1|))) (|has| |#1| (-786)) ((((-794)) . T)) @@ -2216,16 +2216,16 @@ ((((-794)) . T) (((-589 |#4|)) . T)) (((|#2|) . T)) ((((-841 |#1|)) . T) (((-383 (-523))) . T) (($) . T)) -(-3262 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) -(-3262 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3172 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) +(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((((-1087) (-51)) . T)) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) -(-3262 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-25)) (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-784)) (|has| |#2| (-973))) (|has| |#1| (-840)) (|has| |#1| (-840)) (((|#2|) . T)) @@ -2240,12 +2240,12 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (|has| |#1| (-759)) (((#0=(-841 |#1|) #0#) . T) (($ $) . T) ((#1=(-383 (-523)) #1#) . T)) ((((-383 |#2|)) . T)) (|has| |#1| (-784)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1| |#1|) . T) ((#0=(-383 (-523)) #0#) . T) ((#1=(-523) #1#) . T) (($ $) . T)) ((((-841 |#1|)) . T) (($) . T) (((-383 (-523))) . T)) (((|#2|) |has| |#2| (-973)) (((-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973)))) @@ -2255,25 +2255,25 @@ (|has| |#1| (-134)) (((|#2|) . T)) ((((-794)) . T)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) -((((-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))) . T)) -(((#0=(-51)) . T) (((-2 (|:| -1853 (-1087)) (|:| -2433 #0#))) . T)) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) +(((#0=(-51)) . T) (((-2 (|:| -3772 (-1087)) (|:| -2482 #0#))) . T)) (|has| |#1| (-325)) ((((-523)) . T)) ((((-794)) . T)) -(((#0=(-1154 |#1| |#2| |#3| |#4|) $) |has| #0# (-263 #0# #0#))) +(((#0=(-1155 |#1| |#2| |#3| |#4|) $) |has| #0# (-263 #0# #0#))) (|has| |#1| (-339)) (((#0=(-1001) |#1|) . T) ((#0# $) . T) (($ $) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (((#0=(-383 (-523)) #0#) . T) ((#1=(-638) #1#) . T) (($ $) . T)) ((((-292 |#1|)) . T) (($) . T)) (((|#1|) . T) (((-383 (-523))) |has| |#1| (-339))) (|has| |#1| (-1016)) (((|#1|) . T)) -(((|#1|) -3262 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) -(((|#1|) -3262 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) +(((|#1|) -3172 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) +(((|#1|) -3172 (|has| |#2| (-343 |#1|)) (|has| |#2| (-393 |#1|)))) (((|#2|) . T)) ((((-383 (-523))) . T) (((-638)) . T) (($) . T)) (((|#3| |#3|) . T)) @@ -2292,7 +2292,7 @@ (((|#2|) . T)) (((|#1|) . T)) ((((-523)) . T)) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) (((|#2|) . T) (((-523)) |has| |#2| (-585 (-523)))) (((|#1| |#2|) . T)) ((($) . T)) @@ -2300,7 +2300,7 @@ ((($) . T) (((-383 (-523))) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T) (($) . T)) -(((|#1| (-1168 |#1|) (-1168 |#1|)) . T)) +(((|#1| (-1169 |#1|) (-1169 |#1|)) . T)) (((|#1| |#2| |#3| |#4|) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -2329,7 +2329,7 @@ (|has| |#2| (-949)) ((($) . T)) (|has| |#1| (-840)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((($) . T)) (((|#2|) . T)) (((|#1|) . T)) @@ -2337,24 +2337,24 @@ ((($) . T)) (|has| |#1| (-339)) ((((-841 |#1|)) . T)) -((($) -3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) +((($) -3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((|#1|) |has| |#1| (-158)) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) ((($ $) . T) ((#0=(-383 (-523)) #0#) . T)) -(-3262 (|has| |#1| (-344)) (|has| |#1| (-786))) +(-3172 (|has| |#1| (-344)) (|has| |#1| (-786))) (((|#1|) . T)) ((((-794)) . T)) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-383 (-523)) |#1|))) (|has| |#1| (-831 (-1087))))) ((((-383 |#2|) |#3|) . T)) ((($) . T) (((-383 (-523))) . T)) ((((-710) |#1|) . T)) -(((|#2| (-218 (-2676 |#1|) (-710))) . T)) +(((|#2| (-218 (-2810 |#1|) (-710))) . T)) (((|#1| (-495 |#3|)) . T)) ((((-383 (-523))) . T)) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((((-794)) . T)) -(((#0=(-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) #0#) |has| (-2 (|:| -1853 (-1087)) (|:| -2433 (-51))) (-286 (-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))))) +(((#0=(-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) #0#) |has| (-2 (|:| -3772 (-1087)) (|:| -2482 (-51))) (-286 (-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))))) (|has| |#1| (-840)) (|has| |#2| (-339)) -(-3262 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-155 (-355))) . T) (((-203)) . T) (((-355)) . T)) ((((-794)) . T)) (((|#1|) . T)) @@ -2371,11 +2371,11 @@ (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3262 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-284)) (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-37 (-383 (-523)))) (-12 (|has| |#1| (-508)) (|has| |#1| (-767))) ((((-794)) . T)) -((((-1087)) -3262 (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))) (-12 (|has| |#1| (-339)) (|has| |#2| (-831 (-1087)))))) +((((-1087)) -3172 (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))) (-12 (|has| |#1| (-339)) (|has| |#2| (-831 (-1087)))))) (|has| |#1| (-339)) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-383 (-523)) |#1|))) (|has| |#1| (-831 (-1087))))) (|has| |#1| (-339)) @@ -2385,13 +2385,13 @@ (((|#1|) . T)) (((|#2|) |has| |#1| (-339))) (((|#2|) |has| |#1| (-339))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1|) . T)) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) (((|#2|) . T) (((-1087)) -12 (|has| |#1| (-339)) (|has| |#2| (-964 (-1087)))) (((-523)) -12 (|has| |#1| (-339)) (|has| |#2| (-964 (-523)))) (((-383 (-523))) -12 (|has| |#1| (-339)) (|has| |#2| (-964 (-523))))) (((|#2|) . T)) -((((-1087) #0=(-1154 |#1| |#2| |#3| |#4|)) |has| #0# (-484 (-1087) #0#)) ((#0# #0#) |has| #0# (-286 #0#))) +((((-1087) #0=(-1155 |#1| |#2| |#3| |#4|)) |has| #0# (-484 (-1087) #0#)) ((#0# #0#) |has| #0# (-286 #0#))) ((((-562 $) $) . T) (($ $) . T)) ((((-155 (-203))) . T) (((-155 (-355))) . T) (((-1083 (-638))) . T) (((-823 (-355))) . T)) ((((-794)) . T)) @@ -2408,31 +2408,31 @@ (((|#2|) |has| |#1| (-339))) ((((-355)) -12 (|has| |#1| (-339)) (|has| |#2| (-817 (-355)))) (((-523)) -12 (|has| |#1| (-339)) (|has| |#2| (-817 (-523))))) (|has| |#1| (-339)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-339)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) (|has| |#1| (-339)) (|has| |#1| (-515)) (((|#4| |#4|) -12 (|has| |#4| (-286 |#4|)) (|has| |#4| (-1016)))) (((|#3|) . T)) (((|#1|) . T)) -(-3262 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#2|) . T)) (((|#2|) . T)) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 |#1|))) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 |#1|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (|has| |#1| (-37 (-383 (-523)))) (((|#1| |#2|) . T)) (|has| |#1| (-37 (-383 (-523)))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) ((((-1070) |#1|) . T)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-344))) (|has| |#1| (-136)) ((((-536 |#1|)) . T)) ((($) . T)) @@ -2440,7 +2440,7 @@ (|has| |#1| (-515)) (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-37 (-383 (-523)))) -(-3262 (|has| |#1| (-134)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-134)) (|has| |#1| (-325))) (|has| |#1| (-136)) ((((-794)) . T)) ((($) . T)) @@ -2465,13 +2465,13 @@ (|has| |#1| (-730)) (|has| |#1| (-730)) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((((-110)) . T) ((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) ((((-203)) . T) (((-355)) . T) (((-823 (-355))) . T)) ((((-794)) . T)) -((((-1154 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-383 (-523))) . T)) +((((-1155 |#1| |#2| |#3| |#4|)) . T) (($) . T) (((-383 (-523))) . T)) (((|#1|) |has| |#1| (-158)) (($) |has| |#1| (-515)) (((-383 (-523))) |has| |#1| (-515))) ((((-794)) . T)) ((((-794)) . T)) @@ -2486,7 +2486,7 @@ ((((-523)) . T)) ((((-794)) . T)) ((((-523)) . T)) -(-3262 (|has| |#2| (-732)) (|has| |#2| (-784))) +(-3172 (|has| |#2| (-732)) (|has| |#2| (-784))) ((((-155 (-355))) . T) (((-203)) . T) (((-355)) . T)) ((((-794)) . T)) ((((-794)) . T)) @@ -2494,13 +2494,13 @@ ((((-794)) . T)) (|has| |#1| (-136)) (|has| |#1| (-134)) -((($) . T) ((#0=(-1153 |#2| |#3| |#4|)) |has| #0# (-158)) (((-383 (-523))) |has| #0# (-37 (-383 (-523))))) +((($) . T) ((#0=(-1154 |#2| |#3| |#4|)) |has| #0# (-158)) (((-383 (-523))) |has| #0# (-37 (-383 (-523))))) (((|#1|) . T) (($) . T) (((-383 (-523))) . T)) (|has| |#1| (-339)) (|has| |#1| (-339)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-25)) (|has| |#1| (-158)) (|has| |#1| (-339)) (|has| |#1| (-448)) (|has| |#1| (-666)) (|has| |#1| (-831 (-1087))) (|has| |#1| (-973)) (|has| |#1| (-1028)) (|has| |#1| (-1016))) (|has| |#1| (-1063)) ((((-523) |#1|) . T)) (((|#1|) . T)) @@ -2518,8 +2518,8 @@ (((|#1|) . T)) (|has| |#1| (-515)) ((((-383 |#2|)) . T) (((-383 (-523))) . T) (($) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) ((((-355)) . T)) (((|#1|) . T)) (((|#1|) . T)) @@ -2528,7 +2528,7 @@ (|has| |#1| (-515)) (|has| |#1| (-1016)) ((((-719 |#1| (-796 |#2|))) |has| (-719 |#1| (-796 |#2|)) (-286 (-719 |#1| (-796 |#2|))))) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) (((|#1|) . T)) (((|#2| |#3|) . T)) (|has| |#2| (-840)) @@ -2538,12 +2538,12 @@ (|has| |#1| (-211)) (((|#1| (-495 (-1006 (-1087)))) . T)) (|has| |#2| (-339)) -((((-2 (|:| -1853 (-1070)) (|:| -2433 (-51)))) . T)) +((((-2 (|:| -3772 (-1070)) (|:| -2482 (-51)))) . T)) (((|#1|) . T)) (((|#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) ((((-794)) . T)) ((((-794)) . 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T)) @@ -2642,8 +2642,8 @@ ((((-794)) . T)) (|has| |#2| (-759)) (|has| |#2| (-759)) -((((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#2|) |has| |#1| (-339)) (($) . T) ((|#1|) . T)) -(((|#1|) . T) (((-383 (-523))) -3262 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) . T)) +((((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) ((|#2|) |has| |#1| (-339)) (($) . T) ((|#1|) . T)) +(((|#1|) . T) (((-383 (-523))) -3172 (|has| |#1| (-37 (-383 (-523)))) (|has| |#1| (-339))) (($) . T)) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1|) . T) (((-523)) |has| |#1| (-964 (-523))) (((-383 (-523))) |has| |#1| (-964 (-383 (-523))))) ((((-523)) |has| |#1| (-817 (-523))) (((-355)) |has| |#1| (-817 (-355)))) @@ -2669,12 +2669,12 @@ (((|#2| (-710)) . T)) ((((-1087)) . T)) ((((-801 |#1|)) . 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T)) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) ((((-499)) |has| |#2| (-564 (-499))) (((-823 (-355))) |has| |#2| (-564 (-823 (-355)))) (((-823 (-523))) |has| |#2| (-564 (-823 (-523))))) ((((-794)) . T)) ((((-794)) . T)) @@ -2733,11 +2733,11 @@ ((((-383 |#2|) |#3|) . T)) (((|#1|) . T)) (|has| |#1| (-1016)) -(((|#2| (-456 (-2676 |#1|) (-710))) . T)) +(((|#2| (-456 (-2810 |#1|) (-710))) . T)) ((((-523) |#1|) . T)) (((|#2| |#2|) . T)) (((|#1| (-495 (-1087))) . T)) -(-3262 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-523)) . T)) (((|#2|) . T)) (((|#2|) . T)) @@ -2747,9 +2747,9 @@ ((($) . T) (((-383 (-523))) . T)) ((($) . T)) ((($) . T)) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) (((|#1|) . 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T)) @@ -2789,27 +2789,27 @@ (|has| |#1| (-211)) (((|#1| (-495 |#3|)) . T)) (|has| |#1| (-344)) -(((|#2| (-218 (-2676 |#1|) (-710))) . T)) +(((|#2| (-218 (-2810 |#1|) (-710))) . T)) (|has| |#1| (-344)) (|has| |#1| (-344)) (((|#1|) . T) (($) . T)) (((|#1| (-495 |#2|)) . T)) -(-3262 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) (((|#1| (-710)) . 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T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-339)) (|has| |#1| (-339)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) -(-3262 (|has| |#1| (-158)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-158)) (|has| |#1| (-515))) (((|#1| (-523)) . T)) (((|#1| (-383 (-523))) . T)) (((|#1| (-710)) . T)) @@ -3018,16 +3018,16 @@ ((((-823 (-355))) . T) (((-823 (-523))) . T) (((-1087)) . T) (((-499)) . T)) (((|#1|) . T)) ((((-794)) . T)) -(-3262 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) -(-3262 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) +(-3172 (|has| |#2| (-124)) (|has| |#2| (-158)) (|has| |#2| (-339)) (|has| |#2| (-732)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (-12 (|has| |#1| (-21)) (|has| |#2| (-21))) (-12 (|has| |#1| (-23)) (|has| |#2| (-23))) (-12 (|has| |#1| (-124)) (|has| |#2| (-124))) (-12 (|has| |#1| (-732)) (|has| |#2| (-732)))) ((((-523)) . T)) ((((-523)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (((|#1| |#2|) . T)) (((|#1|) . T)) -(-3262 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) +(-3172 (|has| |#2| (-158)) (|has| |#2| (-784)) (|has| |#2| (-973))) ((((-1087)) -12 (|has| |#2| (-831 (-1087))) (|has| |#2| (-973)))) -(-3262 (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) (-12 (|has| |#1| (-666)) (|has| |#2| (-666)))) +(-3172 (-12 (|has| |#1| (-448)) (|has| |#2| (-448))) (-12 (|has| |#1| (-666)) (|has| |#2| (-666)))) (|has| |#1| (-134)) (|has| |#1| (-136)) (|has| |#1| (-339)) @@ -3051,7 +3051,7 @@ ((((-1070) (-1087) (-523) (-203) (-794)) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((|#1| |#2|) . T)) -(-3262 (|has| |#1| (-325)) (|has| |#1| (-344))) +(-3172 (|has| |#1| (-325)) (|has| |#1| (-344))) (((|#1| |#2|) . T)) ((($) . T) ((|#1|) . T)) ((((-794)) . T)) @@ -3059,7 +3059,7 @@ ((($) . T) ((|#1|) . T) (((-383 (-523))) |has| |#1| (-37 (-383 (-523))))) (((|#2|) |has| |#2| (-1016)) (((-523)) -12 (|has| |#2| (-964 (-523))) (|has| |#2| (-1016))) (((-383 (-523))) -12 (|has| |#2| (-964 (-383 (-523)))) (|has| |#2| (-1016)))) ((((-499)) |has| |#1| (-564 (-499)))) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-786)) (|has| |#1| (-1016)))) ((($) . T) (((-383 (-523))) . T)) (|has| |#1| (-840)) (|has| |#1| (-840)) @@ -3068,14 +3068,14 @@ ((((-794)) . T)) (((|#2| |#2|) . T)) (((|#1| |#1|) |has| |#1| (-158))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-515))) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-784))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-515))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-784))) (((|#2|) . T)) -(-3262 (|has| |#1| (-21)) (|has| |#1| (-784))) +(-3172 (|has| |#1| (-21)) (|has| |#1| (-784))) (((|#1|) |has| |#1| (-158))) (((|#1|) . T)) (((|#1|) . T)) -((((-794)) -3262 (-12 (|has| |#1| (-563 (-794))) (|has| |#2| (-563 (-794)))) (-12 (|has| |#1| (-1016)) (|has| |#2| (-1016))))) +((((-794)) -3172 (-12 (|has| |#1| (-563 (-794))) (|has| |#2| (-563 (-794)))) (-12 (|has| |#1| (-1016)) (|has| |#2| (-1016))))) ((((-383 |#2|) |#3|) . T)) ((((-383 (-523))) . T) (($) . T)) (|has| |#1| (-37 (-383 (-523)))) @@ -3087,17 +3087,17 @@ (((|#1|) . T) (((-383 (-523))) . T) (((-523)) . T) (($) . T)) (((#0=(-523) #0#) . T)) ((($) . T) (((-383 (-523))) . T)) -(-3262 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) -(-3262 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) +(-3172 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) +(-3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) (|has| |#4| (-732)) -(-3262 (|has| |#4| (-732)) (|has| |#4| (-784))) +(-3172 (|has| |#4| (-732)) (|has| |#4| (-784))) (|has| |#4| (-784)) (|has| |#3| (-732)) -(-3262 (|has| |#3| (-732)) (|has| |#3| (-784))) +(-3172 (|has| |#3| (-732)) (|has| |#3| (-784))) (|has| |#3| (-784)) ((((-523)) . T)) (((|#2|) . T)) -((((-1087)) -3262 (-12 (|has| (-1085 |#1| |#2| |#3|) (-831 (-1087))) (|has| |#1| (-339))) (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))))) +((((-1087)) -3172 (-12 (|has| (-1085 |#1| |#2| |#3|) (-831 (-1087))) (|has| |#1| (-339))) (-12 (|has| |#1| (-15 * (|#1| (-523) |#1|))) (|has| |#1| (-831 (-1087)))))) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-383 (-523)) |#1|))) (|has| |#1| (-831 (-1087))))) ((((-1087)) -12 (|has| |#1| (-15 * (|#1| (-710) |#1|))) (|has| |#1| (-831 (-1087))))) (((|#1| |#1|) . T) (($ $) . T)) @@ -3112,11 +3112,11 @@ ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) ((((-1052 |#1| |#2|)) . T)) -(((|#2|) . T) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) -((((-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))) . T)) +(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) ((($) . T)) (|has| |#1| (-949)) -(((|#2|) . T) (((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +(((|#2|) . T) (((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) ((((-794)) . T)) ((((-499)) |has| |#2| (-564 (-499))) (((-823 (-523))) |has| |#2| (-564 (-823 (-523)))) (((-823 (-355))) |has| |#2| (-564 (-823 (-355)))) (((-355)) . #0=(|has| |#2| (-949))) (((-203)) . #0#)) ((((-1087) (-51)) . T)) @@ -3128,15 +3128,15 @@ ((((-1085 |#1| |#2| |#3|)) . T)) ((((-1085 |#1| |#2| |#3|)) . T) (((-1078 |#1| |#2| |#3|)) . T)) ((((-794)) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-523) |#1|) . T)) ((((-1085 |#1| |#2| |#3|)) |has| |#1| (-339))) (((|#1| |#2| |#3| |#4|) . T)) (((|#1|) . T)) (((|#2|) . T)) (|has| |#2| (-339)) -(((|#3|) . T) ((|#2|) . T) (($) -3262 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) ((|#4|) -3262 (|has| |#4| (-158)) (|has| |#4| (-339)) (|has| |#4| (-973)))) -(((|#2|) . T) (($) -3262 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((|#3|) -3262 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973)))) +(((|#3|) . T) ((|#2|) . T) (($) -3172 (|has| |#4| (-158)) (|has| |#4| (-784)) (|has| |#4| (-973))) ((|#4|) -3172 (|has| |#4| (-158)) (|has| |#4| (-339)) (|has| |#4| (-973)))) +(((|#2|) . T) (($) -3172 (|has| |#3| (-158)) (|has| |#3| (-784)) (|has| |#3| (-973))) ((|#3|) -3172 (|has| |#3| (-158)) (|has| |#3| (-339)) (|has| |#3| (-973)))) (((|#1|) . T)) (((|#1|) . T)) (|has| |#1| (-339)) @@ -3148,37 +3148,37 @@ ((((-794)) . T)) ((((-794)) . T)) (((|#1|) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) ((((-523) |#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#1|) . T)) (((|#2| $) -12 (|has| |#1| (-339)) (|has| |#2| (-263 |#2| |#2|))) (($ $) . T)) ((($ $) . T)) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-427)) (|has| |#1| (-840))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) ((((-794)) . T)) ((((-794)) . T)) ((((-794)) . T)) (((|#1| (-495 |#2|)) . T)) -((((-2 (|:| -1853 (-1087)) (|:| -2433 (-51)))) . T)) +((((-2 (|:| -3772 (-1087)) (|:| -2482 (-51)))) . T)) (((|#1| (-523)) . T)) (((|#1| (-383 (-523))) . T)) (((|#1| (-710)) . T)) ((((-112 |#1|)) . T) (($) . T) (((-383 (-523))) . T)) -(-3262 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) -(-3262 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) +(-3172 (|has| |#2| (-427)) (|has| |#2| (-515)) (|has| |#2| (-840))) +(-3172 (|has| |#1| (-427)) (|has| |#1| (-515)) (|has| |#1| (-840))) ((($) . T)) (((|#2| (-495 (-796 |#1|))) . T)) ((((-523) |#1|) . T)) (((|#2|) . T)) (((|#2| (-710)) . T)) -((((-794)) -3262 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) +((((-794)) -3172 (|has| |#1| (-563 (-794))) (|has| |#1| (-1016)))) (((|#1|) . T)) (((|#1| |#2|) . T)) ((((-1070) |#1|) . T)) ((((-383 |#2|)) . T)) -((((-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T)) +((((-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T)) (|has| |#1| (-515)) (|has| |#1| (-515)) ((($) . T) ((|#2|) . T)) @@ -3186,12 +3186,12 @@ (((|#1| |#2|) . T)) (((|#2| $) |has| |#2| (-263 |#2| |#2|))) (((|#1| (-589 |#1|)) |has| |#1| (-784))) -(-3262 (|has| |#1| (-211)) (|has| |#1| (-325))) -(-3262 (|has| |#1| (-339)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-211)) (|has| |#1| (-325))) +(-3172 (|has| |#1| (-339)) (|has| |#1| (-325))) (|has| |#1| (-1016)) (((|#1|) . T)) ((((-383 (-523))) . T) (($) . T)) -((((-927 |#1|)) . T) ((|#1|) . T) (((-523)) -3262 (|has| (-927 |#1|) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) -3262 (|has| (-927 |#1|) (-964 (-383 (-523)))) (|has| |#1| (-964 (-383 (-523)))))) +((((-927 |#1|)) . T) ((|#1|) . T) (((-523)) -3172 (|has| (-927 |#1|) (-964 (-523))) (|has| |#1| (-964 (-523)))) (((-383 (-523))) -3172 (|has| (-927 |#1|) (-964 (-383 (-523)))) (|has| |#1| (-964 (-383 (-523)))))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) (((|#1| |#1|) -12 (|has| |#1| (-286 |#1|)) (|has| |#1| (-1016)))) @@ -3202,10 +3202,10 @@ (((|#1|) . T)) (((|#1| |#2| |#3| |#4|) . T)) (((#0=(-1052 |#1| |#2|) #0#) |has| (-1052 |#1| |#2|) (-286 (-1052 |#1| |#2|)))) -(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) #0#) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|))))) +(((|#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((#0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) #0#) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))))) (((#0=(-112 |#1|)) |has| #0# (-286 #0#))) -(-3262 (|has| |#1| (-786)) (|has| |#1| (-1016))) +(-3172 (|has| |#1| (-786)) (|has| |#1| (-1016))) ((($ $) . T)) ((($ $) . T) ((#0=(-796 |#1|) $) . T) ((#0# |#2|) . T)) ((($ $) . T) ((|#2| $) |has| |#1| (-211)) ((|#2| |#1|) |has| |#1| (-211)) ((|#3| |#1|) . T) ((|#3| $) . T)) -(((-605 . -1016) T) ((-241 . -484) 142439) ((-225 . -484) 142382) ((-530 . -107) 142367) ((-495 . -23) T) ((-223 . -1016) 142317) ((-113 . -286) 142274) ((-453 . -484) 142066) ((-633 . -97) T) ((-1053 . -484) 141985) ((-366 . -124) T) ((-1179 . -905) 141954) ((-554 . -462) 141938) ((-568 . -124) T) ((-758 . -782) T) ((-492 . -55) 141888) ((-57 . -484) 141821) ((-488 . -484) 141754) ((-394 . -831) 141713) ((-155 . -973) T) ((-486 . -484) 141646) ((-468 . -484) 141579) ((-467 . -484) 141512) ((-738 . -964) 141299) ((-638 . -37) 141264) ((-319 . -325) T) ((-1011 . -1010) 141248) ((-1011 . -1016) 141226) ((-155 . -221) 141177) ((-155 . -211) 141128) ((-1011 . -1012) 141086) ((-803 . -263) 141044) ((-203 . -734) T) ((-203 . -731) T) ((-633 . -261) NIL) ((-1062 . -1099) 141023) ((-383 . -921) 141007) ((-640 . -21) T) ((-640 . -25) T) ((-1181 . -591) 140981) ((-292 . -147) 140960) ((-292 . -132) 140939) ((-1062 . -102) 140889) ((-126 . -25) T) ((-39 . -209) 140866) ((-112 . -21) T) ((-112 . -25) T) ((-558 . -265) 140842) ((-450 . -265) 140821) ((-1141 . -973) T) ((-791 . -973) T) ((-738 . -314) 140805) ((-113 . -1063) NIL) ((-89 . -563) 140737) ((-452 . -124) T) ((-546 . -1122) T) ((-1141 . -302) 140714) ((-530 . -973) T) ((-1141 . -211) T) ((-605 . -657) 140698) ((-888 . -265) 140675) ((-58 . -33) T) ((-984 . -734) T) ((-984 . -731) T) ((-755 . -666) T) ((-671 . -46) 140640) ((-570 . -37) 140627) ((-331 . -267) T) ((-328 . -267) T) ((-320 . -267) T) ((-241 . -267) 140558) ((-225 . -267) 140489) ((-951 . -97) T) ((-389 . -666) T) ((-113 . -37) 140434) ((-389 . -448) T) ((-330 . -97) T) ((-1117 . -980) T) ((-651 . -980) T) ((-1085 . -46) 140411) ((-1084 . -46) 140381) ((-1078 . -46) 140358) ((-962 . -140) 140304) ((-841 . -267) T) ((-1040 . -46) 140276) ((-633 . -286) NIL) ((-485 . -563) 140258) ((-480 . -563) 140240) ((-478 . -563) 140222) ((-303 . -1016) 140172) ((-652 . -427) 140103) ((-47 . -97) T) ((-1152 . -263) 140088) ((-1131 . -263) 140008) ((-589 . -609) 139992) ((-589 . -594) 139976) ((-315 . -21) T) ((-315 . -25) T) ((-39 . -325) NIL) ((-159 . -21) T) ((-159 . -25) T) ((-589 . -349) 139960) ((-554 . -263) 139937) ((-364 . -97) T) ((-1034 . -132) T) ((-122 . -563) 139869) ((-805 . -1016) T) ((-601 . -387) 139853) ((-654 . -563) 139835) ((-148 . -563) 139817) ((-144 . -563) 139799) ((-1181 . -666) T) ((-1018 . -33) T) ((-802 . -734) NIL) ((-802 . -731) NIL) ((-793 . -786) T) ((-671 . -817) NIL) ((-1190 . -124) T) ((-357 . -124) T) ((-835 . -97) T) ((-671 . -964) 139677) ((-495 . -124) T) ((-1005 . -387) 139661) ((-928 . -462) 139645) ((-113 . -376) 139622) ((-1078 . -1122) 139601) ((-721 . -387) 139585) ((-719 . -387) 139569) ((-874 . -33) T) ((-633 . -1063) NIL) ((-228 . -591) 139406) ((-227 . -591) 139230) ((-756 . -851) 139209) ((-429 . -387) 139193) ((-554 . -19) 139177) ((-1058 . -1116) 139146) ((-1078 . -817) NIL) ((-1078 . -815) 139098) ((-554 . -556) 139075) ((-1109 . -563) 139007) ((-1086 . -563) 138989) ((-60 . -371) T) 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. -563) 110825) ((-614 . -563) 110807) ((-1068 . -286) 110745) ((-453 . -33) T) ((-1009 . -1122) T) ((-452 . -427) T) ((-1005 . -973) T) ((-1053 . -33) T) ((-721 . -973) T) ((-719 . -973) T) ((-590 . -213) 110729) ((-578 . -213) 110675) ((-1141 . -284) 110654) ((-1005 . -302) 110615) ((-429 . -973) T) ((-1089 . -21) T) ((-1005 . -211) 110594) ((-721 . -302) 110571) ((-721 . -211) T) ((-719 . -302) 110543) ((-303 . -594) 110527) ((-671 . -1126) 110506) ((-1089 . -25) T) ((-57 . -33) T) ((-488 . -33) T) ((-486 . -33) T) ((-429 . -302) 110485) ((-303 . -349) 110469) ((-468 . -33) T) ((-467 . -33) T) ((-931 . -1063) NIL) ((-581 . -97) T) ((-557 . -97) T) ((-671 . -515) 110400) ((-331 . -666) T) ((-328 . -666) T) ((-320 . -666) T) ((-241 . -666) T) ((-225 . -666) T) ((-970 . -286) 110308) ((-832 . -1016) 110286) ((-49 . -973) T) ((-1178 . -21) T) ((-1178 . -25) T) ((-1085 . -515) 110265) ((-1084 . -1126) 110244) ((-536 . -973) T) ((-487 . -973) T) ((-1078 . -1126) 110223) ((-337 . -964) 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104907) ((-1131 . -353) 104877) ((-200 . -1035) 104861) ((-1168 . -265) 104838) ((-1117 . -591) 104763) ((-893 . -21) T) ((-893 . -25) T) ((-675 . -21) T) ((-675 . -25) T) ((-655 . -21) T) ((-655 . -25) T) ((-651 . -591) 104728) ((-428 . -21) T) ((-428 . -25) T) ((-315 . -97) T) ((-159 . -97) T) ((-927 . -980) T) ((-801 . -973) T) ((-713 . -97) T) ((-1153 . -339) 104707) ((-1152 . -831) 104613) ((-1132 . -339) 104592) ((-1131 . -831) 104443) ((-951 . -563) 104425) ((-383 . -767) 104378) ((-1085 . -464) 104344) ((-155 . -851) 104275) ((-1084 . -464) 104241) ((-1078 . -464) 104207) ((-652 . -1016) T) ((-1040 . -464) 104173) ((-535 . -979) 104160) ((-523 . -979) 104147) ((-466 . -979) 104112) ((-292 . -267) 104091) ((-289 . -267) T) ((-330 . -563) 104073) ((-394 . -25) T) ((-394 . -21) T) ((-94 . -263) 104052) ((-535 . -107) 104037) ((-523 . -107) 104022) ((-466 . -107) 103978) ((-1087 . -817) 103945) ((-832 . -462) 103929) ((-47 . -563) 103911) ((-47 . -564) 103856) ((-218 . -124) 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. -25) T) ((-130 . -563) 97623) ((-130 . -564) 97582) ((-841 . -284) T) ((-932 . -21) T) ((-900 . -25) T) ((-845 . -21) T) ((-845 . -25) T) ((-403 . -21) T) ((-403 . -25) T) ((-779 . -387) 97566) ((-47 . -973) T) ((-1188 . -1180) 97550) ((-1186 . -1180) 97534) ((-962 . -556) 97509) ((-292 . -564) 97370) ((-292 . -563) 97352) ((-289 . -564) NIL) ((-289 . -563) 97334) ((-47 . -221) T) ((-47 . -211) T) ((-597 . -263) 97295) ((-509 . -213) 97245) ((-128 . -563) 97227) ((-110 . -563) 97209) ((-452 . -37) 97174) ((-1190 . -1187) 97153) ((-1181 . -124) T) ((-1189 . -980) T) ((-1001 . -97) T) ((-86 . -1122) T) ((-471 . -286) NIL) ((-928 . -102) 97137) ((-820 . -1016) T) ((-816 . -1016) T) ((-1168 . -594) 97121) ((-1168 . -349) 97105) ((-303 . -1122) T) ((-546 . -786) T) ((-1054 . -1016) T) ((-1054 . -976) 97045) ((-98 . -484) 96978) ((-858 . -563) 96960) ((-319 . -666) T) ((-30 . -563) 96942) ((-797 . -1016) T) ((-779 . -980) 96921) ((-39 . -591) 96866) ((-203 . -1126) T) ((-383 . -980) T) 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. -840) NIL) ((-1188 . -1187) 92890) ((-1186 . -1187) 92869) ((-721 . -817) NIL) ((-719 . -817) 92728) ((-1181 . -25) T) ((-1181 . -21) T) ((-1120 . -97) 92706) ((-1022 . -371) T) ((-570 . -591) 92693) ((-429 . -817) NIL) ((-617 . -97) 92671) ((-1005 . -964) 92500) ((-802 . -23) T) ((-721 . -964) 92361) ((-719 . -964) 92220) ((-113 . -591) 92165) ((-429 . -964) 92043) ((-592 . -964) 92027) ((-573 . -97) T) ((-200 . -462) 92011) ((-1168 . -33) T) ((-581 . -657) 91995) ((-557 . -657) 91979) ((-613 . -37) 91939) ((-295 . -97) T) ((-83 . -563) 91921) ((-49 . -964) 91905) ((-1034 . -979) 91892) ((-1005 . -353) 91876) ((-58 . -55) 91838) ((-638 . -733) T) ((-638 . -730) T) ((-536 . -964) 91825) ((-487 . -964) 91802) ((-638 . -666) T) ((-292 . -973) 91693) ((-300 . -124) T) ((-289 . -973) T) ((-155 . -1028) T) ((-721 . -353) 91677) ((-719 . -353) 91661) ((-44 . -140) 91611) ((-932 . -921) 91593) ((-429 . -353) 91577) ((-383 . -158) T) ((-292 . -221) 91556) ((-289 . -221) T) ((-289 . -211) 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. -1016) T) ((-196 . -1127) T) ((-927 . -286) 119301) ((-203 . -964) 119261) ((-39 . -267) T) ((-999 . -21) T) ((-999 . -25) T) ((-1034 . -767) T) ((-460 . -515) T) ((-335 . -25) T) ((-196 . -515) T) ((-335 . -21) T) ((-329 . -25) T) ((-329 . -21) T) ((-654 . -591) 119221) ((-321 . -25) T) ((-321 . -21) T) ((-103 . -25) T) ((-103 . -21) T) ((-47 . -980) T) ((-535 . -158) T) ((-523 . -158) T) ((-466 . -158) T) ((-601 . -563) 119203) ((-677 . -676) 119187) ((-312 . -563) 119169) ((-66 . -359) T) ((-66 . -371) T) ((-1018 . -102) 119153) ((-984 . -817) 119135) ((-883 . -817) 119060) ((-596 . -1028) T) ((-570 . -657) 119047) ((-455 . -817) NIL) ((-1058 . -97) T) ((-984 . -964) 119029) ((-92 . -563) 119011) ((-452 . -136) T) ((-883 . -964) 118893) ((-113 . -657) 118838) ((-596 . -23) T) ((-455 . -964) 118716) ((-1005 . -564) NIL) ((-1005 . -563) 118698) ((-721 . -564) NIL) ((-721 . -563) 118659) ((-719 . -564) 118294) ((-719 . -563) 118208) ((-1029 . -585) 118116) ((-436 . -563) 118098) 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. -657) 114526) ((-155 . -831) 114485) ((-638 . -267) T) ((-633 . -158) T) ((-651 . -107) 114441) ((-1195 . -980) T) ((-1142 . -353) 114425) ((-394 . -1127) 114403) ((-289 . -784) NIL) ((-394 . -515) T) ((-203 . -284) T) ((-1132 . -730) 114356) ((-1132 . -733) 114309) ((-1153 . -666) T) ((-1132 . -666) T) ((-47 . -657) 114274) ((-203 . -949) T) ((-327 . -1176) 114251) ((-1155 . -387) 114217) ((-658 . -666) T) ((-1142 . -831) 114160) ((-108 . -563) 114142) ((-108 . -564) 114124) ((-658 . -448) T) ((-456 . -21) 114035) ((-123 . -462) 114019) ((-117 . -462) 114003) ((-456 . -25) 113855) ((-570 . -267) T) ((-540 . -979) 113830) ((-413 . -1016) T) ((-984 . -284) T) ((-113 . -267) T) ((-1020 . -97) T) ((-931 . -97) T) ((-540 . -107) 113798) ((-1054 . -286) 113736) ((-1118 . -973) T) ((-984 . -949) T) ((-64 . -1123) T) ((-977 . -25) T) ((-977 . -21) T) ((-651 . -973) T) ((-361 . -21) T) ((-361 . -25) T) ((-633 . -484) NIL) ((-951 . -158) T) ((-651 . -221) T) ((-984 . -508) T) ((-473 . -97) T) 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. -564) 85381) ((-1052 . -97) T) ((-927 . -979) 85277) ((-39 . -831) 85229) ((-1068 . -556) 85206) ((-1195 . -591) 85193) ((-985 . -140) 85139) ((-803 . -1127) T) ((-927 . -107) 85021) ((-315 . -657) 85005) ((-797 . -563) 84987) ((-159 . -657) 84919) ((-383 . -263) 84877) ((-803 . -515) T) ((-103 . -376) 84859) ((-82 . -360) T) ((-82 . -371) T) ((-640 . -158) T) ((-94 . -666) T) ((-456 . -97) 84670) ((-94 . -448) T) ((-112 . -158) T) ((-1029 . -37) 84640) ((-155 . -585) 84588) ((-977 . -97) T) ((-802 . -25) T) ((-754 . -216) 84567) ((-802 . -21) T) ((-757 . -97) T) ((-390 . -97) T) ((-361 . -97) T) ((-106 . -286) NIL) ((-205 . -97) 84545) ((-123 . -1123) T) ((-117 . -1123) T) ((-961 . -124) T) ((-613 . -343) 84529) ((-927 . -973) T) ((-1142 . -585) 84477) ((-1020 . -563) 84459) ((-931 . -563) 84441) ((-485 . -23) T) ((-480 . -23) T) ((-319 . -284) T) ((-478 . -23) T) ((-298 . -124) T) ((-3 . -1016) T) ((-931 . -564) 84425) ((-927 . -221) 84404) ((-927 . -211) 84383) ((-1195 . -666) T) 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\ No newline at end of file diff --git a/src/share/algebra/compress.daase b/src/share/algebra/compress.daase index bc4d7013..3ec04b2a 100644 --- a/src/share/algebra/compress.daase +++ b/src/share/algebra/compress.daase @@ -1,6 +1,6 @@ -(30 . 3415311727) -(4247 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| +(30 . 3416411995) +(4251 |Enumeration| |Mapping| |Record| |Union| |ofCategory| |isDomain| ATTRIBUTE |package| |domain| |category| CATEGORY |nobranch| AND |Join| |ofType| SIGNATURE "failed" "algebra" |OneDimensionalArrayAggregate&| |OneDimensionalArrayAggregate| |AbelianGroup&| |AbelianGroup| @@ -413,7 +413,7 @@ |SupFractionFactorizer| |SparseUnivariatePolynomial| |SparseUnivariatePuiseuxSeries| |SparseUnivariateTaylorSeries| |Switch| |Symbol| |SymmetricFunctions| |SymmetricPolynomial| - |TheSymbolTable| |SymbolTable| |Syntax| |SystemSolvePackage| + |TheSymbolTable| |SymbolTable| |Syntax| |SystemSolvePackage| |System| |TableauxBumpers| |Tableau| |Table| |TangentExpansions| |TableAggregate&| |TableAggregate| |TabulatedComputationPackage| |TemplateUtilities| |TexFormat1| |TexFormat| |TextFile| |ToolsForSign| @@ -460,650 +460,649 @@ |XPolynomialRing| |XRecursivePolynomial| |ParadoxicalCombinatorsForStreams| |ZeroDimensionalSolvePackage| |IntegerLinearDependence| |IntegerMod| |Enumeration| |Mapping| - |Record| |Union| |splitDenominator| |badValues| |interpolate| - |innerint| |symbolTableOf| |fortranDoubleComplex| - |subscriptedVariables| |reducedQPowers| |yCoordinates| - |tubePointsDefault| |green| |iiasec| |restorePrecision| |fibonacci| - |exprToUPS| |screenResolution| |normalizeAtInfinity| - |leftAlternative?| |palgint| |goodPoint| |factorSquareFreePolynomial| - |legendre| |lowerPolynomial| |f01maf| |wrregime| |zCoord| |notelem| - |bat1| |pow| |measure| |f04axf| |showTheSymbolTable| |deepExpand| - |possiblyInfinite?| |OMgetAtp| |dequeue!| |changeMeasure| - |lazyPremWithDefault| |cAtan| |node?| |pquo| |midpoints| |accuracyIF| - |goto| |nextPrimitivePoly| |constantKernel| |iiacoth| - |mainSquareFreePart| |matrixDimensions| |divergence| |d01gbf| - |linearMatrix| |coefficients| |basisOfCentroid| |meshPar1Var| - |genericRightMinimalPolynomial| |stopTable!| |elliptic?| |opeval| - |round| |getButtonValue| |composite| |ipow| |radicalEigenvector| - |poisson| |entries| |setLabelValue| |cCsch| |factorSFBRlcUnit| - |OMputFloat| |outlineRender| |wordInStrongGenerators| |lazyVariations| - |df2fi| |ksec| |heap| |d03faf| |pToDmp| |removeCosSq| |inrootof| - |rubiksGroup| |const| |exptMod| |updatF| |fixPredicate| |pomopo!| - |aLinear| |coercePreimagesImages| |e02ddf| |center| |csubst| - |inGroundField?| |separateDegrees| |rational?| |backOldPos| Y - |isPower| |complexEigenvalues| |quoted?| |mainMonomial| |cylindrical| - |critB| |commutativeEquality| |lastSubResultantEuclidean| |upperCase| - |startTable!| |polyred| |ratPoly| |createGenericMatrix| |atom?| - |intersect| |semiResultantReduitEuclidean| |quatern| - |internalDecompose| |sincos| |FormatArabic| |solveLinear| |position!| - |safetyMargin| |cExp| |rank| |SturmHabichtSequence| |taylorQuoByVar| - |check| |absolutelyIrreducible?| |d02ejf| |besselI| |setTex!| |every?| - |redmat| |bits| |keys| |writeLine!| |showTypeInOutput| - |generalInfiniteProduct| |singRicDE| |delay| |legendreP| - |squareFreeFactors| |leftFactor| |setMinPoints3D| |mathieu11| |d02gaf| - |showIntensityFunctions| |tanAn| |knownInfBasis| |clipParametric| - |dim| |ravel| |back| |multiplyExponents| |nextNormalPoly| |prem| - |extractTop!| |complete| |rightLcm| |viewSizeDefault| |tanQ| - |mainVariable?| |power!| |reshape| |createZechTable| |c06gcf| |middle| - |mainKernel| |prefixRagits| |getZechTable| |lfextendedint| - |sizeMultiplication| |factorset| |mantissa| |entry?| - |rightExactQuotient| |rspace| |integral| |rationalPoint?| - |eyeDistance| |e04ucf| |reduceLODE| |cscIfCan| |infiniteProduct| - |bivariate?| |biRank| |computeInt| |inconsistent?| |lists| |resetNew| - |leftUnit| |sizeLess?| |adaptive?| |iilog| |mpsode| |f2st| |dflist| - |nthFractionalTerm| |slex| |coHeight| |makeFR| |minimalPolynomial| - |headReduce| |reducedContinuedFraction| |cSec| |imagK| |printingInfo?| - |operator| |setStatus| |outputArgs| |retractable?| |expintfldpoly| - |nextPrime| |allRootsOf| |enterPointData| |putColorInfo| |update| - |separant| |computeBasis| |d02bhf| |setFieldInfo| |KrullNumber| - |decrease| |mirror| |nthRoot| |scalarMatrix| |findBinding| - |ScanFloatIgnoreSpaces| |iisqrt3| |evenInfiniteProduct| |e04fdf| - |bright| |overset?| |frobenius| |OMgetEndApp| |rightTraceMatrix| - |internalIntegrate0| |bfEntry| |tanIfCan| |lowerCase?| |e02gaf| - |drawCurves| |pToHdmp| |identity| |solveRetract| |eigenvector| - |idealiserMatrix| |messagePrint| |operators| |iiGamma| - |processTemplate| |insertMatch| |leftPower| |binaryFunction| - |removeIrreducibleRedundantFactors| |algSplitSimple| |eigenMatrix| - |isobaric?| |d02raf| |denomLODE| |triangularSystems| - |createIrreduciblePoly| |coerce| |debug| |tracePowMod| - |functionIsContinuousAtEndPoints| |antiCommutative?| - |generalizedInverse| |int| |s21baf| |mr| - |inverseIntegralMatrixAtInfinity| |checkRur| |delete| |rightGcd| - |polyRicDE| |construct| |satisfy?| |factorsOfDegree| - |internalSubQuasiComponent?| |basisOfRightNucloid| |iibinom| - |boundOfCauchy| |position| |pol| |OMputEndBVar| - |unprotectedRemoveRedundantFactors| |minPoly| |LiePoly| |ideal| - |copy!| |powerAssociative?| |prinb| |failed?| |selectsecond| |lintgcd| - |revert| |critBonD| |setsubMatrix!| |repeatUntilLoop| |coerceImages| - |leftOne| |cyclicCopy| |arg1| |radicalSolve| |toseLastSubResultant| - |selectNonFiniteRoutines| |components| |leftTraceMatrix| |cos2sec| - |sort!| |sturmSequence| |choosemon| |removeSinSq| |jordanAdmissible?| - |arg2| |orbit| |elementary| |optpair| |startTableInvSet!| |bitCoef| - |iipow| |closedCurve| |homogeneous?| |clip| |substring?| - |removeRoughlyRedundantFactorsInContents| |stoseInvertibleSet| - |reducedDiscriminant| |bumptab| |iicot| |Ci| |tanintegrate| - |createRandomElement| |probablyZeroDim?| |point?| |second| - |complexIntegrate| |conditions| |integralMatrixAtInfinity| - |leftScalarTimes!| |surface| |integer?| |optAttributes| - |subresultantVector| |getCode| |sechIfCan| |fullPartialFraction| - |null| |suffix?| |third| |match| |isList| |distance| |minPoints3D| - |semiLastSubResultantEuclidean| |OMputVariable| |closed?| |exprToXXP| - |polCase| |halfExtendedResultant1| |odd?| |lSpaceBasis| |iiacsch| - |ScanArabic| |selectPDERoutines| |useEisensteinCriterion?| |true| - |s19aaf| |linGenPos| |s14baf| |getOrder| |linearlyDependentOverZ?| - |prefix?| |ScanRoman| |mightHaveRoots| |representationType| |root?| - |log10| |minimumDegree| |roman| |groebnerIdeal| |OMputEndAttr| - |leftRecip| |getGoodPrime| |crest| |nextsousResultant2| |depth| - |outputFixed| |OMputBind| |seriesSolve| |iiabs| |acoshIfCan| - |subTriSet?| |principalIdeal| |cosIfCan| |front| |cCot| |lifting| - |column| |rk4| |getStream| |insertTop!| |iiasin| |binaryTree| |f02axf| - |invmultisect| |divisorCascade| |completeEval| |imagI| - |subresultantSequence| |rootProduct| |primes| |toseSquareFreePart| - |exteriorDifferential| |lastSubResultant| |contours| |cAsinh| |e02ahf| - |infinite?| |subHeight| |digits| |laplacian| |nil?| |mapCoef| - |characteristic| |commaSeparate| |d01asf| |setAdaptive| |cyclotomic| - |rewriteSetByReducingWithParticularGenerators| |cdr| |Not| - |generalizedEigenvectors| |f04atf| |irreducibleFactors| |hermite| - |zeroSetSplitIntoTriangularSystems| |infix?| |dn| |clipBoolean| - |btwFact| |setDifference| |e01saf| |order| |setelt| |algebraicSort| - |ListOfTerms| |headRemainder| |f02fjf| |getPickedPoints| |mask| - |asinhIfCan| |noncommutativeJordanAlgebra?| |computeCycleEntry| - |enqueue!| |innerSolve1| |setIntersection| |linSolve| |overlap| - |product| |setRealSteps| |makeCrit| |associatedEquations| |f02ajf| - |setUnion| |aspFilename| |numberOfFractionalTerms| |copy| |var2Steps| - |parts| |univariatePolynomialsGcds| |addPoint2| |unitNormal| - |iCompose| |powerSum| |say| |commutative?| |slash| |meatAxe| - |stoseInvertible?| |apply| |elRow1!| |inRadical?| |Hausdorff| - |element?| |splitNodeOf!| |extension| |brace| |close!| - |generalPosition| |leftExactQuotient| |uniform| |flatten| ^= - |repeating?| |functionIsOscillatory| |OMgetEndObject| |rootsOf| |vark| - |e01bff| |rules| |outputGeneral| |showArrayValues| |f01rdf| - |symmetricTensors| |autoCoerce| |size| |associates?| |normalizeIfCan| - |UnVectorise| |deepCopy| |exponential| |symmetricSquare| |eq| - |addMatch| |euler| |janko2| |commutator| |spherical| |acothIfCan| - |rischDEsys| |supDimElseRittWu?| |asec| |numerators| |iter| |myDegree| - |s17dlf| |OMputAtp| |expt| |rightMinimalPolynomial| |coerceP| - |zerosOf| |df2st| |solveLinearPolynomialEquationByFractions| |acsc| - |sortConstraints| |value| |hdmpToDmp| |froot| |externalList| - |sylvesterMatrix| |first| |next| |halfExtendedSubResultantGcd1| - |dimensionOfIrreducibleRepresentation| |sinhIfCan| |parent| |sinh| - |laurentIfCan| |concat!| |complexNumeric| |differentialVariables| - |list?| |getSyntaxFormsFromFile| |rest| |usingTable?| |s17dgf| - |OMgetEndAtp| |incrementKthElement| - |rewriteIdealWithQuasiMonicGenerators| |cosh| |minColIndex| |mapSolve| - |extendedEuclidean| |cot2tan| |HermiteIntegrate| |substitute| - |simplifyPower| |computeCycleLength| |getProperty| |numberOfFactors| - |rk4qc| |tanh| |internalAugment| |kernels| |extractPoint| - |removeDuplicates| |wreath| |style| |factorSquareFreeByRecursion| - |outerProduct| |rightCharacteristicPolynomial| - |tryFunctionalDecomposition?| |f01ref| |rk4a| |coth| |subscript| - |iisec| |zeroMatrix| |univariate| |lhs| |character?| |predicates| - |minPoints| |pushdown| |cyclicGroup| |sech| |generalSqFr| |solve1| - |colorFunction| |rhs| |setErrorBound| |indiceSubResultantEuclidean| - |loopPoints| |lfunc| |ef2edf| |rangePascalTriangle| |hue| |csch| - |superscript| |characteristicPolynomial| |submod| |cAcosh| |frst| - |exp| |qqq| |rowEch| |setleaves!| |summation| |iisech| - |withPredicates| |asinh| |removeZeroes| |factor| |inverseColeman| - |c06ebf| |setvalue!| |collectQuasiMonic| |stoseInvertibleSetsqfreg| - |option?| |algebraicDecompose| |swap| |baseRDE| |acosh| |comparison| - |sqrt| |OMread| |or?| |rightRank| |Nul| |atanhIfCan| |getIdentifier| - |atanh| |generalLambert| |explogs2trigs| |real| |mesh| |f04adf| - |tanSum| |bitTruth| |addMatchRestricted| |particularSolution| - |clearTable!| |f04jgf| |standardBasisOfCyclicSubmodule| |acoth| |key| - |weights| |digit| |imag| |leviCivitaSymbol| |palgint0| |s17dhf| - |mkPrim| |splitConstant| |wholeRadix| |ldf2lst| |PDESolve| |asech| - |options| |nullity| |directProduct| |constant?| |fortranCharacter| - |mainMonomials| |printStatement| |genericRightDiscriminant| - |argumentList!| |generalTwoFactor| |exponents| |s18aef| - |exprHasWeightCosWXorSinWX| |resultantEuclideannaif| |insertRoot!| - |normalElement| |totalfract| |create| |kovacic| - |squareFreeLexTriangular| |ceiling| |destruct| |null?| |bracket| - |unitVector| |plusInfinity| |presub| |cPower| |principal?| - |closedCurve?| |groebner| |monicDecomposeIfCan| |unvectorise| - |OMencodingSGML| |compactFraction| |complexElementary| |push| - |minusInfinity| |d01alf| |deleteRoutine!| |quasiMonic?| - |rightScalarTimes!| |asinIfCan| |s17acf| |combineFeatureCompatibility| - |vertConcat| |expandTrigProducts| |infinityNorm| |rdHack1| |equation| - |addPoint| |elColumn2!| |OMgetBVar| |orthonormalBasis| |makeUnit| - |perspective| |symmetricDifference| |sum| |f02agf| |minordet| |mapdiv| - |localReal?| |rename!| |oblateSpheroidal| |OMlistSymbols| - |resetVariableOrder| |listOfMonoms| |monomial| |inspect| - |OMgetVariable| |logical?| |factorFraction| |blue| |pushup| |solve| - |bernoulliB| |startStats!| |expPot| |purelyAlgebraic?| |multivariate| - |univcase| |atanIfCan| |brillhartIrreducible?| |antisymmetricTensors| - |belong?| |pointLists| |baseRDEsys| |leadingSupport| |palgRDE0| - |acosIfCan| |quoByVar| |variables| |primintfldpoly| |chiSquare| - |cAcot| |tanh2coth| |systemSizeIF| |setprevious!| |sorted?| - |quadratic?| |degreePartition| |d01gaf| |lfinfieldint| |printStats!| - |rightPower| |implies| |euclideanSize| |member?| |leftMult| |sdf2lst| - |derivationCoordinates| |selectPolynomials| |primitivePart!| |factors| - |positiveRemainder| |bit?| |SturmHabichtCoefficients| |xor| - |infieldint| |userOrdered?| |complexRoots| |d01amf| |listexp| - |compiledFunction| |f04maf| |primeFrobenius| |prod| |cycleElt| - |gradient| |antiCommutator| |primitiveElement| |finite?| |iomode| - |prindINFO| |OMUnknownCD?| |headReduced?| |harmonic| |pole?| - |interReduce| |purelyTranscendental?| |BasicMethod| |plot| |iiacosh| - |quadraticForm| |stoseLastSubResultant| |doubleResultant| - |radicalRoots| |coord| |localUnquote| |taylor| |s14aaf| |OMgetEndAttr| - |normalize| |mathieu22| |groebSolve| |s17dcf| |associator| |one?| - |monicLeftDivide| |iifact| |errorInfo| |tubePoints| |laurent| |dec| - |tanNa| |row| |cyclicParents| |Gamma| |conical| |leftLcm| |d01ajf| - |triangulate| |evaluate| |ellipticCylindrical| |central?| |shift| - |rightDivide| |fortranInteger| |hasTopPredicate?| |linearPart| - |createNormalPrimitivePoly| |roughBasicSet| |hasSolution?| - |fixedPoints| |iitan| |expenseOfEvaluationIF| |intermediateResultsIF| - |univariatePolynomial| |nthRootIfCan| |monicModulo| |fractRadix| - |showAll?| |stripCommentsAndBlanks| |complement| |coerceL| |varList| - |max| |split| |rootSplit| |times!| |initializeGroupForWordProblem| - |constDsolve| UP2UTS |getRef| |partialQuotients| |alternative?| - |lookup| |radicalSimplify| |getlo| |selectODEIVPRoutines| |normalise| - 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|symbolIfCan| |primitive?| |integerIfCan| |s13adf| |merge!| - |explimitedint| |changeName| |closeComponent| |alphanumeric| |atoms| - |curryLeft| |limit| |copies| |trailingCoefficient| |algebraicOf| - |isAbsolutelyIrreducible?| |FormatRoman| |iiacos| |nonQsign| - |noLinearFactor?| |c02aff| |antisymmetric?| |basisOfMiddleNucleus| - |romberg| |merge| |dioSolve| |makeSUP| |OMgetApp| - |useSingleFactorBound?| |semiResultantEuclideannaif| - |numberOfIrreduciblePoly| |critpOrder| |axesColorDefault| |hdmpToP| - |cap| |recolor| |lepol| |semiDegreeSubResultantEuclidean| |outputList| - |nsqfree| |qinterval| |quasiAlgebraicSet| |primaryDecomp| |cLog| - |associatedSystem| |oddintegers| |applyRules| |e02akf| |csc2sin| - |viewWriteDefault| |constantLeft| |numberOfNormalPoly| |fractionPart| - |sin?| |outputFloating| |plus| |setEpilogue!| |cTanh| |f02aef| - |cosh2sech| |trigs2explogs| |hasoln| |lprop| |mergeFactors| - |semicolonSeparate| |localAbs| |certainlySubVariety?| |symmetricPower| - |univariatePolynomials| |callForm?| |subNodeOf?| |monicRightDivide| - |abelianGroup| |reduction| |e02bbf| |removeSquaresIfCan| - |lflimitedint| |hasHi| |selectIntegrationRoutines| |tableau| - |UpTriBddDenomInv| |medialSet| |mainContent| |makeViewport3D| - |rdregime| |makeSeries| |cross| |mapUp!| |groebnerFactorize| |search| - |nullary| |patternMatchTimes| |unparse| |f07fef| - |resetAttributeButtons| |remove!| |balancedFactorisation| - |splitLinear| |univariateSolve| |rightFactorCandidate| |makingStats?| - |times| |largest| |rroot| |expenseOfEvaluation| |hcrf| |distFact| - |s13aaf| |init| |edf2fi| |Aleph| |OMgetAttr| |clearTheSymbolTable| - |simplify| |getExplanations| |basisOfCenter| |multiEuclidean| |lazy?| - |setMaxPoints| |label| |decompose| |constantOpIfCan| |binomThmExpt| - |physicalLength!| |patternVariable| |low| |prepareDecompose| |e01bef| - |anticoord| |stFunc1| |rightDiscriminant| |fixedPoint| |mindeg| - |generateIrredPoly| |duplicates?| |listOfLists| |rationalPower| - |squareFreePart| |top!| |integerBound| |tValues| |zero?| |children| - |reindex| |relerror| |degree| |fortranLiteralLine| - 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|d01aqf| |mdeg| |selectAndPolynomials| |setMinPoints| |sech2cosh| - |cyclotomicDecomposition| |ratpart| |isQuotient| |pdct| |cCsc| - |firstSubsetGray| |d02kef| |quasiRegular| |identitySquareMatrix| - |subResultantGcdEuclidean| |equiv| |endSubProgram| |cyclic| |polygon| - |createPrimitivePoly| |simpson| |exactQuotient!| |denomRicDE| - |basisOfLeftNucleus| |mainValue| |tanh2trigh| |shiftLeft| |psolve| - |minimize| |intPatternMatch| |cRationalPower| |critMTonD1| |zeroOf| - |countable?| |extendedSubResultantGcd| |lieAdmissible?| |isMult| - |shallowExpand| |failed| |tRange| |var2StepsDefault| |toroidal| - |rightFactorIfCan| |unrankImproperPartitions1| |leftGcd| |tube| - |lifting1| |s18adf| |pr2dmp| |chebyshevT| |reset| - |irreducibleRepresentation| |laurentRep| |declare!| |height| |lambert| - |ridHack1| |palgRDE| |c06frf| |multiple| |stoseInvertibleSetreg| - |prevPrime| |sample| |nthFlag| |mainVariable| |trueEqual| |infLex?| - |applyQuote| |cyclic?| |leftRankPolynomial| |getGraph| - |OMencodingUnknown| |primitivePart| |write| |indicialEquation| - |numerator| |rightRecip| |simplifyExp| |createNormalPoly| - |weierstrass| |checkPrecision| |tab| |diagonals| |ramified?| |e02adf| - |setright!| |pastel| |fixedPointExquo| |insertBottom!| - |leastAffineMultiple| |packageCall| |call| |lagrange| |iiasech| - |henselFact| |rootOfIrreduciblePoly| |lyndon?| |leftMinimalPolynomial| - |createPrimitiveNormalPoly| |vconcat| |explicitEntries?| |remove| - |s17aff| |quadraticNorm| |sturmVariationsOf| |diagonal| |approximate| - |lineColorDefault| |beauzamyBound| |leftCharacteristicPolynomial| - |high| |pdf2ef| |randnum| |splitSquarefree| |whatInfinity| |complex| - |scaleRoots| ~ |binomial| |integers| |trace2PowMod| |monomRDEsys| - |OMgetEndBVar| |last| |recoverAfterFail| ** |singularitiesOf| - |positiveSolve| |llprop| |freeOf?| |rowEchelonLocal| GF2FG |f04mcf| - |assoc| |toseInvertible?| |fracPart| |sqfrFactor| |f01brf| |delta| - |f02abf| |matrixGcd| |GospersMethod| |ReduceOrder| |match?| |prologue| - |cschIfCan| |setref| |OMputError| |positive?| |graphCurves| - |symmetric?| |doubleComplex?| EQ |asecIfCan| |enterInCache| - |primPartElseUnitCanonical!| |hconcat| |realEigenvalues| |graphState| - |toseInvertibleSet| |cyclicEntries| |f04qaf| |LyndonCoordinates| |abs| - |monomial?| |collectUpper| |red| |s17ahf| |collectUnder| |open| - |realRoots| |bezoutDiscriminant| |OMgetBind| |changeThreshhold| - |isExpt| |f01qdf| |variationOfParameters| |findCycle| - |nextPrimitiveNormalPoly| |root| |reduceByQuasiMonic| |swapRows!| - |updateStatus!| |listConjugateBases| |unitNormalize| - |oneDimensionalArray| |eulerPhi| |LyndonBasis| |segment| |nodes| |hex| - |reopen!| |initiallyReduce| |xCoord| |numberOfHues| |square?| |lex| - |trigs| |transcendenceDegree| |triangSolve| |weight| |prime?| - |multiple?| |expr| |hexDigit?| |lambda| |numFunEvals| |reduced?| - |notOperand| |pade| |leadingCoefficientRicDE| |gcdPolynomial| - |invertibleSet| |primlimitedint| |OMgetString| |schwerpunkt| |open?| - |oddlambert| |lowerCase| |tan2cot| |#| |redPo| |jacobi| |eval| - |sin2csc| |removeSinhSq| |mapExpon| |subQuasiComponent?| |s17akf| - |precision| |setPoly| |e01sef| |status| |e01bgf| |changeVar| - |branchPoint?| |shiftRight| |semiSubResultantGcdEuclidean2| - |stronglyReduced?| |numFunEvals3D| |OMputEndObject| |weakBiRank| - |ratDsolve| |numericalOptimization| |variable| |lquo| |graphImage| - |optimize| |doublyTransitive?| |child| |minset| |leastPower| |adjoint| - |moreAlgebraic?| |digamma| |interpret| |algintegrate| |doubleDisc| - |f01rcf| |linear?| |binary| |areEquivalent?| |acotIfCan| - |argumentListOf| |tab1| |OMsend| |OMgetSymbol| - |stiffnessAndStabilityOfODEIF| |internalInfRittWu?| |shellSort| - |leaves| |unary?| |gethi| |maxint| |viewport3D| |symmetricProduct| - |cycleTail| |rootRadius| |selectOptimizationRoutines| |exponent| - |endOfFile?| |internalIntegrate| |someBasis| |f07fdf| |dmpToHdmp| - |subResultantsChain| |palgextint0| |isOp| |startTableGcd!| |iidprod| - |changeNameToObjf| |cCosh| |mainCoefficients| |createNormalElement| - |scopes| |flexible?| |deepestInitial| |delete!| |nextSubsetGray| - |recur| |Zero| |s15aef| |integralLastSubResultant| |formula| |s21bcf| - |att2Result| |f04arf| |bumprow| |integralRepresents| - |modularGcdPrimitive| |duplicates| |One| |irreducible?| |signAround| - |numberOfVariables| |rewriteIdealWithHeadRemainder| |prinshINFO| - |generators| |inf| |hypergeometric0F1| |maxrank| |key?| |bsolve| - |hyperelliptic| |pushdterm| |quadratic| |getMeasure| |hash| - |printHeader| |numer| |countRealRootsMultiple| |minrank| - |rightRegularRepresentation| |polygamma| |df2ef| |testDim| |count| - |repeating| |listLoops| |qelt| |noKaratsuba| |denom| |karatsuba| - |realEigenvectors| |iteratedInitials| |printInfo!| |e02bef| |nrows| - |stopTableInvSet!| |radPoly| |f04mbf| |cAcos| |constantIfCan| - |external?| |testModulus| |lllp| |divisors| |ncols| |ocf2ocdf| - |pseudoDivide| |quotientByP| |xRange| |any| |powmod| |pi| |zero| - |edf2df| |fullDisplay| |cfirst| |ptree| |insertionSort!| |rootBound| - |rootPower| |scripted?| |gramschmidt| |yRange| |OMconnectTCP| - |infinity| |nextIrreduciblePoly| |vedf2vef| |leadingIndex| |scan| - |cotIfCan| |composites| |newTypeLists| |readLineIfCan!| |zRange| - |ode2| |And| |mathieu24| |updatD| |insert| |compdegd| |equiv?| - |pureLex| |reduceBasisAtInfinity| |map!| |octon| |vectorise| |cAsec| - |Or| |c05pbf| |lowerCase!| |uncouplingMatrices| - |inverseIntegralMatrix| |constantOperator| D |qsetelt!| |movedPoints| - |typeLists| |less?| |reverse!| |kernel| |selectfirst| |invertible?| - |jacobiIdentity?| |outputSpacing| |dom| |trim| |newReduc| - |atrapezoidal| |extractIndex| |iroot| |draw| |drawComplexVectorField| - |append| |c06fpf| |lexTriangular| |andOperands| |exponentialOrder| - |removeRoughlyRedundantFactorsInPols| |factorByRecursion| |argscript| - |logGamma| |extendIfCan| |countRealRoots| |zeroDimPrimary?| - |showScalarValues| |rightMult| |f02awf| |firstDenom| |realSolve| - |singular?| |e02agf| |plus!| |stoseInvertible?sqfreg| - |complexNormalize| |deleteProperty!| |yellow| |pointColor| - |divideIfCan!| |mvar| |fortranLiteral| |escape| |maxdeg| |mkcomm| - |viewDeltaYDefault| |schema| |acsch| |cAcsch| |makeObject| |e02aef| - |pack!| |universe| |sPol| |s20adf| |arity| |leftZero| - |changeWeightLevel| |fortran| |firstUncouplingMatrix| |intChoose| - |f02bjf| |lazyResidueClass| |e| LODO2FUN |complexNumericIfCan| - |dihedralGroup| |subMatrix| |coef| |getOperands| |ord| - |factorGroebnerBasis| |characteristicSerie| |increase| |makeResult| - |genericLeftTraceForm| |save| |transcendentalDecompose| - |totalDifferential| |leadingIdeal| |continuedFraction| |print| - |sylvesterSequence| |rootPoly| |graphs| |cn| |pushucoef| - |extendedResultant| |subst| |lieAlgebra?| |singularAtInfinity?| - |exprex| |rightOne| |heapSort| |split!| |shiftRoots| |extractClosed| - |lexico| |meshPar2Var| |coordinates| |gcdcofact| |s17agf| |fTable| - |setClosed| |setleft!| |basisOfCommutingElements| |innerEigenvectors| - |discreteLog| |ParCondList| |initTable!| |tanhIfCan| |rischDE| - |normDeriv2| |fortranTypeOf| |monicDivide| |directory| - |removeSuperfluousQuasiComponents| |lazyPseudoQuotient| - |viewZoomDefault| |goodnessOfFit| |separateFactors| |factorials| - |outputMeasure| |move| |conjugates| |space| |shufflein| - |setMaxPoints3D| |c06gqf| |length| |objects| |subCase?| |subSet| - |setVariableOrder| |writable?| |leftDiscriminant| |implies?| |mapmult| - |scripts| |gderiv| |base| |polar| |lfintegrate| |laplace| - |showFortranOutputStack| |currentSubProgram| |op| |getCurve| - |multiEuclideanTree| |generalizedContinuumHypothesisAssumed?| - |equivOperands| |parametersOf| |addPointLast| - |internalLastSubResultant| |pair?| |e01sbf| |indiceSubResultant| |id| - |dmpToP| |tubeRadius| |coerceS| |setButtonValue| |s20acf| - |bipolarCylindrical| |script| FG2F |ode| |makeViewport2D| - |constructorName| |anfactor| |OMputInteger| |coordinate| LT - |ricDsolve| |viewWriteAvailable| |f07adf| |table| - |factorsOfCyclicGroupSize| |badNum| - |generalizedContinuumHypothesisAssumed| |dequeue| - |genericLeftMinimalPolynomial| |removeRedundantFactorsInContents| - |normalizedAssociate| |iiexp| |new| |makeEq| |mainCharacterization| - |lazyPrem| |maxIndex| |lyndon| |primPartElseUnitCanonical| |constant| - |specialTrigs| |tex| |polyPart| |OMputSymbol| |torsionIfCan| UTS2UP - |quartic| |f01bsf| |matrix| |completeHermite| - |genericLeftDiscriminant| |adaptive3D?| |tower| |OMconnInDevice| - |c06ekf| |twoFactor| |collect| |leftRemainder| |resultant| |size?| - |scanOneDimSubspaces| |bivariatePolynomials| |leftQuotient| RF2UTS - |erf| |internalZeroSetSplit| |iflist2Result| |viewpoint| |dihedral| - |palglimint| |LazardQuotient2| |leftDivide| |impliesOperands| - |reciprocalPolynomial| |systemCommand| |setPredicates| - |exprHasLogarithmicWeights| |subspace| |ODESolve| |rotatex| - |setchildren!| |basisOfRightNucleus| |genericPosition| - |leftFactorIfCan| |alphabetic| |previous| |mapUnivariate| |iExquo| - |property| |mainDefiningPolynomial| |setImagSteps| |unexpand| - |hessian| |stoseSquareFreePart| |read!| |structuralConstants| - |primeFactor| |diagonal?| |eigenvectors| |makeGraphImage| - |associative?| |function| |assign| |createThreeSpace| - |internalSubPolSet?| |top| |resultantEuclidean| |normal| |perfectSqrt| - |symbol?| |condition| |unmakeSUP| |debug3D| |possiblyNewVariety?| - |decreasePrecision| |seed| |continue| |curry| |rightRankPolynomial| - |morphism| |neglist| |e04jaf| |units| |cothIfCan| |getVariableOrder| - |partialNumerators| |s15adf| |generic| |f02bbf| |left| - |stoseIntegralLastSubResultant| |graphStates| |rotate!| - |zeroDimPrime?| |s18acf| |xn| |squareFreePolynomial| |multiset| - |OMgetInteger| |right| |copyInto!| |linearlyDependent?| |makeCos| - |monomialIntegrate| |wordInGenerators| |e01daf| |direction| - |palgintegrate| |f07aef| |chineseRemainder| |acschIfCan| F2FG - |rombergo| |oddInfiniteProduct| |simpleBounds?| |super| |c06fuf| - |pointData| |makeVariable| |sncndn| |cyclotomicFactorization| |d01bbf| - |inR?| |genericLeftNorm| |clipSurface| |resize| |viewport2D| |c05adf| - |e04naf| |code| |deepestTail| |mainForm| |stFuncN| - |rationalApproximation| |cSin| |predicate| |numberOfPrimitivePoly| - |initial| |makeSin| |ScanFloatIgnoreSpacesIfCan| |setEmpty!| |inc| - |basisOfNucleus| |dimension| |genus| |randomLC| |hclf| |string| - |conjugate| |cAcoth| |UP2ifCan| |makeprod| |subtractIfCan| - |intcompBasis| |expIfCan| |s14abf| |OMputString| |factorial| - |transform| |divisor| |subNode?| |currentEnv| |safeFloor| |elt| |in?| - |roughEqualIdeals?| |isTimes| |dominantTerm| |denominators| - |maxPoints| |simpsono| |currentScope| |numeric| |twist| |se2rfi| - |multisect| |ratDenom| |leftTrace| |solid?| |basisOfLeftNucloid| |lp| - |extendedint| |OMreadStr| |radical| |lcm| |sec2cos| - |lastSubResultantElseSplit| |modifyPointData| |rotatez| - |zeroDimensional?| |convergents| |fi2df| NOT |youngGroup| |besselJ| - |divideExponents| |mapDown!| |lazyPseudoRemainder| |dark| |is?| - |topFortranOutputStack| |normInvertible?| OR |LyndonWordsList1| - |float?| |parametric?| |measure2Result| |Is| |showTheIFTable| |dot| - |multMonom| |npcoef| AND |iicsc| |viewDefaults| |palgLODE| - |swapColumns!| |redpps| |gcd| |screenResolution3D| |stFunc2| - |monomialIntPoly| |remainder| |tree| |linearDependence| - |indicialEquations| |eisensteinIrreducible?| |prime| |union| - |rationalFunction| |newLine| |cAsech| |parameters| |solveInField| - |radicalEigenvectors| |quote| |trunc| |makeSketch| |false| - |unitsColorDefault| |raisePolynomial| |subResultantChain| |HenselLift| - |declare| |permutationRepresentation| |invmod| |critT| |crushedSet| - |elliptic| |clipWithRanges| |resultantnaif| |e02dff| - |expressIdealMember| |rootOf| |error| |virtualDegree| |upperCase?| - |bubbleSort!| |df2mf| |categoryFrame| |invertibleElseSplit?| |edf2ef| - |partitions| |rischNormalize| |output| |setTopPredicate| |assert| - |genericRightNorm| |varselect| |Vectorise| |numberOfOperations| - |unit?| |directSum| |orbits| |Si| |symbol| |divideIfCan| - |clearTheIFTable| |maxRowIndex| |dimensionsOf| |OMgetEndError| - |listRepresentation| |getProperties| |e04gcf| |LyndonWordsList| - |unitCanonical| |rationalIfCan| |typeList| |rootSimp| |curve| |s18aff| - |OMputEndBind| |finiteBasis| |symbolTable| |setelt!| |clearCache| - |integer| |getMatch| |OMputObject| |interpretString| - |chainSubResultants| |minGbasis| |imagE| |minus!| - |quasiMonicPolynomials| |tablePow| |antiAssociative?| * |nor| - |lazyPseudoDivide| |nand| |pushFortranOutputStack| - |complexEigenvectors| |printTypes| |fractionFreeGauss!| - |rewriteSetWithReduction| |pushuconst| |approxNthRoot| |increment| - |nextSublist| |var1Steps| |minPol| |expandPower| |drawStyle| - |popFortranOutputStack| |mindegTerm| |permutationGroup| |select!| - |e02zaf| |addiag| |finiteBound| |conditionP| |mat| |roughBase?| - |outputAsFortran| |setlast!| |lazyIntegrate| |e02def| |cardinality| - |coleman| |term?| |fortranDouble| |nextColeman| |errorKind| - |pointColorDefault| |pleskenSplit| |numberOfCycles| |resetBadValues| - |SturmHabicht| |represents| SEGMENT |hexDigit| |iicos| |OMReadError?| - |denominator| |leader| |univariate?| |integrate| |genericLeftTrace| - |BumInSepFFE| |zeroVector| |s13acf| |calcRanges| |returns| - |OMunhandledSymbol| |createPrimitiveElement| |pushNewContour| - |pointColorPalette| |solveid| |s21bdf| |lighting| |printInfo| - |companionBlocks| |dictionary| |addBadValue| |hermiteH| - |totalGroebner| |approxSqrt| |sinhcosh| |kroneckerDelta| |cSinh| - |generator| |LiePolyIfCan| |secIfCan| |separate| |quotient| |cCos| - |exponential1| |chebyshevU| |cons| |insert!| |curveColorPalette| - |setScreenResolution| |cAsin| |Frobenius| |d01akf| |setfirst!| - |postfix| |wholePart| |topPredicate| |c06fqf| |OMclose| |divide| - |coth2tanh| |operation| |d02gbf| |PollardSmallFactor| |SFunction| - |queue| |mathieu23| |OMserve| |subset?| |perfectSquare?| - |semiIndiceSubResultantEuclidean| |retract| |LowTriBddDenomInv| - |plotPolar| |graeffe| |returnTypeOf| |resultantReduitEuclidean| - |bombieriNorm| |tubeRadiusDefault| |e01sff| |radix| |s18def| - |linkToFortran| |rightUnits| |ptFunc| |decimal| |quickSort| - |bernoulli| |ffactor| |changeBase| |parabolic| - |getMultiplicationMatrix| |scale| |integralBasisAtInfinity| - |clipPointsDefault| |nullSpace| |range| |Lazard2| |makeFloatFunction| - |rootNormalize| |contract| |s17def| |bandedHessian| |e01bhf| |modulus| - |prepareSubResAlgo| |zag| |vector| |removeConstantTerm| - |evaluateInverse| |clikeUniv| |ruleset| |untab| |extendedIntegrate| - |retractIfCan| |idealSimplify| |lo| |OMputEndAtp| |nlde| |enumerate| - |differentiate| |viewThetaDefault| |traverse| |rangeIsFinite| - |normalizedDivide| |pmintegrate| |e02dcf| |incr| |pile| |setValue!| - |wholeRagits| |SturmHabichtMultiple| |semiSubResultantGcdEuclidean1| - |radicalEigenvalues| |zeroDim?| |bfKeys| |hi| |stoseInvertible?reg| - |iiacsc| |d03eef| |aQuadratic| |alternating| |rightUnit| |moebiusMu| - |suchThat| |linear| |discriminant| |pdf2df| |wronskianMatrix| - |numberOfComponents| |outputForm| |numberOfMonomials| |leaf?| |qroot| - |tensorProduct| |regime| |c06eaf| |bat| |monomRDE| |cycleEntry| - |semiResultantEuclidean2| |stoseInternalLastSubResultant| - |completeSmith| |polynomial| |stack| |lllip| |limitedIntegrate| - |f02akf| |genericRightTraceForm| - |solveLinearPolynomialEquationByRecursion| |light| - |definingInequation| |primlimintfrac| |cot2trig| |partialDenominators| - |rectangularMatrix| |selectFiniteRoutines| |palglimint0| |s21bbf| - |points| |cartesian| |setAttributeButtonStep| |singleFactorBound| - |ParCond| |lfextlimint| |f01qcf| |uniform01| |pointSizeDefault| - |preprocess| |e02bdf| |problemPoints| |hasPredicate?| - |roughUnitIdeal?| |sup| |overlabel| |extractSplittingLeaf| |Beta| - |OMencodingBinary| |completeEchelonBasis| |sub| |integralMatrix| - |clearDenominator| |trapezoidalo| |degreeSubResultant| - |solveLinearlyOverQ| |diag| |primextendedint| |curve?| |unravel| |map| - |integralAtInfinity?| |squareFree| |imagj| |commonDenominator| - |setColumn!| |cyclicSubmodule| |eigenvalues| |exQuo| - |removeRedundantFactorsInPols| |f01mcf| |real?| |factorList| |randomR| - |realElementary| |iitanh| |stop| |saturate| - |halfExtendedSubResultantGcd2| |reverse| |and?| - |exprHasAlgebraicWeight| |hspace| |removeCoshSq| |normFactors| - |charClass| |yCoord| |useNagFunctions| |/\\| |complexLimit| |dmp2rfi| - |f02aaf| |mathieu12| |leftExtendedGcd| |pascalTriangle| |meshFun2Var| - |selectSumOfSquaresRoutines| |cond| |plenaryPower| |\\/| - |solveLinearPolynomialEquation| |child?| |permutation| |generate| - 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|sort!| |iisinh| |flexible?| + |fortranCompilerName| |fibonacci| |explogs2trigs| |Ei| + |radicalEigenvalues| |bivariatePolynomials| |sturmSequence| + |shanksDiscLogAlgorithm| |mr| |deepestInitial| |basicSet| |exprToUPS| + |debug| |mesh| |zeroDim?| |factor1| |leftQuotient| |choosemon| + |digit?| |paraboloidal| |delete!| |nextsubResultant2| + |screenResolution| |f04adf| |bfKeys| |contains?| RF2UTS |removeSinSq| + |ran| |nextSubsetGray| |minRowIndex| |normalizeAtInfinity| |tanSum| + |OMUnknownSymbol?| |stoseInvertible?reg| |internalZeroSetSplit| + |jordanAdmissible?| |cTan| |factorOfDegree| |recur| |leftAlternative?| + |bitTruth| |iiacsc| |rowEchelon| |iflist2Result| ~= |orbit| |rational| + |s15aef| |OMgetFloat| |palgint| |addMatchRestricted| |d03eef| + |lexGroebner| |viewpoint| |elementary| |coerce| |alphabetic?| + |sts2stst| |replace| |integralLastSubResultant| |goodPoint| |dihedral| + |particularSolution| |expintegrate| |aQuadratic| |leaves| |lo| + |optpair| |construct| |computePowers| 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|hypergeometric0F1| |block| |constant?| |cCsc| |bat| |alphabetic| + |probablyZeroDim?| |setelt| |curryLeft| |leadingExponent| |maxrank| + |append| |fortranCharacter| |firstSubsetGray| |null| |monomRDE| + |mapUnivariate| |incrementBy| |point?| |limit| |key?| |norm| |node| + |d02kef| |mainMonomials| |cycleEntry| |case| |iExquo| |expand| |parts| + |complexIntegrate| |plusInfinity| |copy| |copies| |bsolve| + |totalDegree| |printStatement| |Zero| |semiResultantEuclidean2| + |quasiRegular| |mainDefiningPolynomial| |filterWhile| + |trailingCoefficient| |hyperelliptic| |gcdprim| |isQuotient| + |identitySquareMatrix| |genericRightDiscriminant| |dec| |One| + |stoseInternalLastSubResultant| |setImagSteps| |filterUntil| + |enterPointData| |algebraicOf| |pushdterm| |outputAsTex| |lhs| + |argumentList!| |subResultantGcdEuclidean| |completeSmith| |select| + |unexpand| |putColorInfo| |isAbsolutelyIrreducible?| |doubleRank| + |quadratic| |rhs| |generalTwoFactor| |equiv| |lllip| |hessian| + |separant| |FormatRoman| |padicFraction| |getMeasure| + |limitedIntegrate| |endSubProgram| |stoseSquareFreePart| + |computeBasis| |iiacos| |rst| |printHeader| |hdmpToDmp| |cyclic| + |f02akf| |read!| |d02bhf| |nonQsign| |generic?| + |countRealRootsMultiple| |height| |e| |froot| |genericRightTraceForm| + |elt| |polygon| |structuralConstants| |setFieldInfo| |noLinearFactor?| + |charthRoot| |minrank| |externalList| |createPrimitivePoly| + |solveLinearPolynomialEquationByRecursion| |primeFactor| |equation| + |KrullNumber| |rightRegularRepresentation| |rCoord| |sylvesterMatrix| + |simpson| |light| |makeRecord| |diagonal?| |decrease| + |stripCommentsAndBlanks| |bindings| |polygamma| + |halfExtendedSubResultantGcd1| |definingInequation| |exactQuotient!| + |eigenvectors| |mirror| |complement| |df2ef| |f01qef| + |dimensionOfIrreducibleRepresentation| |primlimintfrac| |denomRicDE| + |makeGraphImage| |nthRoot| |coerceL| |functionIsFracPolynomial?| + |testDim| |sinhIfCan| |associative?| |scalarMatrix| |split| + |repeating| |factorSquareFree| |parent| |curveColorPalette| + |branchIfCan| |assign| |findBinding| |rootSplit| |c06gbf| |listLoops| + |laurentIfCan| |presuper| |setScreenResolution| |createThreeSpace| + |ScanFloatIgnoreSpaces| |dim| |times!| |f02adf| |noKaratsuba| |qelt| + |concat!| |cAsin| |asechIfCan| |internalSubPolSet?| |iisqrt3| + |initializeGroupForWordProblem| |differentialVariables| |droot| + |Frobenius| |resultantEuclidean| |evenInfiniteProduct| |constDsolve| + |euclideanNormalForm| |OMgetString| |xRange| |list?| + |parabolicCylindrical| |d01akf| |perfectSqrt| |e04fdf| UP2UTS + |schwerpunkt| |algint| |getSyntaxFormsFromFile| |yRange| |s18dcf| + |setfirst!| |symbol?| |overset?| |getRef| |property| |latex| |open?| + |postfix| |zRange| |usingTable?| |lazyIrreducibleFactors| |fortran| + |frobenius| |partialQuotients| |mapExponents| |oddlambert| |map!| + |s17dgf| |dfRange| |wholePart| |realZeros| |subCase?| |OMgetEndApp| + |alternative?| |createLowComplexityNormalBasis| |lowerCase| |qsetelt!| + |OMgetEndAtp| |paren| |topPredicate| |negative?| |subSet| + |rightTraceMatrix| |lookup| |units| |primextintfrac| |tan2cot| + |incrementKthElement| |leftUnits| |c06fqf| |mesh?| |setVariableOrder| + |internalIntegrate0| |radicalSimplify| |redPo| + |purelyAlgebraicLeadingMonomial?| + |rewriteIdealWithQuasiMonicGenerators| |OMclose| |cycleSplit!| + |writable?| |maxPoints3D| |bfEntry| |getlo| |setRow!| |jacobi| + |minColIndex| |divide| |coefficient| |leftDiscriminant| + |resultantReduit| |tanIfCan| |selectODEIVPRoutines| |lyndonIfCan| + |sin2csc| |mapSolve| |e02baf| |coth2tanh| |OMsetEncoding| |implies?| + |lowerCase?| |normalise| |removeSinhSq| |colorDef| |extendedEuclidean| + |d02gbf| |acsch| |polyRDE| |lift| |exactQuotient| |mapmult| |e02gaf| + |code| |lazyPquo| |mapExpon| |OMwrite| |comment| |mapBivariate| + |cot2tan| |PollardSmallFactor| |reduce| |gderiv| |coth2trigh| + |substring?| |drawCurves| |rotatey| |selectMultiDimensionalRoutines| + |subQuasiComponent?| |HermiteIntegrate| |SFunction| |corrPoly| |polar| + |log2| |pToHdmp| |arg1| |squareMatrix| |generalizedEigenvector| + |s17akf| |arguments| |simplifyPower| |irreducibleFactor| |queue| + |lfintegrate| |numberOfComputedEntries| |identity| |suffix?| |f2df| + |arg2| |makeTerm| |setPoly| |computeCycleLength| |laplace| |mathieu23| + |fractRagits| |predicate| |extensionDegree| |solveRetract| |interval| + |skewSFunction| |e01sef| |shift| |getProperty| + |createMultiplicationMatrix| |OMserve| |script| + |showFortranOutputStack| |e04dgf| |eigenvector| |prefix?| |second| + |groebgen| |conditions| |e01bgf| |magnitude| |numberOfFactors| + |laguerreL| |subset?| |nthCoef| |currentSubProgram| |idealiserMatrix| + |third| |multinomial| |match| |complex?| |changeVar| |rk4qc| + |perfectSquare?| |expint| |d01apf| |getCurve| |messagePrint| + |polygon?| |branchPoint?| |laguerre| |internalAugment| + |semiIndiceSubResultantEuclidean| |triangular?| |tex| + |multiEuclideanTree| |normalDeriv| |operators| |pop!| + |selectOrPolynomials| |shiftRight| |numeric| |extractPoint| + |modifyPoint| |LowTriBddDenomInv| + |generalizedContinuumHypothesisAssumed?| |setOrder| |iiGamma| |s17adf| + |semiSubResultantGcdEuclidean2| |linearPolynomials| |radical| |wreath| + |nthFactor| |plotPolar| |nullary?| |equivOperands| |processTemplate| + |rootKerSimp| |diagonalProduct| |stronglyReduced?| |style| |graeffe| + |rk4f| |exists?| |parametersOf| |infix?| |insertMatch| |tail| |mix| + |reorder| |numFunEvals3D| |factorSquareFreeByRecursion| |limitedint| + |returnTypeOf| |iiatanh| |addPointLast| |mask| |leftPower| |stirling1| + |integralDerivationMatrix| |OMputEndObject| |parameters| + |rightCharacteristicPolynomial| |reducedSystem| + |resultantReduitEuclidean| |internalLastSubResultant| |connect| + |binaryFunction| |supRittWu?| |weakBiRank| + |stiffnessAndStabilityFactor| |tryFunctionalDecomposition?| + |bombieriNorm| |compBound| |index?| |pair?| + |removeIrreducibleRedundantFactors| |idealiser| |clearTheFTable| + |ratDsolve| |f01ref| |rightRemainder| |tubeRadiusDefault| |e01sbf| + |var1StepsDefault| |algSplitSimple| |expextendedint| |eq?| + |numericalOptimization| |say| |rk4a| |adaptive| |e01sff| + |indiceSubResultant| |geometric| |eigenMatrix| |characteristicSet| + |routines| |lquo| |flatten| |subscript| |radix| |currentCategoryFrame| + |dmpToP| |chiSquare1| |precision| |isobaric?| |exp1| |forLoop| + |graphImage| |formula| |iisec| |s18def| |controlPanel| |tubeRadius| + |getOperator| |d02raf| |readable?| |doublyTransitive?| |setFormula!| + |zeroMatrix| |list| |linkToFortran| |infRittWu?| |binarySearchTree| + |coerceS| |csch| |denomLODE| |any?| |over| |child| |character?| |car| + |log| |rightUnits| |deriv| |setButtonValue| |f02aff| |asinh| |rules| + |triangularSystems| |ode1| |printCode| |minset| |predicates| |cdr| + |curveColor| |ptFunc| |s20acf| |nextLatticePermutation| |acosh| + |createIrreduciblePoly| |OMlistCDs| |leastPower| |setCondition!| + |setDifference| |minPoints| |decimal| |createMultiplicationTable| + |bipolarCylindrical| |cyclicEqual?| |atanh| |tracePowMod| |label| + |monicRightFactorIfCan| |unit| |adjoint| |setIntersection| |pushdown| + |extractBottom!| |quickSort| |arrayStack| FG2F |acoth| + |functionIsContinuousAtEndPoints| |complexNumeric| |trivialIdeal?| + |scalarTypeOf| |moreAlgebraic?| |outerProduct| |setUnion| + |cyclicGroup| |totalLex| |bernoulli| |semiResultantEuclidean1| |ode| + |asech| |antiCommutative?| |viewPosDefault| |binaryTournament| + |digamma| |generalSqFr| |apply| |ffactor| |term| |ref| + |makeViewport2D| |generalizedInverse| |kernels| |prinpolINFO| + |algintegrate| |seriesToOutputForm| |solve1| |changeBase| |shade| + |anfactor| |e04ycf| |int| |linears| |univariate| |doubleDisc| + |showTheRoutinesTable| |parabolic| |colorFunction| |concat| |size| + |printInfo| |comp| |shallowCopy| |OMputInteger| |rotate| |s21baf| + |title| |shuffle| |f01rcf| |outputAsScript| |setErrorBound| + |drawComplex| |getMultiplicationMatrix| |An| |coordinate| + |inverseIntegralMatrixAtInfinity| |bipolar| |primintegrate| |symbol| + |linear?| |indiceSubResultantEuclidean| |bag| |scale| |ricDsolve| + |OMopenFile| |checkRur| |weighted| ^ |factor| |binary| |power| + |loopPoints| |first| |integralBasisAtInfinity| |explicitlyFinite?| + |getDatabase| |viewWriteAvailable| |any| |integer| |rightGcd| + |acscIfCan| |sqrt| |symmetricGroup| |areEquivalent?| |lfunc| |rest| + |validExponential| |clipPointsDefault| |f07adf| |karatsubaOnce| + |polyRicDE| |addmod| |real| |number?| |acotIfCan| |ef2edf| + |substitute| |failed| |nullSpace| |initials| |iiasinh| + |factorsOfCyclicGroupSize| |upperCase!| |imag| |e02ajf| + |argumentListOf| |removeDuplicates| |rangePascalTriangle| |range| + |powern| |badNum| |setPrologue!| |prem| |directProduct| |setrest!| + |bezoutResultant| |tab1| |hue| |cSech| |Lazard2| + |generalizedContinuumHypothesisAssumed| |readLine!| |extractTop!| + |c06gsf| |createLowComplexityTable| |OMsend| |entry| |superscript| + |makeFloatFunction| |subResultantGcd| |dequeue| + |indicialEquationAtInfinity| |complete| |destruct| |initiallyReduced?| + |palginfieldint| |OMgetSymbol| |nary?| |rootNormalize| + |genericLeftMinimalPolynomial| |integralBasis| |rightLcm| + |defineProperty| |stiffnessAndStabilityOfODEIF| + |removeRoughlyRedundantFactorsInPol| |constant| + |numberOfFractionalTerms| |contract| |sinIfCan| ** |shrinkable| + |removeRedundantFactorsInContents| |viewSizeDefault| |find| + |flexibleArray| |internalInfRittWu?| |var2Steps| |autoCoerce| |remove| + |s17def| |imagi| |normalizedAssociate| |dimensions| |tanQ| |optional?| + |shellSort| |tryFunctionalDecomposition| |univariatePolynomialsGcds| + |bandedHessian| |padecf| |iiexp| |unrankImproperPartitions0| + |mainVariable?| |unary?| |implies| EQ |setOfMinN| |erf| |addPoint2| + |last| |indices| |e01bhf| |makeEq| |consnewpol| |power!| |iomode| + |gethi| |curryRight| |xor| |unitNormal| |assoc| |modulus| |color| + |e01baf| |mainCharacterization| |createZechTable| |prindINFO| |maxint| + |OMopenString| |iCompose| |prepareSubResAlgo| |tan2trig| |lazyPrem| + |axes| |c06gcf| |OMUnknownCD?| |prolateSpheroidal| |reset| + |viewport3D| |powerSum| |constantToUnaryFunction| |maxIndex| |middle| + |headReduced?| |nonSingularModel| |symmetricProduct| |commutative?| + |top!| |addiag| |lyndon| |diff| |mainKernel| |harmonic| |condition| + |write| |push!| |cycleTail| |slash| |integerBound| |finiteBound| + |f02xef| |primPartElseUnitCanonical| |prefixRagits| |pole?| + |rootRadius| |zeroSetSplit| |meatAxe| |conditionP| |tValues| + |specialTrigs| |sinh2csch| |getZechTable| |interReduce| |call| |mat| + |stoseInvertible?| ~ |zero?| |polyPart| |normalized?| |lfextendedint| + |purelyTranscendental?| |OMputAttr| |enterInCache| |elRow1!| + |roughBase?| |children| |mkIntegral| |OMputSymbol| + |sizeMultiplication| |length| |BasicMethod| + |primPartElseUnitCanonical!| |smith| |inRadical?| |reindex| |setlast!| + |build| |torsionIfCan| |scripts| |factorset| |plot| |hconcat| + |string?| |Hausdorff| |relerror| |lazyIntegrate| |entry?| |varList| + |iiacosh| |realEigenvalues| |setAdaptive3D| |element?| |e02def| + |degree| |subMatrix| |OMputBVar| |rightExactQuotient| |quadraticForm| + |nodeOf?| |graphState| |open| |splitNodeOf!| |cardinality| + |fortranLiteralLine| |Lazard| |getOperands| |rspace| + |stoseLastSubResultant| |ldf2vmf| |toseInvertibleSet| |extension| + |result| |wordsForStrongGenerators| |coleman| |ord| + |getMultiplicationTable| |integral| |doubleResultant| |coefChoose| + |cyclicEntries| |close!| |s19adf| |term?| |leftNorm| + |factorGroebnerBasis| |rationalPoint?| |radicalRoots| |write!| + |f04qaf| |match?| |generalPosition| |fortranDouble| |matrixConcat3D| + |ranges| |characteristicSerie| |eyeDistance| |LyndonCoordinates| + |coord| |expr| |symFunc| |leftExactQuotient| |bitLength| |nextColeman| + |increase| |reseed| |e04ucf| |localUnquote| |has?| |abs| |uniform| + |OMputApp| |errorKind| |makeResult| |B1solve| |reduceLODE| |s14aaf| + |startPolynomial| |monomial?| |repeating?| |normal?| + |pointColorDefault| |genericLeftTraceForm| |mainVariables| |cscIfCan| + |OMgetEndAttr| |collectUpper| |LazardQuotient| |functionIsOscillatory| + |outputList| |pleskenSplit| |stronglyReduce| |conjug| + |transcendentalDecompose| |infiniteProduct| |red| |normalize| + |sumOfKthPowerDivisors| |variable| |OMgetEndObject| |numberOfCycles| + |bivariateSLPEBR| |iidsum| |totalDifferential| |bivariate?| + |mathieu22| |s17ahf| |floor| |rootsOf| |resetBadValues| |determinant| + |leadingIdeal| |nextItem| |biRank| |groebSolve| |algDsolve| + |collectUnder| |optimize| |vark| |SturmHabicht| |create3Space| + |normalDenom| |continuedFraction| |computeInt| |s17dcf| |realRoots| + |complexForm| |e01bff| |represents| |symmetricRemainder| |s01eaf| + |sylvesterSequence| |plus| |inconsistent?| |associator| + |bezoutDiscriminant| |definingPolynomial| |outputGeneral| |hexDigit| + |coshIfCan| |rootPoly| |quasiRegular?| |resetNew| |one?| |OMgetBind| + |airyBi| |showArrayValues| |init| |iicos| |nextNormalPrimitivePoly| + |algebraicCoefficients?| |graphs| |leftUnit| |monicLeftDivide| + |changeThreshhold| |head| |f01rdf| |OMReadError?| |cycleLength| + |balancedBinaryTree| |pushucoef| |sizeLess?| |iifact| + |mergeDifference| |isExpt| |symmetricTensors| |musserTrials| + |denominator| |iiatan| |extendedResultant| |times| |adaptive?| + |errorInfo| |f01qdf| |nthExpon| |associates?| |univariate?| + |transcendent?| |lieAlgebra?| |d03edf| |iilog| |tubePoints| + |infieldIntegrate| |variationOfParameters| |#| |normalizeIfCan| |eval| + |drawToScale| |integrate| |solid| |singularAtInfinity?| |mpsode| + |tanNa| |semiDiscriminantEuclidean| |findCycle| |UnVectorise| + |genericLeftTrace| |airyAi| |exprex| |listBranches| |f2st| |row| |cup| + |nextPrimitiveNormalPoly| |deepCopy| |edf2efi| |BumInSepFFE| + |bezoutMatrix| |rightOne| |dflist| |monom| |cyclicParents| |root| + |multiplyCoefficients| |exponential| |zeroVector| |besselY| |heapSort| + |returnType!| |nthFractionalTerm| |Gamma| |iFTable| + |reduceByQuasiMonic| |eq| |box| |lambda| |symmetricSquare| |s13acf| + |subPolSet?| |po| |split!| |slex| |conical| |swapRows!| + |quasiComponent| |iter| |addMatch| |rightQuotient| |calcRanges| + |rationalPoints| |shiftRoots| |common| |coHeight| |leftLcm| + |diagonalMatrix| |updateStatus!| |width| |euler| |returns| |powers| + |numericIfCan| |extractClosed| |makeFR| |d01ajf| |redPol| + |listConjugateBases| |janko2| |iisin| |OMunhandledSymbol| |qPot| + |lexico| |minimalPolynomial| |op| |triangulate| |unitNormalize| + |evenlambert| |commutator| |createPrimitiveElement| |safeCeiling| + |iiacot| |meshPar2Var| |headReduce| |evaluate| |oneDimensionalArray| + |nthExponent| |level| |spherical| |moduloP| |pushNewContour| + |integralCoordinates| |coordinates| |reducedContinuedFraction| + |ellipticCylindrical| D |eulerPhi| |nextPartition| |insert| + |acothIfCan| |pointColorPalette| |compound?| |gcdcofact| |normalForm| + |cSec| |central?| |rightTrace| |LyndonBasis| |exp| |optional| + |rischDEsys| |solveid| |c02agf| |regularRepresentation| |s17agf| + |imagK| |rightDivide| |domainOf| |nodes| |supDimElseRittWu?| + |alphanumeric?| |s21bdf| |fTable| |cCoth| |printingInfo?| + |fortranInteger| |hex| |refine| |numerators| |nonLinearPart| + |lighting| |palgextint| |setClosed| |operator| |hasTopPredicate?| + |reopen!| |makeYoungTableau| |double| |myDegree| |numberOfDivisors| + |companionBlocks| |setleft!| |partialFraction| |setStatus| + |linearPart| |traceMatrix| |initiallyReduce| + |basisOfCommutingElements| |s17dlf| |dictionary| |eulerE| |minIndex| + |multiple| |outputArgs| |createNormalPrimitivePoly| + |associatorDependence| |xCoord| |applyQuote| |OMputAtp| + |OMconnOutDevice| |addBadValue| |innerEigenvectors| |OMputEndApp| + |retractable?| |roughBasicSet| |numberOfHues| |identification| |expt| + |f02wef| |hermiteH| |discreteLog| |fortranReal| |expintfldpoly| + |iprint| |hasSolution?| |square?| |sum| |dom| |rightMinimalPolynomial| + |totalGroebner| |fintegrate| |LagrangeInterpolation| |ParCondList| + |nextPrime| |fixedPoints| |print| |RittWuCompare| |lex| |coerceP| + |innerSolve| |approxSqrt| |unaryFunction| |ruleset| |initTable!| + |allRootsOf| |iitan| |invertIfCan| |trigs| |zerosOf| |thetaCoord| + |sinhcosh| |mapGen| |tanhIfCan| |expenseOfEvaluationIF| |cAtanh| + |transcendenceDegree| |declare!| |df2st| |kroneckerDelta| + |euclideanGroebner| |OMgetType| |rischDE| |inGroundField?| + |intermediateResultsIF| |iicoth| |triangSolve| |cSinh| + |solveLinearPolynomialEquationByFractions| |fglmIfCan| |OMcloseConn| + |normDeriv2| |suchThat| |separateDegrees| |univariatePolynomial| + |weight| |module| |sortConstraints| |jordanAlgebra?| |LiePolyIfCan| + |fortranTypeOf| |readIfCan!| |rational?| GE |nthRootIfCan| |extract!| + |prime?| |secIfCan| |more?| |monicDivide| |extend| |backOldPos| GT + |monicModulo| |explicitlyEmpty?| |multiple?| |iiasin| |maxColIndex| + |separate| |removeSuperfluousQuasiComponents| |compose| |isPower| LE + |fractRadix| |hexDigit?| |supersub| |binaryTree| |quotient| |cycle| + |minimumExponent| |lazyPseudoQuotient| |complexEigenvalues| LT + |showAll?| |numericalIntegration| |numFunEvals| |constructorName| + |f02axf| |cCos| |pseudoQuotient| |besselK| |viewZoomDefault| |quoted?| + |cycleRagits| |reduced?| |invmultisect| |superHeight| |exponential1| + |modularFactor| |goodnessOfFit| |mainMonomial| |blue| |notOperand| + |degreeSubResultantEuclidean| |divisorCascade| |stirling2| + |chebyshevU| |separateFactors| |even?| |cylindrical| |pushup| |pade| + |cycles| |completeEval| |coerceListOfPairs| |insert!| |factorials| + |figureUnits| |critB| |solve| |leadingCoefficientRicDE| + |contractSolve| |imagI| |outputMeasure| |completeHensel| + |commutativeEquality| |bernoulliB| |gcdPolynomial| + |monicCompleteDecompose| |subresultantSequence| |setTopPredicate| + |selectIntegrationRoutines| |polarCoordinates| |move| + |lastSubResultantEuclidean| |startStats!| |factorAndSplit| + |invertibleSet| |rootProduct| |genericRightNorm| |tableau| + |sumOfSquares| |or| |conjugates| |upperCase| |expPot| |primlimitedint| + |c05nbf| |segment| |primes| |varselect| |UpTriBddDenomInv| |reflect| + |space| |and| |startTable!| |purelyAlgebraic?| |toseSquareFreePart| + |Vectorise| |medialSet| |complementaryBasis| |shufflein| |function| + |polyred| |univcase| |max| |removeCoshSq| |fixedPointExquo| NOT + |exteriorDifferential| |numberOfOperations| |mainContent| + |setMaxPoints3D| |rquo| |ratPoly| |insertBottom!| |atanIfCan| + |normFactors| |point| OR |lastSubResultant| |unit?| |makeViewport3D| + |c06gqf| |torsion?| |createGenericMatrix| |brillhartIrreducible?| + |charClass| |leastAffineMultiple| AND |contours| |directSum| + |rdregime| |status| |atom?| |antisymmetricTensors| |packageCall| + |yCoord| |cAsinh| |makeSeries| |orbits| |jacobiIdentity?| |imagJ| + |intersect| |useNagFunctions| |belong?| |series| |lagrange| |e02ahf| + |Si| |cross| |outputSpacing| |s19acf| |semiResultantReduitEuclidean| + |pointLists| |iiasech| |complexLimit| |infinite?| |mapUp!| + |divideIfCan| |sqfree| |trim| |quatern| |baseRDEsys| |dmp2rfi| + |henselFact| |subHeight| |groebnerFactorize| |clearTheIFTable| + |newReduc| |linearDependenceOverZ| |internalDecompose| + |leadingSupport| |rootOfIrreduciblePoly| |f02aaf| |stFuncN| |digits| + |nullary| |maxRowIndex| |c06ecf| |atrapezoidal| |interpret| |sincos| + |palgRDE0| |lyndon?| |mathieu12| |min| |rationalApproximation| + |laplacian| |dimensionsOf| |patternMatchTimes| |upDateBranches| + |extractIndex| |FormatArabic| |acosIfCan| |leftMinimalPolynomial| + |leftExtendedGcd| |cSin| |nil?| |unparse| |OMgetEndError| |iroot| + |d02cjf| |solveLinear| |quoByVar| |createPrimitiveNormalPoly| + |pascalTriangle| |numberOfPrimitivePoly| |mapCoef| |f07fef| + |listRepresentation| |drawComplexVectorField| |getBadValues| + |position!| |primintfldpoly| |meshFun2Var| |vconcat| |makeSin| * + |characteristic| |resetAttributeButtons| |getProperties| |c06fpf| + |truncate| |safetyMargin| |lcm| |string| |chiSquare| + |explicitEntries?| |selectSumOfSquaresRoutines| + |ScanFloatIgnoreSpacesIfCan| |commaSeparate| |e04gcf| |remove!| + |lexTriangular| |showRegion| |cExp| |cAcot| |plenaryPower| |s17aff| + |setEmpty!| |d01asf| |balancedFactorisation| |LyndonWordsList| + |increasePrecision| |andOperands| |SturmHabichtSequence| |tanh2coth| + |quadraticNorm| |solveLinearPolynomialEquation| |basisOfNucleus| + |setAdaptive| |splitLinear| |unitCanonical| |exponentialOrder| + |epilogue| |taylorQuoByVar| |gcd| |systemSizeIF| |sturmVariationsOf| + |child?| |dimension| |cyclotomic| |numer| |rationalIfCan| + |univariateSolve| |removeRoughlyRedundantFactorsInPols| |empty| + |union| |check| |setprevious!| |brace| |permutation| |diagonal| + |genus| |rewriteSetByReducingWithParticularGenerators| |denom| + |rightFactorCandidate| |typeList| |factorByRecursion| |taylorIfCan| + |ptree| |false| |absolutelyIrreducible?| |sorted?| + |numberOfComposites| |lineColorDefault| |randomLC| + |generalizedEigenvectors| |rootSimp| |makingStats?| |inverseLaplace| + |argscript| |d02ejf| |quadratic?| |beauzamyBound| |mkAnswer| |hclf| + |f04atf| |pi| |curve| |largest| |logGamma| |OMencodingXML| |besselI| + |degreePartition| |leftCharacteristicPolynomial| |f04asf| |conjugate| + |infinity| |irreducibleFactors| |s18aff| |rroot| |d01fcf| + |extendIfCan| |setTex!| |d01gaf| |value| |omError| |high| |cAcoth| + |hermite| |expenseOfEvaluation| |OMputEndBind| |chvar| + |countRealRoots| |every?| |lfinfieldint| |pdf2ef| |mainPrimitivePart| + |UP2ifCan| |update| |zeroSetSplitIntoTriangularSystems| |finiteBasis| + |hcrf| |zeroDimPrimary?| |halfExtendedResultant2| |redmat| + |printStats!| |randnum| |maxrow| |makeprod| |dn| |kernel| |distFact| + |setelt!| |elem?| |showScalarValues| |bits| |rightPower| + |splitSquarefree| |aromberg| |subtractIfCan| |draw| |clipBoolean| + |s13aaf| |getMatch| |rightMult| |region| |writeLine!| |euclideanSize| + |OMreceive| |whatInfinity| |intcompBasis| |btwFact| |edf2fi| + |OMputObject| |f02awf| |showClipRegion| |showTypeInOutput| |member?| + |scaleRoots| |pseudoRemainder| |expIfCan| |e01saf| |Aleph| + |interpretString| |firstDenom| |numberOfChildren| + |generalInfiniteProduct| |leftMult| |credPol| |binomial| |s14abf| + |order| |OMgetAttr| |chainSubResultants| |expandLog| |realSolve| + |singRicDE| |sdf2lst| |setProperties| |integers| |OMputString| SEGMENT + |makeObject| |position| |algebraicSort| |minGbasis| + |clearTheSymbolTable| |sayLength| |singular?| |delay| + |derivationCoordinates| |trace2PowMod| |sizePascalTriangle| + |factorial| |error| |ListOfTerms| |imagE| |simplify| |setClipValue| + |e02agf| |legendreP| |selectPolynomials| |critMonD1| |monomRDEsys| + |transform| |cn| |assert| |headRemainder| |coef| |minus!| + |getExplanations| |plus!| |isPlus| |squareFreeFactors| + |primitivePart!| |OMgetEndBVar| |sign| |divisor| |directory| |f02fjf| + |basisOfCenter| |quasiMonicPolynomials| |removeSuperfluousCases| + |stoseInvertible?sqfreg| |leftFactor| |factors| |recoverAfterFail| + |birth| |subNode?| |getPickedPoints| |multiEuclidean| |tablePow| + |cAcsc| |complexNormalize| |setMinPoints3D| |positiveRemainder| + |singularitiesOf| |viewDeltaXDefault| |safeFloor| |antiAssociative?| + |asinhIfCan| |lazy?| |retract| |deleteProperty!| |elRow2!| |mathieu11| + |bit?| |rootDirectory| |quotedOperators| |positiveSolve| |in?| + |noncommutativeJordanAlgebra?| |nor| |setMaxPoints| |yellow| |moebius| + |d02gaf| |SturmHabichtCoefficients| |nativeModuleExtension| |llprop| + |extractIfCan| |roughEqualIdeals?| |computeCycleEntry| + |lazyPseudoDivide| |decompose| |pointColor| |aQuartic| + |showIntensityFunctions| |infieldint| |hostPlatform| |freeOf?| + |variable?| |isTimes| F |cons| |constantOpIfCan| |enqueue!| |nand| + |save| |divideIfCan!| |removeZero| |tanAn| |userOrdered?| |totolex| + |rowEchelonLocal| |dominantTerm| |innerSolve1| |binomThmExpt| + |complexEigenvectors| |normal01| |mvar| |knownInfBasis| |complexRoots| + GF2FG |monomials| |denominators| |linSolve| |physicalLength!| + |printTypes| |distdfact| |fortranLiteral| |clipParametric| |d01amf| + |rank| |appendPoint| |f04mcf| |maxPoints| |escape| |overlap| + |fractionFreeGauss!| |patternVariable| |roughSubIdeal?| + |loadNativeModule| |back| |listexp| |toseInvertible?| |difference| + |simpsono| |product| |low| |rewriteSetWithReduction| |rightZero| + |maxdeg| |datalist| |multiplyExponents| |compiledFunction| |fracPart| + |newSubProgram| |currentScope| |setRealSteps| |pushuconst| + |prepareDecompose| |mkcomm| |permanent| |nextNormalPoly| |f04maf| + |sqfrFactor| |limitPlus| |twist| |makeCrit| |approxNthRoot| |e01bef| + |checkForZero| |viewDeltaYDefault| |primeFrobenius| |f01brf| + |OMsupportsCD?| |se2rfi| |associatedEquations| |increment| |anticoord| + |strongGenerators| |schema| |OMgetAtp| |prod| |reify| |f02abf| + |multisect| |f02ajf| |nextSublist| |stFunc1| |fillPascalTriangle| + |cAcsch| |dequeue!| |cycleElt| |lists| |sparsityIF| |matrixGcd| + |ratDenom| |var1Steps| |aspFilename| |rightDiscriminant| + |systemCommand| |e02aef| |htrigs| |checkPrecision| |changeMeasure| + |tower| |gradient| |whileLoop| |GospersMethod| |leftTrace| |matrix| + |minPol| |fixedPoint| |doubleFloatFormat| |pack!| + |lazyPremWithDefault| |antiCommutator| |bandedJacobian| |ReduceOrder| + |solid?| |integralMatrixAtInfinity| |minusInfinity| |expandPower| + |mindeg| |universe| |e04mbf| |cAtan| |primitiveElement| |getConstant| + |prologue| |basisOfLeftNucloid| |leftScalarTimes!| |generateIrredPoly| + |normal| |drawStyle| |sPol| |localIntegralBasis| |node?| |finite?| + |trapezoidal| |cschIfCan| |extendedint| |surface| |duplicates?| + |mindegTerm| |s20adf| |autoReduced?| |pquo| |OMgetEndBind| |setref| + |linear| |OMreadStr| |integer?| |permutationGroup| |listOfLists| + |objectOf| |arity| |midpoints| |exponents| |id| |OMputError| + |buildSyntax| |reverse| |sec2cos| |optAttributes| |select!| BY + |rationalPower| |leftZero| |fmecg| |accuracyIF| |s18aef| |center| + |cond| |positive?| |inverse| |polynomial| |lastSubResultantElseSplit| + |subresultantVector| |e02zaf| |squareFreePart| |setProperty| + |changeWeightLevel| |goto| |exprHasWeightCosWXorSinWX| |table| + |nilFactor| |graphCurves| |modifyPointData| |type| |getCode| |e02bcf| + |firstUncouplingMatrix| |nextPrimitivePoly| |resultantEuclideannaif| + |new| |permutations| |symmetric?| |rotatez| |sechIfCan| |c02aff| |is?| + |ignore?| |intChoose| |constantKernel| |insertRoot!| |doubleComplex?| + |inHallBasis?| |zeroDimensional?| |fullPartialFraction| + |topFortranOutputStack| |antisymmetric?| |bottom!| |f02bjf| |iiacoth| + |normalElement| |cyclePartition| |asecIfCan| |convergents| |isList| + |basisOfMiddleNucleus| |normInvertible?| |basis| |lazyResidueClass| + |inc| |mainSquareFreePart| |totalfract| |fi2df| |distance| + |LyndonWordsList1| |romberg| |orOperands| LODO2FUN |matrixDimensions| + |key| |create| |basisOfLeftNucleus| |cot2trig| |youngGroup| + |minPoints3D| |symbolTable| |float?| |merge| |top| + |complexNumericIfCan| |bumptab1| |divergence| |options| |kovacic| + |partialDenominators| |mainValue| |besselJ| + |semiLastSubResultantEuclidean| |dioSolve| |parametric?| |continue| + |lp| |OMmakeConn| |dihedralGroup| |d01gbf| |squareFreeLexTriangular| + |rectangularMatrix| |tanh2trigh| |divideExponents| |measure2Result| + |OMputVariable| |pushFortranOutputStack| |makeSUP| |linearMatrix| + |filename| |currentEnv| |ceiling| |selectFiniteRoutines| |shiftLeft| + |mapDown!| |popFortranOutputStack| |closed?| |OMgetApp| |Is| |augment| + |karatsuba| |coefficients| |null?| |palglimint0| |psolve| + |lazyPseudoRemainder| |exprToXXP| |useSingleFactorBound?| + |outputAsFortran| |showTheIFTable| |approximants| |realEigenvectors| + |basisOfCentroid| |not?| |bracket| |minimize| |s21bbf| |declare| + |dark| |polCase| |semiResultantEuclideannaif| |dot| |gcdcofactprim| + |iteratedInitials| |meshPar1Var| |parse| |left| |unitVector| + |intPatternMatch| |points| |halfExtendedResultant1| + |numberOfIrreduciblePoly| |multMonom| |component| |printInfo!| + |genericRightMinimalPolynomial| |presub| |right| |cartesian| + |cRationalPower| |stopTableGcd!| |unmakeSUP| |odd?| |critpOrder| + |npcoef| |e02bef| |s17ajf| |initial| |stopTable!| |cPower| + |setAttributeButtonStep| |critMTonD1| |e02daf| |debug3D| |lSpaceBasis| + |iicsc| |axesColorDefault| |gcdPrimitive| |stopTableInvSet!| + |elliptic?| |principal?| |zeroOf| |singleFactorBound| |complexSolve| + |possiblyNewVariety?| |iiacsch| |hdmpToP| |viewDefaults| |radPoly| + |imaginary| |opeval| |closedCurve?| |countable?| |ParCond| + |decreasePrecision| |diophantineSystem| |test| |ScanArabic| |cap| + |palgLODE| |f04mbf| |OMgetObject| |round| |groebner| |pattern| + |lfextlimint| |extendedSubResultantGcd| |integral?| |seed| + |selectPDERoutines| |recolor| |swapColumns!| |cAcos| |putGraph| + |getButtonValue| |monicDecomposeIfCan| |lieAdmissible?| |f01qcf| + |curry| |firstNumer| |useEisensteinCriterion?| |lepol| |redpps| + |constantIfCan| |intensity| |composite| |unvectorise| |isMult| + |uniform01| |rightRankPolynomial| |mulmod| |s19aaf| |output| + |screenResolution3D| |semiDegreeSubResultantEuclidean| |external?| + |pmComplexintegrate| |ipow| |OMencodingSGML| |shallowExpand| + |pointSizeDefault| |morphism| |leadingTerm| = |linGenPos| |nsqfree| + |stFunc2| |testModulus| |cubic| |radicalEigenvector| |compactFraction| + |tRange| |preprocess| |hash| |equality| |neglist| |s14baf| |qinterval| + |monomialIntPoly| |brillhartTrials| |lllp| |tree| |poisson| + |complexElementary| |e02bdf| |var2StepsDefault| |fortranComplex| + |e04jaf| < |vector| |getOrder| |remainder| |quasiAlgebraicSet| + |iiperm| |divisors| |entries| |push| |toroidal| |problemPoints| + |count| |alternatingGroup| |cothIfCan| > |primaryDecomp| + |linearlyDependentOverZ?| |linearDependence| |differentiate| + |ocf2ocdf| |replaceKthElement| |setLabelValue| |d01alf| + |hasPredicate?| |rightFactorIfCan| |ramifiedAtInfinity?| + |getVariableOrder| <= |leader| |ScanRoman| |cLog| |indicialEquations| + |zeroSquareMatrix| |pseudoDivide| |cCsch| |deleteRoutine!| + |roughUnitIdeal?| |unrankImproperPartitions1| |partialNumerators| + |transpose| >= |exquo| |mightHaveRoots| |associatedSystem| + |eisensteinIrreducible?| |ddFact| |quotientByP| |index| + |factorSFBRlcUnit| |quasiMonic?| |sup| |leftGcd| + |clearFortranOutputStack| |s15adf| |div| |representationType| |prime| + |oddintegers| |powmod| |maximumExponent| |OMputFloat| + |rightScalarTimes!| |overlabel| |tube| |generic| |decomposeFunc| |quo| + |root?| |applyRules| |rationalFunction| |binding| |edf2df| + |outlineRender| |body| |asinIfCan| |lifting1| |extractSplittingLeaf| + |f02bbf| |rarrow| + |newLine| |minimumDegree| |fullDisplay| |e02akf| + |asimpson| |clearCache| |pair| |wordInStrongGenerators| |s17acf| + |s18adf| |Beta| |hMonic| |stoseIntegralLastSubResultant| |rem| - + |roman| |cAsech| |csc2sin| |OMParseError?| |cfirst| + |combineFeatureCompatibility| |lazyVariations| |compile| |nil| + |OMencodingBinary| |pr2dmp| |OMbindTCP| |graphStates| / + |groebnerIdeal| |solveInField| |viewWriteDefault| |socf2socdf| + |insertionSort!| |df2fi| |vertConcat| |chebyshevT| + |completeEchelonBasis| |rotate!| |zoom| |OMputEndAttr| |constantLeft| + |radicalEigenvectors| |toScale| |rootBound| |ksec| + |expandTrigProducts| |irreducibleRepresentation| |sub| |zeroDimPrime?| + |partition| |leftRecip| |numberOfNormalPoly| |quote| |rootPower| + |dAndcExp| |heap| |integralMatrix| |infinityNorm| |d02bbf| + |laurentRep| |s18acf| |approximate| |getGoodPrime| |fractionPart| + |trunc| |iicosh| |scripted?| |d03faf| |complex| |rdHack1| + |clearDenominator| |lambert| |xn| |showAllElements| |crest| + |makeSketch| |sin?| |imagk| |gramschmidt| |pToDmp| |addPoint| + |trapezoidalo| |ridHack1| |squareFreePolynomial| |elements| + |nextsousResultant2| |outputFloating| |unitsColorDefault| |tubePlot| + |OMconnectTCP| |removeCosSq| |elColumn2!| |palgRDE| + |degreeSubResultant| |fill!| |multiset| |outputFixed| + |raisePolynomial| |setEpilogue!| |nextIrreduciblePoly| |cosSinInfo| + |inrootof| |message| |obj| |OMgetBVar| |c06frf| |solveLinearlyOverQ| + |qfactor| |OMgetInteger| |OMputBind| |cTanh| |subResultantChain| + |vedf2vef| |removeDuplicates!| |rubiksGroup| |orthonormalBasis| + |cache| |diag| |stoseInvertibleSetreg| |copyInto!| + |constantCoefficientRicDE| |seriesSolve| |HenselLift| |f02aef| + |leadingIndex| |blankSeparate| |const| |makeUnit| |primextendedint| + |prevPrime| |linearlyDependent?| |rename| |not| |iiabs| + |permutationRepresentation| |cosh2sech| |linearAssociatedOrder| |scan| + |char| |exptMod| |perspective| |curve?| |sample| |makeCos| |swap!| + |acoshIfCan| |invmod| |trigs2explogs| |palgLODE0| |cotIfCan| |updatF| + |name| |symmetricDifference| |unravel| |nthFlag| |monomialIntegrate| + |csch2sinh| |subTriSet?| |critT| |hasoln| |horizConcat| |composites| + |fixPredicate| |float| |f02agf| |integralAtInfinity?| |mainVariable| + |makeop| |wordInGenerators| |search| |principalIdeal| |crushedSet| + |lprop| |setProperty!| |newTypeLists| |pomopo!| |stack| |minordet| + |trueEqual| |squareFree| |e01daf| |midpoint| |nil| |infinite| + |arbitraryExponent| |approximate| |complex| |shallowMutable| + |canonical| |noetherian| |central| |partiallyOrderedSet| + |arbitraryPrecision| |canonicalsClosed| |noZeroDivisors| + |rightUnitary| |leftUnitary| |additiveValuation| |unitsKnown| + |canonicalUnitNormal| |multiplicativeValuation| |finiteAggregate| + |shallowlyMutable| |commutative|)
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(($ $ (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) 168) (($ (-589 $)) 167) (($ (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) $) 136) (($ $ $) 135)) (-1691 (((-794) $) 18 (-3172 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-563 (-794))) (|has| |#2| (-563 (-794))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-563 (-794)))))) (-2612 (((-589 $) $) 122)) (-3313 (((-108) $ $) 130 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016)))) (-2417 (($ (-589 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) 42)) (-2546 (((-3 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) "failed") |#1| $) 108)) (-2308 (((-108) (-1 (-108) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) $) 33 (|has| $ (-6 -4248))) (((-108) (-1 (-108) |#2|) $) 76 (|has| $ (-6 -4248))) (((-108) (-1 (-108) (-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) $) 111 (|has| $ (-6 -4248)))) (-4006 (((-108) $ $) 195 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-786)))) (-3980 (((-108) $ $) 194 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-786)))) (-3941 (((-108) $ $) 20 (-3172 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T) ((-102 #0=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T) ((-97) -3262 (|has| |#2| (-1016)) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-1016)) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-786))) ((-563 (-794)) -3262 (|has| |#2| (-1016)) (|has| |#2| (-563 (-794))) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-1016)) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-786)) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-563 (-794)))) ((-140 #1=(-2 (|:| -1853 |#1|) (|:| -2433 |#2|))) . T) ((-564 (-499)) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-564 (-499))) ((-207 #0#) . T) ((-213 #0#) . T) ((-263 #2=(-523) #1#) . T) ((-263 |#1| |#2|) . T) ((-265 #2# #1#) . T) ((-265 |#1| |#2|) . T) ((-286 #1#) -12 (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)))) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-1016))) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-259 #1#) . T) ((-349 #1#) . T) ((-462 #1#) . T) ((-462 |#2|) . T) ((-556 #2# #1#) . T) ((-556 |#1| |#2|) . T) ((-484 #1# #1#) -12 (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-286 (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)))) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-1016))) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-560 |#1| |#2|) . T) ((-594 #1#) . T) ((-609 #1#) . T) ((-786) |has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-786)) ((-938 #1#) . T) ((-1016) -3262 (|has| |#2| (-1016)) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-1016)) (|has| (-2 (|:| -1853 |#1|) (|:| -2433 |#2|)) (-786))) ((-1061 #1#) . T) ((-1099 |#1| |#2|) . T) ((-1122) . T) ((-1156 #1#) . T)) -((-1458 (((-794) $) NIL) (($ (-523)) NIL) (($ |#2|) 10))) -(((-36 |#1| |#2|) (-10 -8 (-15 -1458 (|#1| |#2|)) (-15 -1458 (|#1| (-523))) (-15 -1458 ((-794) |#1|))) (-37 |#2|) (-158)) (T -36)) -NIL -(-10 -8 (-15 -1458 (|#1| |#2|)) (-15 -1458 (|#1| (-523))) (-15 -1458 ((-794) |#1|))) -((-3924 (((-108) $ $) 7)) (-2295 (((-108) $) 16)) (-3212 (((-3 $ "failed") $ $) 19)) (-2518 (($) 17 T CONST)) (-2121 (((-3 $ "failed") $) 34)) (-2023 (((-108) $) 31)) (-3779 (((-1070) $) 9)) (-2783 (((-1034) $) 10)) (-1458 (((-794) $) 11) (($ (-523)) 28) (($ |#1|) 37)) (-1621 (((-710)) 29)) (-2364 (($ $ (-852)) 26) (($ $ (-710)) 33)) (-2756 (($) 18 T CONST)) (-2767 (($) 30 T CONST)) (-3983 (((-108) $ $) 6)) (-4087 (($ $) 22) (($ $ $) 21)) (-4075 (($ $ $) 14)) (** (($ $ (-852)) 25) (($ $ (-710)) 32)) (* (($ (-852) $) 13) (($ (-710) $) 15) (($ (-523) $) 20) (($ $ $) 24) (($ $ |#1|) 39) (($ |#1| $) 38))) +((-2546 (*1 *2 *3 *1) (|partial| -12 (-4 *1 (-35 *3 *4)) (-4 *3 (-1016)) (-4 *4 (-1016)) (-5 *2 (-2 (|:| -3772 *3) (|:| -2482 *4)))))) +(-13 (-1100 |t#1| |t#2|) (-609 (-2 (|:| -3772 |t#1|) (|:| -2482 |t#2|))) (-10 -8 (-15 -2546 ((-3 (-2 (|:| -3772 |t#1|) (|:| -2482 |t#2|)) "failed") |t#1| $)))) +(((-33) . T) ((-102 #0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((-97) -3172 (|has| |#2| (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-786))) ((-563 (-794)) -3172 (|has| |#2| (-1016)) (|has| |#2| (-563 (-794))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-786)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-563 (-794)))) ((-140 #1=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((-564 (-499)) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-564 (-499))) ((-207 #0#) . T) ((-213 #0#) . T) ((-263 #2=(-523) #1#) . T) ((-263 |#1| |#2|) . T) ((-265 #2# #1#) . T) ((-265 |#1| |#2|) . T) ((-286 #1#) -12 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-259 #1#) . T) ((-349 #1#) . T) ((-462 #1#) . T) ((-462 |#2|) . T) ((-556 #2# #1#) . T) ((-556 |#1| |#2|) . T) ((-484 #1# #1#) -12 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-560 |#1| |#2|) . T) ((-594 #1#) . T) ((-609 #1#) . T) ((-786) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-786)) ((-938 #1#) . T) ((-1016) -3172 (|has| |#2| (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-786))) ((-1061 #1#) . T) ((-1100 |#1| |#2|) . T) ((-1123) . T) ((-1157 #1#) . T)) +((-1691 (((-794) $) NIL) (($ (-523)) NIL) (($ |#2|) 10))) +(((-36 |#1| |#2|) (-10 -8 (-15 -1691 (|#1| |#2|)) (-15 -1691 (|#1| (-523))) (-15 -1691 ((-794) |#1|))) (-37 |#2|) (-158)) (T -36)) +NIL +(-10 -8 (-15 -1691 (|#1| |#2|)) (-15 -1691 (|#1| (-523))) (-15 -1691 ((-794) |#1|))) +((-1680 (((-108) $ $) 7)) (-2603 (((-108) $) 16)) (-3405 (((-3 $ "failed") $ $) 19)) (-4189 (($) 17 T CONST)) (-1444 (((-3 $ "failed") $) 34)) (-2769 (((-108) $) 31)) (-2032 (((-1070) $) 9)) (-3951 (((-1034) $) 10)) (-1691 (((-794) $) 11) (($ (-523)) 28) (($ |#1|) 37)) (-3272 (((-710)) 29)) (-2423 (($ $ (-852)) 26) (($ $ (-710)) 33)) (-1879 (($) 18 T CONST)) (-1891 (($) 30 T CONST)) (-3941 (((-108) $ $) 6)) (-4060 (($ $) 22) (($ $ $) 21)) (-4045 (($ $ $) 14)) (** (($ $ (-852)) 25) (($ $ (-710)) 32)) (* (($ (-852) $) 13) (($ (-710) $) 15) (($ (-523) $) 20) (($ $ $) 24) (($ $ |#1|) 39) (($ |#1| $) 38))) (((-37 |#1|) (-129) (-158)) (T -37)) -((-1458 (*1 *1 *2) (-12 (-4 *1 (-37 *2)) (-4 *2 (-158))))) -(-13 (-973) (-657 |t#1|) (-10 -8 (-15 -1458 ($ |t#1|)))) +((-1691 (*1 *1 *2) (-12 (-4 *1 (-37 *2)) (-4 *2 (-158))))) +(-13 (-973) (-657 |t#1|) (-10 -8 (-15 -1691 ($ |t#1|)))) (((-21) . 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T) ((-23) . T) ((-25) . T) ((-37 #0=(-383 (-523))) -3262 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-37 |#1|) . T) ((-37 $) -3262 (|has| |#1| (-515)) (|has| |#1| (-325)) (|has| |#1| (-339)) (|has| |#1| (-284))) ((-34) |has| |#1| (-1108)) ((-91) |has| |#1| (-1108)) ((-97) . T) ((-107 #0# #0#) -3262 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-124) . T) ((-134) -3262 (|has| |#1| (-325)) (|has| |#1| (-134))) ((-136) |has| |#1| (-136)) ((-563 (-794)) . T) ((-158) . T) ((-564 (-155 (-203))) |has| |#1| (-949)) ((-564 (-155 (-355))) |has| |#1| (-949)) ((-564 (-499)) |has| |#1| (-564 (-499))) ((-564 (-823 (-355))) |has| |#1| (-564 (-823 (-355)))) ((-564 (-823 (-523))) |has| |#1| (-564 (-823 (-523)))) ((-564 #1=(-1083 |#1|)) . T) ((-209 |#1|) . 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T) ((-840) -12 (|has| |#1| (-284)) (|has| |#1| (-840))) ((-851) -3262 (|has| |#1| (-325)) (|has| |#1| (-339)) (|has| |#1| (-284))) ((-930) -12 (|has| |#1| (-930)) (|has| |#1| (-1108))) ((-964 (-383 (-523))) |has| |#1| (-964 (-383 (-523)))) ((-964 (-523)) |has| |#1| (-964 (-523))) ((-964 |#1|) . T) ((-979 #0#) -3262 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-979 |#1|) . T) ((-979 $) . T) ((-973) . T) ((-980) . T) ((-1028) . T) ((-1016) . T) ((-1063) |has| |#1| (-325)) ((-1108) |has| |#1| (-1108)) ((-1111) |has| |#1| (-1108)) ((-1122) . 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|%noBranch|))) +(((-21) . T) ((-23) . T) ((-25) . T) ((-37 #0=(-383 (-523))) -3172 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-37 |#1|) . T) ((-37 $) -3172 (|has| |#1| (-515)) (|has| |#1| (-325)) (|has| |#1| (-339)) (|has| |#1| (-284))) ((-34) |has| |#1| (-1109)) ((-91) |has| |#1| (-1109)) ((-97) . T) ((-107 #0# #0#) -3172 (|has| |#1| (-325)) (|has| |#1| (-339))) ((-107 |#1| |#1|) . T) ((-107 $ $) . T) ((-124) . T) ((-134) -3172 (|has| |#1| (-325)) (|has| |#1| (-134))) ((-136) |has| |#1| (-136)) ((-563 (-794)) . T) ((-158) . T) ((-564 (-155 (-203))) |has| |#1| (-949)) ((-564 (-155 (-355))) |has| |#1| (-949)) ((-564 (-499)) |has| |#1| (-564 (-499))) ((-564 (-823 (-355))) |has| |#1| (-564 (-823 (-355)))) ((-564 (-823 (-523))) |has| |#1| (-564 (-823 (-523)))) ((-564 #1=(-1083 |#1|)) . T) ((-209 |#1|) . 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(-732)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-33) . T) ((-37 |#2|) |has| |#2| (-158)) ((-97) -3262 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3262 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-107 $ $) |has| |#2| (-158)) ((-124) -3262 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124))) ((-563 (-794)) -3262 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-563 (-794))) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-563 (-1168 |#2|)) . T) ((-158) |has| |#2| (-158)) ((-209 |#2|) |has| |#2| (-973)) ((-211) -12 (|has| |#2| (-211)) (|has| |#2| (-973))) ((-263 #0=(-523) |#2|) . T) ((-265 #0# |#2|) . T) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-344) |has| |#2| (-344)) ((-353 |#2|) |has| |#2| (-973)) ((-387 |#2|) |has| |#2| (-1016)) ((-462 |#2|) . T) ((-556 #0# |#2|) . 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(-732)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-33) . T) ((-37 |#2|) |has| |#2| (-158)) ((-97) -3172 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-107 |#2| |#2|) -3172 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-107 $ $) |has| |#2| (-158)) ((-124) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124))) ((-563 (-794)) -3172 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-563 (-794))) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-563 (-1169 |#2|)) . T) ((-158) |has| |#2| (-158)) ((-209 |#2|) |has| |#2| (-973)) ((-211) -12 (|has| |#2| (-211)) (|has| |#2| (-973))) ((-263 #0=(-523) |#2|) . T) ((-265 #0# |#2|) . T) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-344) |has| |#2| (-344)) ((-353 |#2|) |has| |#2| (-973)) ((-387 |#2|) |has| |#2| (-1016)) ((-462 |#2|) . T) ((-556 #0# |#2|) . T) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-591 |#2|) -3172 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-591 $) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-585 (-523)) -12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973))) ((-585 |#2|) |has| |#2| (-973)) ((-657 |#2|) -3172 (|has| |#2| (-339)) (|has| |#2| (-158))) ((-666) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-730) |has| |#2| (-784)) ((-731) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-732) |has| |#2| (-732)) ((-733) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-734) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-784) |has| |#2| (-784)) ((-786) -3172 (|has| |#2| (-784)) (|has| |#2| (-732))) ((-831 (-1087)) -12 (|has| |#2| (-831 (-1087))) (|has| |#2| (-973))) ((-964 (-383 (-523))) -12 (|has| |#2| (-964 (-383 (-523)))) (|has| |#2| (-1016))) ((-964 (-523)) -12 (|has| |#2| (-964 (-523))) (|has| |#2| (-1016))) ((-964 |#2|) |has| |#2| (-1016)) ((-979 |#2|) -3172 (|has| |#2| (-973)) (|has| |#2| (-339)) (|has| |#2| (-158))) ((-979 $) |has| |#2| (-158)) ((-973) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-980) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-1028) -3172 (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-158))) ((-1016) -3172 (|has| |#2| (-1016)) (|has| |#2| (-973)) (|has| |#2| (-784)) (|has| |#2| (-732)) (|has| |#2| (-344)) (|has| |#2| (-339)) (|has| |#2| (-158)) (|has| |#2| (-124)) (|has| |#2| (-25))) ((-1123) . T) ((-1176 |#2|) |has| |#2| (-339))) +((-4184 (((-218 |#1| |#3|) (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|) 21)) (-2116 ((|#3| (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|) 23)) (-1345 (((-218 |#1| |#3|) (-1 |#3| |#2|) (-218 |#1| |#2|)) 18))) +(((-217 |#1| |#2| |#3|) (-10 -7 (-15 -4184 ((-218 |#1| |#3|) (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|)) (-15 -2116 (|#3| (-1 |#3| |#2| |#3|) (-218 |#1| |#2|) |#3|)) (-15 -1345 ((-218 |#1| |#3|) (-1 |#3| |#2|) (-218 |#1| |#2|)))) (-710) (-1123) (-1123)) (T -217)) +((-1345 (*1 *2 *3 *4) (-12 (-5 *3 (-1 *7 *6)) (-5 *4 (-218 *5 *6)) (-14 *5 (-710)) (-4 *6 (-1123)) (-4 *7 (-1123)) (-5 *2 (-218 *5 *7)) (-5 *1 (-217 *5 *6 *7)))) (-2116 (*1 *2 *3 *4 *2) (-12 (-5 *3 (-1 *2 *6 *2)) (-5 *4 (-218 *5 *6)) (-14 *5 (-710)) (-4 *6 (-1123)) (-4 *2 (-1123)) (-5 *1 (-217 *5 *6 *2)))) (-4184 (*1 *2 *3 *4 *5) (-12 (-5 *3 (-1 *5 *7 *5)) (-5 *4 (-218 *6 *7)) (-14 *6 (-710)) (-4 *7 (-1123)) (-4 *5 (-1123)) (-5 *2 (-218 *6 *5)) (-5 *1 (-217 *6 *7 *5))))) +(-10 -7 (-15 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(-1016)))) (((-383 (-523)) $) NIL (-12 (|has| |#2| (-964 (-383 (-523)))) (|has| |#2| (-1016)))) ((|#2| $) 27 (|has| |#2| (-1016)))) (-2243 (((-629 (-523)) (-629 $)) NIL (-12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973)))) (((-2 (|:| -2600 (-629 (-523))) (|:| |vec| (-1169 (-523)))) (-629 $) (-1169 $)) NIL (-12 (|has| |#2| (-585 (-523))) (|has| |#2| (-973)))) (((-2 (|:| -2600 (-629 |#2|)) (|:| |vec| (-1169 |#2|))) (-629 $) (-1169 $)) NIL (|has| |#2| (-973))) (((-629 |#2|) (-629 $)) NIL (|has| |#2| (-973)))) (-1444 (((-3 $ "failed") $) 53 (|has| |#2| (-973)))) (-1631 (($) NIL (|has| |#2| (-344)))) (-2053 ((|#2| $ (-523) |#2|) NIL (|has| $ (-6 -4249)))) (-2000 ((|#2| $ (-523)) 51)) (-3712 (((-108) $) NIL (|has| |#2| (-784)))) (-1871 (((-589 |#2|) $) 15 (|has| $ (-6 -4248)))) (-2769 (((-108) $) NIL (|has| |#2| (-973)))) (-2057 (((-108) $) NIL (|has| |#2| (-784)))) (-3051 (((-108) $ (-710)) NIL)) (-2965 (((-523) $) 20 (|has| (-523) (-786)))) (-3239 (($ $ $) NIL (-3172 (|has| |#2| (-732)) 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T) ((-102 #0=(-2 (|:| -3772 |#1|) (|:| -2482 |#2|))) . T) ((-97) -3172 (|has| |#2| (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-563 (-794)) -3172 (|has| |#2| (-1016)) (|has| |#2| (-563 (-794))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-563 (-794)))) ((-140 #0#) . T) ((-564 (-499)) |has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-564 (-499))) ((-207 #0#) . T) ((-213 #0#) . T) ((-263 |#1| |#2|) . T) ((-265 |#1| |#2|) . T) ((-286 #0#) -12 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-286 |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-462 #0#) . T) ((-462 |#2|) . T) ((-556 |#1| |#2|) . T) ((-484 #0# #0#) -12 (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-286 (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)))) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-484 |#2| |#2|) -12 (|has| |#2| (-286 |#2|)) (|has| |#2| (-1016))) ((-560 |#1| |#2|) . T) ((-1016) -3172 (|has| |#2| (-1016)) (|has| (-2 (|:| -3772 |#1|) (|:| -2482 |#2|)) (-1016))) ((-1123) . 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T) ((-23) . T) ((-46 |#1| #0=(-523)) . T) ((-25) . T) ((-37 #1=(-383 (-523))) -3172 (|has| |#1| (-339)) (|has| |#1| (-37 (-383 (-523))))) ((-37 |#1|) |has| |#1| (-158)) ((-37 |#2|) |has| |#1| (-339)) ((-37 $) -3172 (|has| |#1| (-515)) (|has| |#1| (-339))) ((-34) |has| |#1| (-37 (-383 (-523)))) ((-91) |has| |#1| (-37 (-383 (-523)))) ((-97) . T) ((-107 #1# #1#) -3172 (|has| |#1| (-339)) (|has| |#1| (-37 (-383 (-523))))) ((-107 |#1| |#1|) . T) ((-107 |#2| |#2|) |has| |#1| (-339)) ((-107 $ $) -3172 (|has| |#1| (-515)) (|has| |#1| (-339)) (|has| |#1| (-158))) ((-124) . T) ((-134) -3172 (-12 (|has| |#1| (-339)) (|has| |#2| (-134))) (|has| |#1| (-134))) ((-136) -3172 (-12 (|has| |#1| (-339)) (|has| |#2| (-136))) (|has| |#1| (-136))) ((-563 (-794)) . T) ((-158) -3172 (|has| |#1| (-515)) (|has| |#1| (-339)) (|has| |#1| (-158))) ((-564 (-203)) -12 (|has| |#1| (-339)) (|has| |#2| (-949))) ((-564 (-355)) -12 (|has| |#1| (-339)) (|has| |#2| (-949))) ((-564 (-499)) -12 (|has| |#1| (-339)) (|has| |#2| (-564 (-499)))) ((-564 (-823 (-355))) -12 (|has| |#1| (-339)) (|has| |#2| (-564 (-823 (-355))))) ((-564 (-823 (-523))) -12 (|has| |#1| (-339)) (|has| |#2| (-564 (-823 (-523))))) ((-209 |#2|) |has| |#1| (-339)) ((-211) -3172 (-12 (|has| |#1| (-339)) (|has| |#2| (-211))) (|has| |#1| (-15 * (|#1| (-523) |#1|)))) ((-221) |has| |#1| (-339)) ((-261) |has| |#1| (-37 (-383 (-523)))) ((-263 |#2| $) -12 (|has| |#1| (-339)) (|has| |#2| (-263 |#2| |#2|))) ((-263 $ $) |has| (-523) (-1028)) ((-267) -3172 (|has| |#1| (-515)) (|has| |#1| (-339))) ((-284) |has| |#1| (-339)) ((-286 |#2|) -12 (|has| |#1| (-339)) (|has| |#2| (-286 |#2|))) ((-339) |has| |#1| (-339)) ((-314 |#2|) |has| |#1| (-339)) ((-353 |#2|) |has| |#1| (-339)) ((-376 |#2|) |has| |#1| (-339)) ((-427) |has| |#1| (-339)) ((-464) |has| |#1| (-37 (-383 (-523)))) ((-484 (-1087) |#2|) -12 (|has| |#1| (-339)) (|has| |#2| (-484 (-1087) |#2|))) ((-484 |#2| |#2|) -12 (|has| |#1| (-339)) (|has| |#2| (-286 |#2|))) ((-515) -3172 (|has| |#1| (-515)) (|has| |#1| (-339))) ((-591 #1#) -3172 (|has| |#1| (-339)) (|has| |#1| (-37 (-383 (-523))))) ((-591 |#1|) . T) ((-591 |#2|) |has| |#1| (-339)) ((-591 $) . T) ((-585 (-523)) -12 (|has| |#1| (-339)) (|has| |#2| (-585 (-523)))) ((-585 |#2|) |has| |#1| (-339)) ((-657 #1#) -3172 (|has| |#1| (-339)) (|has| |#1| (-37 (-383 (-523))))) ((-657 |#1|) |has| |#1| (-158)) ((-657 |#2|) |has| |#1| (-339)) ((-657 $) -3172 (|has| |#1| (-515)) (|has| |#1| (-339))) ((-666) . 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STREAM1 (NIL T) -7 NIL NIL) (-1064 2666834 2667015 2667246 "STINPROD" 2667634 NIL STINPROD (NIL T) -7 NIL NIL) (-1063 2666413 2666597 2666627 "STEP" 2666707 T STEP (NIL) -9 NIL 2666785) (-1062 2659956 2666312 2666389 "STBL" 2666394 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1061 2655132 2659179 2659222 "STAGG" 2659375 NIL STAGG (NIL T) -9 NIL 2659464) (-1060 2652834 2653436 2654308 "STAGG-" 2654313 NIL STAGG- (NIL T T) -8 NIL NIL) (-1059 2651029 2652604 2652696 "STACK" 2652777 NIL STACK (NIL T) -8 NIL NIL) (-1058 2643760 2649176 2649631 "SREGSET" 2650659 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1057 2636200 2637568 2639080 "SRDCMPK" 2642366 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1056 2629168 2633641 2633671 "SRAGG" 2634974 T SRAGG (NIL) -9 NIL 2635582) (-1055 2628185 2628440 2628819 "SRAGG-" 2628824 NIL SRAGG- (NIL T) -8 NIL NIL) (-1054 2622634 2627104 2627531 "SQMATRIX" 2627804 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1053 2616386 2619354 2620080 "SPLTREE" 2621980 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1052 2612376 2613042 2613688 "SPLNODE" 2615812 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1051 2611423 2611656 2611686 "SPFCAT" 2612130 T SPFCAT (NIL) -9 NIL NIL) (-1050 2610160 2610370 2610634 "SPECOUT" 2611181 T SPECOUT (NIL) -7 NIL NIL) (-1049 2609921 2609961 2610030 "SPADPRSR" 2610113 T SPADPRSR (NIL) -7 NIL NIL) (-1048 2601944 2603691 2603733 "SPACEC" 2608056 NIL SPACEC (NIL T) -9 NIL 2609872) (-1047 2600116 2601877 2601925 "SPACE3" 2601930 NIL SPACE3 (NIL T) -8 NIL NIL) (-1046 2598868 2599039 2599330 "SORTPAK" 2599921 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1045 2596924 2597227 2597645 "SOLVETRA" 2598532 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1044 2595935 2596157 2596431 "SOLVESER" 2596697 NIL SOLVESER (NIL T) -7 NIL NIL) (-1043 2591155 2592036 2593038 "SOLVERAD" 2594987 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1042 2586970 2587579 2588308 "SOLVEFOR" 2590522 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1041 2581270 2586322 2586418 "SNTSCAT" 2586423 NIL SNTSCAT (NIL T T T T) -9 NIL 2586493) (-1040 2575375 2579601 2579991 "SMTS" 2580960 NIL SMTS (NIL T T T) -8 NIL NIL) (-1039 2569786 2575264 2575340 "SMP" 2575345 NIL SMP (NIL T T) -8 NIL NIL) (-1038 2567945 2568246 2568644 "SMITH" 2569483 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1037 2560910 2565106 2565208 "SMATCAT" 2566548 NIL SMATCAT (NIL NIL T T T) -9 NIL 2567097) (-1036 2557851 2558674 2559851 "SMATCAT-" 2559856 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1035 2555565 2557088 2557131 "SKAGG" 2557392 NIL SKAGG (NIL T) -9 NIL 2557527) (-1034 2551623 2554669 2554947 "SINT" 2555309 T SINT (NIL) -8 NIL NIL) (-1033 2551395 2551433 2551499 "SIMPAN" 2551579 T SIMPAN (NIL) -7 NIL NIL) (-1032 2550233 2550454 2550729 "SIGNRF" 2551154 NIL SIGNRF (NIL T) -7 NIL NIL) (-1031 2549042 2549193 2549483 "SIGNEF" 2550062 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1030 2546732 2547186 2547692 "SHP" 2548583 NIL SHP (NIL T NIL) -7 NIL NIL) (-1029 2540585 2546633 2546709 "SHDP" 2546714 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1028 2540075 2540267 2540297 "SGROUP" 2540449 T SGROUP (NIL) -9 NIL 2540536) (-1027 2539845 2539897 2540001 "SGROUP-" 2540006 NIL SGROUP- (NIL T) -8 NIL NIL) (-1026 2536681 2537378 2538101 "SGCF" 2539144 T SGCF (NIL) -7 NIL NIL) (-1025 2531080 2536132 2536228 "SFRTCAT" 2536233 NIL SFRTCAT (NIL T T T T) -9 NIL 2536271) (-1024 2524540 2525555 2526689 "SFRGCD" 2530063 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1023 2517706 2518777 2519961 "SFQCMPK" 2523473 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1022 2517328 2517417 2517527 "SFORT" 2517647 NIL SFORT (NIL T T) -8 NIL NIL) (-1021 2516473 2517168 2517289 "SEXOF" 2517294 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1020 2515607 2516354 2516422 "SEX" 2516427 T SEX (NIL) -8 NIL NIL) (-1019 2510384 2511073 2511168 "SEXCAT" 2514939 NIL SEXCAT (NIL T T T T T) -9 NIL 2515558) (-1018 2507564 2510318 2510366 "SET" 2510371 NIL SET (NIL T) -8 NIL NIL) (-1017 2505815 2506277 2506582 "SETMN" 2507305 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1016 2505423 2505549 2505579 "SETCAT" 2505696 T SETCAT (NIL) -9 NIL 2505780) (-1015 2505203 2505255 2505354 "SETCAT-" 2505359 NIL SETCAT- (NIL T) -8 NIL NIL) (-1014 2501591 2503665 2503708 "SETAGG" 2504578 NIL SETAGG (NIL T) -9 NIL 2504918) (-1013 2501049 2501165 2501402 "SETAGG-" 2501407 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1012 2500253 2500546 2500607 "SEGXCAT" 2500893 NIL SEGXCAT (NIL T T) -9 NIL 2501013) (-1011 2499309 2499919 2500101 "SEG" 2500106 NIL SEG (NIL T) -8 NIL NIL) (-1010 2498216 2498429 2498472 "SEGCAT" 2499054 NIL SEGCAT (NIL T) -9 NIL 2499292) (-1009 2497265 2497595 2497795 "SEGBIND" 2498051 NIL SEGBIND (NIL T) -8 NIL NIL) (-1008 2496886 2496945 2497058 "SEGBIND2" 2497200 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1007 2496105 2496231 2496435 "SEG2" 2496730 NIL SEG2 (NIL T T) -7 NIL NIL) (-1006 2495542 2496040 2496087 "SDVAR" 2496092 NIL SDVAR (NIL T) -8 NIL NIL) (-1005 2487794 2495315 2495443 "SDPOL" 2495448 NIL SDPOL (NIL T) -8 NIL NIL) (-1004 2486387 2486653 2486972 "SCPKG" 2487509 NIL SCPKG (NIL T) -7 NIL NIL) (-1003 2485524 2485703 2485903 "SCOPE" 2486209 T SCOPE (NIL) -8 NIL NIL) (-1002 2484745 2484878 2485057 "SCACHE" 2485379 NIL SCACHE (NIL T) -7 NIL NIL) (-1001 2484184 2484505 2484590 "SAOS" 2484682 T SAOS (NIL) -8 NIL NIL) (-1000 2483749 2483784 2483957 "SAERFFC" 2484143 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-999 2477645 2483648 2483726 "SAE" 2483731 NIL SAE (NIL T T NIL) -8 NIL NIL) (-998 2477241 2477276 2477433 "SAEFACT" 2477604 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-997 2475567 2475881 2476280 "RURPK" 2476907 NIL RURPK (NIL T NIL) -7 NIL NIL) (-996 2474220 2474497 2474804 "RULESET" 2475403 NIL RULESET (NIL T T T) -8 NIL NIL) (-995 2471428 2471931 2472392 "RULE" 2473902 NIL RULE (NIL T T T) -8 NIL NIL) (-994 2471070 2471225 2471306 "RULECOLD" 2471380 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-993 2465962 2466756 2467672 "RSETGCD" 2470269 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-992 2455277 2460329 2460423 "RSETCAT" 2464488 NIL RSETCAT (NIL T T T T) -9 NIL 2465585) (-991 2453208 2453747 2454567 "RSETCAT-" 2454572 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-990 2445638 2447013 2448529 "RSDCMPK" 2451807 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-989 2443656 2444097 2444169 "RRCC" 2445245 NIL RRCC (NIL T T) -9 NIL 2445589) (-988 2443010 2443184 2443460 "RRCC-" 2443465 NIL RRCC- (NIL T T T) -8 NIL NIL) (-987 2417377 2427002 2427066 "RPOLCAT" 2437568 NIL RPOLCAT (NIL T T T) -9 NIL 2440726) (-986 2408881 2411219 2414337 "RPOLCAT-" 2414342 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-985 2399947 2407111 2407591 "ROUTINE" 2408421 T ROUTINE (NIL) -8 NIL NIL) (-984 2396652 2399503 2399650 "ROMAN" 2399820 T ROMAN (NIL) -8 NIL NIL) (-983 2394938 2395523 2395780 "ROIRC" 2396458 NIL ROIRC (NIL T T) -8 NIL NIL) (-982 2391343 2393647 2393675 "RNS" 2393971 T RNS (NIL) -9 NIL 2394241) (-981 2389857 2390240 2390771 "RNS-" 2390844 NIL RNS- (NIL T) -8 NIL NIL) (-980 2389283 2389691 2389719 "RNG" 2389724 T RNG (NIL) -9 NIL 2389745) (-979 2388681 2389043 2389083 "RMODULE" 2389143 NIL RMODULE (NIL T) -9 NIL 2389185) (-978 2387533 2387627 2387957 "RMCAT2" 2388582 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-977 2384247 2386716 2387037 "RMATRIX" 2387268 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-976 2377244 2379478 2379590 "RMATCAT" 2382899 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2383881) (-975 2376623 2376770 2377073 "RMATCAT-" 2377078 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-974 2376193 2376268 2376394 "RINTERP" 2376542 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-973 2375244 2375808 2375836 "RING" 2375946 T RING (NIL) -9 NIL 2376040) (-972 2375039 2375083 2375177 "RING-" 2375182 NIL RING- (NIL T) -8 NIL NIL) (-971 2373887 2374124 2374380 "RIDIST" 2374803 T RIDIST (NIL) -7 NIL NIL) (-970 2365209 2373361 2373564 "RGCHAIN" 2373736 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-969 2362214 2362828 2363496 "RF" 2364573 NIL RF (NIL T) -7 NIL NIL) (-968 2361863 2361926 2362027 "RFFACTOR" 2362145 NIL RFFACTOR (NIL T) -7 NIL NIL) (-967 2361591 2361626 2361721 "RFFACT" 2361822 NIL RFFACT (NIL T) -7 NIL NIL) (-966 2359721 2360085 2360465 "RFDIST" 2361231 T RFDIST (NIL) -7 NIL NIL) (-965 2359179 2359271 2359431 "RETSOL" 2359623 NIL RETSOL (NIL T T) -7 NIL NIL) (-964 2358772 2358852 2358893 "RETRACT" 2359083 NIL RETRACT (NIL T) -9 NIL NIL) (-963 2358624 2358649 2358733 "RETRACT-" 2358738 NIL RETRACT- (NIL T T) -8 NIL NIL) (-962 2351482 2358281 2358406 "RESULT" 2358519 T RESULT (NIL) -8 NIL NIL) (-961 2350067 2350756 2350953 "RESRING" 2351385 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-960 2349707 2349756 2349852 "RESLATC" 2350004 NIL RESLATC (NIL T) -7 NIL NIL) (-959 2349416 2349450 2349555 "REPSQ" 2349666 NIL REPSQ (NIL T) -7 NIL NIL) (-958 2346847 2347427 2348027 "REP" 2348836 T REP (NIL) -7 NIL NIL) (-957 2346548 2346582 2346691 "REPDB" 2346806 NIL REPDB (NIL T) -7 NIL NIL) (-956 2340493 2341872 2343092 "REP2" 2345360 NIL REP2 (NIL T) -7 NIL NIL) (-955 2336899 2337580 2338385 "REP1" 2339720 NIL REP1 (NIL T) -7 NIL NIL) (-954 2329645 2335060 2335512 "REGSET" 2336530 NIL REGSET (NIL T T T T) -8 NIL NIL) (-953 2328466 2328801 2329049 "REF" 2329430 NIL REF (NIL T) -8 NIL NIL) (-952 2327847 2327950 2328115 "REDORDER" 2328350 NIL REDORDER (NIL T T) -7 NIL NIL) (-951 2323816 2327081 2327302 "RECLOS" 2327678 NIL RECLOS (NIL T) -8 NIL NIL) (-950 2322873 2323054 2323267 "REALSOLV" 2323623 T REALSOLV (NIL) -7 NIL NIL) (-949 2322721 2322762 2322790 "REAL" 2322795 T REAL (NIL) -9 NIL 2322830) (-948 2319212 2320014 2320896 "REAL0Q" 2321886 NIL REAL0Q (NIL T) -7 NIL NIL) (-947 2314823 2315811 2316870 "REAL0" 2318193 NIL REAL0 (NIL T) -7 NIL NIL) (-946 2314231 2314303 2314508 "RDIV" 2314745 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-945 2313304 2313478 2313689 "RDIST" 2314053 NIL RDIST (NIL T) -7 NIL NIL) (-944 2311908 2312195 2312564 "RDETRS" 2313012 NIL RDETRS (NIL T T) -7 NIL NIL) (-943 2309729 2310183 2310718 "RDETR" 2311450 NIL RDETR (NIL T T) -7 NIL NIL) (-942 2308345 2308623 2309024 "RDEEFS" 2309445 NIL RDEEFS (NIL T T) -7 NIL NIL) (-941 2306845 2307151 2307580 "RDEEF" 2308033 NIL RDEEF (NIL T T) -7 NIL NIL) (-940 2301130 2304062 2304090 "RCFIELD" 2305367 T RCFIELD (NIL) -9 NIL 2306097) (-939 2299199 2299703 2300396 "RCFIELD-" 2300469 NIL RCFIELD- (NIL T) -8 NIL NIL) (-938 2295531 2297316 2297357 "RCAGG" 2298428 NIL RCAGG (NIL T) -9 NIL 2298893) (-937 2295162 2295256 2295416 "RCAGG-" 2295421 NIL RCAGG- (NIL T T) -8 NIL NIL) (-936 2294507 2294618 2294780 "RATRET" 2295046 NIL RATRET (NIL T) -7 NIL NIL) (-935 2294064 2294131 2294250 "RATFACT" 2294435 NIL RATFACT (NIL T) -7 NIL NIL) (-934 2293379 2293499 2293649 "RANDSRC" 2293934 T RANDSRC (NIL) -7 NIL NIL) (-933 2293116 2293160 2293231 "RADUTIL" 2293328 T RADUTIL (NIL) -7 NIL NIL) (-932 2286123 2291859 2292176 "RADIX" 2292831 NIL RADIX (NIL NIL) -8 NIL NIL) (-931 2277693 2285967 2286095 "RADFF" 2286100 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-930 2277345 2277420 2277448 "RADCAT" 2277605 T RADCAT (NIL) -9 NIL NIL) (-929 2277130 2277178 2277275 "RADCAT-" 2277280 NIL RADCAT- (NIL T) -8 NIL NIL) (-928 2275281 2276905 2276994 "QUEUE" 2277074 NIL QUEUE (NIL T) -8 NIL NIL) (-927 2271778 2275218 2275263 "QUAT" 2275268 NIL QUAT (NIL T) -8 NIL NIL) (-926 2271416 2271459 2271586 "QUATCT2" 2271729 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-925 2265210 2268590 2268630 "QUATCAT" 2269409 NIL QUATCAT (NIL T) -9 NIL 2270174) (-924 2261354 2262391 2263778 "QUATCAT-" 2263872 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-923 2258875 2260439 2260480 "QUAGG" 2260855 NIL QUAGG (NIL T) -9 NIL 2261030) (-922 2257800 2258273 2258445 "QFORM" 2258747 NIL QFORM (NIL NIL T) -8 NIL NIL) (-921 2249097 2254355 2254395 "QFCAT" 2255053 NIL QFCAT (NIL T) -9 NIL 2256046) (-920 2244669 2245870 2247461 "QFCAT-" 2247555 NIL QFCAT- (NIL T T) -8 NIL NIL) (-919 2244307 2244350 2244477 "QFCAT2" 2244620 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-918 2243767 2243877 2244007 "QEQUAT" 2244197 T QEQUAT (NIL) -8 NIL NIL) (-917 2236953 2238024 2239206 "QCMPACK" 2242700 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-916 2234529 2234950 2235378 "QALGSET" 2236608 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-915 2233774 2233948 2234180 "QALGSET2" 2234349 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-914 2232465 2232688 2233005 "PWFFINTB" 2233547 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-913 2230653 2230821 2231174 "PUSHVAR" 2232279 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-912 2226571 2227625 2227666 "PTRANFN" 2229550 NIL PTRANFN (NIL T) -9 NIL NIL) (-911 2224983 2225274 2225595 "PTPACK" 2226282 NIL PTPACK (NIL T) -7 NIL NIL) (-910 2224619 2224676 2224783 "PTFUNC2" 2224920 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-909 2219096 2223437 2223477 "PTCAT" 2223845 NIL PTCAT (NIL T) -9 NIL 2224007) (-908 2218754 2218789 2218913 "PSQFR" 2219055 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-907 2217349 2217647 2217981 "PSEUDLIN" 2218452 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-906 2204157 2206521 2208844 "PSETPK" 2215109 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-905 2197244 2199958 2200052 "PSETCAT" 2203033 NIL PSETCAT (NIL T T T T) -9 NIL 2203847) (-904 2195082 2195716 2196535 "PSETCAT-" 2196540 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-903 2194431 2194596 2194624 "PSCURVE" 2194892 T PSCURVE (NIL) -9 NIL 2195059) (-902 2190883 2192409 2192473 "PSCAT" 2193309 NIL PSCAT (NIL T T T) -9 NIL 2193549) (-901 2189947 2190163 2190562 "PSCAT-" 2190567 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-900 2188600 2189232 2189446 "PRTITION" 2189753 T PRTITION (NIL) -8 NIL NIL) (-899 2177698 2179904 2182092 "PRS" 2186462 NIL PRS (NIL T T) -7 NIL NIL) (-898 2175557 2177049 2177089 "PRQAGG" 2177272 NIL PRQAGG (NIL T) -9 NIL 2177374) (-897 2175128 2175230 2175258 "PROPLOG" 2175443 T PROPLOG (NIL) -9 NIL NIL) (-896 2172251 2172816 2173343 "PROPFRML" 2174633 NIL PROPFRML (NIL T) -8 NIL NIL) (-895 2171711 2171821 2171951 "PROPERTY" 2172141 T PROPERTY (NIL) -8 NIL NIL) (-894 2165485 2169877 2170697 "PRODUCT" 2170937 NIL PRODUCT (NIL T T) -8 NIL NIL) (-893 2162761 2164945 2165178 "PR" 2165296 NIL PR (NIL T T) -8 NIL NIL) (-892 2162557 2162589 2162648 "PRINT" 2162722 T PRINT (NIL) -7 NIL NIL) (-891 2161897 2162014 2162166 "PRIMES" 2162437 NIL PRIMES (NIL T) -7 NIL NIL) (-890 2159962 2160363 2160829 "PRIMELT" 2161476 NIL PRIMELT (NIL T) -7 NIL NIL) (-889 2159691 2159740 2159768 "PRIMCAT" 2159892 T PRIMCAT (NIL) -9 NIL NIL) (-888 2155852 2159629 2159674 "PRIMARR" 2159679 NIL PRIMARR (NIL T) -8 NIL NIL) (-887 2154859 2155037 2155265 "PRIMARR2" 2155670 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-886 2154502 2154558 2154669 "PREASSOC" 2154797 NIL PREASSOC (NIL T T) -7 NIL NIL) (-885 2153977 2154110 2154138 "PPCURVE" 2154343 T PPCURVE (NIL) -9 NIL 2154479) (-884 2151336 2151735 2152327 "POLYROOT" 2153558 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-883 2145242 2150942 2151101 "POLY" 2151209 NIL POLY (NIL T) -8 NIL NIL) (-882 2144627 2144685 2144918 "POLYLIFT" 2145178 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-881 2140912 2141361 2141989 "POLYCATQ" 2144172 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-880 2127953 2133350 2133414 "POLYCAT" 2136899 NIL POLYCAT (NIL T T T) -9 NIL 2138826) (-879 2121404 2123265 2125648 "POLYCAT-" 2125653 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-878 2120993 2121061 2121180 "POLY2UP" 2121330 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-877 2120629 2120686 2120793 "POLY2" 2120930 NIL POLY2 (NIL T T) -7 NIL NIL) (-876 2119314 2119553 2119829 "POLUTIL" 2120403 NIL POLUTIL (NIL T T) -7 NIL NIL) (-875 2117676 2117953 2118283 "POLTOPOL" 2119036 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-874 2113199 2117613 2117658 "POINT" 2117663 NIL POINT (NIL T) -8 NIL NIL) (-873 2111386 2111743 2112118 "PNTHEORY" 2112844 T PNTHEORY (NIL) -7 NIL NIL) (-872 2109814 2110111 2110520 "PMTOOLS" 2111084 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-871 2109407 2109485 2109602 "PMSYM" 2109730 NIL PMSYM (NIL T) -7 NIL NIL) (-870 2108917 2108986 2109160 "PMQFCAT" 2109332 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-869 2108272 2108382 2108538 "PMPRED" 2108794 NIL PMPRED (NIL T) -7 NIL NIL) (-868 2107668 2107754 2107915 "PMPREDFS" 2108173 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-867 2106314 2106522 2106906 "PMPLCAT" 2107430 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-866 2105846 2105925 2106077 "PMLSAGG" 2106229 NIL PMLSAGG (NIL T T T) -7 NIL NIL) (-865 2105323 2105399 2105579 "PMKERNEL" 2105764 NIL PMKERNEL (NIL T T) -7 NIL NIL) (-864 2104940 2105015 2105128 "PMINS" 2105242 NIL PMINS (NIL T) -7 NIL NIL) (-863 2104370 2104439 2104654 "PMFS" 2104865 NIL PMFS (NIL T T T) -7 NIL NIL) (-862 2103601 2103719 2103923 "PMDOWN" 2104247 NIL PMDOWN (NIL T T T) -7 NIL NIL) (-861 2102764 2102923 2103105 "PMASS" 2103439 T PMASS (NIL) -7 NIL NIL) (-860 2102038 2102149 2102312 "PMASSFS" 2102650 NIL PMASSFS (NIL T T) -7 NIL NIL) (-859 2101693 2101761 2101855 "PLOTTOOL" 2101964 T PLOTTOOL (NIL) -7 NIL NIL) (-858 2096315 2097504 2098652 "PLOT" 2100565 T PLOT (NIL) -8 NIL NIL) (-857 2092129 2093163 2094084 "PLOT3D" 2095414 T PLOT3D (NIL) -8 NIL NIL) (-856 2091041 2091218 2091453 "PLOT1" 2091933 NIL PLOT1 (NIL T) -7 NIL NIL) (-855 2066436 2071107 2075958 "PLEQN" 2086307 NIL PLEQN (NIL T 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2018395 2019086 "PDEPROB" 2019832 T PDEPROB (NIL) -8 NIL NIL) (-828 2015216 2015712 2016261 "PDEPACK" 2017116 T PDEPACK (NIL) -7 NIL NIL) (-827 2014128 2014318 2014569 "PDECOMP" 2015015 NIL PDECOMP (NIL T T) -7 NIL NIL) (-826 2011740 2012555 2012583 "PDECAT" 2013368 T PDECAT (NIL) -9 NIL 2014079) (-825 2011493 2011526 2011615 "PCOMP" 2011701 NIL PCOMP (NIL T T) -7 NIL NIL) (-824 2009700 2010296 2010592 "PBWLB" 2011223 NIL PBWLB (NIL T) -8 NIL NIL) (-823 2002209 2003777 2005113 "PATTERN" 2008385 NIL PATTERN (NIL T) -8 NIL NIL) (-822 2001841 2001898 2002007 "PATTERN2" 2002146 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-821 1999598 1999986 2000443 "PATTERN1" 2001430 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-820 1996993 1997547 1998028 "PATRES" 1999163 NIL PATRES (NIL T T) -8 NIL NIL) (-819 1996557 1996624 1996756 "PATRES2" 1996920 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-818 1994454 1994854 1995259 "PATMATCH" 1996226 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-817 1993991 1994174 1994215 "PATMAB" 1994322 NIL PATMAB (NIL T) -9 NIL 1994405) (-816 1992536 1992845 1993103 "PATLRES" 1993796 NIL PATLRES (NIL T T T) -8 NIL NIL) (-815 1992082 1992205 1992246 "PATAB" 1992251 NIL PATAB (NIL T) -9 NIL 1992423) (-814 1989563 1990095 1990668 "PARTPERM" 1991529 T PARTPERM (NIL) -7 NIL NIL) (-813 1989184 1989247 1989349 "PARSURF" 1989494 NIL PARSURF (NIL T) -8 NIL NIL) (-812 1988816 1988873 1988982 "PARSU2" 1989121 NIL PARSU2 (NIL T T) -7 NIL NIL) (-811 1988580 1988620 1988687 "PARSER" 1988769 T PARSER (NIL) -7 NIL NIL) (-810 1988201 1988264 1988366 "PARSCURV" 1988511 NIL PARSCURV (NIL T) -8 NIL NIL) (-809 1987833 1987890 1987999 "PARSC2" 1988138 NIL PARSC2 (NIL T T) -7 NIL NIL) (-808 1987472 1987530 1987627 "PARPCURV" 1987769 NIL PARPCURV (NIL T) -8 NIL NIL) (-807 1987104 1987161 1987270 "PARPC2" 1987409 NIL PARPC2 (NIL T T) -7 NIL NIL) (-806 1986624 1986710 1986829 "PAN2EXPR" 1987005 T PAN2EXPR (NIL) -7 NIL NIL) (-805 1985430 1985745 1985973 "PALETTE" 1986416 T PALETTE (NIL) -8 NIL NIL) (-804 1983898 1984435 1984795 "PAIR" 1985116 NIL PAIR (NIL T T) -8 NIL NIL) (-803 1977748 1983157 1983351 "PADICRC" 1983753 NIL PADICRC (NIL NIL T) -8 NIL NIL) (-802 1970956 1977094 1977278 "PADICRAT" 1977596 NIL PADICRAT (NIL NIL) -8 NIL NIL) (-801 1969260 1970893 1970938 "PADIC" 1970943 NIL PADIC (NIL NIL) -8 NIL NIL) (-800 1966465 1968039 1968079 "PADICCT" 1968660 NIL PADICCT (NIL NIL) -9 NIL 1968942) (-799 1965422 1965622 1965890 "PADEPAC" 1966252 NIL PADEPAC (NIL T NIL NIL) -7 NIL NIL) (-798 1964634 1964767 1964973 "PADE" 1965284 NIL PADE (NIL T T T) -7 NIL NIL) (-797 1962645 1963477 1963792 "OWP" 1964402 NIL OWP (NIL T NIL NIL NIL) -8 NIL NIL) (-796 1961754 1962250 1962422 "OVAR" 1962513 NIL OVAR (NIL NIL) -8 NIL NIL) (-795 1961018 1961139 1961300 "OUT" 1961613 T OUT (NIL) -7 NIL NIL) (-794 1950064 1952243 1954413 "OUTFORM" 1958868 T OUTFORM (NIL) -8 NIL NIL) (-793 1949472 1949793 1949882 "OSI" 1949995 T OSI (NIL) -8 NIL NIL) (-792 1948217 1948444 1948729 "ORTHPOL" 1949219 NIL ORTHPOL (NIL T) 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(-779 1923095 1925169 1925578 "ORDCOMP" 1926207 NIL ORDCOMP (NIL T) -8 NIL NIL) (-778 1922361 1922488 1922674 "ORDCOMP2" 1922955 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-777 1918869 1919751 1920588 "OPTPROB" 1921544 T OPTPROB (NIL) -8 NIL NIL) (-776 1915711 1916340 1917034 "OPTPACK" 1918195 T OPTPACK (NIL) -7 NIL NIL) (-775 1913437 1914173 1914201 "OPTCAT" 1915016 T OPTCAT (NIL) -9 NIL 1915662) (-774 1913205 1913244 1913310 "OPQUERY" 1913391 T OPQUERY (NIL) -7 NIL NIL) (-773 1910341 1911532 1912032 "OP" 1912737 NIL OP (NIL T) -8 NIL NIL) (-772 1907106 1909138 1909507 "ONECOMP" 1910005 NIL ONECOMP (NIL T) -8 NIL NIL) (-771 1906411 1906526 1906700 "ONECOMP2" 1906978 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-770 1905830 1905936 1906066 "OMSERVER" 1906301 T OMSERVER (NIL) -7 NIL NIL) (-769 1902719 1905271 1905311 "OMSAGG" 1905372 NIL OMSAGG (NIL T) -9 NIL 1905436) (-768 1901342 1901605 1901887 "OMPKG" 1902457 T OMPKG (NIL) -7 NIL NIL) (-767 1900772 1900875 1900903 "OM" 1901202 T OM (NIL) -9 NIL 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1830268 "ODEEF" 1832339 NIL ODEEF (NIL T T) -7 NIL NIL) (-740 1827861 1827950 1828179 "ODECONST" 1828429 NIL ODECONST (NIL T T T) -7 NIL NIL) (-739 1826019 1826652 1826680 "ODECAT" 1827283 T ODECAT (NIL) -9 NIL 1827812) (-738 1822891 1825731 1825850 "OCT" 1825932 NIL OCT (NIL T) -8 NIL NIL) (-737 1822529 1822572 1822699 "OCTCT2" 1822842 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-736 1817363 1819801 1819841 "OC" 1820937 NIL OC (NIL T) -9 NIL 1821794) (-735 1814590 1815338 1816328 "OC-" 1816422 NIL OC- (NIL T T) -8 NIL NIL) (-734 1813969 1814411 1814439 "OCAMON" 1814444 T OCAMON (NIL) -9 NIL 1814465) (-733 1813423 1813830 1813858 "OASGP" 1813863 T OASGP (NIL) -9 NIL 1813883) (-732 1812711 1813174 1813202 "OAMONS" 1813242 T OAMONS (NIL) -9 NIL 1813285) (-731 1812152 1812559 1812587 "OAMON" 1812592 T OAMON (NIL) -9 NIL 1812612) (-730 1811457 1811949 1811977 "OAGROUP" 1811982 T OAGROUP (NIL) -9 NIL 1812002) (-729 1811147 1811197 1811285 "NUMTUBE" 1811401 NIL NUMTUBE (NIL T) -7 NIL NIL) (-728 1804720 1806238 1807774 "NUMQUAD" 1809631 T NUMQUAD (NIL) -7 NIL NIL) (-727 1800476 1801464 1802489 "NUMODE" 1803715 T NUMODE (NIL) -7 NIL NIL) (-726 1797880 1798726 1798754 "NUMINT" 1799671 T NUMINT (NIL) -9 NIL 1800427) (-725 1796828 1797025 1797243 "NUMFMT" 1797682 T NUMFMT (NIL) -7 NIL NIL) (-724 1783210 1786144 1788674 "NUMERIC" 1794337 NIL NUMERIC (NIL T) -7 NIL NIL) (-723 1777611 1782663 1782757 "NTSCAT" 1782762 NIL NTSCAT (NIL T T T T) -9 NIL 1782800) (-722 1776805 1776970 1777163 "NTPOLFN" 1777450 NIL NTPOLFN (NIL T) -7 NIL NIL) (-721 1764621 1773647 1774457 "NSUP" 1776027 NIL NSUP (NIL T) -8 NIL NIL) (-720 1764257 1764314 1764421 "NSUP2" 1764558 NIL NSUP2 (NIL T T) -7 NIL NIL) (-719 1754219 1764036 1764166 "NSMP" 1764171 NIL NSMP (NIL T T) -8 NIL NIL) (-718 1752651 1752952 1753309 "NREP" 1753907 NIL NREP (NIL T) -7 NIL NIL) (-717 1751242 1751494 1751852 "NPCOEF" 1752394 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-716 1750308 1750423 1750639 "NORMRETR" 1751123 NIL NORMRETR (NIL T 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1735224 T NASRING (NIL) -9 NIL 1735298) (-702 1734142 1734186 1734280 "NASRING-" 1734285 NIL NASRING- (NIL T) -8 NIL NIL) (-701 1733296 1733795 1733823 "NARNG" 1733940 T NARNG (NIL) -9 NIL 1734031) (-700 1732988 1733055 1733189 "NARNG-" 1733194 NIL NARNG- (NIL T) -8 NIL NIL) (-699 1731867 1732074 1732309 "NAGSP" 1732773 T NAGSP (NIL) -7 NIL NIL) (-698 1723291 1724937 1726572 "NAGS" 1730252 T NAGS (NIL) -7 NIL NIL) (-697 1721855 1722159 1722486 "NAGF07" 1722984 T NAGF07 (NIL) -7 NIL NIL) (-696 1716437 1717717 1719013 "NAGF04" 1720579 T NAGF04 (NIL) -7 NIL NIL) (-695 1709469 1711067 1712684 "NAGF02" 1714840 T NAGF02 (NIL) -7 NIL NIL) (-694 1704733 1705823 1706930 "NAGF01" 1708382 T NAGF01 (NIL) -7 NIL NIL) (-693 1698393 1699951 1701528 "NAGE04" 1703176 T NAGE04 (NIL) -7 NIL NIL) (-692 1689634 1691737 1693849 "NAGE02" 1696301 T NAGE02 (NIL) -7 NIL NIL) (-691 1685627 1686564 1687518 "NAGE01" 1688700 T NAGE01 (NIL) -7 NIL NIL) (-690 1683434 1683965 1684520 "NAGD03" 1685092 T NAGD03 (NIL) -7 NIL NIL) (-689 1675220 1677139 1679084 "NAGD02" 1681509 T NAGD02 (NIL) -7 NIL NIL) (-688 1669079 1670492 1671920 "NAGD01" 1673812 T NAGD01 (NIL) -7 NIL NIL) (-687 1665336 1666146 1666971 "NAGC06" 1668274 T NAGC06 (NIL) -7 NIL NIL) (-686 1663813 1664142 1664495 "NAGC05" 1665003 T NAGC05 (NIL) -7 NIL NIL) (-685 1663197 1663314 1663456 "NAGC02" 1663691 T NAGC02 (NIL) -7 NIL NIL) (-684 1662259 1662816 1662856 "NAALG" 1662935 NIL NAALG (NIL T) -9 NIL 1662996) (-683 1662094 1662123 1662213 "NAALG-" 1662218 NIL NAALG- (NIL T T) -8 NIL NIL) (-682 1656044 1657152 1658339 "MULTSQFR" 1660990 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-681 1655363 1655438 1655622 "MULTFACT" 1655956 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-680 1648557 1652468 1652520 "MTSCAT" 1653580 NIL MTSCAT (NIL T T) -9 NIL 1654094) (-679 1648269 1648323 1648415 "MTHING" 1648497 NIL MTHING (NIL T) -7 NIL NIL) (-678 1648061 1648094 1648154 "MSYSCMD" 1648229 T MSYSCMD (NIL) -7 NIL NIL) (-677 1644173 1646816 1647136 "MSET" 1647774 NIL MSET (NIL T) -8 NIL NIL) (-676 1641269 1643735 1643776 "MSETAGG" 1643781 NIL MSETAGG (NIL T) -9 NIL 1643815) (-675 1637125 1638667 1639408 "MRING" 1640572 NIL MRING (NIL T T) -8 NIL NIL) (-674 1636695 1636762 1636891 "MRF2" 1637052 NIL MRF2 (NIL T T T) -7 NIL NIL) (-673 1636313 1636348 1636492 "MRATFAC" 1636654 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-672 1633925 1634220 1634651 "MPRFF" 1636018 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-671 1627945 1633780 1633876 "MPOLY" 1633881 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-670 1627435 1627470 1627678 "MPCPF" 1627904 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-669 1626951 1626994 1627177 "MPC3" 1627386 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-668 1626152 1626233 1626452 "MPC2" 1626866 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-667 1624453 1624790 1625180 "MONOTOOL" 1625812 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-666 1623578 1623913 1623941 "MONOID" 1624218 T MONOID (NIL) -9 NIL 1624390) (-665 1622956 1623119 1623362 "MONOID-" 1623367 NIL MONOID- (NIL T) -8 NIL NIL) (-664 1613937 1619923 1619982 "MONOGEN" 1620656 NIL MONOGEN (NIL T T) -9 NIL 1621112) (-663 1611155 1611890 1612890 "MONOGEN-" 1613009 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-662 1610015 1610435 1610463 "MONADWU" 1610855 T MONADWU (NIL) -9 NIL 1611093) (-661 1609387 1609546 1609794 "MONADWU-" 1609799 NIL MONADWU- (NIL T) -8 NIL NIL) (-660 1608773 1608991 1609019 "MONAD" 1609226 T MONAD (NIL) -9 NIL 1609338) (-659 1608458 1608536 1608668 "MONAD-" 1608673 NIL MONAD- (NIL T) -8 NIL NIL) (-658 1606709 1607371 1607650 "MOEBIUS" 1608211 NIL MOEBIUS (NIL T) -8 NIL NIL) (-657 1606103 1606481 1606521 "MODULE" 1606526 NIL MODULE (NIL T) -9 NIL 1606552) (-656 1605671 1605767 1605957 "MODULE-" 1605962 NIL MODULE- (NIL T T) -8 NIL NIL) (-655 1603342 1604037 1604363 "MODRING" 1605496 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-654 1600298 1601463 1601980 "MODOP" 1602874 NIL MODOP (NIL T T) -8 NIL NIL) (-653 1598485 1598937 1599278 "MODMONOM" 1600097 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-652 1588163 1596689 1597111 "MODMON" 1598113 NIL MODMON (NIL T T) -8 NIL NIL) (-651 1585289 1587007 1587283 "MODFIELD" 1588038 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-650 1584293 1584570 1584760 "MMLFORM" 1585119 T MMLFORM (NIL) -8 NIL NIL) (-649 1583819 1583862 1584041 "MMAP" 1584244 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-648 1582056 1582833 1582873 "MLO" 1583290 NIL MLO (NIL T) -9 NIL 1583531) (-647 1579423 1579938 1580540 "MLIFT" 1581537 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-646 1578814 1578898 1579052 "MKUCFUNC" 1579334 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-645 1578413 1578483 1578606 "MKRECORD" 1578737 NIL MKRECORD (NIL T T) -7 NIL NIL) (-644 1577461 1577622 1577850 "MKFUNC" 1578224 NIL MKFUNC (NIL T) -7 NIL NIL) (-643 1576849 1576953 1577109 "MKFLCFN" 1577344 NIL MKFLCFN (NIL T) -7 NIL NIL) (-642 1576275 1576642 1576731 "MKCHSET" 1576793 NIL MKCHSET (NIL T) -8 NIL NIL) (-641 1575552 1575654 1575839 "MKBCFUNC" 1576168 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-640 1572236 1575106 1575242 "MINT" 1575436 T MINT (NIL) -8 NIL NIL) (-639 1571048 1571291 1571568 "MHROWRED" 1571991 NIL MHROWRED (NIL T) -7 NIL NIL) (-638 1566319 1569493 1569917 "MFLOAT" 1570644 T MFLOAT (NIL) -8 NIL NIL) (-637 1565676 1565752 1565923 "MFINFACT" 1566231 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-636 1561991 1562839 1563723 "MESH" 1564812 T MESH (NIL) -7 NIL NIL) (-635 1560381 1560693 1561046 "MDDFACT" 1561678 NIL MDDFACT (NIL T) -7 NIL NIL) (-634 1557224 1559541 1559582 "MDAGG" 1559837 NIL MDAGG (NIL T) -9 NIL 1559980) (-633 1546922 1556517 1556724 "MCMPLX" 1557037 T MCMPLX (NIL) -8 NIL NIL) (-632 1546063 1546209 1546409 "MCDEN" 1546771 NIL MCDEN (NIL T T) -7 NIL NIL) (-631 1543953 1544223 1544603 "MCALCFN" 1545793 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-630 1541575 1542098 1542659 "MATSTOR" 1543424 NIL MATSTOR (NIL T) -7 NIL NIL) (-629 1537584 1540950 1541197 "MATRIX" 1541360 NIL MATRIX (NIL T) -8 NIL NIL) (-628 1533354 1534057 1534793 "MATLIN" 1536941 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-627 1523552 1526690 1526766 "MATCAT" 1531604 NIL MATCAT (NIL T T T) -9 NIL 1533021) (-626 1519917 1520930 1522285 "MATCAT-" 1522290 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-625 1518519 1518672 1519003 "MATCAT2" 1519752 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-624 1516631 1516955 1517339 "MAPPKG3" 1518194 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-623 1515612 1515785 1516007 "MAPPKG2" 1516455 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-622 1514111 1514395 1514722 "MAPPKG1" 1515318 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-621 1513722 1513780 1513903 "MAPHACK3" 1514047 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-620 1513314 1513375 1513489 "MAPHACK2" 1513654 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-619 1512752 1512855 1512997 "MAPHACK1" 1513205 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-618 1510860 1511454 1511757 "MAGMA" 1512481 NIL MAGMA (NIL T) -8 NIL NIL) (-617 1507334 1509104 1509564 "M3D" 1510433 NIL M3D (NIL T) -8 NIL NIL) (-616 1501490 1505705 1505746 "LZSTAGG" 1506528 NIL LZSTAGG (NIL T) -9 NIL 1506823) (-615 1497463 1498621 1500078 "LZSTAGG-" 1500083 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-614 1494579 1495356 1495842 "LWORD" 1497009 NIL LWORD (NIL T) -8 NIL NIL) (-613 1487739 1494350 1494484 "LSQM" 1494489 NIL LSQM (NIL NIL T) -8 NIL NIL) (-612 1486963 1487102 1487330 "LSPP" 1487594 NIL LSPP (NIL T T T T) -7 NIL NIL) (-611 1484775 1485076 1485532 "LSMP" 1486652 NIL LSMP (NIL T T T T) -7 NIL NIL) (-610 1481554 1482228 1482958 "LSMP1" 1484077 NIL LSMP1 (NIL T) -7 NIL NIL) (-609 1475481 1480723 1480764 "LSAGG" 1480826 NIL LSAGG (NIL T) -9 NIL 1480904) (-608 1472176 1473100 1474313 "LSAGG-" 1474318 NIL LSAGG- (NIL T T) -8 NIL NIL) (-607 1469802 1471320 1471569 "LPOLY" 1471971 NIL LPOLY (NIL T T) -8 NIL NIL) (-606 1469384 1469469 1469592 "LPEFRAC" 1469711 NIL LPEFRAC (NIL T) -7 NIL NIL) (-605 1467731 1468478 1468731 "LO" 1469216 NIL LO (NIL T T T) -8 NIL NIL) (-604 1467385 1467497 1467525 "LOGIC" 1467636 T LOGIC (NIL) -9 NIL 1467716) (-603 1467247 1467270 1467341 "LOGIC-" 1467346 NIL LOGIC- (NIL T) -8 NIL NIL) (-602 1466440 1466580 1466773 "LODOOPS" 1467103 NIL LODOOPS (NIL T T) -7 NIL NIL) (-601 1463858 1466357 1466422 "LODO" 1466427 NIL LODO (NIL T NIL) -8 NIL NIL) (-600 1462404 1462639 1462990 "LODOF" 1463605 NIL LODOF (NIL T T) -7 NIL NIL) (-599 1458824 1461260 1461300 "LODOCAT" 1461732 NIL LODOCAT (NIL T) -9 NIL 1461943) (-598 1458558 1458616 1458742 "LODOCAT-" 1458747 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-597 1455872 1458399 1458517 "LODO2" 1458522 NIL LODO2 (NIL T T) -8 NIL NIL) (-596 1453301 1455809 1455854 "LODO1" 1455859 NIL LODO1 (NIL T) -8 NIL NIL) (-595 1452164 1452329 1452640 "LODEEF" 1453124 NIL LODEEF (NIL T T T) -7 NIL NIL) (-594 1447451 1450295 1450336 "LNAGG" 1451283 NIL LNAGG (NIL T) -9 NIL 1451727) (-593 1446598 1446812 1447154 "LNAGG-" 1447159 NIL LNAGG- (NIL T T) -8 NIL NIL) (-592 1442763 1443525 1444163 "LMOPS" 1446014 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-591 1442161 1442523 1442563 "LMODULE" 1442623 NIL LMODULE (NIL T) -9 NIL 1442665) (-590 1439407 1441806 1441929 "LMDICT" 1442071 NIL LMDICT (NIL T) -8 NIL NIL) (-589 1432634 1438353 1438651 "LIST" 1439142 NIL LIST (NIL T) -8 NIL NIL) (-588 1432159 1432233 1432372 "LIST3" 1432554 NIL LIST3 (NIL T T T) -7 NIL NIL) (-587 1431166 1431344 1431572 "LIST2" 1431977 NIL LIST2 (NIL T T) -7 NIL NIL) (-586 1429300 1429612 1430011 "LIST2MAP" 1430813 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-585 1428013 1428693 1428733 "LINEXP" 1428986 NIL LINEXP (NIL T) -9 NIL 1429134) (-584 1426660 1426920 1427217 "LINDEP" 1427765 NIL LINDEP (NIL T T) -7 NIL NIL) (-583 1423427 1424146 1424923 "LIMITRF" 1425915 NIL LIMITRF (NIL T) -7 NIL NIL) (-582 1421707 1422002 1422417 "LIMITPS" 1423122 NIL LIMITPS (NIL T T) -7 NIL NIL) (-581 1416162 1421218 1421446 "LIE" 1421528 NIL LIE (NIL T T) -8 NIL NIL) (-580 1415213 1415656 1415696 "LIECAT" 1415836 NIL LIECAT (NIL T) -9 NIL 1415987) (-579 1415054 1415081 1415169 "LIECAT-" 1415174 NIL LIECAT- (NIL T T) -8 NIL NIL) (-578 1407666 1414503 1414668 "LIB" 1414909 T LIB (NIL) -8 NIL NIL) (-577 1403303 1404184 1405119 "LGROBP" 1406783 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-576 1401169 1401443 1401805 "LF" 1403024 NIL LF (NIL T T) -7 NIL NIL) (-575 1400009 1400701 1400729 "LFCAT" 1400936 T LFCAT (NIL) -9 NIL 1401075) (-574 1396921 1397547 1398233 "LEXTRIPK" 1399375 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-573 1393627 1394491 1394994 "LEXP" 1396501 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-572 1392025 1392338 1392739 "LEADCDET" 1393309 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-571 1391221 1391295 1391522 "LAZM3PK" 1391946 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-570 1386137 1389300 1389837 "LAUPOL" 1390734 NIL LAUPOL (NIL T T) -8 NIL NIL) (-569 1385704 1385748 1385915 "LAPLACE" 1386087 NIL LAPLACE (NIL T T) -7 NIL NIL) (-568 1383632 1384805 1385056 "LA" 1385537 NIL LA (NIL T T T) -8 NIL NIL) (-567 1382695 1383289 1383329 "LALG" 1383390 NIL LALG (NIL T) -9 NIL 1383448) (-566 1382410 1382469 1382604 "LALG-" 1382609 NIL LALG- (NIL T T) -8 NIL NIL) (-565 1381320 1381507 1381804 "KOVACIC" 1382210 NIL KOVACIC (NIL T T) -7 NIL NIL) (-564 1381155 1381179 1381220 "KONVERT" 1381282 NIL KONVERT (NIL T) -9 NIL NIL) (-563 1380990 1381014 1381055 "KOERCE" 1381117 NIL KOERCE (NIL T) -9 NIL NIL) (-562 1378724 1379484 1379877 "KERNEL" 1380629 NIL KERNEL (NIL T) -8 NIL NIL) (-561 1378226 1378307 1378437 "KERNEL2" 1378638 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-560 1372078 1376766 1376820 "KDAGG" 1377197 NIL KDAGG (NIL T T) -9 NIL 1377403) (-559 1371607 1371731 1371936 "KDAGG-" 1371941 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-558 1364782 1371268 1371423 "KAFILE" 1371485 NIL KAFILE (NIL T) -8 NIL NIL) (-557 1359237 1364293 1364521 "JORDAN" 1364603 NIL JORDAN (NIL T T) -8 NIL NIL) (-556 1355537 1357443 1357497 "IXAGG" 1358426 NIL IXAGG (NIL T T) -9 NIL 1358885) (-555 1354456 1354762 1355181 "IXAGG-" 1355186 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-554 1350041 1354378 1354437 "IVECTOR" 1354442 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-553 1348807 1349044 1349310 "ITUPLE" 1349808 NIL ITUPLE (NIL T) -8 NIL NIL) (-552 1347243 1347420 1347726 "ITRIGMNP" 1348629 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-551 1345988 1346192 1346475 "ITFUN3" 1347019 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-550 1345620 1345677 1345786 "ITFUN2" 1345925 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-549 1343422 1344493 1344790 "ITAYLOR" 1345355 NIL ITAYLOR (NIL T) -8 NIL NIL) (-548 1332410 1337608 1338767 "ISUPS" 1342295 NIL ISUPS (NIL T) -8 NIL NIL) (-547 1331514 1331654 1331890 "ISUMP" 1332257 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-546 1326778 1331315 1331394 "ISTRING" 1331467 NIL ISTRING (NIL NIL) -8 NIL NIL) (-545 1325991 1326072 1326287 "IRURPK" 1326692 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-544 1324927 1325128 1325368 "IRSN" 1325771 T IRSN (NIL) -7 NIL NIL) (-543 1322962 1323317 1323752 "IRRF2F" 1324565 NIL IRRF2F (NIL T) -7 NIL NIL) (-542 1322709 1322747 1322823 "IRREDFFX" 1322918 NIL IRREDFFX (NIL T) -7 NIL NIL) (-541 1321324 1321583 1321882 "IROOT" 1322442 NIL IROOT (NIL T) -7 NIL NIL) (-540 1317962 1319013 1319703 "IR" 1320666 NIL IR (NIL T) -8 NIL NIL) (-539 1315575 1316070 1316636 "IR2" 1317440 NIL IR2 (NIL T T) -7 NIL NIL) (-538 1314651 1314764 1314984 "IR2F" 1315458 NIL IR2F (NIL T T) -7 NIL NIL) (-537 1314442 1314476 1314536 "IPRNTPK" 1314611 T IPRNTPK (NIL) -7 NIL NIL) (-536 1310996 1314331 1314400 "IPF" 1314405 NIL IPF (NIL NIL) -8 NIL NIL) (-535 1309313 1310921 1310978 "IPADIC" 1310983 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-534 1308812 1308870 1309059 "INVLAPLA" 1309249 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-533 1298461 1300814 1303200 "INTTR" 1306476 NIL INTTR (NIL T T) -7 NIL NIL) (-532 1294809 1295550 1296413 "INTTOOLS" 1297647 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-531 1294395 1294486 1294603 "INTSLPE" 1294712 T INTSLPE (NIL) -7 NIL NIL) (-530 1292345 1294318 1294377 "INTRVL" 1294382 NIL INTRVL (NIL T) -8 NIL NIL) (-529 1289952 1290464 1291038 "INTRF" 1291830 NIL INTRF (NIL T) -7 NIL NIL) (-528 1289367 1289464 1289605 "INTRET" 1289850 NIL INTRET (NIL T) -7 NIL NIL) (-527 1287369 1287758 1288227 "INTRAT" 1288975 NIL INTRAT (NIL T T) -7 NIL NIL) (-526 1284602 1285185 1285810 "INTPM" 1286854 NIL INTPM (NIL T T) -7 NIL NIL) (-525 1281311 1281910 1282654 "INTPAF" 1283988 NIL INTPAF (NIL T T T) -7 NIL NIL) (-524 1276554 1277500 1278535 "INTPACK" 1280296 T INTPACK (NIL) -7 NIL NIL) (-523 1273408 1276283 1276410 "INT" 1276447 T INT (NIL) -8 NIL NIL) (-522 1272660 1272812 1273020 "INTHERTR" 1273250 NIL INTHERTR (NIL T T) -7 NIL NIL) (-521 1272099 1272179 1272367 "INTHERAL" 1272574 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-520 1269945 1270388 1270845 "INTHEORY" 1271662 T INTHEORY (NIL) -7 NIL NIL) (-519 1261268 1262888 1264666 "INTG0" 1268297 NIL INTG0 (NIL T T T) -7 NIL NIL) (-518 1241841 1246631 1251441 "INTFTBL" 1256478 T INTFTBL (NIL) -8 NIL NIL) (-517 1241090 1241228 1241401 "INTFACT" 1241700 NIL INTFACT (NIL T) -7 NIL NIL) (-516 1238481 1238927 1239490 "INTEF" 1240644 NIL INTEF (NIL T T) -7 NIL NIL) (-515 1236943 1237692 1237720 "INTDOM" 1238021 T INTDOM (NIL) -9 NIL 1238228) (-514 1236312 1236486 1236728 "INTDOM-" 1236733 NIL INTDOM- (NIL T) -8 NIL NIL) (-513 1232805 1234737 1234791 "INTCAT" 1235590 NIL INTCAT (NIL T) -9 NIL 1235909) (-512 1232278 1232380 1232508 "INTBIT" 1232697 T INTBIT (NIL) -7 NIL NIL) (-511 1230953 1231107 1231420 "INTALG" 1232123 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-510 1230410 1230500 1230670 "INTAF" 1230857 NIL INTAF (NIL T T) -7 NIL NIL) (-509 1223864 1230220 1230360 "INTABL" 1230365 NIL INTABL (NIL T T T) -8 NIL NIL) (-508 1218815 1221544 1221572 "INS" 1222540 T INS (NIL) -9 NIL 1223221) (-507 1216055 1216826 1217800 "INS-" 1217873 NIL INS- (NIL T) -8 NIL NIL) (-506 1214834 1215061 1215358 "INPSIGN" 1215808 NIL INPSIGN (NIL T T) -7 NIL NIL) (-505 1213952 1214069 1214266 "INPRODPF" 1214714 NIL INPRODPF (NIL T T) -7 NIL NIL) (-504 1212846 1212963 1213200 "INPRODFF" 1213832 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-503 1211846 1211998 1212258 "INNMFACT" 1212682 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-502 1211043 1211140 1211328 "INMODGCD" 1211745 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-501 1209552 1209796 1210120 "INFSP" 1210788 NIL INFSP (NIL T T T) -7 NIL NIL) (-500 1208736 1208853 1209036 "INFPROD0" 1209432 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-499 1205746 1206905 1207396 "INFORM" 1208253 T INFORM (NIL) -8 NIL NIL) (-498 1205356 1205416 1205514 "INFORM1" 1205681 NIL INFORM1 (NIL T) -7 NIL NIL) (-497 1204879 1204968 1205082 "INFINITY" 1205262 T INFINITY (NIL) -7 NIL NIL) (-496 1203497 1203745 1204066 "INEP" 1204627 NIL INEP (NIL T T T) -7 NIL NIL) (-495 1202773 1203394 1203459 "INDE" 1203464 NIL INDE (NIL T) -8 NIL NIL) (-494 1202337 1202405 1202522 "INCRMAPS" 1202700 NIL INCRMAPS (NIL T) -7 NIL NIL) (-493 1197648 1198573 1199517 "INBFF" 1201425 NIL INBFF (NIL T) -7 NIL NIL) (-492 1194143 1197493 1197596 "IMATRIX" 1197601 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-491 1192855 1192978 1193293 "IMATQF" 1193999 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-490 1191075 1191302 1191639 "IMATLIN" 1192611 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-489 1185701 1190999 1191057 "ILIST" 1191062 NIL ILIST (NIL T NIL) -8 NIL NIL) (-488 1183654 1185561 1185674 "IIARRAY2" 1185679 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-487 1179022 1183565 1183629 "IFF" 1183634 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-486 1174065 1178314 1178502 "IFARRAY" 1178879 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-485 1173272 1173969 1174042 "IFAMON" 1174047 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-484 1172856 1172921 1172975 "IEVALAB" 1173182 NIL IEVALAB (NIL T T) -9 NIL NIL) (-483 1172531 1172599 1172759 "IEVALAB-" 1172764 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-482 1172189 1172445 1172508 "IDPO" 1172513 NIL IDPO (NIL T T) -8 NIL NIL) (-481 1171466 1172078 1172153 "IDPOAMS" 1172158 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-480 1170800 1171355 1171430 "IDPOAM" 1171435 NIL IDPOAM (NIL T T) -8 NIL NIL) (-479 1169886 1170136 1170189 "IDPC" 1170602 NIL IDPC (NIL T T) -9 NIL 1170751) (-478 1169382 1169778 1169851 "IDPAM" 1169856 NIL IDPAM (NIL T T) -8 NIL NIL) (-477 1168785 1169274 1169347 "IDPAG" 1169352 NIL IDPAG (NIL T T) -8 NIL NIL) (-476 1165040 1165888 1166783 "IDECOMP" 1167942 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-475 1157914 1158963 1160010 "IDEAL" 1164076 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-474 1157078 1157190 1157389 "ICDEN" 1157798 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-473 1156177 1156558 1156705 "ICARD" 1156951 T ICARD (NIL) -8 NIL NIL) (-472 1154249 1154562 1154965 "IBPTOOLS" 1155854 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-471 1149863 1153869 1153982 "IBITS" 1154168 NIL IBITS (NIL NIL) -8 NIL NIL) (-470 1146586 1147162 1147857 "IBATOOL" 1149280 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-469 1144366 1144827 1145360 "IBACHIN" 1146121 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-468 1142243 1144212 1144315 "IARRAY2" 1144320 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-467 1138396 1142169 1142226 "IARRAY1" 1142231 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-466 1132335 1136814 1137292 "IAN" 1137938 T IAN (NIL) -8 NIL NIL) (-465 1131846 1131903 1132076 "IALGFACT" 1132272 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-464 1131374 1131487 1131515 "HYPCAT" 1131722 T HYPCAT (NIL) -9 NIL NIL) (-463 1130912 1131029 1131215 "HYPCAT-" 1131220 NIL HYPCAT- (NIL T) -8 NIL NIL) (-462 1127592 1128923 1128964 "HOAGG" 1129945 NIL HOAGG (NIL T) -9 NIL 1130624) (-461 1126186 1126585 1127111 "HOAGG-" 1127116 NIL HOAGG- (NIL T T) -8 NIL NIL) (-460 1120017 1125627 1125793 "HEXADEC" 1126040 T HEXADEC (NIL) -8 NIL NIL) (-459 1118765 1118987 1119250 "HEUGCD" 1119794 NIL HEUGCD (NIL T) -7 NIL NIL) (-458 1117868 1118602 1118732 "HELLFDIV" 1118737 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-457 1116096 1117645 1117733 "HEAP" 1117812 NIL HEAP (NIL T) -8 NIL NIL) (-456 1109963 1116011 1116073 "HDP" 1116078 NIL HDP (NIL NIL T) -8 NIL NIL) (-455 1103675 1109600 1109751 "HDMP" 1109864 NIL HDMP (NIL NIL T) -8 NIL NIL) (-454 1103000 1103139 1103303 "HB" 1103531 T HB (NIL) -7 NIL NIL) (-453 1096497 1102846 1102950 "HASHTBL" 1102955 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-452 1094250 1096125 1096304 "HACKPI" 1096338 T HACKPI (NIL) -8 NIL NIL) (-451 1089946 1094104 1094216 "GTSET" 1094221 NIL GTSET (NIL T T T T) -8 NIL NIL) (-450 1083472 1089824 1089922 "GSTBL" 1089927 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-449 1075705 1082508 1082772 "GSERIES" 1083263 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-448 1074728 1075181 1075209 "GROUP" 1075470 T GROUP (NIL) -9 NIL 1075629) (-447 1073844 1074067 1074411 "GROUP-" 1074416 NIL GROUP- (NIL T) -8 NIL NIL) (-446 1072213 1072532 1072919 "GROEBSOL" 1073521 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-445 1071154 1071416 1071467 "GRMOD" 1071996 NIL GRMOD (NIL T T) -9 NIL 1072164) (-444 1070922 1070958 1071086 "GRMOD-" 1071091 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-443 1066250 1067276 1068276 "GRIMAGE" 1069942 T GRIMAGE (NIL) -8 NIL NIL) (-442 1064717 1064977 1065301 "GRDEF" 1065946 T GRDEF (NIL) -7 NIL NIL) (-441 1064161 1064277 1064418 "GRAY" 1064596 T GRAY (NIL) -7 NIL NIL) (-440 1063395 1063775 1063826 "GRALG" 1063979 NIL GRALG (NIL T T) -9 NIL 1064071) (-439 1063056 1063129 1063292 "GRALG-" 1063297 NIL GRALG- (NIL T T T) -8 NIL NIL) (-438 1059864 1062645 1062821 "GPOLSET" 1062963 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-437 1059220 1059277 1059534 "GOSPER" 1059801 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-436 1054979 1055658 1056184 "GMODPOL" 1058919 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-435 1053984 1054168 1054406 "GHENSEL" 1054791 NIL GHENSEL (NIL T T) -7 NIL NIL) (-434 1048050 1048893 1049919 "GENUPS" 1053068 NIL GENUPS (NIL T T) -7 NIL NIL) (-433 1047747 1047798 1047887 "GENUFACT" 1047993 NIL GENUFACT (NIL T) -7 NIL NIL) (-432 1047159 1047236 1047401 "GENPGCD" 1047665 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-431 1046633 1046668 1046881 "GENMFACT" 1047118 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-430 1045201 1045456 1045763 "GENEEZ" 1046376 NIL GENEEZ (NIL T T) -7 NIL NIL) (-429 1039075 1044814 1044975 "GDMP" 1045124 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-428 1028457 1032846 1033952 "GCNAALG" 1038058 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-427 1026879 1027751 1027779 "GCDDOM" 1028034 T GCDDOM (NIL) -9 NIL 1028191) (-426 1026349 1026476 1026691 "GCDDOM-" 1026696 NIL GCDDOM- (NIL T) -8 NIL NIL) (-425 1025021 1025206 1025510 "GB" 1026128 NIL GB (NIL T T T T) -7 NIL NIL) (-424 1013641 1015967 1018359 "GBINTERN" 1022712 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-423 1011478 1011770 1012191 "GBF" 1013316 NIL GBF (NIL T T T T) -7 NIL NIL) (-422 1010259 1010424 1010691 "GBEUCLID" 1011294 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-421 1009608 1009733 1009882 "GAUSSFAC" 1010130 T GAUSSFAC (NIL) -7 NIL NIL) (-420 1007985 1008287 1008600 "GALUTIL" 1009327 NIL GALUTIL (NIL T) -7 NIL NIL) (-419 1006302 1006576 1006899 "GALPOLYU" 1007712 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-418 1003691 1003981 1004386 "GALFACTU" 1005999 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-417 995497 996996 998604 "GALFACT" 1002123 NIL GALFACT (NIL T) -7 NIL NIL) (-416 992885 993543 993571 "FVFUN" 994727 T FVFUN (NIL) -9 NIL 995447) (-415 992151 992333 992361 "FVC" 992652 T FVC (NIL) -9 NIL 992835) (-414 991793 991948 992029 "FUNCTION" 992103 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-413 989463 990014 990503 "FT" 991324 T FT (NIL) -8 NIL NIL) (-412 988281 988764 988967 "FTEM" 989280 T FTEM (NIL) -8 NIL NIL) (-411 986546 986834 987236 "FSUPFACT" 987973 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-410 984943 985232 985564 "FST" 986234 T FST (NIL) -8 NIL NIL) (-409 984118 984224 984418 "FSRED" 984825 NIL FSRED (NIL T T) -7 NIL NIL) (-408 982797 983052 983406 "FSPRMELT" 983833 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-407 979882 980320 980819 "FSPECF" 982360 NIL FSPECF (NIL T T) -7 NIL NIL) (-406 962256 970813 970853 "FS" 974691 NIL FS (NIL T) -9 NIL 976973) (-405 950906 953896 957952 "FS-" 958249 NIL FS- (NIL T T) -8 NIL NIL) (-404 950422 950476 950652 "FSINT" 950847 NIL FSINT (NIL T T) -7 NIL NIL) (-403 948703 949415 949718 "FSERIES" 950201 NIL FSERIES (NIL T T) -8 NIL NIL) (-402 947721 947837 948067 "FSCINT" 948583 NIL FSCINT (NIL T T) -7 NIL NIL) (-401 943956 946666 946707 "FSAGG" 947077 NIL FSAGG (NIL T) -9 NIL 947336) (-400 941718 942319 943115 "FSAGG-" 943210 NIL FSAGG- (NIL T T) -8 NIL NIL) (-399 940760 940903 941130 "FSAGG2" 941571 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-398 938419 938698 939251 "FS2UPS" 940478 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-397 938005 938048 938201 "FS2" 938370 NIL FS2 (NIL T T T T) -7 NIL NIL) (-396 936865 937036 937344 "FS2EXPXP" 937830 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-395 936291 936406 936558 "FRUTIL" 936745 NIL FRUTIL (NIL T) -7 NIL NIL) (-394 927712 931790 933146 "FR" 934967 NIL FR (NIL T) -8 NIL NIL) (-393 922789 925432 925472 "FRNAALG" 926868 NIL FRNAALG (NIL T) -9 NIL 927475) (-392 918468 919538 920813 "FRNAALG-" 921563 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-391 918106 918149 918276 "FRNAAF2" 918419 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-390 916471 916963 917257 "FRMOD" 917919 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-389 914194 914862 915178 "FRIDEAL" 916262 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-388 913393 913480 913767 "FRIDEAL2" 914101 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-387 912651 913059 913100 "FRETRCT" 913105 NIL FRETRCT (NIL T) -9 NIL 913276) (-386 911763 911994 912345 "FRETRCT-" 912350 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-385 908973 910193 910252 "FRAMALG" 911134 NIL FRAMALG (NIL T T) -9 NIL 911426) (-384 907106 907562 908192 "FRAMALG-" 908415 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-383 901008 906581 906857 "FRAC" 906862 NIL FRAC (NIL T) -8 NIL NIL) (-382 900644 900701 900808 "FRAC2" 900945 NIL FRAC2 (NIL T T) -7 NIL NIL) (-381 900280 900337 900444 "FR2" 900581 NIL FR2 (NIL T T) -7 NIL NIL) (-380 894954 897867 897895 "FPS" 899014 T FPS (NIL) -9 NIL 899570) (-379 894403 894512 894676 "FPS-" 894822 NIL FPS- (NIL T) -8 NIL NIL) (-378 891852 893549 893577 "FPC" 893802 T FPC (NIL) -9 NIL 893944) (-377 891645 891685 891782 "FPC-" 891787 NIL FPC- (NIL T) -8 NIL NIL) (-376 890524 891134 891175 "FPATMAB" 891180 NIL FPATMAB (NIL T) -9 NIL 891332) (-375 888224 888700 889126 "FPARFRAC" 890161 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-374 883619 884116 884798 "FORTRAN" 887656 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-373 881335 881835 882374 "FORT" 883100 T FORT (NIL) -7 NIL NIL) (-372 879011 879573 879601 "FORTFN" 880661 T FORTFN (NIL) -9 NIL 881285) (-371 878775 878825 878853 "FORTCAT" 878912 T FORTCAT (NIL) -9 NIL 878974) (-370 876835 877318 877717 "FORMULA" 878396 T FORMULA (NIL) -8 NIL NIL) (-369 876623 876653 876722 "FORMULA1" 876799 NIL FORMULA1 (NIL T) -7 NIL NIL) (-368 876146 876198 876371 "FORDER" 876565 NIL FORDER (NIL T T T T) -7 NIL NIL) (-367 875242 875406 875599 "FOP" 875973 T FOP (NIL) -7 NIL NIL) (-366 873850 874522 874696 "FNLA" 875124 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-365 872519 872908 872936 "FNCAT" 873508 T FNCAT (NIL) -9 NIL 873801) (-364 872085 872478 872506 "FNAME" 872511 T FNAME (NIL) -8 NIL NIL) (-363 870745 871718 871746 "FMTC" 871751 T FMTC (NIL) -9 NIL 871786) (-362 867063 868270 868898 "FMONOID" 870150 NIL FMONOID (NIL T) -8 NIL NIL) (-361 866283 866806 866954 "FM" 866959 NIL FM (NIL T T) -8 NIL NIL) (-360 863707 864353 864381 "FMFUN" 865525 T FMFUN (NIL) -9 NIL 866233) (-359 862976 863157 863185 "FMC" 863475 T FMC (NIL) -9 NIL 863657) (-358 860206 861040 861093 "FMCAT" 862275 NIL FMCAT (NIL T T) -9 NIL 862769) (-357 859101 859974 860073 "FM1" 860151 NIL FM1 (NIL T T) -8 NIL NIL) (-356 856875 857291 857785 "FLOATRP" 858652 NIL FLOATRP (NIL T) -7 NIL NIL) (-355 850361 854531 855161 "FLOAT" 856265 T FLOAT (NIL) -8 NIL NIL) (-354 847799 848299 848877 "FLOATCP" 849828 NIL FLOATCP (NIL T) -7 NIL NIL) (-353 846588 847436 847476 "FLINEXP" 847481 NIL FLINEXP (NIL T) -9 NIL 847574) (-352 845743 845978 846305 "FLINEXP-" 846310 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-351 844819 844963 845187 "FLASORT" 845595 NIL FLASORT (NIL T T) -7 NIL NIL) (-350 842038 842880 842932 "FLALG" 844159 NIL FLALG (NIL T T) -9 NIL 844626) (-349 835823 839525 839566 "FLAGG" 840828 NIL FLAGG (NIL T) -9 NIL 841480) (-348 834549 834888 835378 "FLAGG-" 835383 NIL FLAGG- (NIL T T) -8 NIL NIL) (-347 833591 833734 833961 "FLAGG2" 834402 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-346 830564 831582 831641 "FINRALG" 832769 NIL FINRALG (NIL T T) -9 NIL 833277) (-345 829724 829953 830292 "FINRALG-" 830297 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-344 829131 829344 829372 "FINITE" 829568 T FINITE (NIL) -9 NIL 829675) (-343 821591 823752 823792 "FINAALG" 827459 NIL FINAALG (NIL T) -9 NIL 828912) (-342 816932 817973 819117 "FINAALG-" 820496 NIL FINAALG- (NIL T T) -8 NIL NIL) (-341 816327 816687 816790 "FILE" 816862 NIL FILE (NIL T) -8 NIL NIL) (-340 815012 815324 815378 "FILECAT" 816062 NIL FILECAT (NIL T T) -9 NIL 816278) (-339 812875 814431 814459 "FIELD" 814499 T FIELD (NIL) -9 NIL 814579) (-338 811495 811880 812391 "FIELD-" 812396 NIL FIELD- (NIL T) -8 NIL NIL) (-337 809310 810132 810478 "FGROUP" 811182 NIL FGROUP (NIL T) -8 NIL NIL) (-336 808400 808564 808784 "FGLMICPK" 809142 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-335 804202 808325 808382 "FFX" 808387 NIL FFX (NIL T NIL) -8 NIL NIL) (-334 803803 803864 803999 "FFSLPE" 804135 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-333 799798 800575 801371 "FFPOLY" 803039 NIL FFPOLY (NIL T) -7 NIL NIL) (-332 799302 799338 799547 "FFPOLY2" 799756 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-331 795124 799221 799284 "FFP" 799289 NIL FFP (NIL T NIL) -8 NIL NIL) (-330 790492 795035 795099 "FF" 795104 NIL FF (NIL NIL NIL) -8 NIL NIL) (-329 785588 789835 790025 "FFNBX" 790346 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-328 780498 784723 784981 "FFNBP" 785442 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-327 775101 779782 779993 "FFNB" 780331 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-326 773933 774131 774446 "FFINTBAS" 774898 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-325 770157 772397 772425 "FFIELDC" 773045 T FFIELDC (NIL) -9 NIL 773421) (-324 768820 769190 769687 "FFIELDC-" 769692 NIL FFIELDC- (NIL T) -8 NIL NIL) (-323 768390 768435 768559 "FFHOM" 768762 NIL FFHOM (NIL T T T) -7 NIL NIL) (-322 766088 766572 767089 "FFF" 767905 NIL FFF (NIL T) -7 NIL NIL) (-321 761676 765830 765931 "FFCGX" 766031 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-320 757278 761408 761515 "FFCGP" 761619 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-319 752431 757005 757113 "FFCG" 757214 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-318 734377 743500 743586 "FFCAT" 748751 NIL FFCAT (NIL T T T) -9 NIL 750238) (-317 729575 730622 731936 "FFCAT-" 733166 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-316 728986 729029 729264 "FFCAT2" 729526 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-315 718186 721976 723193 "FEXPR" 727841 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-314 717186 717621 717662 "FEVALAB" 717746 NIL FEVALAB (NIL T) -9 NIL 718007) (-313 716345 716555 716893 "FEVALAB-" 716898 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-312 714938 715728 715931 "FDIV" 716244 NIL FDIV (NIL T T T T) -8 NIL NIL) (-311 712005 712720 712835 "FDIVCAT" 714403 NIL FDIVCAT (NIL T T T T) -9 NIL 714840) (-310 711767 711794 711964 "FDIVCAT-" 711969 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-309 710987 711074 711351 "FDIV2" 711674 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-308 709673 709932 710221 "FCPAK1" 710718 T FCPAK1 (NIL) -7 NIL NIL) (-307 708801 709173 709314 "FCOMP" 709564 NIL FCOMP (NIL T) -8 NIL NIL) (-306 692437 695850 699411 "FC" 705260 T FC (NIL) -8 NIL NIL) (-305 685033 689079 689119 "FAXF" 690921 NIL FAXF (NIL T) -9 NIL 691612) (-304 682312 682967 683792 "FAXF-" 684257 NIL FAXF- (NIL T T) -8 NIL NIL) (-303 677412 681688 681864 "FARRAY" 682169 NIL FARRAY (NIL T) -8 NIL NIL) (-302 672803 674874 674926 "FAMR" 675938 NIL FAMR (NIL T T) -9 NIL 676398) (-301 671694 671996 672430 "FAMR-" 672435 NIL FAMR- (NIL T T T) -8 NIL NIL) (-300 670890 671616 671669 "FAMONOID" 671674 NIL FAMONOID (NIL T) -8 NIL NIL) (-299 668723 669407 669460 "FAMONC" 670401 NIL FAMONC (NIL T T) -9 NIL 670786) (-298 667415 668477 668614 "FAGROUP" 668619 NIL FAGROUP (NIL T) -8 NIL NIL) (-297 665218 665537 665939 "FACUTIL" 667096 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-296 664317 664502 664724 "FACTFUNC" 665028 NIL FACTFUNC (NIL T) -7 NIL NIL) (-295 656637 663568 663780 "EXPUPXS" 664173 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-294 654120 654660 655246 "EXPRTUBE" 656071 T EXPRTUBE (NIL) -7 NIL NIL) (-293 650314 650906 651643 "EXPRODE" 653459 NIL EXPRODE (NIL T T) -7 NIL NIL) (-292 635473 648973 649399 "EXPR" 649920 NIL EXPR (NIL T) -8 NIL NIL) (-291 629901 630488 631300 "EXPR2UPS" 634771 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-290 629537 629594 629701 "EXPR2" 629838 NIL EXPR2 (NIL T T) -7 NIL NIL) (-289 620891 628674 628969 "EXPEXPAN" 629375 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-288 620718 620848 620877 "EXIT" 620882 T EXIT (NIL) -8 NIL NIL) (-287 620345 620407 620520 "EVALCYC" 620650 NIL EVALCYC (NIL T) -7 NIL NIL) (-286 619886 620004 620045 "EVALAB" 620215 NIL EVALAB (NIL T) -9 NIL 620319) (-285 619367 619489 619710 "EVALAB-" 619715 NIL EVALAB- (NIL T T) -8 NIL NIL) (-284 616830 618142 618170 "EUCDOM" 618725 T EUCDOM (NIL) -9 NIL 619075) (-283 615235 615677 616267 "EUCDOM-" 616272 NIL EUCDOM- (NIL T) -8 NIL NIL) (-282 602813 605561 608301 "ESTOOLS" 612515 T ESTOOLS (NIL) -7 NIL NIL) (-281 602449 602506 602613 "ESTOOLS2" 602750 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-280 602200 602242 602322 "ESTOOLS1" 602401 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-279 596138 597862 597890 "ES" 600654 T ES (NIL) -9 NIL 602060) (-278 591086 592372 594189 "ES-" 594353 NIL ES- (NIL T) -8 NIL NIL) (-277 587461 588221 589001 "ESCONT" 590326 T ESCONT (NIL) -7 NIL NIL) (-276 587206 587238 587320 "ESCONT1" 587423 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-275 586881 586931 587031 "ES2" 587150 NIL ES2 (NIL T T) -7 NIL NIL) (-274 586511 586569 586678 "ES1" 586817 NIL ES1 (NIL T T) -7 NIL NIL) (-273 585727 585856 586032 "ERROR" 586355 T ERROR (NIL) -7 NIL NIL) (-272 579230 585586 585677 "EQTBL" 585682 NIL EQTBL (NIL T T) -8 NIL NIL) (-271 571667 574548 575995 "EQ" 577816 NIL -2608 (NIL T) -8 NIL NIL) (-270 571299 571356 571465 "EQ2" 571604 NIL EQ2 (NIL T T) -7 NIL NIL) (-269 566591 567637 568730 "EP" 570238 NIL EP (NIL T) -7 NIL NIL) (-268 565174 565474 565791 "ENV" 566294 T ENV (NIL) -8 NIL NIL) (-267 564334 564898 564926 "ENTIRER" 564931 T ENTIRER (NIL) -9 NIL 564976) (-266 560790 562289 562659 "EMR" 564133 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-265 559934 560119 560173 "ELTAGG" 560553 NIL ELTAGG (NIL T T) -9 NIL 560764) (-264 559653 559715 559856 "ELTAGG-" 559861 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-263 559442 559471 559525 "ELTAB" 559609 NIL ELTAB (NIL T T) -9 NIL NIL) (-262 558568 558714 558913 "ELFUTS" 559293 NIL ELFUTS (NIL T T) -7 NIL NIL) (-261 558310 558366 558394 "ELEMFUN" 558499 T ELEMFUN (NIL) -9 NIL NIL) (-260 558180 558201 558269 "ELEMFUN-" 558274 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-259 553072 556281 556322 "ELAGG" 557262 NIL ELAGG (NIL T) -9 NIL 557725) (-258 551357 551791 552454 "ELAGG-" 552459 NIL ELAGG- (NIL T T) -8 NIL NIL) (-257 550014 550294 550589 "ELABEXPR" 551082 T ELABEXPR (NIL) -8 NIL NIL) (-256 542882 544681 545508 "EFUPXS" 549290 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-255 536332 538133 538943 "EFULS" 542158 NIL EFULS (NIL T T T) -8 NIL NIL) (-254 533763 534121 534599 "EFSTRUC" 535964 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-253 522835 524400 525960 "EF" 532278 NIL EF (NIL T T) -7 NIL NIL) (-252 521936 522320 522469 "EAB" 522706 T EAB (NIL) -8 NIL NIL) (-251 521149 521895 521923 "E04UCFA" 521928 T E04UCFA (NIL) -8 NIL NIL) (-250 520362 521108 521136 "E04NAFA" 521141 T E04NAFA (NIL) -8 NIL NIL) (-249 519575 520321 520349 "E04MBFA" 520354 T E04MBFA (NIL) -8 NIL NIL) (-248 518788 519534 519562 "E04JAFA" 519567 T E04JAFA (NIL) -8 NIL NIL) (-247 518003 518747 518775 "E04GCFA" 518780 T E04GCFA (NIL) -8 NIL NIL) (-246 517218 517962 517990 "E04FDFA" 517995 T E04FDFA (NIL) -8 NIL NIL) (-245 516431 517177 517205 "E04DGFA" 517210 T E04DGFA (NIL) -8 NIL NIL) (-244 510616 511961 513323 "E04AGNT" 515089 T E04AGNT (NIL) -7 NIL NIL) (-243 509343 509823 509863 "DVARCAT" 510338 NIL DVARCAT (NIL T) -9 NIL 510536) (-242 508547 508759 509073 "DVARCAT-" 509078 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-241 501409 508349 508476 "DSMP" 508481 NIL DSMP (NIL T T T) -8 NIL NIL) (-240 496219 497354 498422 "DROPT" 500361 T DROPT (NIL) -8 NIL NIL) (-239 495884 495943 496041 "DROPT1" 496154 NIL DROPT1 (NIL T) -7 NIL NIL) (-238 490999 492125 493262 "DROPT0" 494767 T DROPT0 (NIL) -7 NIL NIL) (-237 489344 489669 490055 "DRAWPT" 490633 T DRAWPT (NIL) -7 NIL NIL) (-236 483931 484854 485933 "DRAW" 488318 NIL DRAW (NIL T) -7 NIL NIL) (-235 483564 483617 483735 "DRAWHACK" 483872 NIL DRAWHACK (NIL T) -7 NIL NIL) (-234 482295 482564 482855 "DRAWCX" 483293 T DRAWCX (NIL) -7 NIL NIL) (-233 481813 481881 482031 "DRAWCURV" 482221 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-232 472285 474243 476358 "DRAWCFUN" 479718 T DRAWCFUN (NIL) -7 NIL NIL) (-231 469099 470981 471022 "DQAGG" 471651 NIL DQAGG (NIL T) -9 NIL 471924) (-230 457606 464344 464426 "DPOLCAT" 466264 NIL DPOLCAT (NIL T T T T) -9 NIL 466808) (-229 452446 453792 455749 "DPOLCAT-" 455754 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-228 446530 452308 452405 "DPMO" 452410 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-227 440517 446311 446477 "DPMM" 446482 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-226 440030 440128 440248 "DOMAIN" 440417 T DOMAIN (NIL) -8 NIL NIL) (-225 433742 439667 439818 "DMP" 439931 NIL DMP (NIL NIL T) -8 NIL NIL) (-224 433342 433398 433542 "DLP" 433680 NIL DLP (NIL T) -7 NIL NIL) (-223 426986 432443 432670 "DLIST" 433147 NIL DLIST (NIL T) -8 NIL NIL) (-222 423833 425842 425883 "DLAGG" 426433 NIL DLAGG (NIL T) -9 NIL 426662) (-221 422543 423235 423263 "DIVRING" 423413 T DIVRING (NIL) -9 NIL 423521) (-220 421531 421784 422177 "DIVRING-" 422182 NIL DIVRING- (NIL T) -8 NIL NIL) (-219 419633 419990 420396 "DISPLAY" 421145 T DISPLAY (NIL) -7 NIL NIL) (-218 413522 419547 419610 "DIRPROD" 419615 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-217 412370 412573 412838 "DIRPROD2" 413315 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-216 402001 408006 408059 "DIRPCAT" 408467 NIL DIRPCAT (NIL NIL T) -9 NIL 409294) (-215 399327 399969 400850 "DIRPCAT-" 401187 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-214 398614 398774 398960 "DIOSP" 399161 T DIOSP (NIL) -7 NIL NIL) (-213 395317 397527 397568 "DIOPS" 398002 NIL DIOPS (NIL T) -9 NIL 398231) (-212 394866 394980 395171 "DIOPS-" 395176 NIL DIOPS- (NIL T T) -8 NIL NIL) (-211 393738 394376 394404 "DIFRING" 394591 T DIFRING (NIL) -9 NIL 394700) (-210 393384 393461 393613 "DIFRING-" 393618 NIL DIFRING- (NIL T) -8 NIL NIL) (-209 391174 392456 392496 "DIFEXT" 392855 NIL DIFEXT (NIL T) -9 NIL 393148) (-208 389460 389888 390553 "DIFEXT-" 390558 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-207 386783 388993 389034 "DIAGG" 389039 NIL DIAGG (NIL T) -9 NIL 389059) (-206 386167 386324 386576 "DIAGG-" 386581 NIL DIAGG- (NIL T T) -8 NIL NIL) (-205 381632 385126 385403 "DHMATRIX" 385936 NIL DHMATRIX (NIL T) -8 NIL NIL) (-204 377244 378153 379163 "DFSFUN" 380642 T DFSFUN (NIL) -7 NIL NIL) (-203 372030 375958 376323 "DFLOAT" 376899 T DFLOAT (NIL) -8 NIL NIL) (-202 370263 370544 370939 "DFINTTLS" 371738 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-201 367296 368298 368696 "DERHAM" 369930 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-200 365145 367071 367160 "DEQUEUE" 367240 NIL DEQUEUE (NIL T) -8 NIL NIL) (-199 364363 364496 364691 "DEGRED" 365007 NIL DEGRED (NIL T T) -7 NIL NIL) (-198 360763 361508 362360 "DEFINTRF" 363591 NIL DEFINTRF (NIL T) -7 NIL NIL) (-197 358294 358763 359361 "DEFINTEF" 360282 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-196 352125 357735 357901 "DECIMAL" 358148 T DECIMAL (NIL) -8 NIL NIL) (-195 349637 350095 350601 "DDFACT" 351669 NIL DDFACT (NIL T T) -7 NIL NIL) (-194 349233 349276 349427 "DBLRESP" 349588 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-193 346943 347277 347646 "DBASE" 348991 NIL DBASE (NIL T) -8 NIL NIL) (-192 346078 346902 346930 "D03FAFA" 346935 T D03FAFA (NIL) -8 NIL NIL) (-191 345214 346037 346065 "D03EEFA" 346070 T D03EEFA (NIL) -8 NIL NIL) (-190 343164 343630 344119 "D03AGNT" 344745 T D03AGNT (NIL) -7 NIL NIL) (-189 342482 343123 343151 "D02EJFA" 343156 T D02EJFA (NIL) -8 NIL NIL) (-188 341800 342441 342469 "D02CJFA" 342474 T D02CJFA (NIL) -8 NIL NIL) (-187 341118 341759 341787 "D02BHFA" 341792 T D02BHFA (NIL) -8 NIL NIL) (-186 340436 341077 341105 "D02BBFA" 341110 T D02BBFA (NIL) -8 NIL NIL) (-185 333634 335222 336828 "D02AGNT" 338850 T D02AGNT (NIL) -7 NIL NIL) (-184 331403 331925 332471 "D01WGTS" 333108 T D01WGTS (NIL) -7 NIL NIL) (-183 330506 331362 331390 "D01TRNS" 331395 T D01TRNS (NIL) -8 NIL NIL) (-182 329609 330465 330493 "D01GBFA" 330498 T D01GBFA (NIL) -8 NIL NIL) (-181 328712 329568 329596 "D01FCFA" 329601 T D01FCFA (NIL) -8 NIL NIL) (-180 327815 328671 328699 "D01ASFA" 328704 T D01ASFA (NIL) -8 NIL NIL) (-179 326918 327774 327802 "D01AQFA" 327807 T D01AQFA (NIL) -8 NIL NIL) (-178 326021 326877 326905 "D01APFA" 326910 T D01APFA (NIL) -8 NIL NIL) (-177 325124 325980 326008 "D01ANFA" 326013 T D01ANFA (NIL) -8 NIL NIL) (-176 324227 325083 325111 "D01AMFA" 325116 T D01AMFA (NIL) -8 NIL NIL) (-175 323330 324186 324214 "D01ALFA" 324219 T D01ALFA (NIL) -8 NIL NIL) (-174 322433 323289 323317 "D01AKFA" 323322 T D01AKFA (NIL) -8 NIL NIL) (-173 321536 322392 322420 "D01AJFA" 322425 T D01AJFA (NIL) -8 NIL NIL) (-172 314840 316389 317948 "D01AGNT" 319997 T D01AGNT (NIL) -7 NIL NIL) (-171 314177 314305 314457 "CYCLOTOM" 314708 T CYCLOTOM (NIL) -7 NIL NIL) (-170 310912 311625 312352 "CYCLES" 313470 T CYCLES (NIL) -7 NIL NIL) (-169 310224 310358 310529 "CVMP" 310773 NIL CVMP (NIL T) -7 NIL NIL) (-168 308006 308263 308638 "CTRIGMNP" 309952 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-167 307611 307694 307799 "CTORCALL" 307921 T CTORCALL (NIL) -8 NIL NIL) (-166 306985 307084 307237 "CSTTOOLS" 307508 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-165 302784 303441 304199 "CRFP" 306297 NIL CRFP (NIL T T) -7 NIL NIL) (-164 301831 302016 302244 "CRAPACK" 302588 NIL CRAPACK (NIL T) -7 NIL NIL) (-163 301215 301316 301520 "CPMATCH" 301707 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-162 300940 300968 301074 "CPIMA" 301181 NIL CPIMA (NIL T T T) -7 NIL NIL) (-161 297304 297976 298694 "COORDSYS" 300275 NIL COORDSYS (NIL T) -7 NIL NIL) (-160 296688 296817 296967 "CONTOUR" 297174 T CONTOUR (NIL) -8 NIL NIL) (-159 292549 294691 295183 "CONTFRAC" 296228 NIL CONTFRAC (NIL T) -8 NIL NIL) (-158 291703 292267 292295 "COMRING" 292300 T COMRING (NIL) -9 NIL 292351) (-157 290784 291061 291245 "COMPPROP" 291539 T COMPPROP (NIL) -8 NIL NIL) (-156 290445 290480 290608 "COMPLPAT" 290743 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-155 280426 290254 290363 "COMPLEX" 290368 NIL COMPLEX (NIL T) -8 NIL NIL) (-154 280062 280119 280226 "COMPLEX2" 280363 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-153 279780 279815 279913 "COMPFACT" 280021 NIL COMPFACT (NIL T T) -7 NIL NIL) (-152 264115 274409 274449 "COMPCAT" 275451 NIL COMPCAT (NIL T) -9 NIL 276844) (-151 253630 256554 260181 "COMPCAT-" 260537 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-150 253361 253389 253491 "COMMUPC" 253596 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-149 253156 253189 253248 "COMMONOP" 253322 T COMMONOP (NIL) -7 NIL NIL) (-148 252739 252907 252994 "COMM" 253089 T COMM (NIL) -8 NIL NIL) (-147 251988 252182 252210 "COMBOPC" 252548 T COMBOPC (NIL) -9 NIL 252723) (-146 250884 251094 251336 "COMBINAT" 251778 NIL COMBINAT (NIL T) -7 NIL NIL) (-145 247082 247655 248295 "COMBF" 250306 NIL COMBF (NIL T T) -7 NIL NIL) (-144 245868 246198 246433 "COLOR" 246867 T COLOR (NIL) -8 NIL NIL) (-143 245508 245555 245680 "CMPLXRT" 245815 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-142 241010 242038 243118 "CLIP" 244448 T CLIP (NIL) -7 NIL NIL) (-141 239348 240118 240356 "CLIF" 240838 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-140 235571 237495 237536 "CLAGG" 238465 NIL CLAGG (NIL T) -9 NIL 239001) (-139 233993 234450 235033 "CLAGG-" 235038 NIL CLAGG- (NIL T T) -8 NIL NIL) (-138 233537 233622 233762 "CINTSLPE" 233902 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-137 231038 231509 232057 "CHVAR" 233065 NIL CHVAR (NIL T T T) -7 NIL NIL) (-136 230261 230825 230853 "CHARZ" 230858 T CHARZ (NIL) -9 NIL 230872) (-135 230015 230055 230133 "CHARPOL" 230215 NIL CHARPOL (NIL T) -7 NIL NIL) (-134 229122 229719 229747 "CHARNZ" 229794 T CHARNZ (NIL) -9 NIL 229849) (-133 227147 227812 228147 "CHAR" 228807 T CHAR (NIL) -8 NIL NIL) (-132 226873 226934 226962 "CFCAT" 227073 T CFCAT (NIL) -9 NIL NIL) (-131 226118 226229 226411 "CDEN" 226757 NIL CDEN (NIL T T T) -7 NIL NIL) (-130 222110 225271 225551 "CCLASS" 225858 T CCLASS (NIL) -8 NIL NIL) (-129 222029 222055 222090 "CATEGORY" 222095 T -10 (NIL) -8 NIL NIL) (-128 217082 218058 218811 "CARTEN" 221332 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-127 216190 216338 216559 "CARTEN2" 216929 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 214487 215342 215598 "CARD" 215954 T CARD (NIL) -8 NIL NIL) (-125 213860 214188 214216 "CACHSET" 214348 T CACHSET (NIL) -9 NIL 214425) (-124 213357 213653 213681 "CABMON" 213731 T CABMON (NIL) -9 NIL 213787) (-123 210914 213049 213156 "BTREE" 213283 NIL BTREE (NIL T) -8 NIL NIL) (-122 208412 210562 210684 "BTOURN" 210824 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205831 207884 207925 "BTCAT" 207993 NIL BTCAT (NIL T) -9 NIL 208070) (-120 205498 205578 205727 "BTCAT-" 205732 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200719 204590 204618 "BTAGG" 204874 T BTAGG (NIL) -9 NIL 205053) (-118 200142 200286 200516 "BTAGG-" 200521 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197186 199420 199635 "BSTREE" 199959 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196324 196450 196634 "BRILL" 197042 NIL BRILL (NIL T) -7 NIL NIL) (-115 193026 195053 195094 "BRAGG" 195743 NIL BRAGG (NIL T) -9 NIL 196000) (-114 191555 191961 192516 "BRAGG-" 192521 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184763 190901 191085 "BPADICRT" 191403 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183067 184700 184745 "BPADIC" 184750 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182767 182797 182910 "BOUNDZRO" 183031 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178282 179373 180240 "BOP" 181920 T BOP (NIL) -8 NIL NIL) (-109 175903 176347 176867 "BOP1" 177795 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174522 175233 175456 "BOOLEAN" 175700 T BOOLEAN (NIL) -8 NIL NIL) (-107 173889 174267 174319 "BMODULE" 174324 NIL BMODULE (NIL T T) -9 NIL 174388) (-106 169699 173687 173760 "BITS" 173836 T BITS (NIL) -8 NIL NIL) (-105 168796 169231 169383 "BINFILE" 169567 T BINFILE (NIL) -8 NIL NIL) (-104 168208 168330 168472 "BINDING" 168674 T BINDING (NIL) -8 NIL NIL) (-103 162043 167652 167817 "BINARY" 168063 T BINARY (NIL) -8 NIL NIL) (-102 159871 161299 161340 "BGAGG" 161600 NIL BGAGG (NIL T) -9 NIL 161737) (-101 159702 159734 159825 "BGAGG-" 159830 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158800 159086 159291 "BFUNCT" 159517 T BFUNCT (NIL) -8 NIL NIL) (-99 157501 157679 157964 "BEZOUT" 158624 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154026 156361 156689 "BBTREE" 157204 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153764 153817 153843 "BASTYPE" 153960 T BASTYPE (NIL) -9 NIL NIL) (-96 153619 153648 153718 "BASTYPE-" 153723 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153057 153133 153283 "BALFACT" 153530 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151879 152476 152661 "AUTOMOR" 152902 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151605 151610 151636 "ATTREG" 151641 T ATTREG (NIL) -9 NIL NIL) (-92 149884 150302 150654 "ATTRBUT" 151271 T ATTRBUT (NIL) -8 NIL NIL) (-91 149420 149533 149559 "ATRIG" 149760 T ATRIG (NIL) -9 NIL NIL) (-90 149229 149270 149357 "ATRIG-" 149362 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147426 149005 149093 "ASTACK" 149172 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145931 146228 146593 "ASSOCEQ" 147108 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144963 145590 145714 "ASP9" 145838 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144727 144911 144950 "ASP8" 144955 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143597 144332 144474 "ASP80" 144616 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142496 143232 143364 "ASP7" 143496 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141452 142173 142291 "ASP78" 142409 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140423 141132 141249 "ASP77" 141366 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139338 140061 140192 "ASP74" 140323 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138239 138973 139105 "ASP73" 139237 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137194 137916 138034 "ASP6" 138152 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136143 136871 136989 "ASP55" 137107 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135093 135817 135936 "ASP50" 136055 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134181 134794 134904 "ASP4" 135014 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133269 133882 133992 "ASP49" 134102 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132054 132808 132976 "ASP42" 133158 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130832 131587 131757 "ASP41" 131941 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129784 130509 130627 "ASP35" 130745 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129549 129732 129771 "ASP34" 129776 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129286 129353 129429 "ASP33" 129504 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128182 128921 129053 "ASP31" 129185 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127947 128130 128169 "ASP30" 128174 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127682 127751 127827 "ASP29" 127902 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127447 127630 127669 "ASP28" 127674 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127212 127395 127434 "ASP27" 127439 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126296 126910 127021 "ASP24" 127132 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125213 125937 126067 "ASP20" 126197 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124301 124914 125024 "ASP1" 125134 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123245 123975 124094 "ASP19" 124213 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122982 123049 123125 "ASP12" 123200 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121835 122581 122725 "ASP10" 122869 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119734 121679 121770 "ARRAY2" 121775 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115550 119382 119496 "ARRAY1" 119651 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114582 114755 114976 "ARRAY12" 115373 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108942 110813 110888 "ARR2CAT" 113518 NIL ARR2CAT (NIL T T T) -9 NIL 114276) (-54 106376 107120 108074 "ARR2CAT-" 108079 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105136 105286 105589 "APPRULE" 106214 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104789 104837 104955 "APPLYORE" 105082 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103763 104054 104249 "ANY" 104612 T ANY (NIL) -8 NIL NIL) (-50 103041 103164 103321 "ANY1" 103637 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100573 101491 101816 "ANTISYM" 102766 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100088 100277 100374 "ANON" 100494 T ANON (NIL) -8 NIL NIL) (-47 94165 98633 99084 "AN" 99655 T AN (NIL) -8 NIL NIL) (-46 90519 91917 91967 "AMR" 92706 NIL AMR (NIL T T) -9 NIL 93305) (-45 89632 89853 90215 "AMR-" 90220 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74182 89549 89610 "ALIST" 89615 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71019 73776 73945 "ALGSC" 74100 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67575 68129 68736 "ALGPKG" 70459 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66852 66953 67137 "ALGMFACT" 67461 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63282 63936 "ALGMANIP" 66376 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file +((-3 3139883 3139888 3139893 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-2 3139868 3139873 3139878 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1 3139853 3139858 3139863 NIL NIL NIL NIL (NIL) -8 NIL NIL) (0 3139838 3139843 3139848 NIL NIL NIL NIL (NIL) -8 NIL NIL) (-1195 3138968 3139713 3139790 "ZMOD" 3139795 NIL ZMOD (NIL NIL) -8 NIL NIL) (-1194 3138078 3138242 3138451 "ZLINDEP" 3138800 NIL ZLINDEP (NIL T) -7 NIL NIL) (-1193 3127482 3129227 3131179 "ZDSOLVE" 3136227 NIL ZDSOLVE (NIL T NIL NIL) -7 NIL NIL) (-1192 3126728 3126869 3127058 "YSTREAM" 3127328 NIL YSTREAM (NIL T) -7 NIL NIL) (-1191 3124497 3126033 3126236 "XRPOLY" 3126571 NIL XRPOLY (NIL T T) -8 NIL NIL) (-1190 3120959 3122288 3122870 "XPR" 3123961 NIL XPR (NIL T T) -8 NIL NIL) (-1189 3118673 3120294 3120497 "XPOLY" 3120790 NIL XPOLY (NIL T) -8 NIL NIL) (-1188 3116487 3117865 3117919 "XPOLYC" 3118204 NIL XPOLYC (NIL T T) -9 NIL 3118317) (-1187 3112859 3115004 3115392 "XPBWPOLY" 3116145 NIL XPBWPOLY (NIL T T) -8 NIL NIL) (-1186 3108787 3111100 3111142 "XF" 3111763 NIL XF (NIL T) -9 NIL 3112162) (-1185 3108408 3108496 3108665 "XF-" 3108670 NIL XF- (NIL T T) -8 NIL NIL) (-1184 3103788 3105087 3105141 "XFALG" 3107289 NIL XFALG (NIL T T) -9 NIL 3108076) (-1183 3102925 3103029 3103233 "XEXPPKG" 3103680 NIL XEXPPKG (NIL T T T) -7 NIL NIL) (-1182 3101024 3102776 3102871 "XDPOLY" 3102876 NIL XDPOLY (NIL T T) -8 NIL NIL) (-1181 3099903 3100513 3100555 "XALG" 3100617 NIL XALG (NIL T) -9 NIL 3100736) (-1180 3093379 3097887 3098380 "WUTSET" 3099495 NIL WUTSET (NIL T T T T) -8 NIL NIL) (-1179 3091191 3091998 3092349 "WP" 3093161 NIL WP (NIL T T T T NIL NIL NIL) -8 NIL NIL) (-1178 3090077 3090275 3090570 "WFFINTBS" 3090988 NIL WFFINTBS (NIL T T T T) -7 NIL NIL) (-1177 3087981 3088408 3088870 "WEIER" 3089649 NIL WEIER (NIL T) -7 NIL NIL) (-1176 3087130 3087554 3087596 "VSPACE" 3087732 NIL VSPACE (NIL T) -9 NIL 3087806) (-1175 3086968 3086995 3087086 "VSPACE-" 3087091 NIL VSPACE- (NIL T T) -8 NIL NIL) (-1174 3086714 3086757 3086828 "VOID" 3086919 T VOID (NIL) -8 NIL NIL) (-1173 3084850 3085209 3085615 "VIEW" 3086330 T VIEW (NIL) -7 NIL NIL) (-1172 3081275 3081913 3082650 "VIEWDEF" 3084135 T VIEWDEF (NIL) -7 NIL NIL) (-1171 3070614 3072823 3074996 "VIEW3D" 3079124 T VIEW3D (NIL) -8 NIL NIL) (-1170 3062896 3064525 3066104 "VIEW2D" 3069057 T VIEW2D (NIL) -8 NIL NIL) (-1169 3058305 3062666 3062758 "VECTOR" 3062839 NIL VECTOR (NIL T) -8 NIL NIL) (-1168 3056882 3057141 3057459 "VECTOR2" 3058035 NIL VECTOR2 (NIL T T) -7 NIL NIL) (-1167 3050422 3054674 3054717 "VECTCAT" 3055705 NIL VECTCAT (NIL T) -9 NIL 3056289) (-1166 3049436 3049690 3050080 "VECTCAT-" 3050085 NIL VECTCAT- (NIL T T) -8 NIL NIL) (-1165 3048917 3049087 3049207 "VARIABLE" 3049351 NIL VARIABLE (NIL NIL) -8 NIL NIL) (-1164 3048850 3048855 3048885 "UTYPE" 3048890 T UTYPE (NIL) -9 NIL NIL) (-1163 3047685 3047839 3048100 "UTSODETL" 3048676 NIL UTSODETL (NIL T T T T) -7 NIL NIL) (-1162 3045125 3045585 3046109 "UTSODE" 3047226 NIL UTSODE (NIL T T) -7 NIL NIL) (-1161 3036969 3042765 3043253 "UTS" 3044694 NIL UTS (NIL T NIL NIL) -8 NIL NIL) (-1160 3028314 3033679 3033721 "UTSCAT" 3034822 NIL UTSCAT (NIL T) -9 NIL 3035579) (-1159 3025669 3026385 3027373 "UTSCAT-" 3027378 NIL UTSCAT- (NIL T T) -8 NIL NIL) (-1158 3025300 3025343 3025474 "UTS2" 3025620 NIL UTS2 (NIL T T T T) -7 NIL NIL) (-1157 3019576 3022141 3022184 "URAGG" 3024254 NIL URAGG (NIL T) -9 NIL 3024976) (-1156 3016515 3017378 3018501 "URAGG-" 3018506 NIL URAGG- (NIL T T) -8 NIL NIL) (-1155 3012201 3015132 3015603 "UPXSSING" 3016179 NIL UPXSSING (NIL T T NIL NIL) -8 NIL NIL) (-1154 3004092 3011322 3011602 "UPXS" 3011978 NIL UPXS (NIL T NIL NIL) -8 NIL NIL) (-1153 2997121 3003997 3004068 "UPXSCONS" 3004073 NIL UPXSCONS (NIL T T) -8 NIL NIL) (-1152 2987410 2994240 2994301 "UPXSCCA" 2994950 NIL UPXSCCA (NIL T T) -9 NIL 2995191) (-1151 2987049 2987134 2987307 "UPXSCCA-" 2987312 NIL UPXSCCA- (NIL T T T) -8 NIL NIL) (-1150 2977260 2983863 2983905 "UPXSCAT" 2984548 NIL UPXSCAT (NIL T) -9 NIL 2985156) (-1149 2976694 2976773 2976950 "UPXS2" 2977175 NIL UPXS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1148 2975348 2975601 2975952 "UPSQFREE" 2976437 NIL UPSQFREE (NIL T T) -7 NIL NIL) (-1147 2969239 2972294 2972348 "UPSCAT" 2973497 NIL UPSCAT (NIL T T) -9 NIL 2974271) (-1146 2968444 2968651 2968977 "UPSCAT-" 2968982 NIL UPSCAT- (NIL T T T) -8 NIL NIL) (-1145 2954530 2962567 2962609 "UPOLYC" 2964687 NIL UPOLYC (NIL T) -9 NIL 2965908) (-1144 2945860 2948285 2951431 "UPOLYC-" 2951436 NIL UPOLYC- (NIL T T) -8 NIL NIL) (-1143 2945491 2945534 2945665 "UPOLYC2" 2945811 NIL UPOLYC2 (NIL T T T T) -7 NIL NIL) (-1142 2936910 2945060 2945197 "UP" 2945401 NIL UP (NIL NIL T) -8 NIL NIL) (-1141 2936253 2936360 2936523 "UPMP" 2936799 NIL UPMP (NIL T T) -7 NIL NIL) (-1140 2935806 2935887 2936026 "UPDIVP" 2936166 NIL UPDIVP (NIL T T) -7 NIL NIL) (-1139 2934374 2934623 2934939 "UPDECOMP" 2935555 NIL UPDECOMP (NIL T T) -7 NIL NIL) (-1138 2933609 2933721 2933906 "UPCDEN" 2934258 NIL UPCDEN (NIL T T T) -7 NIL NIL) (-1137 2933132 2933201 2933348 "UP2" 2933534 NIL UP2 (NIL NIL T NIL T) -7 NIL NIL) (-1136 2931649 2932336 2932613 "UNISEG" 2932890 NIL UNISEG (NIL T) -8 NIL NIL) (-1135 2930864 2930991 2931196 "UNISEG2" 2931492 NIL UNISEG2 (NIL T T) -7 NIL NIL) (-1134 2929924 2930104 2930330 "UNIFACT" 2930680 NIL UNIFACT (NIL T) -7 NIL NIL) (-1133 2913820 2929105 2929355 "ULS" 2929731 NIL ULS (NIL T NIL NIL) -8 NIL NIL) (-1132 2901785 2913725 2913796 "ULSCONS" 2913801 NIL ULSCONS (NIL T T) -8 NIL NIL) (-1131 2884535 2896548 2896609 "ULSCCAT" 2897321 NIL ULSCCAT (NIL T T) -9 NIL 2897617) (-1130 2883586 2883831 2884218 "ULSCCAT-" 2884223 NIL ULSCCAT- (NIL T T T) -8 NIL NIL) (-1129 2873576 2880093 2880135 "ULSCAT" 2880991 NIL ULSCAT (NIL T) -9 NIL 2881721) (-1128 2873010 2873089 2873266 "ULS2" 2873491 NIL ULS2 (NIL T T NIL NIL NIL NIL) -7 NIL NIL) (-1127 2871408 2872375 2872405 "UFD" 2872617 T UFD (NIL) -9 NIL 2872731) (-1126 2871202 2871248 2871343 "UFD-" 2871348 NIL UFD- (NIL T) -8 NIL NIL) (-1125 2870284 2870467 2870683 "UDVO" 2871008 T UDVO (NIL) -7 NIL NIL) (-1124 2868100 2868509 2868980 "UDPO" 2869848 NIL UDPO (NIL T) -7 NIL NIL) (-1123 2868033 2868038 2868068 "TYPE" 2868073 T TYPE (NIL) -9 NIL NIL) (-1122 2867004 2867206 2867446 "TWOFACT" 2867827 NIL TWOFACT (NIL T) -7 NIL NIL) (-1121 2865942 2866279 2866542 "TUPLE" 2866776 NIL TUPLE (NIL T) -8 NIL NIL) (-1120 2863633 2864152 2864691 "TUBETOOL" 2865425 T TUBETOOL (NIL) -7 NIL NIL) (-1119 2862482 2862687 2862928 "TUBE" 2863426 NIL TUBE (NIL T) -8 NIL NIL) (-1118 2857206 2861460 2861742 "TS" 2862234 NIL TS (NIL T) -8 NIL NIL) (-1117 2845910 2850002 2850098 "TSETCAT" 2855332 NIL TSETCAT (NIL T T T T) -9 NIL 2856863) (-1116 2840645 2842243 2844133 "TSETCAT-" 2844138 NIL TSETCAT- (NIL T T T T T) -8 NIL NIL) (-1115 2834908 2835754 2836696 "TRMANIP" 2839781 NIL TRMANIP (NIL T T) -7 NIL NIL) (-1114 2834349 2834412 2834575 "TRIMAT" 2834840 NIL TRIMAT (NIL T T T T) -7 NIL NIL) (-1113 2832155 2832392 2832755 "TRIGMNIP" 2834098 NIL TRIGMNIP (NIL T T) -7 NIL NIL) (-1112 2831675 2831788 2831818 "TRIGCAT" 2832031 T TRIGCAT (NIL) -9 NIL NIL) (-1111 2831344 2831423 2831564 "TRIGCAT-" 2831569 NIL TRIGCAT- (NIL T) -8 NIL NIL) (-1110 2828243 2830204 2830484 "TREE" 2831099 NIL TREE (NIL T) -8 NIL NIL) (-1109 2827517 2828045 2828075 "TRANFUN" 2828110 T TRANFUN (NIL) -9 NIL 2828176) (-1108 2826796 2826987 2827267 "TRANFUN-" 2827272 NIL TRANFUN- (NIL T) -8 NIL NIL) (-1107 2826600 2826632 2826693 "TOPSP" 2826757 T TOPSP (NIL) -7 NIL NIL) (-1106 2825952 2826067 2826220 "TOOLSIGN" 2826481 NIL TOOLSIGN (NIL T) -7 NIL NIL) (-1105 2824613 2825129 2825368 "TEXTFILE" 2825735 T TEXTFILE (NIL) -8 NIL NIL) (-1104 2822478 2822992 2823430 "TEX" 2824197 T TEX (NIL) -8 NIL NIL) (-1103 2822259 2822290 2822362 "TEX1" 2822441 NIL TEX1 (NIL T) -7 NIL NIL) (-1102 2821907 2821970 2822060 "TEMUTL" 2822191 T TEMUTL (NIL) -7 NIL NIL) (-1101 2820061 2820341 2820666 "TBCMPPK" 2821630 NIL TBCMPPK (NIL T T) -7 NIL NIL) (-1100 2811950 2818222 2818278 "TBAGG" 2818678 NIL TBAGG (NIL T T) -9 NIL 2818889) (-1099 2807020 2808508 2810262 "TBAGG-" 2810267 NIL TBAGG- (NIL T T T) -8 NIL NIL) (-1098 2806404 2806511 2806656 "TANEXP" 2806909 NIL TANEXP (NIL T) -7 NIL NIL) (-1097 2799905 2806261 2806354 "TABLE" 2806359 NIL TABLE (NIL T T) -8 NIL NIL) (-1096 2799318 2799416 2799554 "TABLEAU" 2799802 NIL TABLEAU (NIL T) -8 NIL NIL) (-1095 2793926 2795146 2796394 "TABLBUMP" 2798104 NIL TABLBUMP (NIL T) -7 NIL NIL) (-1094 2793354 2793454 2793582 "SYSTEM" 2793820 T SYSTEM (NIL) -7 NIL NIL) (-1093 2789817 2790512 2791295 "SYSSOLP" 2792605 NIL SYSSOLP (NIL T) -7 NIL NIL) (-1092 2786108 2786816 2787550 "SYNTAX" 2789105 T SYNTAX (NIL) -8 NIL NIL) (-1091 2783242 2783850 2784488 "SYMTAB" 2785492 T SYMTAB (NIL) -8 NIL NIL) (-1090 2778491 2779393 2780376 "SYMS" 2782281 T SYMS (NIL) -8 NIL NIL) (-1089 2775724 2777951 2778180 "SYMPOLY" 2778296 NIL SYMPOLY (NIL T) -8 NIL NIL) (-1088 2775244 2775319 2775441 "SYMFUNC" 2775636 NIL SYMFUNC (NIL T) -7 NIL NIL) (-1087 2771221 2772481 2773303 "SYMBOL" 2774444 T SYMBOL (NIL) -8 NIL NIL) (-1086 2764760 2766449 2768169 "SWITCH" 2769523 T SWITCH (NIL) -8 NIL NIL) (-1085 2757990 2763587 2763889 "SUTS" 2764515 NIL SUTS (NIL T NIL NIL) -8 NIL NIL) (-1084 2749880 2757111 2757391 "SUPXS" 2757767 NIL SUPXS (NIL T NIL NIL) -8 NIL NIL) (-1083 2741372 2749501 2749626 "SUP" 2749789 NIL SUP (NIL T) -8 NIL NIL) (-1082 2740531 2740658 2740875 "SUPFRACF" 2741240 NIL SUPFRACF (NIL T T T T) -7 NIL NIL) (-1081 2740156 2740215 2740326 "SUP2" 2740466 NIL SUP2 (NIL T T) -7 NIL NIL) (-1080 2738574 2738848 2739210 "SUMRF" 2739855 NIL SUMRF (NIL T) -7 NIL NIL) (-1079 2737891 2737957 2738155 "SUMFS" 2738495 NIL SUMFS (NIL T T) -7 NIL NIL) (-1078 2721827 2737072 2737322 "SULS" 2737698 NIL SULS (NIL T NIL NIL) -8 NIL NIL) (-1077 2721149 2721352 2721492 "SUCH" 2721735 NIL SUCH (NIL T T) -8 NIL NIL) (-1076 2715076 2716088 2717046 "SUBSPACE" 2720237 NIL SUBSPACE (NIL NIL T) -8 NIL NIL) (-1075 2714506 2714596 2714760 "SUBRESP" 2714964 NIL SUBRESP (NIL T T) -7 NIL NIL) (-1074 2707875 2709171 2710482 "STTF" 2713242 NIL STTF (NIL T) -7 NIL NIL) (-1073 2702048 2703168 2704315 "STTFNC" 2706775 NIL STTFNC (NIL T) -7 NIL NIL) (-1072 2693399 2695266 2697059 "STTAYLOR" 2700289 NIL STTAYLOR (NIL T) -7 NIL NIL) (-1071 2686643 2693263 2693346 "STRTBL" 2693351 NIL STRTBL (NIL T) -8 NIL NIL) (-1070 2682034 2686598 2686629 "STRING" 2686634 T STRING (NIL) -8 NIL NIL) (-1069 2676923 2681408 2681438 "STRICAT" 2681497 T STRICAT (NIL) -9 NIL 2681559) (-1068 2669639 2674446 2675066 "STREAM" 2676338 NIL STREAM (NIL T) -8 NIL NIL) (-1067 2669149 2669226 2669370 "STREAM3" 2669556 NIL STREAM3 (NIL T T T) -7 NIL NIL) (-1066 2668131 2668314 2668549 "STREAM2" 2668962 NIL STREAM2 (NIL T T) -7 NIL NIL) (-1065 2667819 2667871 2667964 "STREAM1" 2668073 NIL STREAM1 (NIL T) -7 NIL NIL) (-1064 2666835 2667016 2667247 "STINPROD" 2667635 NIL STINPROD (NIL T) -7 NIL NIL) (-1063 2666414 2666598 2666628 "STEP" 2666708 T STEP (NIL) -9 NIL 2666786) (-1062 2659957 2666313 2666390 "STBL" 2666395 NIL STBL (NIL T T NIL) -8 NIL NIL) (-1061 2655133 2659180 2659223 "STAGG" 2659376 NIL STAGG (NIL T) -9 NIL 2659465) (-1060 2652835 2653437 2654309 "STAGG-" 2654314 NIL STAGG- (NIL T T) -8 NIL NIL) (-1059 2651030 2652605 2652697 "STACK" 2652778 NIL STACK (NIL T) -8 NIL NIL) (-1058 2643761 2649177 2649632 "SREGSET" 2650660 NIL SREGSET (NIL T T T T) -8 NIL NIL) (-1057 2636201 2637569 2639081 "SRDCMPK" 2642367 NIL SRDCMPK (NIL T T T T T) -7 NIL NIL) (-1056 2629169 2633642 2633672 "SRAGG" 2634975 T SRAGG (NIL) -9 NIL 2635583) (-1055 2628186 2628441 2628820 "SRAGG-" 2628825 NIL SRAGG- (NIL T) -8 NIL NIL) (-1054 2622635 2627105 2627532 "SQMATRIX" 2627805 NIL SQMATRIX (NIL NIL T) -8 NIL NIL) (-1053 2616387 2619355 2620081 "SPLTREE" 2621981 NIL SPLTREE (NIL T T) -8 NIL NIL) (-1052 2612377 2613043 2613689 "SPLNODE" 2615813 NIL SPLNODE (NIL T T) -8 NIL NIL) (-1051 2611424 2611657 2611687 "SPFCAT" 2612131 T SPFCAT (NIL) -9 NIL NIL) (-1050 2610161 2610371 2610635 "SPECOUT" 2611182 T SPECOUT (NIL) -7 NIL NIL) (-1049 2609922 2609962 2610031 "SPADPRSR" 2610114 T SPADPRSR (NIL) -7 NIL NIL) (-1048 2601945 2603692 2603734 "SPACEC" 2608057 NIL SPACEC (NIL T) -9 NIL 2609873) (-1047 2600117 2601878 2601926 "SPACE3" 2601931 NIL SPACE3 (NIL T) -8 NIL NIL) (-1046 2598869 2599040 2599331 "SORTPAK" 2599922 NIL SORTPAK (NIL T T) -7 NIL NIL) (-1045 2596925 2597228 2597646 "SOLVETRA" 2598533 NIL SOLVETRA (NIL T) -7 NIL NIL) (-1044 2595936 2596158 2596432 "SOLVESER" 2596698 NIL SOLVESER (NIL T) -7 NIL NIL) (-1043 2591156 2592037 2593039 "SOLVERAD" 2594988 NIL SOLVERAD (NIL T) -7 NIL NIL) (-1042 2586971 2587580 2588309 "SOLVEFOR" 2590523 NIL SOLVEFOR (NIL T T) -7 NIL NIL) (-1041 2581271 2586323 2586419 "SNTSCAT" 2586424 NIL SNTSCAT (NIL T T T T) -9 NIL 2586494) (-1040 2575375 2579602 2579992 "SMTS" 2580961 NIL SMTS (NIL T T T) -8 NIL NIL) (-1039 2569785 2575264 2575340 "SMP" 2575345 NIL SMP (NIL T T) -8 NIL NIL) (-1038 2567944 2568245 2568643 "SMITH" 2569482 NIL SMITH (NIL T T T T) -7 NIL NIL) (-1037 2560909 2565105 2565207 "SMATCAT" 2566547 NIL SMATCAT (NIL NIL T T T) -9 NIL 2567096) (-1036 2557850 2558673 2559850 "SMATCAT-" 2559855 NIL SMATCAT- (NIL T NIL T T T) -8 NIL NIL) (-1035 2555564 2557087 2557130 "SKAGG" 2557391 NIL SKAGG (NIL T) -9 NIL 2557526) (-1034 2551622 2554668 2554946 "SINT" 2555308 T SINT (NIL) -8 NIL NIL) (-1033 2551394 2551432 2551498 "SIMPAN" 2551578 T SIMPAN (NIL) -7 NIL NIL) (-1032 2550232 2550453 2550728 "SIGNRF" 2551153 NIL SIGNRF (NIL T) -7 NIL NIL) (-1031 2549041 2549192 2549482 "SIGNEF" 2550061 NIL SIGNEF (NIL T T) -7 NIL NIL) (-1030 2546731 2547185 2547691 "SHP" 2548582 NIL SHP (NIL T NIL) -7 NIL NIL) (-1029 2540584 2546632 2546708 "SHDP" 2546713 NIL SHDP (NIL NIL NIL T) -8 NIL NIL) (-1028 2540074 2540266 2540296 "SGROUP" 2540448 T SGROUP (NIL) -9 NIL 2540535) (-1027 2539844 2539896 2540000 "SGROUP-" 2540005 NIL SGROUP- (NIL T) -8 NIL NIL) (-1026 2536680 2537377 2538100 "SGCF" 2539143 T SGCF (NIL) -7 NIL NIL) (-1025 2531079 2536131 2536227 "SFRTCAT" 2536232 NIL SFRTCAT (NIL T T T T) -9 NIL 2536270) (-1024 2524539 2525554 2526688 "SFRGCD" 2530062 NIL SFRGCD (NIL T T T T T) -7 NIL NIL) (-1023 2517705 2518776 2519960 "SFQCMPK" 2523472 NIL SFQCMPK (NIL T T T T T) -7 NIL NIL) (-1022 2517327 2517416 2517526 "SFORT" 2517646 NIL SFORT (NIL T T) -8 NIL NIL) (-1021 2516472 2517167 2517288 "SEXOF" 2517293 NIL SEXOF (NIL T T T T T) -8 NIL NIL) (-1020 2515606 2516353 2516421 "SEX" 2516426 T SEX (NIL) -8 NIL NIL) (-1019 2510383 2511072 2511167 "SEXCAT" 2514938 NIL SEXCAT (NIL T T T T T) -9 NIL 2515557) (-1018 2507563 2510317 2510365 "SET" 2510370 NIL SET (NIL T) -8 NIL NIL) (-1017 2505814 2506276 2506581 "SETMN" 2507304 NIL SETMN (NIL NIL NIL) -8 NIL NIL) (-1016 2505422 2505548 2505578 "SETCAT" 2505695 T SETCAT (NIL) -9 NIL 2505779) (-1015 2505202 2505254 2505353 "SETCAT-" 2505358 NIL SETCAT- (NIL T) -8 NIL NIL) (-1014 2501590 2503664 2503707 "SETAGG" 2504577 NIL SETAGG (NIL T) -9 NIL 2504917) (-1013 2501048 2501164 2501401 "SETAGG-" 2501406 NIL SETAGG- (NIL T T) -8 NIL NIL) (-1012 2500252 2500545 2500606 "SEGXCAT" 2500892 NIL SEGXCAT (NIL T T) -9 NIL 2501012) (-1011 2499308 2499918 2500100 "SEG" 2500105 NIL SEG (NIL T) -8 NIL NIL) (-1010 2498215 2498428 2498471 "SEGCAT" 2499053 NIL SEGCAT (NIL T) -9 NIL 2499291) (-1009 2497264 2497594 2497794 "SEGBIND" 2498050 NIL SEGBIND (NIL T) -8 NIL NIL) (-1008 2496885 2496944 2497057 "SEGBIND2" 2497199 NIL SEGBIND2 (NIL T T) -7 NIL NIL) (-1007 2496104 2496230 2496434 "SEG2" 2496729 NIL SEG2 (NIL T T) -7 NIL NIL) (-1006 2495541 2496039 2496086 "SDVAR" 2496091 NIL SDVAR (NIL T) -8 NIL NIL) (-1005 2487793 2495314 2495442 "SDPOL" 2495447 NIL SDPOL (NIL T) -8 NIL NIL) (-1004 2486386 2486652 2486971 "SCPKG" 2487508 NIL SCPKG (NIL T) -7 NIL NIL) (-1003 2485523 2485702 2485902 "SCOPE" 2486208 T SCOPE (NIL) -8 NIL NIL) (-1002 2484744 2484877 2485056 "SCACHE" 2485378 NIL SCACHE (NIL T) -7 NIL NIL) (-1001 2484183 2484504 2484589 "SAOS" 2484681 T SAOS (NIL) -8 NIL NIL) (-1000 2483748 2483783 2483956 "SAERFFC" 2484142 NIL SAERFFC (NIL T T T) -7 NIL NIL) (-999 2477644 2483647 2483725 "SAE" 2483730 NIL SAE (NIL T T NIL) -8 NIL NIL) (-998 2477240 2477275 2477432 "SAEFACT" 2477603 NIL SAEFACT (NIL T T T) -7 NIL NIL) (-997 2475566 2475880 2476279 "RURPK" 2476906 NIL RURPK (NIL T NIL) -7 NIL NIL) (-996 2474219 2474496 2474803 "RULESET" 2475402 NIL RULESET (NIL T T T) -8 NIL NIL) (-995 2471427 2471930 2472391 "RULE" 2473901 NIL RULE (NIL T T T) -8 NIL NIL) (-994 2471069 2471224 2471305 "RULECOLD" 2471379 NIL RULECOLD (NIL NIL) -8 NIL NIL) (-993 2465961 2466755 2467671 "RSETGCD" 2470268 NIL RSETGCD (NIL T T T T T) -7 NIL NIL) (-992 2455276 2460328 2460422 "RSETCAT" 2464487 NIL RSETCAT (NIL T T T T) -9 NIL 2465584) (-991 2453207 2453746 2454566 "RSETCAT-" 2454571 NIL RSETCAT- (NIL T T T T T) -8 NIL NIL) (-990 2445637 2447012 2448528 "RSDCMPK" 2451806 NIL RSDCMPK (NIL T T T T T) -7 NIL NIL) (-989 2443655 2444096 2444168 "RRCC" 2445244 NIL RRCC (NIL T T) -9 NIL 2445588) (-988 2443009 2443183 2443459 "RRCC-" 2443464 NIL RRCC- (NIL T T T) -8 NIL NIL) (-987 2417376 2427001 2427065 "RPOLCAT" 2437567 NIL RPOLCAT (NIL T T T) -9 NIL 2440725) (-986 2408880 2411218 2414336 "RPOLCAT-" 2414341 NIL RPOLCAT- (NIL T T T T) -8 NIL NIL) (-985 2399946 2407110 2407590 "ROUTINE" 2408420 T ROUTINE (NIL) -8 NIL NIL) (-984 2396651 2399502 2399649 "ROMAN" 2399819 T ROMAN (NIL) -8 NIL NIL) (-983 2394937 2395522 2395779 "ROIRC" 2396457 NIL ROIRC (NIL T T) -8 NIL NIL) (-982 2391342 2393646 2393674 "RNS" 2393970 T RNS (NIL) -9 NIL 2394240) (-981 2389856 2390239 2390770 "RNS-" 2390843 NIL RNS- (NIL T) -8 NIL NIL) (-980 2389282 2389690 2389718 "RNG" 2389723 T RNG (NIL) -9 NIL 2389744) (-979 2388680 2389042 2389082 "RMODULE" 2389142 NIL RMODULE (NIL T) -9 NIL 2389184) (-978 2387532 2387626 2387956 "RMCAT2" 2388581 NIL RMCAT2 (NIL NIL NIL T T T T T T T T) -7 NIL NIL) (-977 2384246 2386715 2387036 "RMATRIX" 2387267 NIL RMATRIX (NIL NIL NIL T) -8 NIL NIL) (-976 2377243 2379477 2379589 "RMATCAT" 2382898 NIL RMATCAT (NIL NIL NIL T T T) -9 NIL 2383880) (-975 2376622 2376769 2377072 "RMATCAT-" 2377077 NIL RMATCAT- (NIL T NIL NIL T T T) -8 NIL NIL) (-974 2376192 2376267 2376393 "RINTERP" 2376541 NIL RINTERP (NIL NIL T) -7 NIL NIL) (-973 2375243 2375807 2375835 "RING" 2375945 T RING (NIL) -9 NIL 2376039) (-972 2375038 2375082 2375176 "RING-" 2375181 NIL RING- (NIL T) -8 NIL NIL) (-971 2373886 2374123 2374379 "RIDIST" 2374802 T RIDIST (NIL) -7 NIL NIL) (-970 2365208 2373360 2373563 "RGCHAIN" 2373735 NIL RGCHAIN (NIL T NIL) -8 NIL NIL) (-969 2362213 2362827 2363495 "RF" 2364572 NIL RF (NIL T) -7 NIL NIL) (-968 2361862 2361925 2362026 "RFFACTOR" 2362144 NIL RFFACTOR (NIL T) -7 NIL NIL) (-967 2361590 2361625 2361720 "RFFACT" 2361821 NIL RFFACT (NIL T) -7 NIL NIL) (-966 2359720 2360084 2360464 "RFDIST" 2361230 T RFDIST (NIL) -7 NIL NIL) (-965 2359178 2359270 2359430 "RETSOL" 2359622 NIL RETSOL (NIL T T) -7 NIL NIL) (-964 2358771 2358851 2358892 "RETRACT" 2359082 NIL RETRACT (NIL T) -9 NIL NIL) (-963 2358623 2358648 2358732 "RETRACT-" 2358737 NIL RETRACT- (NIL T T) -8 NIL NIL) (-962 2351481 2358280 2358405 "RESULT" 2358518 T RESULT (NIL) -8 NIL NIL) (-961 2350066 2350755 2350952 "RESRING" 2351384 NIL RESRING (NIL T T T T NIL) -8 NIL NIL) (-960 2349706 2349755 2349851 "RESLATC" 2350003 NIL RESLATC (NIL T) -7 NIL NIL) (-959 2349415 2349449 2349554 "REPSQ" 2349665 NIL REPSQ (NIL T) -7 NIL NIL) (-958 2346846 2347426 2348026 "REP" 2348835 T REP (NIL) -7 NIL NIL) (-957 2346547 2346581 2346690 "REPDB" 2346805 NIL REPDB (NIL T) -7 NIL NIL) (-956 2340492 2341871 2343091 "REP2" 2345359 NIL REP2 (NIL T) -7 NIL NIL) (-955 2336898 2337579 2338384 "REP1" 2339719 NIL REP1 (NIL T) -7 NIL NIL) (-954 2329644 2335059 2335511 "REGSET" 2336529 NIL REGSET (NIL T T T T) -8 NIL NIL) (-953 2328465 2328800 2329048 "REF" 2329429 NIL REF (NIL T) -8 NIL NIL) (-952 2327846 2327949 2328114 "REDORDER" 2328349 NIL REDORDER (NIL T T) -7 NIL NIL) (-951 2323815 2327080 2327301 "RECLOS" 2327677 NIL RECLOS (NIL T) -8 NIL NIL) (-950 2322872 2323053 2323266 "REALSOLV" 2323622 T REALSOLV (NIL) -7 NIL NIL) (-949 2322720 2322761 2322789 "REAL" 2322794 T REAL (NIL) -9 NIL 2322829) (-948 2319211 2320013 2320895 "REAL0Q" 2321885 NIL REAL0Q (NIL T) -7 NIL NIL) (-947 2314822 2315810 2316869 "REAL0" 2318192 NIL REAL0 (NIL T) -7 NIL NIL) (-946 2314230 2314302 2314507 "RDIV" 2314744 NIL RDIV (NIL T T T T T) -7 NIL NIL) (-945 2313303 2313477 2313688 "RDIST" 2314052 NIL RDIST (NIL T) -7 NIL NIL) (-944 2311907 2312194 2312563 "RDETRS" 2313011 NIL RDETRS (NIL T T) -7 NIL NIL) (-943 2309728 2310182 2310717 "RDETR" 2311449 NIL RDETR (NIL T T) -7 NIL NIL) (-942 2308344 2308622 2309023 "RDEEFS" 2309444 NIL RDEEFS (NIL T T) -7 NIL NIL) (-941 2306844 2307150 2307579 "RDEEF" 2308032 NIL RDEEF (NIL T T) -7 NIL NIL) (-940 2301129 2304061 2304089 "RCFIELD" 2305366 T RCFIELD (NIL) -9 NIL 2306096) (-939 2299198 2299702 2300395 "RCFIELD-" 2300468 NIL RCFIELD- (NIL T) -8 NIL NIL) (-938 2295530 2297315 2297356 "RCAGG" 2298427 NIL RCAGG (NIL T) -9 NIL 2298892) (-937 2295161 2295255 2295415 "RCAGG-" 2295420 NIL RCAGG- (NIL T T) -8 NIL NIL) (-936 2294506 2294617 2294779 "RATRET" 2295045 NIL RATRET (NIL T) -7 NIL NIL) (-935 2294063 2294130 2294249 "RATFACT" 2294434 NIL RATFACT (NIL T) -7 NIL NIL) (-934 2293378 2293498 2293648 "RANDSRC" 2293933 T RANDSRC (NIL) -7 NIL NIL) (-933 2293115 2293159 2293230 "RADUTIL" 2293327 T RADUTIL (NIL) -7 NIL NIL) (-932 2286122 2291858 2292175 "RADIX" 2292830 NIL RADIX (NIL NIL) -8 NIL NIL) (-931 2277692 2285966 2286094 "RADFF" 2286099 NIL RADFF (NIL T T T NIL NIL) -8 NIL NIL) (-930 2277344 2277419 2277447 "RADCAT" 2277604 T RADCAT (NIL) -9 NIL NIL) (-929 2277129 2277177 2277274 "RADCAT-" 2277279 NIL RADCAT- (NIL T) -8 NIL NIL) (-928 2275280 2276904 2276993 "QUEUE" 2277073 NIL QUEUE (NIL T) -8 NIL NIL) (-927 2271777 2275217 2275262 "QUAT" 2275267 NIL QUAT (NIL T) -8 NIL NIL) (-926 2271415 2271458 2271585 "QUATCT2" 2271728 NIL QUATCT2 (NIL T T T T) -7 NIL NIL) (-925 2265209 2268589 2268629 "QUATCAT" 2269408 NIL QUATCAT (NIL T) -9 NIL 2270173) (-924 2261353 2262390 2263777 "QUATCAT-" 2263871 NIL QUATCAT- (NIL T T) -8 NIL NIL) (-923 2258874 2260438 2260479 "QUAGG" 2260854 NIL QUAGG (NIL T) -9 NIL 2261029) (-922 2257799 2258272 2258444 "QFORM" 2258746 NIL QFORM (NIL NIL T) -8 NIL NIL) (-921 2249096 2254354 2254394 "QFCAT" 2255052 NIL QFCAT (NIL T) -9 NIL 2256045) (-920 2244668 2245869 2247460 "QFCAT-" 2247554 NIL QFCAT- (NIL T T) -8 NIL NIL) (-919 2244306 2244349 2244476 "QFCAT2" 2244619 NIL QFCAT2 (NIL T T T T) -7 NIL NIL) (-918 2243766 2243876 2244006 "QEQUAT" 2244196 T QEQUAT (NIL) -8 NIL NIL) (-917 2236952 2238023 2239205 "QCMPACK" 2242699 NIL QCMPACK (NIL T T T T T) -7 NIL NIL) (-916 2234528 2234949 2235377 "QALGSET" 2236607 NIL QALGSET (NIL T T T T) -8 NIL NIL) (-915 2233773 2233947 2234179 "QALGSET2" 2234348 NIL QALGSET2 (NIL NIL NIL) -7 NIL NIL) (-914 2232464 2232687 2233004 "PWFFINTB" 2233546 NIL PWFFINTB (NIL T T T T) -7 NIL NIL) (-913 2230652 2230820 2231173 "PUSHVAR" 2232278 NIL PUSHVAR (NIL T T T T) -7 NIL NIL) (-912 2226570 2227624 2227665 "PTRANFN" 2229549 NIL PTRANFN (NIL T) -9 NIL NIL) (-911 2224982 2225273 2225594 "PTPACK" 2226281 NIL PTPACK (NIL T) -7 NIL NIL) (-910 2224618 2224675 2224782 "PTFUNC2" 2224919 NIL PTFUNC2 (NIL T T) -7 NIL NIL) (-909 2219095 2223436 2223476 "PTCAT" 2223844 NIL PTCAT (NIL T) -9 NIL 2224006) (-908 2218753 2218788 2218912 "PSQFR" 2219054 NIL PSQFR (NIL T T T T) -7 NIL NIL) (-907 2217348 2217646 2217980 "PSEUDLIN" 2218451 NIL PSEUDLIN (NIL T) -7 NIL NIL) (-906 2204156 2206520 2208843 "PSETPK" 2215108 NIL PSETPK (NIL T T T T) -7 NIL NIL) (-905 2197243 2199957 2200051 "PSETCAT" 2203032 NIL PSETCAT (NIL T T T T) -9 NIL 2203846) (-904 2195081 2195715 2196534 "PSETCAT-" 2196539 NIL PSETCAT- (NIL T T T T T) -8 NIL NIL) (-903 2194430 2194595 2194623 "PSCURVE" 2194891 T PSCURVE (NIL) -9 NIL 2195058) (-902 2190882 2192408 2192472 "PSCAT" 2193308 NIL PSCAT (NIL T T T) -9 NIL 2193548) (-901 2189946 2190162 2190561 "PSCAT-" 2190566 NIL PSCAT- (NIL T T T T) -8 NIL NIL) (-900 2188599 2189231 2189445 "PRTITION" 2189752 T PRTITION (NIL) -8 NIL NIL) (-899 2177697 2179903 2182091 "PRS" 2186461 NIL PRS (NIL T T) -7 NIL NIL) (-898 2175556 2177048 2177088 "PRQAGG" 2177271 NIL PRQAGG (NIL T) -9 NIL 2177373) (-897 2175127 2175229 2175257 "PROPLOG" 2175442 T PROPLOG (NIL) -9 NIL NIL) (-896 2172250 2172815 2173342 "PROPFRML" 2174632 NIL PROPFRML (NIL T) -8 NIL NIL) (-895 2171710 2171820 2171950 "PROPERTY" 2172140 T PROPERTY (NIL) -8 NIL NIL) (-894 2165484 2169876 2170696 "PRODUCT" 2170936 NIL PRODUCT (NIL T T) -8 NIL NIL) (-893 2162760 2164944 2165177 "PR" 2165295 NIL PR (NIL T T) -8 NIL NIL) (-892 2162556 2162588 2162647 "PRINT" 2162721 T PRINT (NIL) -7 NIL NIL) (-891 2161896 2162013 2162165 "PRIMES" 2162436 NIL PRIMES (NIL T) -7 NIL NIL) (-890 2159961 2160362 2160828 "PRIMELT" 2161475 NIL PRIMELT (NIL T) -7 NIL NIL) (-889 2159690 2159739 2159767 "PRIMCAT" 2159891 T PRIMCAT (NIL) -9 NIL NIL) (-888 2155851 2159628 2159673 "PRIMARR" 2159678 NIL PRIMARR (NIL T) -8 NIL NIL) (-887 2154858 2155036 2155264 "PRIMARR2" 2155669 NIL PRIMARR2 (NIL T T) -7 NIL NIL) (-886 2154501 2154557 2154668 "PREASSOC" 2154796 NIL PREASSOC (NIL T T) -7 NIL NIL) (-885 2153976 2154109 2154137 "PPCURVE" 2154342 T PPCURVE (NIL) -9 NIL 2154478) (-884 2151335 2151734 2152326 "POLYROOT" 2153557 NIL POLYROOT (NIL T T T T T) -7 NIL NIL) (-883 2145241 2150941 2151100 "POLY" 2151208 NIL POLY (NIL T) -8 NIL NIL) (-882 2144626 2144684 2144917 "POLYLIFT" 2145177 NIL POLYLIFT (NIL T T T T T) -7 NIL NIL) (-881 2140911 2141360 2141988 "POLYCATQ" 2144171 NIL POLYCATQ (NIL T T T T T) -7 NIL NIL) (-880 2127952 2133349 2133413 "POLYCAT" 2136898 NIL POLYCAT (NIL T T T) -9 NIL 2138825) (-879 2121403 2123264 2125647 "POLYCAT-" 2125652 NIL POLYCAT- (NIL T T T T) -8 NIL NIL) (-878 2120992 2121060 2121179 "POLY2UP" 2121329 NIL POLY2UP (NIL NIL T) -7 NIL NIL) (-877 2120628 2120685 2120792 "POLY2" 2120929 NIL POLY2 (NIL T T) -7 NIL NIL) (-876 2119313 2119552 2119828 "POLUTIL" 2120402 NIL POLUTIL (NIL T T) -7 NIL NIL) (-875 2117675 2117952 2118282 "POLTOPOL" 2119035 NIL POLTOPOL (NIL NIL T) -7 NIL NIL) (-874 2113198 2117612 2117657 "POINT" 2117662 NIL POINT (NIL T) -8 NIL NIL) (-873 2111385 2111742 2112117 "PNTHEORY" 2112843 T PNTHEORY (NIL) -7 NIL NIL) (-872 2109813 2110110 2110519 "PMTOOLS" 2111083 NIL PMTOOLS (NIL T T T) -7 NIL NIL) (-871 2109406 2109484 2109601 "PMSYM" 2109729 NIL PMSYM (NIL T) -7 NIL NIL) (-870 2108916 2108985 2109159 "PMQFCAT" 2109331 NIL PMQFCAT (NIL T T T) -7 NIL NIL) (-869 2108271 2108381 2108537 "PMPRED" 2108793 NIL PMPRED (NIL T) -7 NIL NIL) (-868 2107667 2107753 2107914 "PMPREDFS" 2108172 NIL PMPREDFS (NIL T T T) -7 NIL NIL) (-867 2106313 2106521 2106905 "PMPLCAT" 2107429 NIL PMPLCAT (NIL T T T T T) -7 NIL NIL) (-866 2105845 2105924 2106076 "PMLSAGG" 2106228 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2065596 "PINTERPA" 2065700 NIL PINTERPA (NIL T T) -7 NIL NIL) (-852 2064673 2065240 2065333 "PI" 2065373 T PI (NIL) -8 NIL NIL) (-851 2063065 2064050 2064078 "PID" 2064260 T PID (NIL) -9 NIL 2064394) (-850 2062790 2062827 2062915 "PICOERCE" 2063022 NIL PICOERCE (NIL T) -7 NIL NIL) (-849 2062111 2062249 2062425 "PGROEB" 2062646 NIL PGROEB (NIL T) -7 NIL NIL) (-848 2057698 2058512 2059417 "PGE" 2061226 T PGE (NIL) -7 NIL NIL) (-847 2055822 2056068 2056434 "PGCD" 2057415 NIL PGCD (NIL T T T T) -7 NIL NIL) (-846 2055160 2055263 2055424 "PFRPAC" 2055706 NIL PFRPAC (NIL T) -7 NIL NIL) (-845 2051775 2053708 2054061 "PFR" 2054839 NIL PFR (NIL T) -8 NIL NIL) (-844 2050164 2050408 2050733 "PFOTOOLS" 2051522 NIL PFOTOOLS (NIL T T) -7 NIL NIL) (-843 2048697 2048936 2049287 "PFOQ" 2049921 NIL PFOQ (NIL T T T) -7 NIL NIL) (-842 2047174 2047386 2047748 "PFO" 2048481 NIL PFO (NIL T T T T T) -7 NIL NIL) (-841 2043697 2047063 2047132 "PF" 2047137 NIL PF (NIL NIL) -8 NIL NIL) (-840 2041126 2042407 2042435 "PFECAT" 2043020 T PFECAT (NIL) -9 NIL 2043404) (-839 2040571 2040725 2040939 "PFECAT-" 2040944 NIL PFECAT- (NIL T) -8 NIL NIL) (-838 2039175 2039426 2039727 "PFBRU" 2040320 NIL PFBRU (NIL T T) -7 NIL NIL) (-837 2037042 2037393 2037825 "PFBR" 2038826 NIL PFBR (NIL T T T T) -7 NIL NIL) (-836 2032894 2034418 2035094 "PERM" 2036399 NIL PERM (NIL T) -8 NIL NIL) (-835 2028159 2029101 2029971 "PERMGRP" 2032057 NIL PERMGRP (NIL T) -8 NIL NIL) (-834 2026230 2027223 2027264 "PERMCAT" 2027710 NIL PERMCAT (NIL T) -9 NIL 2028015) (-833 2025885 2025926 2026049 "PERMAN" 2026183 NIL PERMAN (NIL NIL T) -7 NIL NIL) (-832 2023325 2025454 2025585 "PENDTREE" 2025787 NIL PENDTREE (NIL T) -8 NIL NIL) (-831 2021398 2022176 2022217 "PDRING" 2022874 NIL PDRING (NIL T) -9 NIL 2023159) (-830 2020501 2020719 2021081 "PDRING-" 2021086 NIL PDRING- (NIL T T) -8 NIL NIL) (-829 2017643 2018393 2019084 "PDEPROB" 2019830 T PDEPROB (NIL) -8 NIL NIL) (-828 2015214 2015710 2016259 "PDEPACK" 2017114 T PDEPACK (NIL) -7 NIL NIL) (-827 2014126 2014316 2014567 "PDECOMP" 2015013 NIL PDECOMP (NIL T T) -7 NIL NIL) (-826 2011738 2012553 2012581 "PDECAT" 2013366 T PDECAT (NIL) -9 NIL 2014077) (-825 2011491 2011524 2011613 "PCOMP" 2011699 NIL PCOMP (NIL T T) -7 NIL NIL) (-824 2009698 2010294 2010590 "PBWLB" 2011221 NIL PBWLB (NIL T) -8 NIL NIL) (-823 2002206 2003775 2005111 "PATTERN" 2008383 NIL PATTERN (NIL T) -8 NIL NIL) (-822 2001838 2001895 2002004 "PATTERN2" 2002143 NIL PATTERN2 (NIL T T) -7 NIL NIL) (-821 1999595 1999983 2000440 "PATTERN1" 2001427 NIL PATTERN1 (NIL T T) -7 NIL NIL) (-820 1996990 1997544 1998025 "PATRES" 1999160 NIL PATRES (NIL T T) -8 NIL NIL) (-819 1996554 1996621 1996753 "PATRES2" 1996917 NIL PATRES2 (NIL T T T) -7 NIL NIL) (-818 1994451 1994851 1995256 "PATMATCH" 1996223 NIL PATMATCH (NIL T T T) -7 NIL NIL) (-817 1993988 1994171 1994212 "PATMAB" 1994319 NIL PATMAB (NIL T) -9 NIL 1994402) (-816 1992533 1992842 1993100 "PATLRES" 1993793 NIL PATLRES (NIL T T T) -8 NIL NIL) (-815 1992079 1992202 1992243 "PATAB" 1992248 NIL PATAB (NIL T) -9 NIL 1992420) (-814 1989560 1990092 1990665 "PARTPERM" 1991526 T PARTPERM (NIL) -7 NIL NIL) (-813 1989181 1989244 1989346 "PARSURF" 1989491 NIL PARSURF (NIL T) -8 NIL NIL) (-812 1988813 1988870 1988979 "PARSU2" 1989118 NIL PARSU2 (NIL T T) -7 NIL NIL) (-811 1988577 1988617 1988684 "PARSER" 1988766 T PARSER (NIL) -7 NIL NIL) (-810 1988198 1988261 1988363 "PARSCURV" 1988508 NIL PARSCURV (NIL T) -8 NIL NIL) (-809 1987830 1987887 1987996 "PARSC2" 1988135 NIL PARSC2 (NIL T T) -7 NIL NIL) (-808 1987469 1987527 1987624 "PARPCURV" 1987766 NIL PARPCURV (NIL T) -8 NIL NIL) (-807 1987101 1987158 1987267 "PARPC2" 1987406 NIL PARPC2 (NIL T T) -7 NIL NIL) (-806 1986621 1986707 1986826 "PAN2EXPR" 1987002 T PAN2EXPR (NIL) -7 NIL NIL) (-805 1985427 1985742 1985970 "PALETTE" 1986413 T PALETTE (NIL) -8 NIL NIL) (-804 1983895 1984432 1984792 "PAIR" 1985113 NIL PAIR (NIL T T) -8 NIL NIL) (-803 1977745 1983154 1983348 "PADICRC" 1983750 NIL PADICRC 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1945412 "ORESUP" 1945535 NIL ORESUP (NIL T NIL NIL) -8 NIL NIL) (-789 1940524 1941024 1941584 "OREPCTO" 1942478 NIL OREPCTO (NIL T T) -7 NIL NIL) (-788 1934434 1936640 1936680 "OREPCAT" 1939001 NIL OREPCAT (NIL T) -9 NIL 1940104) (-787 1931582 1932364 1933421 "OREPCAT-" 1933426 NIL OREPCAT- (NIL T T) -8 NIL NIL) (-786 1930760 1931032 1931060 "ORDSET" 1931369 T ORDSET (NIL) -9 NIL 1931533) (-785 1930279 1930401 1930594 "ORDSET-" 1930599 NIL ORDSET- (NIL T) -8 NIL NIL) (-784 1928893 1929694 1929722 "ORDRING" 1929924 T ORDRING (NIL) -9 NIL 1930048) (-783 1928538 1928632 1928776 "ORDRING-" 1928781 NIL ORDRING- (NIL T) -8 NIL NIL) (-782 1927914 1928395 1928423 "ORDMON" 1928428 T ORDMON (NIL) -9 NIL 1928449) (-781 1927076 1927223 1927418 "ORDFUNS" 1927763 NIL ORDFUNS (NIL NIL T) -7 NIL NIL) (-780 1926588 1926947 1926975 "ORDFIN" 1926980 T ORDFIN (NIL) -9 NIL 1927001) (-779 1923100 1925174 1925583 "ORDCOMP" 1926212 NIL ORDCOMP (NIL T) -8 NIL NIL) (-778 1922366 1922493 1922679 "ORDCOMP2" 1922960 NIL ORDCOMP2 (NIL T T) -7 NIL NIL) (-777 1918874 1919756 1920593 "OPTPROB" 1921549 T OPTPROB (NIL) -8 NIL NIL) (-776 1915716 1916345 1917039 "OPTPACK" 1918200 T OPTPACK (NIL) -7 NIL NIL) (-775 1913442 1914178 1914206 "OPTCAT" 1915021 T OPTCAT (NIL) -9 NIL 1915667) (-774 1913210 1913249 1913315 "OPQUERY" 1913396 T OPQUERY (NIL) -7 NIL NIL) (-773 1910346 1911537 1912037 "OP" 1912742 NIL OP (NIL T) -8 NIL NIL) (-772 1907111 1909143 1909512 "ONECOMP" 1910010 NIL ONECOMP (NIL T) -8 NIL NIL) (-771 1906416 1906531 1906705 "ONECOMP2" 1906983 NIL ONECOMP2 (NIL T T) -7 NIL NIL) (-770 1905835 1905941 1906071 "OMSERVER" 1906306 T OMSERVER (NIL) -7 NIL NIL) (-769 1902724 1905276 1905316 "OMSAGG" 1905377 NIL OMSAGG (NIL T) -9 NIL 1905441) (-768 1901347 1901610 1901892 "OMPKG" 1902462 T OMPKG (NIL) -7 NIL NIL) (-767 1900777 1900880 1900908 "OM" 1901207 T OM (NIL) -9 NIL NIL) (-766 1899316 1900329 1900497 "OMLO" 1900658 NIL OMLO (NIL T T) -8 NIL NIL) (-765 1898246 1898393 1898619 "OMEXPR" 1899142 NIL OMEXPR (NIL T) -7 NIL NIL) (-764 1897564 1897792 1897928 "OMERR" 1898130 T OMERR (NIL) -8 NIL NIL) (-763 1896742 1896985 1897145 "OMERRK" 1897424 T OMERRK (NIL) -8 NIL NIL) (-762 1896220 1896419 1896527 "OMENC" 1896654 T OMENC (NIL) -8 NIL NIL) (-761 1890115 1891300 1892471 "OMDEV" 1895069 T OMDEV (NIL) -8 NIL NIL) (-760 1889184 1889355 1889549 "OMCONN" 1889941 T OMCONN (NIL) -8 NIL NIL) (-759 1887800 1888786 1888814 "OINTDOM" 1888819 T OINTDOM (NIL) -9 NIL 1888840) (-758 1883562 1884792 1885507 "OFMONOID" 1887117 NIL OFMONOID (NIL T) -8 NIL NIL) (-757 1883000 1883499 1883544 "ODVAR" 1883549 NIL ODVAR (NIL T) -8 NIL NIL) (-756 1880125 1882497 1882682 "ODR" 1882875 NIL ODR (NIL T T NIL) -8 NIL NIL) (-755 1872431 1879904 1880028 "ODPOL" 1880033 NIL ODPOL (NIL T) -8 NIL NIL) (-754 1866254 1872303 1872408 "ODP" 1872413 NIL ODP (NIL NIL T NIL) -8 NIL NIL) (-753 1865020 1865235 1865510 "ODETOOLS" 1866028 NIL ODETOOLS (NIL T T) -7 NIL NIL) (-752 1861989 1862645 1863361 "ODESYS" 1864353 NIL ODESYS (NIL T T) -7 NIL NIL) (-751 1856893 1857801 1858824 "ODERTRIC" 1861064 NIL ODERTRIC (NIL T T) -7 NIL NIL) (-750 1856319 1856401 1856595 "ODERED" 1856805 NIL ODERED (NIL T T T T T) -7 NIL NIL) (-749 1853221 1853769 1854444 "ODERAT" 1855742 NIL ODERAT (NIL T T) -7 NIL NIL) (-748 1850189 1850653 1851249 "ODEPRRIC" 1852750 NIL ODEPRRIC (NIL T T T T) -7 NIL NIL) (-747 1848060 1848627 1849136 "ODEPROB" 1849700 T ODEPROB (NIL) -8 NIL NIL) (-746 1844592 1845075 1845721 "ODEPRIM" 1847539 NIL ODEPRIM (NIL T T T T) -7 NIL NIL) (-745 1843845 1843947 1844205 "ODEPAL" 1844484 NIL ODEPAL (NIL T T T T) -7 NIL NIL) (-744 1840047 1840828 1841682 "ODEPACK" 1843011 T ODEPACK (NIL) -7 NIL NIL) (-743 1839084 1839191 1839419 "ODEINT" 1839936 NIL ODEINT (NIL T T) -7 NIL NIL) (-742 1833185 1834610 1836057 "ODEIFTBL" 1837657 T ODEIFTBL (NIL) -8 NIL NIL) (-741 1828529 1829315 1830273 "ODEEF" 1832344 NIL ODEEF (NIL T T) -7 NIL NIL) (-740 1827866 1827955 1828184 "ODECONST" 1828434 NIL ODECONST (NIL T T T) -7 NIL NIL) (-739 1826024 1826657 1826685 "ODECAT" 1827288 T ODECAT (NIL) -9 NIL 1827817) (-738 1822896 1825736 1825855 "OCT" 1825937 NIL OCT (NIL T) -8 NIL NIL) (-737 1822534 1822577 1822704 "OCTCT2" 1822847 NIL OCTCT2 (NIL T T T T) -7 NIL NIL) (-736 1817368 1819806 1819846 "OC" 1820942 NIL OC (NIL T) -9 NIL 1821799) (-735 1814595 1815343 1816333 "OC-" 1816427 NIL OC- (NIL T T) -8 NIL NIL) (-734 1813974 1814416 1814444 "OCAMON" 1814449 T OCAMON (NIL) -9 NIL 1814470) (-733 1813428 1813835 1813863 "OASGP" 1813868 T OASGP (NIL) -9 NIL 1813888) (-732 1812716 1813179 1813207 "OAMONS" 1813247 T OAMONS (NIL) -9 NIL 1813290) (-731 1812157 1812564 1812592 "OAMON" 1812597 T OAMON (NIL) -9 NIL 1812617) (-730 1811462 1811954 1811982 "OAGROUP" 1811987 T OAGROUP (NIL) -9 NIL 1812007) (-729 1811152 1811202 1811290 "NUMTUBE" 1811406 NIL NUMTUBE (NIL T) -7 NIL NIL) (-728 1804725 1806243 1807779 "NUMQUAD" 1809636 T NUMQUAD (NIL) -7 NIL NIL) (-727 1800481 1801469 1802494 "NUMODE" 1803720 T NUMODE (NIL) -7 NIL NIL) (-726 1797885 1798731 1798759 "NUMINT" 1799676 T NUMINT (NIL) -9 NIL 1800432) (-725 1796833 1797030 1797248 "NUMFMT" 1797687 T NUMFMT (NIL) -7 NIL NIL) (-724 1783215 1786149 1788679 "NUMERIC" 1794342 NIL NUMERIC (NIL T) -7 NIL NIL) (-723 1777616 1782668 1782762 "NTSCAT" 1782767 NIL NTSCAT (NIL T T T T) -9 NIL 1782805) (-722 1776810 1776975 1777168 "NTPOLFN" 1777455 NIL NTPOLFN (NIL T) -7 NIL NIL) (-721 1764626 1773652 1774462 "NSUP" 1776032 NIL NSUP (NIL T) -8 NIL NIL) (-720 1764262 1764319 1764426 "NSUP2" 1764563 NIL NSUP2 (NIL T T) -7 NIL NIL) (-719 1754224 1764041 1764171 "NSMP" 1764176 NIL NSMP (NIL T T) -8 NIL NIL) (-718 1752656 1752957 1753314 "NREP" 1753912 NIL NREP (NIL T) -7 NIL NIL) (-717 1751247 1751499 1751857 "NPCOEF" 1752399 NIL NPCOEF (NIL T T T T T) -7 NIL NIL) (-716 1750313 1750428 1750644 "NORMRETR" 1751128 NIL NORMRETR (NIL T T T T NIL) -7 NIL NIL) (-715 1748366 1748656 1749063 "NORMPK" 1750021 NIL NORMPK (NIL T T T T T) -7 NIL NIL) (-714 1748051 1748079 1748203 "NORMMA" 1748332 NIL NORMMA (NIL T T T T) -7 NIL NIL) (-713 1747878 1748008 1748037 "NONE" 1748042 T NONE (NIL) -8 NIL NIL) (-712 1747667 1747696 1747765 "NONE1" 1747842 NIL NONE1 (NIL T) -7 NIL NIL) (-711 1747152 1747214 1747399 "NODE1" 1747599 NIL NODE1 (NIL T T) -7 NIL NIL) (-710 1745445 1746315 1746570 "NNI" 1746917 T NNI (NIL) -8 NIL NIL) (-709 1743865 1744178 1744542 "NLINSOL" 1745113 NIL NLINSOL (NIL T) -7 NIL NIL) (-708 1740033 1741000 1741922 "NIPROB" 1742963 T NIPROB (NIL) -8 NIL NIL) (-707 1738790 1739024 1739326 "NFINTBAS" 1739795 NIL NFINTBAS (NIL T T) -7 NIL NIL) (-706 1737498 1737729 1738010 "NCODIV" 1738558 NIL NCODIV (NIL T T) -7 NIL NIL) (-705 1737260 1737297 1737372 "NCNTFRAC" 1737455 NIL NCNTFRAC (NIL T) -7 NIL NIL) (-704 1735440 1735804 1736224 "NCEP" 1736885 NIL NCEP (NIL T) -7 NIL NIL) (-703 1734352 1735091 1735119 "NASRING" 1735229 T NASRING (NIL) -9 NIL 1735303) (-702 1734147 1734191 1734285 "NASRING-" 1734290 NIL NASRING- (NIL T) -8 NIL NIL) (-701 1733301 1733800 1733828 "NARNG" 1733945 T NARNG (NIL) -9 NIL 1734036) (-700 1732993 1733060 1733194 "NARNG-" 1733199 NIL NARNG- (NIL T) -8 NIL NIL) (-699 1731872 1732079 1732314 "NAGSP" 1732778 T NAGSP (NIL) -7 NIL NIL) (-698 1723296 1724942 1726577 "NAGS" 1730257 T NAGS (NIL) -7 NIL NIL) (-697 1721860 1722164 1722491 "NAGF07" 1722989 T NAGF07 (NIL) -7 NIL NIL) (-696 1716442 1717722 1719018 "NAGF04" 1720584 T NAGF04 (NIL) -7 NIL NIL) (-695 1709474 1711072 1712689 "NAGF02" 1714845 T NAGF02 (NIL) -7 NIL NIL) (-694 1704738 1705828 1706935 "NAGF01" 1708387 T NAGF01 (NIL) -7 NIL NIL) (-693 1698398 1699956 1701533 "NAGE04" 1703181 T NAGE04 (NIL) -7 NIL NIL) (-692 1689639 1691742 1693854 "NAGE02" 1696306 T NAGE02 (NIL) -7 NIL NIL) (-691 1685632 1686569 1687523 "NAGE01" 1688705 T NAGE01 (NIL) -7 NIL NIL) (-690 1683439 1683970 1684525 "NAGD03" 1685097 T NAGD03 (NIL) -7 NIL NIL) (-689 1675225 1677144 1679089 "NAGD02" 1681514 T NAGD02 (NIL) -7 NIL NIL) (-688 1669084 1670497 1671925 "NAGD01" 1673817 T NAGD01 (NIL) -7 NIL NIL) (-687 1665341 1666151 1666976 "NAGC06" 1668279 T NAGC06 (NIL) -7 NIL NIL) (-686 1663818 1664147 1664500 "NAGC05" 1665008 T NAGC05 (NIL) -7 NIL NIL) (-685 1663202 1663319 1663461 "NAGC02" 1663696 T NAGC02 (NIL) -7 NIL NIL) (-684 1662264 1662821 1662861 "NAALG" 1662940 NIL NAALG (NIL T) -9 NIL 1663001) (-683 1662099 1662128 1662218 "NAALG-" 1662223 NIL NAALG- (NIL T T) -8 NIL NIL) (-682 1656049 1657157 1658344 "MULTSQFR" 1660995 NIL MULTSQFR (NIL T T T T) -7 NIL NIL) (-681 1655368 1655443 1655627 "MULTFACT" 1655961 NIL MULTFACT (NIL T T T T) -7 NIL NIL) (-680 1648562 1652473 1652525 "MTSCAT" 1653585 NIL MTSCAT (NIL T T) -9 NIL 1654099) (-679 1648274 1648328 1648420 "MTHING" 1648502 NIL MTHING (NIL T) -7 NIL NIL) (-678 1648066 1648099 1648159 "MSYSCMD" 1648234 T MSYSCMD (NIL) -7 NIL NIL) (-677 1644178 1646821 1647141 "MSET" 1647779 NIL MSET (NIL T) -8 NIL NIL) (-676 1641274 1643740 1643781 "MSETAGG" 1643786 NIL MSETAGG (NIL T) -9 NIL 1643820) (-675 1637130 1638672 1639413 "MRING" 1640577 NIL MRING (NIL T T) -8 NIL NIL) (-674 1636700 1636767 1636896 "MRF2" 1637057 NIL MRF2 (NIL T T T) -7 NIL NIL) (-673 1636318 1636353 1636497 "MRATFAC" 1636659 NIL MRATFAC (NIL T T T T) -7 NIL NIL) (-672 1633930 1634225 1634656 "MPRFF" 1636023 NIL MPRFF (NIL T T T T) -7 NIL NIL) (-671 1627950 1633785 1633881 "MPOLY" 1633886 NIL MPOLY (NIL NIL T) -8 NIL NIL) (-670 1627440 1627475 1627683 "MPCPF" 1627909 NIL MPCPF (NIL T T T T) -7 NIL NIL) (-669 1626956 1626999 1627182 "MPC3" 1627391 NIL MPC3 (NIL T T T T T T T) -7 NIL NIL) (-668 1626157 1626238 1626457 "MPC2" 1626871 NIL MPC2 (NIL T T T T T T T) -7 NIL NIL) (-667 1624458 1624795 1625185 "MONOTOOL" 1625817 NIL MONOTOOL (NIL T T) -7 NIL NIL) (-666 1623583 1623918 1623946 "MONOID" 1624223 T MONOID (NIL) -9 NIL 1624395) (-665 1622961 1623124 1623367 "MONOID-" 1623372 NIL MONOID- (NIL T) -8 NIL NIL) (-664 1613942 1619928 1619987 "MONOGEN" 1620661 NIL MONOGEN (NIL T T) -9 NIL 1621117) (-663 1611160 1611895 1612895 "MONOGEN-" 1613014 NIL MONOGEN- (NIL T T T) -8 NIL NIL) (-662 1610020 1610440 1610468 "MONADWU" 1610860 T MONADWU (NIL) -9 NIL 1611098) (-661 1609392 1609551 1609799 "MONADWU-" 1609804 NIL MONADWU- (NIL T) -8 NIL NIL) (-660 1608778 1608996 1609024 "MONAD" 1609231 T MONAD (NIL) -9 NIL 1609343) (-659 1608463 1608541 1608673 "MONAD-" 1608678 NIL MONAD- (NIL T) -8 NIL NIL) (-658 1606714 1607376 1607655 "MOEBIUS" 1608216 NIL MOEBIUS (NIL T) -8 NIL NIL) (-657 1606108 1606486 1606526 "MODULE" 1606531 NIL MODULE (NIL T) -9 NIL 1606557) (-656 1605676 1605772 1605962 "MODULE-" 1605967 NIL MODULE- (NIL T T) -8 NIL NIL) (-655 1603347 1604042 1604368 "MODRING" 1605501 NIL MODRING (NIL T T NIL NIL NIL) -8 NIL NIL) (-654 1600303 1601468 1601985 "MODOP" 1602879 NIL MODOP (NIL T T) -8 NIL NIL) (-653 1598490 1598942 1599283 "MODMONOM" 1600102 NIL MODMONOM (NIL T T NIL) -8 NIL NIL) (-652 1588169 1596694 1597116 "MODMON" 1598118 NIL MODMON (NIL T T) -8 NIL NIL) (-651 1585295 1587013 1587289 "MODFIELD" 1588044 NIL MODFIELD (NIL T T NIL NIL NIL) -8 NIL NIL) (-650 1584299 1584576 1584766 "MMLFORM" 1585125 T MMLFORM (NIL) -8 NIL NIL) (-649 1583825 1583868 1584047 "MMAP" 1584250 NIL MMAP (NIL T T T T T T) -7 NIL NIL) (-648 1582062 1582839 1582879 "MLO" 1583296 NIL MLO (NIL T) -9 NIL 1583537) (-647 1579429 1579944 1580546 "MLIFT" 1581543 NIL MLIFT (NIL T T T T) -7 NIL NIL) (-646 1578820 1578904 1579058 "MKUCFUNC" 1579340 NIL MKUCFUNC (NIL T T T) -7 NIL NIL) (-645 1578419 1578489 1578612 "MKRECORD" 1578743 NIL MKRECORD (NIL T T) -7 NIL NIL) (-644 1577467 1577628 1577856 "MKFUNC" 1578230 NIL MKFUNC (NIL T) -7 NIL NIL) (-643 1576855 1576959 1577115 "MKFLCFN" 1577350 NIL MKFLCFN (NIL T) -7 NIL NIL) (-642 1576281 1576648 1576737 "MKCHSET" 1576799 NIL MKCHSET (NIL T) -8 NIL NIL) (-641 1575558 1575660 1575845 "MKBCFUNC" 1576174 NIL MKBCFUNC (NIL T T T T) -7 NIL NIL) (-640 1572242 1575112 1575248 "MINT" 1575442 T MINT (NIL) -8 NIL NIL) (-639 1571054 1571297 1571574 "MHROWRED" 1571997 NIL MHROWRED (NIL T) -7 NIL NIL) (-638 1566325 1569499 1569923 "MFLOAT" 1570650 T MFLOAT (NIL) -8 NIL NIL) (-637 1565682 1565758 1565929 "MFINFACT" 1566237 NIL MFINFACT (NIL T T T T) -7 NIL NIL) (-636 1561997 1562845 1563729 "MESH" 1564818 T MESH (NIL) -7 NIL NIL) (-635 1560387 1560699 1561052 "MDDFACT" 1561684 NIL MDDFACT (NIL T) -7 NIL NIL) (-634 1557230 1559547 1559588 "MDAGG" 1559843 NIL MDAGG (NIL T) -9 NIL 1559986) (-633 1546928 1556523 1556730 "MCMPLX" 1557043 T MCMPLX (NIL) -8 NIL NIL) (-632 1546069 1546215 1546415 "MCDEN" 1546777 NIL MCDEN (NIL T T) -7 NIL NIL) (-631 1543959 1544229 1544609 "MCALCFN" 1545799 NIL MCALCFN (NIL T T T T) -7 NIL NIL) (-630 1541581 1542104 1542665 "MATSTOR" 1543430 NIL MATSTOR (NIL T) -7 NIL NIL) (-629 1537590 1540956 1541203 "MATRIX" 1541366 NIL MATRIX (NIL T) -8 NIL NIL) (-628 1533360 1534063 1534799 "MATLIN" 1536947 NIL MATLIN (NIL T T T T) -7 NIL NIL) (-627 1523558 1526696 1526772 "MATCAT" 1531610 NIL MATCAT (NIL T T T) -9 NIL 1533027) (-626 1519923 1520936 1522291 "MATCAT-" 1522296 NIL MATCAT- (NIL T T T T) -8 NIL NIL) (-625 1518525 1518678 1519009 "MATCAT2" 1519758 NIL MATCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-624 1516637 1516961 1517345 "MAPPKG3" 1518200 NIL MAPPKG3 (NIL T T T) -7 NIL NIL) (-623 1515618 1515791 1516013 "MAPPKG2" 1516461 NIL MAPPKG2 (NIL T T) -7 NIL NIL) (-622 1514117 1514401 1514728 "MAPPKG1" 1515324 NIL MAPPKG1 (NIL T) -7 NIL NIL) (-621 1513728 1513786 1513909 "MAPHACK3" 1514053 NIL MAPHACK3 (NIL T T T) -7 NIL NIL) (-620 1513320 1513381 1513495 "MAPHACK2" 1513660 NIL MAPHACK2 (NIL T T) -7 NIL NIL) (-619 1512758 1512861 1513003 "MAPHACK1" 1513211 NIL MAPHACK1 (NIL T) -7 NIL NIL) (-618 1510866 1511460 1511763 "MAGMA" 1512487 NIL MAGMA (NIL T) -8 NIL NIL) (-617 1507340 1509110 1509570 "M3D" 1510439 NIL M3D (NIL T) -8 NIL NIL) (-616 1501496 1505711 1505752 "LZSTAGG" 1506534 NIL LZSTAGG (NIL T) -9 NIL 1506829) (-615 1497469 1498627 1500084 "LZSTAGG-" 1500089 NIL LZSTAGG- (NIL T T) -8 NIL NIL) (-614 1494585 1495362 1495848 "LWORD" 1497015 NIL LWORD (NIL T) -8 NIL NIL) (-613 1487745 1494356 1494490 "LSQM" 1494495 NIL LSQM (NIL NIL T) -8 NIL NIL) (-612 1486969 1487108 1487336 "LSPP" 1487600 NIL LSPP (NIL T T T T) -7 NIL NIL) (-611 1484781 1485082 1485538 "LSMP" 1486658 NIL LSMP (NIL T T T T) -7 NIL NIL) (-610 1481560 1482234 1482964 "LSMP1" 1484083 NIL LSMP1 (NIL T) -7 NIL NIL) (-609 1475487 1480729 1480770 "LSAGG" 1480832 NIL LSAGG (NIL T) -9 NIL 1480910) (-608 1472182 1473106 1474319 "LSAGG-" 1474324 NIL LSAGG- (NIL T T) -8 NIL NIL) (-607 1469808 1471326 1471575 "LPOLY" 1471977 NIL LPOLY (NIL T T) -8 NIL NIL) (-606 1469390 1469475 1469598 "LPEFRAC" 1469717 NIL LPEFRAC (NIL T) -7 NIL NIL) (-605 1467737 1468484 1468737 "LO" 1469222 NIL LO (NIL T T T) -8 NIL NIL) (-604 1467391 1467503 1467531 "LOGIC" 1467642 T LOGIC (NIL) -9 NIL 1467722) (-603 1467253 1467276 1467347 "LOGIC-" 1467352 NIL LOGIC- (NIL T) -8 NIL NIL) (-602 1466446 1466586 1466779 "LODOOPS" 1467109 NIL LODOOPS (NIL T T) -7 NIL NIL) (-601 1463864 1466363 1466428 "LODO" 1466433 NIL LODO (NIL T NIL) -8 NIL NIL) (-600 1462410 1462645 1462996 "LODOF" 1463611 NIL LODOF (NIL T T) -7 NIL NIL) (-599 1458830 1461266 1461306 "LODOCAT" 1461738 NIL LODOCAT (NIL T) -9 NIL 1461949) (-598 1458564 1458622 1458748 "LODOCAT-" 1458753 NIL LODOCAT- (NIL T T) -8 NIL NIL) (-597 1455878 1458405 1458523 "LODO2" 1458528 NIL LODO2 (NIL T T) -8 NIL NIL) (-596 1453307 1455815 1455860 "LODO1" 1455865 NIL LODO1 (NIL T) -8 NIL NIL) (-595 1452170 1452335 1452646 "LODEEF" 1453130 NIL LODEEF (NIL T T T) -7 NIL NIL) (-594 1447457 1450301 1450342 "LNAGG" 1451289 NIL LNAGG (NIL T) -9 NIL 1451733) (-593 1446604 1446818 1447160 "LNAGG-" 1447165 NIL LNAGG- (NIL T T) -8 NIL NIL) (-592 1442769 1443531 1444169 "LMOPS" 1446020 NIL LMOPS (NIL T T NIL) -8 NIL NIL) (-591 1442167 1442529 1442569 "LMODULE" 1442629 NIL LMODULE (NIL T) -9 NIL 1442671) (-590 1439413 1441812 1441935 "LMDICT" 1442077 NIL LMDICT (NIL T) -8 NIL NIL) (-589 1432640 1438359 1438657 "LIST" 1439148 NIL LIST (NIL T) -8 NIL NIL) (-588 1432165 1432239 1432378 "LIST3" 1432560 NIL LIST3 (NIL T T T) -7 NIL NIL) (-587 1431172 1431350 1431578 "LIST2" 1431983 NIL LIST2 (NIL T T) -7 NIL NIL) (-586 1429306 1429618 1430017 "LIST2MAP" 1430819 NIL LIST2MAP (NIL T T) -7 NIL NIL) (-585 1428019 1428699 1428739 "LINEXP" 1428992 NIL LINEXP (NIL T) -9 NIL 1429140) (-584 1426666 1426926 1427223 "LINDEP" 1427771 NIL LINDEP (NIL T T) -7 NIL NIL) (-583 1423433 1424152 1424929 "LIMITRF" 1425921 NIL LIMITRF (NIL T) -7 NIL NIL) (-582 1421713 1422008 1422423 "LIMITPS" 1423128 NIL LIMITPS (NIL T T) -7 NIL NIL) (-581 1416168 1421224 1421452 "LIE" 1421534 NIL LIE (NIL T T) -8 NIL NIL) (-580 1415219 1415662 1415702 "LIECAT" 1415842 NIL LIECAT (NIL T) -9 NIL 1415993) (-579 1415060 1415087 1415175 "LIECAT-" 1415180 NIL LIECAT- (NIL T T) -8 NIL NIL) (-578 1407672 1414509 1414674 "LIB" 1414915 T LIB (NIL) -8 NIL NIL) (-577 1403309 1404190 1405125 "LGROBP" 1406789 NIL LGROBP (NIL NIL T) -7 NIL NIL) (-576 1401175 1401449 1401811 "LF" 1403030 NIL LF (NIL T T) -7 NIL NIL) (-575 1400015 1400707 1400735 "LFCAT" 1400942 T LFCAT (NIL) -9 NIL 1401081) (-574 1396927 1397553 1398239 "LEXTRIPK" 1399381 NIL LEXTRIPK (NIL T NIL) -7 NIL NIL) (-573 1393633 1394497 1395000 "LEXP" 1396507 NIL LEXP (NIL T T NIL) -8 NIL NIL) (-572 1392031 1392344 1392745 "LEADCDET" 1393315 NIL LEADCDET (NIL T T T T) -7 NIL NIL) (-571 1391227 1391301 1391528 "LAZM3PK" 1391952 NIL LAZM3PK (NIL T T T T T T) -7 NIL NIL) (-570 1386144 1389306 1389843 "LAUPOL" 1390740 NIL LAUPOL (NIL T T) -8 NIL NIL) (-569 1385711 1385755 1385922 "LAPLACE" 1386094 NIL LAPLACE (NIL T T) -7 NIL NIL) (-568 1383639 1384812 1385063 "LA" 1385544 NIL LA (NIL T T T) -8 NIL NIL) (-567 1382702 1383296 1383336 "LALG" 1383397 NIL LALG (NIL T) -9 NIL 1383455) (-566 1382417 1382476 1382611 "LALG-" 1382616 NIL LALG- (NIL T T) -8 NIL NIL) (-565 1381327 1381514 1381811 "KOVACIC" 1382217 NIL KOVACIC (NIL T T) -7 NIL NIL) (-564 1381162 1381186 1381227 "KONVERT" 1381289 NIL KONVERT (NIL T) -9 NIL NIL) (-563 1380997 1381021 1381062 "KOERCE" 1381124 NIL KOERCE (NIL T) -9 NIL NIL) (-562 1378731 1379491 1379884 "KERNEL" 1380636 NIL KERNEL (NIL T) -8 NIL NIL) (-561 1378233 1378314 1378444 "KERNEL2" 1378645 NIL KERNEL2 (NIL T T) -7 NIL NIL) (-560 1372085 1376773 1376827 "KDAGG" 1377204 NIL KDAGG (NIL T T) -9 NIL 1377410) (-559 1371614 1371738 1371943 "KDAGG-" 1371948 NIL KDAGG- (NIL T T T) -8 NIL NIL) (-558 1364789 1371275 1371430 "KAFILE" 1371492 NIL KAFILE (NIL T) -8 NIL NIL) (-557 1359244 1364300 1364528 "JORDAN" 1364610 NIL JORDAN (NIL T T) -8 NIL NIL) (-556 1355544 1357450 1357504 "IXAGG" 1358433 NIL IXAGG (NIL T T) -9 NIL 1358892) (-555 1354463 1354769 1355188 "IXAGG-" 1355193 NIL IXAGG- (NIL T T T) -8 NIL NIL) (-554 1350048 1354385 1354444 "IVECTOR" 1354449 NIL IVECTOR (NIL T NIL) -8 NIL NIL) (-553 1348814 1349051 1349317 "ITUPLE" 1349815 NIL ITUPLE (NIL T) -8 NIL NIL) (-552 1347250 1347427 1347733 "ITRIGMNP" 1348636 NIL ITRIGMNP (NIL T T T) -7 NIL NIL) (-551 1345995 1346199 1346482 "ITFUN3" 1347026 NIL ITFUN3 (NIL T T T) -7 NIL NIL) (-550 1345627 1345684 1345793 "ITFUN2" 1345932 NIL ITFUN2 (NIL T T) -7 NIL NIL) (-549 1343429 1344500 1344797 "ITAYLOR" 1345362 NIL ITAYLOR (NIL T) -8 NIL NIL) (-548 1332417 1337615 1338774 "ISUPS" 1342302 NIL ISUPS (NIL T) -8 NIL NIL) (-547 1331521 1331661 1331897 "ISUMP" 1332264 NIL ISUMP (NIL T T T T) -7 NIL NIL) (-546 1326785 1331322 1331401 "ISTRING" 1331474 NIL ISTRING (NIL NIL) -8 NIL NIL) (-545 1325998 1326079 1326294 "IRURPK" 1326699 NIL IRURPK (NIL T T T T T) -7 NIL NIL) (-544 1324934 1325135 1325375 "IRSN" 1325778 T IRSN (NIL) -7 NIL NIL) (-543 1322969 1323324 1323759 "IRRF2F" 1324572 NIL IRRF2F (NIL T) -7 NIL NIL) (-542 1322716 1322754 1322830 "IRREDFFX" 1322925 NIL IRREDFFX (NIL T) -7 NIL NIL) (-541 1321331 1321590 1321889 "IROOT" 1322449 NIL IROOT (NIL T) -7 NIL NIL) (-540 1317969 1319020 1319710 "IR" 1320673 NIL IR (NIL T) -8 NIL NIL) (-539 1315582 1316077 1316643 "IR2" 1317447 NIL IR2 (NIL T T) -7 NIL NIL) (-538 1314658 1314771 1314991 "IR2F" 1315465 NIL IR2F (NIL T T) -7 NIL NIL) (-537 1314449 1314483 1314543 "IPRNTPK" 1314618 T IPRNTPK (NIL) -7 NIL NIL) (-536 1311003 1314338 1314407 "IPF" 1314412 NIL IPF (NIL NIL) -8 NIL NIL) (-535 1309320 1310928 1310985 "IPADIC" 1310990 NIL IPADIC (NIL NIL NIL) -8 NIL NIL) (-534 1308819 1308877 1309066 "INVLAPLA" 1309256 NIL INVLAPLA (NIL T T) -7 NIL NIL) (-533 1298468 1300821 1303207 "INTTR" 1306483 NIL INTTR (NIL T T) -7 NIL NIL) (-532 1294816 1295557 1296420 "INTTOOLS" 1297654 NIL INTTOOLS (NIL T T) -7 NIL NIL) (-531 1294402 1294493 1294610 "INTSLPE" 1294719 T INTSLPE (NIL) -7 NIL NIL) (-530 1292352 1294325 1294384 "INTRVL" 1294389 NIL INTRVL (NIL T) -8 NIL NIL) (-529 1289959 1290471 1291045 "INTRF" 1291837 NIL INTRF (NIL T) -7 NIL NIL) (-528 1289374 1289471 1289612 "INTRET" 1289857 NIL INTRET (NIL T) -7 NIL NIL) (-527 1287376 1287765 1288234 "INTRAT" 1288982 NIL INTRAT (NIL T T) -7 NIL NIL) (-526 1284609 1285192 1285817 "INTPM" 1286861 NIL INTPM (NIL T T) -7 NIL NIL) (-525 1281318 1281917 1282661 "INTPAF" 1283995 NIL INTPAF (NIL T T T) -7 NIL NIL) (-524 1276561 1277507 1278542 "INTPACK" 1280303 T INTPACK (NIL) -7 NIL NIL) (-523 1273415 1276290 1276417 "INT" 1276454 T INT (NIL) -8 NIL NIL) (-522 1272667 1272819 1273027 "INTHERTR" 1273257 NIL INTHERTR (NIL T T) -7 NIL NIL) (-521 1272106 1272186 1272374 "INTHERAL" 1272581 NIL INTHERAL (NIL T T T T) -7 NIL NIL) (-520 1269952 1270395 1270852 "INTHEORY" 1271669 T INTHEORY (NIL) -7 NIL NIL) (-519 1261275 1262895 1264673 "INTG0" 1268304 NIL INTG0 (NIL T T T) -7 NIL NIL) (-518 1241848 1246638 1251448 "INTFTBL" 1256485 T INTFTBL (NIL) -8 NIL NIL) (-517 1241097 1241235 1241408 "INTFACT" 1241707 NIL INTFACT (NIL T) -7 NIL NIL) (-516 1238488 1238934 1239497 "INTEF" 1240651 NIL INTEF (NIL T T) -7 NIL NIL) (-515 1236950 1237699 1237727 "INTDOM" 1238028 T INTDOM (NIL) -9 NIL 1238235) (-514 1236319 1236493 1236735 "INTDOM-" 1236740 NIL INTDOM- (NIL T) -8 NIL NIL) (-513 1232812 1234744 1234798 "INTCAT" 1235597 NIL INTCAT (NIL T) -9 NIL 1235916) (-512 1232285 1232387 1232515 "INTBIT" 1232704 T INTBIT (NIL) -7 NIL NIL) (-511 1230960 1231114 1231427 "INTALG" 1232130 NIL INTALG (NIL T T T T T) -7 NIL NIL) (-510 1230417 1230507 1230677 "INTAF" 1230864 NIL INTAF (NIL T T) -7 NIL NIL) (-509 1223871 1230227 1230367 "INTABL" 1230372 NIL INTABL (NIL T T T) -8 NIL NIL) (-508 1218822 1221551 1221579 "INS" 1222547 T INS (NIL) -9 NIL 1223228) (-507 1216062 1216833 1217807 "INS-" 1217880 NIL INS- (NIL T) -8 NIL NIL) (-506 1214841 1215068 1215365 "INPSIGN" 1215815 NIL INPSIGN (NIL T T) -7 NIL NIL) (-505 1213959 1214076 1214273 "INPRODPF" 1214721 NIL INPRODPF (NIL T T) -7 NIL NIL) (-504 1212853 1212970 1213207 "INPRODFF" 1213839 NIL INPRODFF (NIL T T T T) -7 NIL NIL) (-503 1211853 1212005 1212265 "INNMFACT" 1212689 NIL INNMFACT (NIL T T T T) -7 NIL NIL) (-502 1211050 1211147 1211335 "INMODGCD" 1211752 NIL INMODGCD (NIL T T NIL NIL) -7 NIL NIL) (-501 1209559 1209803 1210127 "INFSP" 1210795 NIL INFSP (NIL T T T) -7 NIL NIL) (-500 1208743 1208860 1209043 "INFPROD0" 1209439 NIL INFPROD0 (NIL T T) -7 NIL NIL) (-499 1205753 1206912 1207403 "INFORM" 1208260 T INFORM (NIL) -8 NIL NIL) (-498 1205363 1205423 1205521 "INFORM1" 1205688 NIL INFORM1 (NIL T) -7 NIL NIL) (-497 1204886 1204975 1205089 "INFINITY" 1205269 T INFINITY (NIL) -7 NIL NIL) (-496 1203504 1203752 1204073 "INEP" 1204634 NIL INEP (NIL T T T) -7 NIL NIL) (-495 1202780 1203401 1203466 "INDE" 1203471 NIL INDE (NIL T) -8 NIL NIL) (-494 1202344 1202412 1202529 "INCRMAPS" 1202707 NIL INCRMAPS (NIL T) -7 NIL NIL) (-493 1197655 1198580 1199524 "INBFF" 1201432 NIL INBFF (NIL T) -7 NIL NIL) (-492 1194150 1197500 1197603 "IMATRIX" 1197608 NIL IMATRIX (NIL T NIL NIL) -8 NIL NIL) (-491 1192862 1192985 1193300 "IMATQF" 1194006 NIL IMATQF (NIL T T T T T T T T) -7 NIL NIL) (-490 1191082 1191309 1191646 "IMATLIN" 1192618 NIL IMATLIN (NIL T T T T) -7 NIL NIL) (-489 1185708 1191006 1191064 "ILIST" 1191069 NIL ILIST (NIL T NIL) -8 NIL NIL) (-488 1183661 1185568 1185681 "IIARRAY2" 1185686 NIL IIARRAY2 (NIL T NIL NIL T T) -8 NIL NIL) (-487 1179029 1183572 1183636 "IFF" 1183641 NIL IFF (NIL NIL NIL) -8 NIL NIL) (-486 1174072 1178321 1178509 "IFARRAY" 1178886 NIL IFARRAY (NIL T NIL) -8 NIL NIL) (-485 1173279 1173976 1174049 "IFAMON" 1174054 NIL IFAMON (NIL T T NIL) -8 NIL NIL) (-484 1172863 1172928 1172982 "IEVALAB" 1173189 NIL IEVALAB (NIL T T) -9 NIL NIL) (-483 1172538 1172606 1172766 "IEVALAB-" 1172771 NIL IEVALAB- (NIL T T T) -8 NIL NIL) (-482 1172196 1172452 1172515 "IDPO" 1172520 NIL IDPO (NIL T T) -8 NIL NIL) (-481 1171473 1172085 1172160 "IDPOAMS" 1172165 NIL IDPOAMS (NIL T T) -8 NIL NIL) (-480 1170807 1171362 1171437 "IDPOAM" 1171442 NIL IDPOAM (NIL T T) -8 NIL NIL) (-479 1169893 1170143 1170196 "IDPC" 1170609 NIL IDPC (NIL T T) -9 NIL 1170758) (-478 1169389 1169785 1169858 "IDPAM" 1169863 NIL IDPAM (NIL T T) -8 NIL NIL) (-477 1168792 1169281 1169354 "IDPAG" 1169359 NIL IDPAG (NIL T T) -8 NIL NIL) (-476 1165047 1165895 1166790 "IDECOMP" 1167949 NIL IDECOMP (NIL NIL NIL) -7 NIL NIL) (-475 1157920 1158970 1160017 "IDEAL" 1164083 NIL IDEAL (NIL T T T T) -8 NIL NIL) (-474 1157084 1157196 1157395 "ICDEN" 1157804 NIL ICDEN (NIL T T T T) -7 NIL NIL) (-473 1156183 1156564 1156711 "ICARD" 1156957 T ICARD (NIL) -8 NIL NIL) (-472 1154255 1154568 1154971 "IBPTOOLS" 1155860 NIL IBPTOOLS (NIL T T T T) -7 NIL NIL) (-471 1149869 1153875 1153988 "IBITS" 1154174 NIL IBITS (NIL NIL) -8 NIL NIL) (-470 1146592 1147168 1147863 "IBATOOL" 1149286 NIL IBATOOL (NIL T T T) -7 NIL NIL) (-469 1144372 1144833 1145366 "IBACHIN" 1146127 NIL IBACHIN (NIL T T T) -7 NIL NIL) (-468 1142249 1144218 1144321 "IARRAY2" 1144326 NIL IARRAY2 (NIL T NIL NIL) -8 NIL NIL) (-467 1138402 1142175 1142232 "IARRAY1" 1142237 NIL IARRAY1 (NIL T NIL) -8 NIL NIL) (-466 1132341 1136820 1137298 "IAN" 1137944 T IAN (NIL) -8 NIL NIL) (-465 1131852 1131909 1132082 "IALGFACT" 1132278 NIL IALGFACT (NIL T T T T) -7 NIL NIL) (-464 1131380 1131493 1131521 "HYPCAT" 1131728 T HYPCAT (NIL) -9 NIL NIL) (-463 1130918 1131035 1131221 "HYPCAT-" 1131226 NIL HYPCAT- (NIL T) -8 NIL NIL) (-462 1127598 1128929 1128970 "HOAGG" 1129951 NIL HOAGG (NIL T) -9 NIL 1130630) (-461 1126192 1126591 1127117 "HOAGG-" 1127122 NIL HOAGG- (NIL T T) -8 NIL NIL) (-460 1120023 1125633 1125799 "HEXADEC" 1126046 T HEXADEC (NIL) -8 NIL NIL) (-459 1118771 1118993 1119256 "HEUGCD" 1119800 NIL HEUGCD (NIL T) -7 NIL NIL) (-458 1117874 1118608 1118738 "HELLFDIV" 1118743 NIL HELLFDIV (NIL T T T T) -8 NIL NIL) (-457 1116102 1117651 1117739 "HEAP" 1117818 NIL HEAP (NIL T) -8 NIL NIL) (-456 1109969 1116017 1116079 "HDP" 1116084 NIL HDP (NIL NIL T) -8 NIL NIL) (-455 1103681 1109606 1109757 "HDMP" 1109870 NIL HDMP (NIL NIL T) -8 NIL NIL) (-454 1103006 1103145 1103309 "HB" 1103537 T HB (NIL) -7 NIL NIL) (-453 1096503 1102852 1102956 "HASHTBL" 1102961 NIL HASHTBL (NIL T T NIL) -8 NIL NIL) (-452 1094256 1096131 1096310 "HACKPI" 1096344 T HACKPI (NIL) -8 NIL NIL) (-451 1089952 1094110 1094222 "GTSET" 1094227 NIL GTSET (NIL T T T T) -8 NIL NIL) (-450 1083478 1089830 1089928 "GSTBL" 1089933 NIL GSTBL (NIL T T T NIL) -8 NIL NIL) (-449 1075711 1082514 1082778 "GSERIES" 1083269 NIL GSERIES (NIL T NIL NIL) -8 NIL NIL) (-448 1074734 1075187 1075215 "GROUP" 1075476 T GROUP (NIL) -9 NIL 1075635) (-447 1073850 1074073 1074417 "GROUP-" 1074422 NIL GROUP- (NIL T) -8 NIL NIL) (-446 1072219 1072538 1072925 "GROEBSOL" 1073527 NIL GROEBSOL (NIL NIL T T) -7 NIL NIL) (-445 1071160 1071422 1071473 "GRMOD" 1072002 NIL GRMOD (NIL T T) -9 NIL 1072170) (-444 1070928 1070964 1071092 "GRMOD-" 1071097 NIL GRMOD- (NIL T T T) -8 NIL NIL) (-443 1066254 1067282 1068282 "GRIMAGE" 1069948 T GRIMAGE (NIL) -8 NIL NIL) (-442 1064721 1064981 1065305 "GRDEF" 1065950 T GRDEF (NIL) -7 NIL NIL) (-441 1064165 1064281 1064422 "GRAY" 1064600 T GRAY (NIL) -7 NIL NIL) (-440 1063399 1063779 1063830 "GRALG" 1063983 NIL GRALG (NIL T T) -9 NIL 1064075) (-439 1063060 1063133 1063296 "GRALG-" 1063301 NIL GRALG- (NIL T T T) -8 NIL NIL) (-438 1059868 1062649 1062825 "GPOLSET" 1062967 NIL GPOLSET (NIL T T T T) -8 NIL NIL) (-437 1059224 1059281 1059538 "GOSPER" 1059805 NIL GOSPER (NIL T T T T T) -7 NIL NIL) (-436 1054983 1055662 1056188 "GMODPOL" 1058923 NIL GMODPOL (NIL NIL T T T NIL T) -8 NIL NIL) (-435 1053988 1054172 1054410 "GHENSEL" 1054795 NIL GHENSEL (NIL T T) -7 NIL NIL) (-434 1048054 1048897 1049923 "GENUPS" 1053072 NIL GENUPS (NIL T T) -7 NIL NIL) (-433 1047751 1047802 1047891 "GENUFACT" 1047997 NIL GENUFACT (NIL T) -7 NIL NIL) (-432 1047163 1047240 1047405 "GENPGCD" 1047669 NIL GENPGCD (NIL T T T T) -7 NIL NIL) (-431 1046637 1046672 1046885 "GENMFACT" 1047122 NIL GENMFACT (NIL T T T T T) -7 NIL NIL) (-430 1045205 1045460 1045767 "GENEEZ" 1046380 NIL GENEEZ (NIL T T) -7 NIL NIL) (-429 1039079 1044818 1044979 "GDMP" 1045128 NIL GDMP (NIL NIL T T) -8 NIL NIL) (-428 1028461 1032850 1033956 "GCNAALG" 1038062 NIL GCNAALG (NIL T NIL NIL NIL) -8 NIL NIL) (-427 1026883 1027755 1027783 "GCDDOM" 1028038 T GCDDOM (NIL) -9 NIL 1028195) (-426 1026353 1026480 1026695 "GCDDOM-" 1026700 NIL GCDDOM- (NIL T) -8 NIL NIL) (-425 1025025 1025210 1025514 "GB" 1026132 NIL GB (NIL T T T T) -7 NIL NIL) (-424 1013645 1015971 1018363 "GBINTERN" 1022716 NIL GBINTERN (NIL T T T T) -7 NIL NIL) (-423 1011482 1011774 1012195 "GBF" 1013320 NIL GBF (NIL T T T T) -7 NIL NIL) (-422 1010263 1010428 1010695 "GBEUCLID" 1011298 NIL GBEUCLID (NIL T T T T) -7 NIL NIL) (-421 1009612 1009737 1009886 "GAUSSFAC" 1010134 T GAUSSFAC (NIL) -7 NIL NIL) (-420 1007989 1008291 1008604 "GALUTIL" 1009331 NIL GALUTIL (NIL T) -7 NIL NIL) (-419 1006306 1006580 1006903 "GALPOLYU" 1007716 NIL GALPOLYU (NIL T T) -7 NIL NIL) (-418 1003695 1003985 1004390 "GALFACTU" 1006003 NIL GALFACTU (NIL T T T) -7 NIL NIL) (-417 995501 997000 998608 "GALFACT" 1002127 NIL GALFACT (NIL T) -7 NIL NIL) (-416 992889 993547 993575 "FVFUN" 994731 T FVFUN (NIL) -9 NIL 995451) (-415 992155 992337 992365 "FVC" 992656 T FVC (NIL) -9 NIL 992839) (-414 991797 991952 992033 "FUNCTION" 992107 NIL FUNCTION (NIL NIL) -8 NIL NIL) (-413 989467 990018 990507 "FT" 991328 T FT (NIL) -8 NIL NIL) (-412 988285 988768 988971 "FTEM" 989284 T FTEM (NIL) -8 NIL NIL) (-411 986550 986838 987240 "FSUPFACT" 987977 NIL FSUPFACT (NIL T T T) -7 NIL NIL) (-410 984947 985236 985568 "FST" 986238 T FST (NIL) -8 NIL NIL) (-409 984122 984228 984422 "FSRED" 984829 NIL FSRED (NIL T T) -7 NIL NIL) (-408 982801 983056 983410 "FSPRMELT" 983837 NIL FSPRMELT (NIL T T) -7 NIL NIL) (-407 979886 980324 980823 "FSPECF" 982364 NIL FSPECF (NIL T T) -7 NIL NIL) (-406 962260 970817 970857 "FS" 974695 NIL FS (NIL T) -9 NIL 976977) (-405 950910 953900 957956 "FS-" 958253 NIL FS- (NIL T T) -8 NIL NIL) (-404 950426 950480 950656 "FSINT" 950851 NIL FSINT (NIL T T) -7 NIL NIL) (-403 948707 949419 949722 "FSERIES" 950205 NIL FSERIES (NIL T T) -8 NIL NIL) (-402 947725 947841 948071 "FSCINT" 948587 NIL FSCINT (NIL T T) -7 NIL NIL) (-401 943960 946670 946711 "FSAGG" 947081 NIL FSAGG (NIL T) -9 NIL 947340) (-400 941722 942323 943119 "FSAGG-" 943214 NIL FSAGG- (NIL T T) -8 NIL NIL) (-399 940764 940907 941134 "FSAGG2" 941575 NIL FSAGG2 (NIL T T T T) -7 NIL NIL) (-398 938423 938702 939255 "FS2UPS" 940482 NIL FS2UPS (NIL T T T T T NIL) -7 NIL NIL) (-397 938009 938052 938205 "FS2" 938374 NIL FS2 (NIL T T T T) -7 NIL NIL) (-396 936869 937040 937348 "FS2EXPXP" 937834 NIL FS2EXPXP (NIL T T NIL NIL) -7 NIL NIL) (-395 936295 936410 936562 "FRUTIL" 936749 NIL FRUTIL (NIL T) -7 NIL NIL) (-394 927715 931794 933150 "FR" 934971 NIL FR (NIL T) -8 NIL NIL) (-393 922792 925435 925475 "FRNAALG" 926871 NIL FRNAALG (NIL T) -9 NIL 927478) (-392 918471 919541 920816 "FRNAALG-" 921566 NIL FRNAALG- (NIL T T) -8 NIL NIL) (-391 918109 918152 918279 "FRNAAF2" 918422 NIL FRNAAF2 (NIL T T T T) -7 NIL NIL) (-390 916474 916966 917260 "FRMOD" 917922 NIL FRMOD (NIL T T T T NIL) -8 NIL NIL) (-389 914197 914865 915181 "FRIDEAL" 916265 NIL FRIDEAL (NIL T T T T) -8 NIL NIL) (-388 913396 913483 913770 "FRIDEAL2" 914104 NIL FRIDEAL2 (NIL T T T T T T T T) -7 NIL NIL) (-387 912654 913062 913103 "FRETRCT" 913108 NIL FRETRCT (NIL T) -9 NIL 913279) (-386 911766 911997 912348 "FRETRCT-" 912353 NIL FRETRCT- (NIL T T) -8 NIL NIL) (-385 908976 910196 910255 "FRAMALG" 911137 NIL FRAMALG (NIL T T) -9 NIL 911429) (-384 907109 907565 908195 "FRAMALG-" 908418 NIL FRAMALG- (NIL T T T) -8 NIL NIL) (-383 901011 906584 906860 "FRAC" 906865 NIL FRAC (NIL T) -8 NIL NIL) (-382 900647 900704 900811 "FRAC2" 900948 NIL FRAC2 (NIL T T) -7 NIL NIL) (-381 900283 900340 900447 "FR2" 900584 NIL FR2 (NIL T T) -7 NIL NIL) (-380 894957 897870 897898 "FPS" 899017 T FPS (NIL) -9 NIL 899573) (-379 894406 894515 894679 "FPS-" 894825 NIL FPS- (NIL T) -8 NIL NIL) (-378 891855 893552 893580 "FPC" 893805 T FPC (NIL) -9 NIL 893947) (-377 891648 891688 891785 "FPC-" 891790 NIL FPC- (NIL T) -8 NIL NIL) (-376 890527 891137 891178 "FPATMAB" 891183 NIL FPATMAB (NIL T) -9 NIL 891335) (-375 888227 888703 889129 "FPARFRAC" 890164 NIL FPARFRAC (NIL T T) -8 NIL NIL) (-374 883622 884119 884801 "FORTRAN" 887659 NIL FORTRAN (NIL NIL NIL NIL NIL) -8 NIL NIL) (-373 881338 881838 882377 "FORT" 883103 T FORT (NIL) -7 NIL NIL) (-372 879014 879576 879604 "FORTFN" 880664 T FORTFN (NIL) -9 NIL 881288) (-371 878778 878828 878856 "FORTCAT" 878915 T FORTCAT (NIL) -9 NIL 878977) (-370 876838 877321 877720 "FORMULA" 878399 T FORMULA (NIL) -8 NIL NIL) (-369 876626 876656 876725 "FORMULA1" 876802 NIL FORMULA1 (NIL T) -7 NIL NIL) (-368 876149 876201 876374 "FORDER" 876568 NIL FORDER (NIL T T T T) -7 NIL NIL) (-367 875245 875409 875602 "FOP" 875976 T FOP (NIL) -7 NIL NIL) (-366 873853 874525 874699 "FNLA" 875127 NIL FNLA (NIL NIL NIL T) -8 NIL NIL) (-365 872522 872911 872939 "FNCAT" 873511 T FNCAT (NIL) -9 NIL 873804) (-364 872088 872481 872509 "FNAME" 872514 T FNAME (NIL) -8 NIL NIL) (-363 870748 871721 871749 "FMTC" 871754 T FMTC (NIL) -9 NIL 871789) (-362 867066 868273 868901 "FMONOID" 870153 NIL FMONOID (NIL T) -8 NIL NIL) (-361 866286 866809 866957 "FM" 866962 NIL FM (NIL T T) -8 NIL NIL) (-360 863710 864356 864384 "FMFUN" 865528 T FMFUN (NIL) -9 NIL 866236) (-359 862979 863160 863188 "FMC" 863478 T FMC (NIL) -9 NIL 863660) (-358 860209 861043 861096 "FMCAT" 862278 NIL FMCAT (NIL T T) -9 NIL 862772) (-357 859104 859977 860076 "FM1" 860154 NIL FM1 (NIL T T) -8 NIL NIL) (-356 856878 857294 857788 "FLOATRP" 858655 NIL FLOATRP (NIL T) -7 NIL NIL) (-355 850364 854534 855164 "FLOAT" 856268 T FLOAT (NIL) -8 NIL NIL) (-354 847802 848302 848880 "FLOATCP" 849831 NIL FLOATCP (NIL T) -7 NIL NIL) (-353 846591 847439 847479 "FLINEXP" 847484 NIL FLINEXP (NIL T) -9 NIL 847577) (-352 845746 845981 846308 "FLINEXP-" 846313 NIL FLINEXP- (NIL T T) -8 NIL NIL) (-351 844822 844966 845190 "FLASORT" 845598 NIL FLASORT (NIL T T) -7 NIL NIL) (-350 842041 842883 842935 "FLALG" 844162 NIL FLALG (NIL T T) -9 NIL 844629) (-349 835826 839528 839569 "FLAGG" 840831 NIL FLAGG (NIL T) -9 NIL 841483) (-348 834552 834891 835381 "FLAGG-" 835386 NIL FLAGG- (NIL T T) -8 NIL NIL) (-347 833594 833737 833964 "FLAGG2" 834405 NIL FLAGG2 (NIL T T T T) -7 NIL NIL) (-346 830567 831585 831644 "FINRALG" 832772 NIL FINRALG (NIL T T) -9 NIL 833280) (-345 829727 829956 830295 "FINRALG-" 830300 NIL FINRALG- (NIL T T T) -8 NIL NIL) (-344 829134 829347 829375 "FINITE" 829571 T FINITE (NIL) -9 NIL 829678) (-343 821594 823755 823795 "FINAALG" 827462 NIL FINAALG (NIL T) -9 NIL 828915) (-342 816935 817976 819120 "FINAALG-" 820499 NIL FINAALG- (NIL T T) -8 NIL NIL) (-341 816330 816690 816793 "FILE" 816865 NIL FILE (NIL T) -8 NIL NIL) (-340 815015 815327 815381 "FILECAT" 816065 NIL FILECAT (NIL T T) -9 NIL 816281) (-339 812878 814434 814462 "FIELD" 814502 T FIELD (NIL) -9 NIL 814582) (-338 811498 811883 812394 "FIELD-" 812399 NIL FIELD- (NIL T) -8 NIL NIL) (-337 809313 810135 810481 "FGROUP" 811185 NIL FGROUP (NIL T) -8 NIL NIL) (-336 808403 808567 808787 "FGLMICPK" 809145 NIL FGLMICPK (NIL T NIL) -7 NIL NIL) (-335 804205 808328 808385 "FFX" 808390 NIL FFX (NIL T NIL) -8 NIL NIL) (-334 803806 803867 804002 "FFSLPE" 804138 NIL FFSLPE (NIL T T T) -7 NIL NIL) (-333 799799 800578 801374 "FFPOLY" 803042 NIL FFPOLY (NIL T) -7 NIL NIL) (-332 799303 799339 799548 "FFPOLY2" 799757 NIL FFPOLY2 (NIL T T) -7 NIL NIL) (-331 795125 799222 799285 "FFP" 799290 NIL FFP (NIL T NIL) -8 NIL NIL) (-330 790493 795036 795100 "FF" 795105 NIL FF (NIL NIL NIL) -8 NIL NIL) (-329 785589 789836 790026 "FFNBX" 790347 NIL FFNBX (NIL T NIL) -8 NIL NIL) (-328 780499 784724 784982 "FFNBP" 785443 NIL FFNBP (NIL T NIL) -8 NIL NIL) (-327 775102 779783 779994 "FFNB" 780332 NIL FFNB (NIL NIL NIL) -8 NIL NIL) (-326 773934 774132 774447 "FFINTBAS" 774899 NIL FFINTBAS (NIL T T T) -7 NIL NIL) (-325 770158 772398 772426 "FFIELDC" 773046 T FFIELDC (NIL) -9 NIL 773422) (-324 768821 769191 769688 "FFIELDC-" 769693 NIL FFIELDC- (NIL T) -8 NIL NIL) (-323 768391 768436 768560 "FFHOM" 768763 NIL FFHOM (NIL T T T) -7 NIL NIL) (-322 766089 766573 767090 "FFF" 767906 NIL FFF (NIL T) -7 NIL NIL) (-321 761677 765831 765932 "FFCGX" 766032 NIL FFCGX (NIL T NIL) -8 NIL NIL) (-320 757279 761409 761516 "FFCGP" 761620 NIL FFCGP (NIL T NIL) -8 NIL NIL) (-319 752432 757006 757114 "FFCG" 757215 NIL FFCG (NIL NIL NIL) -8 NIL NIL) (-318 734378 743501 743587 "FFCAT" 748752 NIL FFCAT (NIL T T T) -9 NIL 750239) (-317 729576 730623 731937 "FFCAT-" 733167 NIL FFCAT- (NIL T T T T) -8 NIL NIL) (-316 728987 729030 729265 "FFCAT2" 729527 NIL FFCAT2 (NIL T T T T T T T T) -7 NIL NIL) (-315 718187 721977 723194 "FEXPR" 727842 NIL FEXPR (NIL NIL NIL T) -8 NIL NIL) (-314 717187 717622 717663 "FEVALAB" 717747 NIL FEVALAB (NIL T) -9 NIL 718008) (-313 716346 716556 716894 "FEVALAB-" 716899 NIL FEVALAB- (NIL T T) -8 NIL NIL) (-312 714939 715729 715932 "FDIV" 716245 NIL FDIV (NIL T T T T) -8 NIL NIL) (-311 712006 712721 712836 "FDIVCAT" 714404 NIL FDIVCAT (NIL T T T T) -9 NIL 714841) (-310 711768 711795 711965 "FDIVCAT-" 711970 NIL FDIVCAT- (NIL T T T T T) -8 NIL NIL) (-309 710988 711075 711352 "FDIV2" 711675 NIL FDIV2 (NIL T T T T T T T T) -7 NIL NIL) (-308 709674 709933 710222 "FCPAK1" 710719 T FCPAK1 (NIL) -7 NIL NIL) (-307 708802 709174 709315 "FCOMP" 709565 NIL FCOMP (NIL T) -8 NIL NIL) (-306 692438 695851 699412 "FC" 705261 T FC (NIL) -8 NIL NIL) (-305 685034 689080 689120 "FAXF" 690922 NIL FAXF (NIL T) -9 NIL 691613) (-304 682313 682968 683793 "FAXF-" 684258 NIL FAXF- (NIL T T) -8 NIL NIL) (-303 677413 681689 681865 "FARRAY" 682170 NIL FARRAY (NIL T) -8 NIL NIL) (-302 672804 674875 674927 "FAMR" 675939 NIL FAMR (NIL T T) -9 NIL 676399) (-301 671695 671997 672431 "FAMR-" 672436 NIL FAMR- (NIL T T T) -8 NIL NIL) (-300 670891 671617 671670 "FAMONOID" 671675 NIL FAMONOID (NIL T) -8 NIL NIL) (-299 668724 669408 669461 "FAMONC" 670402 NIL FAMONC (NIL T T) -9 NIL 670787) (-298 667416 668478 668615 "FAGROUP" 668620 NIL FAGROUP (NIL T) -8 NIL NIL) (-297 665219 665538 665940 "FACUTIL" 667097 NIL FACUTIL (NIL T T T T) -7 NIL NIL) (-296 664318 664503 664725 "FACTFUNC" 665029 NIL FACTFUNC (NIL T) -7 NIL NIL) (-295 656638 663569 663781 "EXPUPXS" 664174 NIL EXPUPXS (NIL T NIL NIL) -8 NIL NIL) (-294 654121 654661 655247 "EXPRTUBE" 656072 T EXPRTUBE (NIL) -7 NIL NIL) (-293 650315 650907 651644 "EXPRODE" 653460 NIL EXPRODE (NIL T T) -7 NIL NIL) (-292 635474 648974 649400 "EXPR" 649921 NIL EXPR (NIL T) -8 NIL NIL) (-291 629902 630489 631301 "EXPR2UPS" 634772 NIL EXPR2UPS (NIL T T) -7 NIL NIL) (-290 629538 629595 629702 "EXPR2" 629839 NIL EXPR2 (NIL T T) -7 NIL NIL) (-289 620892 628675 628970 "EXPEXPAN" 629376 NIL EXPEXPAN (NIL T T NIL NIL) -8 NIL NIL) (-288 620719 620849 620878 "EXIT" 620883 T EXIT (NIL) -8 NIL NIL) (-287 620346 620408 620521 "EVALCYC" 620651 NIL EVALCYC (NIL T) -7 NIL NIL) (-286 619887 620005 620046 "EVALAB" 620216 NIL EVALAB (NIL T) -9 NIL 620320) (-285 619368 619490 619711 "EVALAB-" 619716 NIL EVALAB- (NIL T T) -8 NIL NIL) (-284 616831 618143 618171 "EUCDOM" 618726 T EUCDOM (NIL) -9 NIL 619076) (-283 615236 615678 616268 "EUCDOM-" 616273 NIL EUCDOM- (NIL T) -8 NIL NIL) (-282 602814 605562 608302 "ESTOOLS" 612516 T ESTOOLS (NIL) -7 NIL NIL) (-281 602450 602507 602614 "ESTOOLS2" 602751 NIL ESTOOLS2 (NIL T T) -7 NIL NIL) (-280 602201 602243 602323 "ESTOOLS1" 602402 NIL ESTOOLS1 (NIL T) -7 NIL NIL) (-279 596139 597863 597891 "ES" 600655 T ES (NIL) -9 NIL 602061) (-278 591087 592373 594190 "ES-" 594354 NIL ES- (NIL T) -8 NIL NIL) (-277 587462 588222 589002 "ESCONT" 590327 T ESCONT (NIL) -7 NIL NIL) (-276 587207 587239 587321 "ESCONT1" 587424 NIL ESCONT1 (NIL NIL NIL) -7 NIL NIL) (-275 586882 586932 587032 "ES2" 587151 NIL ES2 (NIL T T) -7 NIL NIL) (-274 586512 586570 586679 "ES1" 586818 NIL ES1 (NIL T T) -7 NIL NIL) (-273 585728 585857 586033 "ERROR" 586356 T ERROR (NIL) -7 NIL NIL) (-272 579231 585587 585678 "EQTBL" 585683 NIL EQTBL (NIL T T) -8 NIL NIL) (-271 571668 574549 575996 "EQ" 577817 NIL -2531 (NIL T) -8 NIL NIL) (-270 571300 571357 571466 "EQ2" 571605 NIL EQ2 (NIL T T) -7 NIL NIL) (-269 566592 567638 568731 "EP" 570239 NIL EP (NIL T) -7 NIL NIL) (-268 565175 565475 565792 "ENV" 566295 T ENV (NIL) -8 NIL NIL) (-267 564335 564899 564927 "ENTIRER" 564932 T ENTIRER (NIL) -9 NIL 564977) (-266 560791 562290 562660 "EMR" 564134 NIL EMR (NIL T T T NIL NIL NIL) -8 NIL NIL) (-265 559935 560120 560174 "ELTAGG" 560554 NIL ELTAGG (NIL T T) -9 NIL 560765) (-264 559654 559716 559857 "ELTAGG-" 559862 NIL ELTAGG- (NIL T T T) -8 NIL NIL) (-263 559443 559472 559526 "ELTAB" 559610 NIL ELTAB (NIL T T) -9 NIL NIL) (-262 558569 558715 558914 "ELFUTS" 559294 NIL ELFUTS (NIL T T) -7 NIL NIL) (-261 558311 558367 558395 "ELEMFUN" 558500 T ELEMFUN (NIL) -9 NIL NIL) (-260 558181 558202 558270 "ELEMFUN-" 558275 NIL ELEMFUN- (NIL T) -8 NIL NIL) (-259 553073 556282 556323 "ELAGG" 557263 NIL ELAGG (NIL T) -9 NIL 557726) (-258 551358 551792 552455 "ELAGG-" 552460 NIL ELAGG- (NIL T T) -8 NIL NIL) (-257 550015 550295 550590 "ELABEXPR" 551083 T ELABEXPR (NIL) -8 NIL NIL) (-256 542883 544682 545509 "EFUPXS" 549291 NIL EFUPXS (NIL T T T T) -8 NIL NIL) (-255 536333 538134 538944 "EFULS" 542159 NIL EFULS (NIL T T T) -8 NIL NIL) (-254 533764 534122 534600 "EFSTRUC" 535965 NIL EFSTRUC (NIL T T) -7 NIL NIL) (-253 522836 524401 525961 "EF" 532279 NIL EF (NIL T T) -7 NIL NIL) (-252 521937 522321 522470 "EAB" 522707 T EAB (NIL) -8 NIL NIL) (-251 521150 521896 521924 "E04UCFA" 521929 T E04UCFA (NIL) -8 NIL NIL) (-250 520363 521109 521137 "E04NAFA" 521142 T E04NAFA (NIL) -8 NIL NIL) (-249 519576 520322 520350 "E04MBFA" 520355 T E04MBFA (NIL) -8 NIL NIL) (-248 518789 519535 519563 "E04JAFA" 519568 T E04JAFA (NIL) -8 NIL NIL) (-247 518004 518748 518776 "E04GCFA" 518781 T E04GCFA (NIL) -8 NIL NIL) (-246 517219 517963 517991 "E04FDFA" 517996 T E04FDFA (NIL) -8 NIL NIL) (-245 516432 517178 517206 "E04DGFA" 517211 T E04DGFA (NIL) -8 NIL NIL) (-244 510617 511962 513324 "E04AGNT" 515090 T E04AGNT (NIL) -7 NIL NIL) (-243 509344 509824 509864 "DVARCAT" 510339 NIL DVARCAT (NIL T) -9 NIL 510537) (-242 508548 508760 509074 "DVARCAT-" 509079 NIL DVARCAT- (NIL T T) -8 NIL NIL) (-241 501410 508350 508477 "DSMP" 508482 NIL DSMP (NIL T T T) -8 NIL NIL) (-240 496220 497355 498423 "DROPT" 500362 T DROPT (NIL) -8 NIL NIL) (-239 495885 495944 496042 "DROPT1" 496155 NIL DROPT1 (NIL T) -7 NIL NIL) (-238 491000 492126 493263 "DROPT0" 494768 T DROPT0 (NIL) -7 NIL NIL) (-237 489345 489670 490056 "DRAWPT" 490634 T DRAWPT (NIL) -7 NIL NIL) (-236 483932 484855 485934 "DRAW" 488319 NIL DRAW (NIL T) -7 NIL NIL) (-235 483565 483618 483736 "DRAWHACK" 483873 NIL DRAWHACK (NIL T) -7 NIL NIL) (-234 482296 482565 482856 "DRAWCX" 483294 T DRAWCX (NIL) -7 NIL NIL) (-233 481814 481882 482032 "DRAWCURV" 482222 NIL DRAWCURV (NIL T T) -7 NIL NIL) (-232 472286 474244 476359 "DRAWCFUN" 479719 T DRAWCFUN (NIL) -7 NIL NIL) (-231 469100 470982 471023 "DQAGG" 471652 NIL DQAGG (NIL T) -9 NIL 471925) (-230 457607 464345 464427 "DPOLCAT" 466265 NIL DPOLCAT (NIL T T T T) -9 NIL 466809) (-229 452447 453793 455750 "DPOLCAT-" 455755 NIL DPOLCAT- (NIL T T T T T) -8 NIL NIL) (-228 446531 452309 452406 "DPMO" 452411 NIL DPMO (NIL NIL T T) -8 NIL NIL) (-227 440518 446312 446478 "DPMM" 446483 NIL DPMM (NIL NIL T T T) -8 NIL NIL) (-226 440031 440129 440249 "DOMAIN" 440418 T DOMAIN (NIL) -8 NIL NIL) (-225 433743 439668 439819 "DMP" 439932 NIL DMP (NIL NIL T) -8 NIL NIL) (-224 433343 433399 433543 "DLP" 433681 NIL DLP (NIL T) -7 NIL NIL) (-223 426987 432444 432671 "DLIST" 433148 NIL DLIST (NIL T) -8 NIL NIL) (-222 423834 425843 425884 "DLAGG" 426434 NIL DLAGG (NIL T) -9 NIL 426663) (-221 422544 423236 423264 "DIVRING" 423414 T DIVRING (NIL) -9 NIL 423522) (-220 421532 421785 422178 "DIVRING-" 422183 NIL DIVRING- (NIL T) -8 NIL NIL) (-219 419634 419991 420397 "DISPLAY" 421146 T DISPLAY (NIL) -7 NIL NIL) (-218 413523 419548 419611 "DIRPROD" 419616 NIL DIRPROD (NIL NIL T) -8 NIL NIL) (-217 412371 412574 412839 "DIRPROD2" 413316 NIL DIRPROD2 (NIL NIL T T) -7 NIL NIL) (-216 402002 408007 408060 "DIRPCAT" 408468 NIL DIRPCAT (NIL NIL T) -9 NIL 409295) (-215 399328 399970 400851 "DIRPCAT-" 401188 NIL DIRPCAT- (NIL T NIL T) -8 NIL NIL) (-214 398615 398775 398961 "DIOSP" 399162 T DIOSP (NIL) -7 NIL NIL) (-213 395318 397528 397569 "DIOPS" 398003 NIL DIOPS (NIL T) -9 NIL 398232) (-212 394867 394981 395172 "DIOPS-" 395177 NIL DIOPS- (NIL T T) -8 NIL NIL) (-211 393739 394377 394405 "DIFRING" 394592 T DIFRING (NIL) -9 NIL 394701) (-210 393385 393462 393614 "DIFRING-" 393619 NIL DIFRING- (NIL T) -8 NIL NIL) (-209 391175 392457 392497 "DIFEXT" 392856 NIL DIFEXT (NIL T) -9 NIL 393149) (-208 389461 389889 390554 "DIFEXT-" 390559 NIL DIFEXT- (NIL T T) -8 NIL NIL) (-207 386784 388994 389035 "DIAGG" 389040 NIL DIAGG (NIL T) -9 NIL 389060) (-206 386168 386325 386577 "DIAGG-" 386582 NIL DIAGG- (NIL T T) -8 NIL NIL) (-205 381633 385127 385404 "DHMATRIX" 385937 NIL DHMATRIX (NIL T) -8 NIL NIL) (-204 377245 378154 379164 "DFSFUN" 380643 T DFSFUN (NIL) -7 NIL NIL) (-203 372031 375959 376324 "DFLOAT" 376900 T DFLOAT (NIL) -8 NIL NIL) (-202 370264 370545 370940 "DFINTTLS" 371739 NIL DFINTTLS (NIL T T) -7 NIL NIL) (-201 367297 368299 368697 "DERHAM" 369931 NIL DERHAM (NIL T NIL) -8 NIL NIL) (-200 365146 367072 367161 "DEQUEUE" 367241 NIL DEQUEUE (NIL T) -8 NIL NIL) (-199 364364 364497 364692 "DEGRED" 365008 NIL DEGRED (NIL T T) -7 NIL NIL) (-198 360764 361509 362361 "DEFINTRF" 363592 NIL DEFINTRF (NIL T) -7 NIL NIL) (-197 358295 358764 359362 "DEFINTEF" 360283 NIL DEFINTEF (NIL T T) -7 NIL NIL) (-196 352126 357736 357902 "DECIMAL" 358149 T DECIMAL (NIL) -8 NIL NIL) (-195 349638 350096 350602 "DDFACT" 351670 NIL DDFACT (NIL T T) -7 NIL NIL) (-194 349234 349277 349428 "DBLRESP" 349589 NIL DBLRESP (NIL T T T T) -7 NIL NIL) (-193 346944 347278 347647 "DBASE" 348992 NIL DBASE (NIL T) -8 NIL NIL) (-192 346079 346903 346931 "D03FAFA" 346936 T D03FAFA (NIL) -8 NIL NIL) (-191 345215 346038 346066 "D03EEFA" 346071 T D03EEFA (NIL) -8 NIL NIL) (-190 343165 343631 344120 "D03AGNT" 344746 T D03AGNT (NIL) -7 NIL NIL) (-189 342483 343124 343152 "D02EJFA" 343157 T D02EJFA (NIL) -8 NIL NIL) (-188 341801 342442 342470 "D02CJFA" 342475 T D02CJFA (NIL) -8 NIL NIL) (-187 341119 341760 341788 "D02BHFA" 341793 T D02BHFA (NIL) -8 NIL NIL) (-186 340437 341078 341106 "D02BBFA" 341111 T D02BBFA (NIL) -8 NIL NIL) (-185 333635 335223 336829 "D02AGNT" 338851 T D02AGNT (NIL) -7 NIL NIL) (-184 331404 331926 332472 "D01WGTS" 333109 T D01WGTS (NIL) -7 NIL NIL) (-183 330507 331363 331391 "D01TRNS" 331396 T D01TRNS (NIL) -8 NIL NIL) (-182 329610 330466 330494 "D01GBFA" 330499 T D01GBFA (NIL) -8 NIL NIL) (-181 328713 329569 329597 "D01FCFA" 329602 T D01FCFA (NIL) -8 NIL NIL) (-180 327816 328672 328700 "D01ASFA" 328705 T D01ASFA (NIL) -8 NIL NIL) (-179 326919 327775 327803 "D01AQFA" 327808 T D01AQFA (NIL) -8 NIL NIL) (-178 326022 326878 326906 "D01APFA" 326911 T D01APFA (NIL) -8 NIL NIL) (-177 325125 325981 326009 "D01ANFA" 326014 T D01ANFA (NIL) -8 NIL NIL) (-176 324228 325084 325112 "D01AMFA" 325117 T D01AMFA (NIL) -8 NIL NIL) (-175 323331 324187 324215 "D01ALFA" 324220 T D01ALFA (NIL) -8 NIL NIL) (-174 322434 323290 323318 "D01AKFA" 323323 T D01AKFA (NIL) -8 NIL NIL) (-173 321537 322393 322421 "D01AJFA" 322426 T D01AJFA (NIL) -8 NIL NIL) (-172 314841 316390 317949 "D01AGNT" 319998 T D01AGNT (NIL) -7 NIL NIL) (-171 314178 314306 314458 "CYCLOTOM" 314709 T CYCLOTOM (NIL) -7 NIL NIL) (-170 310913 311626 312353 "CYCLES" 313471 T CYCLES (NIL) -7 NIL NIL) (-169 310225 310359 310530 "CVMP" 310774 NIL CVMP (NIL T) -7 NIL NIL) (-168 308007 308264 308639 "CTRIGMNP" 309953 NIL CTRIGMNP (NIL T T) -7 NIL NIL) (-167 307612 307695 307800 "CTORCALL" 307922 T CTORCALL (NIL) -8 NIL NIL) (-166 306986 307085 307238 "CSTTOOLS" 307509 NIL CSTTOOLS (NIL T T) -7 NIL NIL) (-165 302785 303442 304200 "CRFP" 306298 NIL CRFP (NIL T T) -7 NIL NIL) (-164 301832 302017 302245 "CRAPACK" 302589 NIL CRAPACK (NIL T) -7 NIL NIL) (-163 301216 301317 301521 "CPMATCH" 301708 NIL CPMATCH (NIL T T T) -7 NIL NIL) (-162 300941 300969 301075 "CPIMA" 301182 NIL CPIMA (NIL T T T) -7 NIL NIL) (-161 297305 297977 298695 "COORDSYS" 300276 NIL COORDSYS (NIL T) -7 NIL NIL) (-160 296689 296818 296968 "CONTOUR" 297175 T CONTOUR (NIL) -8 NIL NIL) (-159 292550 294692 295184 "CONTFRAC" 296229 NIL CONTFRAC (NIL T) -8 NIL NIL) (-158 291704 292268 292296 "COMRING" 292301 T COMRING (NIL) -9 NIL 292352) (-157 290785 291062 291246 "COMPPROP" 291540 T COMPPROP (NIL) -8 NIL NIL) (-156 290446 290481 290609 "COMPLPAT" 290744 NIL COMPLPAT (NIL T T T) -7 NIL NIL) (-155 280427 290255 290364 "COMPLEX" 290369 NIL COMPLEX (NIL T) -8 NIL NIL) (-154 280063 280120 280227 "COMPLEX2" 280364 NIL COMPLEX2 (NIL T T) -7 NIL NIL) (-153 279781 279816 279914 "COMPFACT" 280022 NIL COMPFACT (NIL T T) -7 NIL NIL) (-152 264116 274410 274450 "COMPCAT" 275452 NIL COMPCAT (NIL T) -9 NIL 276845) (-151 253631 256555 260182 "COMPCAT-" 260538 NIL COMPCAT- (NIL T T) -8 NIL NIL) (-150 253362 253390 253492 "COMMUPC" 253597 NIL COMMUPC (NIL T T T) -7 NIL NIL) (-149 253157 253190 253249 "COMMONOP" 253323 T COMMONOP (NIL) -7 NIL NIL) (-148 252740 252908 252995 "COMM" 253090 T COMM (NIL) -8 NIL NIL) (-147 251989 252183 252211 "COMBOPC" 252549 T COMBOPC (NIL) -9 NIL 252724) (-146 250885 251095 251337 "COMBINAT" 251779 NIL COMBINAT (NIL T) -7 NIL NIL) (-145 247083 247656 248296 "COMBF" 250307 NIL COMBF (NIL T T) -7 NIL NIL) (-144 245869 246199 246434 "COLOR" 246868 T COLOR (NIL) -8 NIL NIL) (-143 245509 245556 245681 "CMPLXRT" 245816 NIL CMPLXRT (NIL T T) -7 NIL NIL) (-142 241011 242039 243119 "CLIP" 244449 T CLIP (NIL) -7 NIL NIL) (-141 239349 240119 240357 "CLIF" 240839 NIL CLIF (NIL NIL T NIL) -8 NIL NIL) (-140 235572 237496 237537 "CLAGG" 238466 NIL CLAGG (NIL T) -9 NIL 239002) (-139 233994 234451 235034 "CLAGG-" 235039 NIL CLAGG- (NIL T T) -8 NIL NIL) (-138 233538 233623 233763 "CINTSLPE" 233903 NIL CINTSLPE (NIL T T) -7 NIL NIL) (-137 231039 231510 232058 "CHVAR" 233066 NIL CHVAR (NIL T T T) -7 NIL NIL) (-136 230262 230826 230854 "CHARZ" 230859 T CHARZ (NIL) -9 NIL 230873) (-135 230016 230056 230134 "CHARPOL" 230216 NIL CHARPOL (NIL T) -7 NIL NIL) (-134 229123 229720 229748 "CHARNZ" 229795 T CHARNZ (NIL) -9 NIL 229850) (-133 227148 227813 228148 "CHAR" 228808 T CHAR (NIL) -8 NIL NIL) (-132 226874 226935 226963 "CFCAT" 227074 T CFCAT (NIL) -9 NIL NIL) (-131 226119 226230 226412 "CDEN" 226758 NIL CDEN (NIL T T T) -7 NIL NIL) (-130 222111 225272 225552 "CCLASS" 225859 T CCLASS (NIL) -8 NIL NIL) (-129 222030 222056 222091 "CATEGORY" 222096 T -10 (NIL) -8 NIL NIL) (-128 217082 218059 218812 "CARTEN" 221333 NIL CARTEN (NIL NIL NIL T) -8 NIL NIL) (-127 216190 216338 216559 "CARTEN2" 216929 NIL CARTEN2 (NIL NIL NIL T T) -7 NIL NIL) (-126 214488 215342 215598 "CARD" 215954 T CARD (NIL) -8 NIL NIL) (-125 213861 214189 214217 "CACHSET" 214349 T CACHSET (NIL) -9 NIL 214426) (-124 213358 213654 213682 "CABMON" 213732 T CABMON (NIL) -9 NIL 213788) (-123 210915 213050 213157 "BTREE" 213284 NIL BTREE (NIL T) -8 NIL NIL) (-122 208413 210563 210685 "BTOURN" 210825 NIL BTOURN (NIL T) -8 NIL NIL) (-121 205832 207885 207926 "BTCAT" 207994 NIL BTCAT (NIL T) -9 NIL 208071) (-120 205499 205579 205728 "BTCAT-" 205733 NIL BTCAT- (NIL T T) -8 NIL NIL) (-119 200720 204591 204619 "BTAGG" 204875 T BTAGG (NIL) -9 NIL 205054) (-118 200143 200287 200517 "BTAGG-" 200522 NIL BTAGG- (NIL T) -8 NIL NIL) (-117 197187 199421 199636 "BSTREE" 199960 NIL BSTREE (NIL T) -8 NIL NIL) (-116 196325 196451 196635 "BRILL" 197043 NIL BRILL (NIL T) -7 NIL NIL) (-115 193027 195054 195095 "BRAGG" 195744 NIL BRAGG (NIL T) -9 NIL 196001) (-114 191556 191962 192517 "BRAGG-" 192522 NIL BRAGG- (NIL T T) -8 NIL NIL) (-113 184764 190902 191086 "BPADICRT" 191404 NIL BPADICRT (NIL NIL) -8 NIL NIL) (-112 183068 184701 184746 "BPADIC" 184751 NIL BPADIC (NIL NIL) -8 NIL NIL) (-111 182768 182798 182911 "BOUNDZRO" 183032 NIL BOUNDZRO (NIL T T) -7 NIL NIL) (-110 178283 179374 180241 "BOP" 181921 T BOP (NIL) -8 NIL NIL) (-109 175904 176348 176868 "BOP1" 177796 NIL BOP1 (NIL T) -7 NIL NIL) (-108 174523 175234 175457 "BOOLEAN" 175701 T BOOLEAN (NIL) -8 NIL NIL) (-107 173890 174268 174320 "BMODULE" 174325 NIL BMODULE (NIL T T) -9 NIL 174389) (-106 169700 173688 173761 "BITS" 173837 T BITS (NIL) -8 NIL NIL) (-105 168797 169232 169384 "BINFILE" 169568 T BINFILE (NIL) -8 NIL NIL) (-104 168209 168331 168473 "BINDING" 168675 T BINDING (NIL) -8 NIL NIL) (-103 162044 167653 167818 "BINARY" 168064 T BINARY (NIL) -8 NIL NIL) (-102 159872 161300 161341 "BGAGG" 161601 NIL BGAGG (NIL T) -9 NIL 161738) (-101 159703 159735 159826 "BGAGG-" 159831 NIL BGAGG- (NIL T T) -8 NIL NIL) (-100 158801 159087 159292 "BFUNCT" 159518 T BFUNCT (NIL) -8 NIL NIL) (-99 157502 157680 157965 "BEZOUT" 158625 NIL BEZOUT (NIL T T T T T) -7 NIL NIL) (-98 154027 156362 156690 "BBTREE" 157205 NIL BBTREE (NIL T) -8 NIL NIL) (-97 153765 153818 153844 "BASTYPE" 153961 T BASTYPE (NIL) -9 NIL NIL) (-96 153620 153649 153719 "BASTYPE-" 153724 NIL BASTYPE- (NIL T) -8 NIL NIL) (-95 153058 153134 153284 "BALFACT" 153531 NIL BALFACT (NIL T T) -7 NIL NIL) (-94 151880 152477 152662 "AUTOMOR" 152903 NIL AUTOMOR (NIL T) -8 NIL NIL) (-93 151606 151611 151637 "ATTREG" 151642 T ATTREG (NIL) -9 NIL NIL) (-92 149885 150303 150655 "ATTRBUT" 151272 T ATTRBUT (NIL) -8 NIL NIL) (-91 149421 149534 149560 "ATRIG" 149761 T ATRIG (NIL) -9 NIL NIL) (-90 149230 149271 149358 "ATRIG-" 149363 NIL ATRIG- (NIL T) -8 NIL NIL) (-89 147427 149006 149094 "ASTACK" 149173 NIL ASTACK (NIL T) -8 NIL NIL) (-88 145932 146229 146594 "ASSOCEQ" 147109 NIL ASSOCEQ (NIL T T) -7 NIL NIL) (-87 144964 145591 145715 "ASP9" 145839 NIL ASP9 (NIL NIL) -8 NIL NIL) (-86 144728 144912 144951 "ASP8" 144956 NIL ASP8 (NIL NIL) -8 NIL NIL) (-85 143598 144333 144475 "ASP80" 144617 NIL ASP80 (NIL NIL) -8 NIL NIL) (-84 142497 143233 143365 "ASP7" 143497 NIL ASP7 (NIL NIL) -8 NIL NIL) (-83 141453 142174 142292 "ASP78" 142410 NIL ASP78 (NIL NIL) -8 NIL NIL) (-82 140424 141133 141250 "ASP77" 141367 NIL ASP77 (NIL NIL) -8 NIL NIL) (-81 139338 140062 140193 "ASP74" 140324 NIL ASP74 (NIL NIL) -8 NIL NIL) (-80 138239 138973 139105 "ASP73" 139237 NIL ASP73 (NIL NIL) -8 NIL NIL) (-79 137194 137916 138034 "ASP6" 138152 NIL ASP6 (NIL NIL) -8 NIL NIL) (-78 136143 136871 136989 "ASP55" 137107 NIL ASP55 (NIL NIL) -8 NIL NIL) (-77 135093 135817 135936 "ASP50" 136055 NIL ASP50 (NIL NIL) -8 NIL NIL) (-76 134181 134794 134904 "ASP4" 135014 NIL ASP4 (NIL NIL) -8 NIL NIL) (-75 133269 133882 133992 "ASP49" 134102 NIL ASP49 (NIL NIL) -8 NIL NIL) (-74 132054 132808 132976 "ASP42" 133158 NIL ASP42 (NIL NIL NIL NIL) -8 NIL NIL) (-73 130832 131587 131757 "ASP41" 131941 NIL ASP41 (NIL NIL NIL NIL) -8 NIL NIL) (-72 129784 130509 130627 "ASP35" 130745 NIL ASP35 (NIL NIL) -8 NIL NIL) (-71 129549 129732 129771 "ASP34" 129776 NIL ASP34 (NIL NIL) -8 NIL NIL) (-70 129286 129353 129429 "ASP33" 129504 NIL ASP33 (NIL NIL) -8 NIL NIL) (-69 128182 128921 129053 "ASP31" 129185 NIL ASP31 (NIL NIL) -8 NIL NIL) (-68 127947 128130 128169 "ASP30" 128174 NIL ASP30 (NIL NIL) -8 NIL NIL) (-67 127682 127751 127827 "ASP29" 127902 NIL ASP29 (NIL NIL) -8 NIL NIL) (-66 127447 127630 127669 "ASP28" 127674 NIL ASP28 (NIL NIL) -8 NIL NIL) (-65 127212 127395 127434 "ASP27" 127439 NIL ASP27 (NIL NIL) -8 NIL NIL) (-64 126296 126910 127021 "ASP24" 127132 NIL ASP24 (NIL NIL) -8 NIL NIL) (-63 125213 125937 126067 "ASP20" 126197 NIL ASP20 (NIL NIL) -8 NIL NIL) (-62 124301 124914 125024 "ASP1" 125134 NIL ASP1 (NIL NIL) -8 NIL NIL) (-61 123245 123975 124094 "ASP19" 124213 NIL ASP19 (NIL NIL) -8 NIL NIL) (-60 122982 123049 123125 "ASP12" 123200 NIL ASP12 (NIL NIL) -8 NIL NIL) (-59 121835 122581 122725 "ASP10" 122869 NIL ASP10 (NIL NIL) -8 NIL NIL) (-58 119734 121679 121770 "ARRAY2" 121775 NIL ARRAY2 (NIL T) -8 NIL NIL) (-57 115550 119382 119496 "ARRAY1" 119651 NIL ARRAY1 (NIL T) -8 NIL NIL) (-56 114582 114755 114976 "ARRAY12" 115373 NIL ARRAY12 (NIL T T) -7 NIL NIL) (-55 108942 110813 110888 "ARR2CAT" 113518 NIL ARR2CAT (NIL T T T) -9 NIL 114276) (-54 106376 107120 108074 "ARR2CAT-" 108079 NIL ARR2CAT- (NIL T T T T) -8 NIL NIL) (-53 105136 105286 105589 "APPRULE" 106214 NIL APPRULE (NIL T T T) -7 NIL NIL) (-52 104789 104837 104955 "APPLYORE" 105082 NIL APPLYORE (NIL T T T) -7 NIL NIL) (-51 103763 104054 104249 "ANY" 104612 T ANY (NIL) -8 NIL NIL) (-50 103041 103164 103321 "ANY1" 103637 NIL ANY1 (NIL T) -7 NIL NIL) (-49 100573 101491 101816 "ANTISYM" 102766 NIL ANTISYM (NIL T NIL) -8 NIL NIL) (-48 100088 100277 100374 "ANON" 100494 T ANON (NIL) -8 NIL NIL) (-47 94165 98633 99084 "AN" 99655 T AN (NIL) -8 NIL NIL) (-46 90519 91917 91967 "AMR" 92706 NIL AMR (NIL T T) -9 NIL 93305) (-45 89632 89853 90215 "AMR-" 90220 NIL AMR- (NIL T T T) -8 NIL NIL) (-44 74182 89549 89610 "ALIST" 89615 NIL ALIST (NIL T T) -8 NIL NIL) (-43 71019 73776 73945 "ALGSC" 74100 NIL ALGSC (NIL T NIL NIL NIL) -8 NIL NIL) (-42 67575 68129 68736 "ALGPKG" 70459 NIL ALGPKG (NIL T T) -7 NIL NIL) (-41 66852 66953 67137 "ALGMFACT" 67461 NIL ALGMFACT (NIL T T T) -7 NIL NIL) (-40 62602 63282 63936 "ALGMANIP" 66376 NIL ALGMANIP (NIL T T) -7 NIL NIL) (-39 53921 62228 62378 "ALGFF" 62535 NIL ALGFF (NIL T T T NIL) -8 NIL NIL) (-38 53117 53248 53427 "ALGFACT" 53779 NIL ALGFACT (NIL T) -7 NIL NIL) (-37 52108 52718 52756 "ALGEBRA" 52816 NIL ALGEBRA (NIL T) -9 NIL 52874) (-36 51826 51885 52017 "ALGEBRA-" 52022 NIL ALGEBRA- (NIL T T) -8 NIL NIL) (-35 34087 49830 49882 "ALAGG" 50018 NIL ALAGG (NIL T T) -9 NIL 50179) (-34 33623 33736 33762 "AHYP" 33963 T AHYP (NIL) -9 NIL NIL) (-33 32554 32802 32828 "AGG" 33327 T AGG (NIL) -9 NIL 33606) (-32 31988 32150 32364 "AGG-" 32369 NIL AGG- (NIL T) -8 NIL NIL) (-31 29675 30093 30510 "AF" 31631 NIL AF (NIL T T) -7 NIL NIL) (-30 28944 29202 29358 "ACPLOT" 29537 T ACPLOT (NIL) -8 NIL NIL) (-29 18411 26357 26408 "ACFS" 27119 NIL ACFS (NIL T) -9 NIL 27358) (-28 16425 16915 17690 "ACFS-" 17695 NIL ACFS- (NIL T T) -8 NIL NIL) (-27 12693 14649 14675 "ACF" 15554 T ACF (NIL) -9 NIL 15966) (-26 11397 11731 12224 "ACF-" 12229 NIL ACF- (NIL T) -8 NIL NIL) (-25 10996 11165 11191 "ABELSG" 11283 T ABELSG (NIL) -9 NIL 11348) (-24 10863 10888 10954 "ABELSG-" 10959 NIL ABELSG- (NIL T) -8 NIL NIL) (-23 10233 10494 10520 "ABELMON" 10690 T ABELMON (NIL) -9 NIL 10802) (-22 9897 9981 10119 "ABELMON-" 10124 NIL ABELMON- (NIL T) -8 NIL NIL) (-21 9232 9578 9604 "ABELGRP" 9729 T ABELGRP (NIL) -9 NIL 9811) (-20 8695 8824 9040 "ABELGRP-" 9045 NIL ABELGRP- (NIL T) -8 NIL NIL) (-19 4333 8035 8074 "A1AGG" 8079 NIL A1AGG (NIL T) -9 NIL 8119) (-18 30 1251 2813 "A1AGG-" 2818 NIL A1AGG- (NIL T T) -8 NIL NIL))
\ No newline at end of file diff --git a/src/share/algebra/operation.daase b/src/share/algebra/operation.daase index 49405576..8f45d042 100644 --- a/src/share/algebra/operation.daase +++ b/src/share/algebra/operation.daase @@ -1,547 +1,671 @@ -(725939 . 3415311731) -(((*1 *1 *2 *3 *3 *3 *3) - (-12 (-5 *2 (-1 (-874 (-203)) (-203))) (-5 *3 (-1011 (-203))) - (-5 *1 (-857)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-874 (-203)) (-203))) (-5 *3 (-1011 (-203))) - (-5 *1 (-857)))) - ((*1 *1 *2 *3 *3 *3) - (-12 (-5 *2 (-1 (-874 (-203)) (-203))) (-5 *3 (-1011 (-203))) - (-5 *1 (-858)))) - ((*1 *1 *2 *3) - (-12 (-5 *2 (-1 (-874 (-203)) (-203))) (-5 *3 (-1011 (-203))) - (-5 *1 (-858))))) -(((*1 *1) (-5 *1 (-413)))) -(((*1 *1 *1 *2) - (-12 (-5 *2 (-108)) (-5 *1 (-1052 *3 *4)) (-4 *3 (-13 (-1016) (-33))) - (-4 *4 (-13 (-1016) (-33)))))) -(((*1 *1 *1 *1) - (-12 (|has| *1 (-6 -4245)) (-4 *1 (-222 *2)) (-4 *2 (-1122))))) -(((*1 *1 *1) - (-12 (-4 *1 (-987 *2 *3 *4)) (-4 *2 (-973)) (-4 *3 (-732)) - (-4 *4 (-786))))) -(((*1 *1 *1 *1 *1) (-5 *1 (-794))) - ((*1 *1 *1 *2) (-12 (-5 *2 (-589 (-794))) (-5 *1 (-794))))) -(((*1 *2 *3 *3 *3 *4 *3 *3 *4 *4 *4 *5) - (-12 (-5 *3 (-203)) (-5 *4 (-523)) - (-5 *5 (-3 (|:| |fn| (-364)) (|:| |fp| (-62 G)))) (-5 *2 (-962)) - (-5 *1 (-688))))) -(((*1 *2 *3) - (-12 (-5 *3 (-1 *6 *4)) (-4 *4 (-1016)) (-4 *6 (-1016)) - (-5 *2 (-1 *6 *4 *5)) (-5 *1 (-624 *4 *5 *6)) (-4 *5 (-1016))))) -(((*1 *2 *2 *3) - (-12 (-5 *2 (-629 *3)) (-4 *3 (-284)) (-5 *1 (-639 *3))))) -(((*1 *2 *3) - (|partial| -12 - (-5 *3 - (-2 (|:| |var| (-1087)) (|:| |fn| (-292 (-203))) - (|:| -3499 (-1011 (-779 (-203)))) (|:| |abserr| (-203)) - (|:| |relerr| (-203)))) - (-5 *2 - (-2 - (|:| |endPointContinuity| - (-3 (|:| |continuous| "Continuous at the end points") - (|:| |lowerSingular| - "There is a singularity at the lower end point") - (|:| |upperSingular| - "There is a singularity at the upper end point") - (|:| |bothSingular| - "There are singularities at both end points") - (|:| |notEvaluated| - "End point continuity not yet evaluated"))) - (|:| |singularitiesStream| - (-3 (|:| |str| (-1068 (-203))) - (|:| |notEvaluated| - "Internal singularities not yet evaluated"))) - (|:| -3499 - (-3 (|:| |finite| "The range is finite") - (|:| |lowerInfinite| "The bottom of range is infinite") - (|:| |upperInfinite| "The top of range is infinite") - (|:| |bothInfinite| - "Both top and bottom points are infinite") - (|:| |notEvaluated| "Range not yet evaluated"))))) - (-5 *1 (-518))))) -(((*1 *2 *2) (|partial| -12 (-4 *1 (-912 *2)) (-4 *2 (-1108))))) -(((*1 *2 *3) - (-12 (-5 *3 (-589 (-562 *5))) (-4 *4 (-786)) (-5 *2 (-562 *5)) - (-5 *1 (-532 *4 *5)) (-4 *5 (-406 *4))))) -(((*1 *2 *1) (-12 (-4 *1 (-343 *2)) (-4 *2 (-158))))) +(726160 . 3416412000) (((*1 *2 *3) + (-12 (-5 *3 (-2 (|:| -3844 (-383 (-523))) (|:| -3855 (-383 (-523))))) + (-5 *2 (-383 (-523))) (-5 *1 (-947 *4)) (-4 *4 (-1145 (-523)))))) +(((*1 *2 *3 *3 *4 *4 *4 *3) + (-12 (-5 *3 (-523)) (-5 *4 (-629 (-203))) (-5 *2 (-962)) + (-5 *1 (-691))))) +(((*1 *2 *3) (-12 (-5 *2 (-394 *3)) (-5 *1 (-517 *3)) (-4 *3 (-508)))) + ((*1 *2 *3) (-12 (-4 *4 (-732)) (-4 *5 (-786)) (-4 *6 (-284)) (-5 *2 (-394 *3)) - (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-880 *6 *4 *5))))) + (-5 *1 (-682 *4 *5 *6 *3)) (-4 *3 (-880 *6 *4 *5)))) + ((*1 *2 *3) + (-12 (-4 *4 (-732)) (-4 *5 (-786)) (-4 *6 (-284)) + (-4 *7 (-880 *6 *4 *5)) (-5 *2 (-394 (-1083 *7))) + (-5 *1 (-682 *4 *5 *6 *7)) (-5 *3 (-1083 *7)))) + ((*1 *2 *1) + (-12 (-4 *3 (-427)) (-4 *3 (-973)) (-4 *4 (-732)) (-4 *5 (-786)) + (-5 *2 (-394 *1)) (-4 *1 (-880 *3 *4 *5)))) + ((*1 *2 *3) + (-12 (-4 *4 (-786)) (-4 *5 (-732)) (-4 *6 (-427)) (-5 *2 (-394 *3)) + (-5 *1 (-908 *4 *5 *6 *3)) (-4 *3 (-880 *6 *5 *4)))) + ((*1 *2 *3) + (-12 (-4 *4 (-732)) (-4 *5 (-786)) (-4 *6 (-427)) + (-4 *7 (-880 *6 *4 *5)) (-5 *2 (-394 (-1083 (-383 *7)))) + (-5 *1 (-1082 *4 *5 *6 *7)) (-5 *3 (-1083 (-383 *7))))) + ((*1 *2 *1) (-12 (-5 *2 (-394 *1)) (-4 *1 (-1127)))) + ((*1 *2 *3) + (-12 (-4 *4 (-515)) (-5 *2 (-394 *3)) (-5 *1 (-1148 *4 *3)) + (-4 *3 (-13 (-1145 *4) (-515) (-10 -8 (-15 -3310 ($ $ $))))))) + ((*1 *2 *3) + (-12 (-5 *3 (-970 *4 *5)) (-4 *4 (-13 (-784) (-284) (-136) (-949))) + (-14 *5 (-589 (-1087))) + (-5 *2 + (-589 (-1058 *4 (-495 (-796 *6)) (-796 *6) (-719 *4 (-796 *6))))) + (-5 *1 (-1193 *4 *5 *6)) (-14 *6 (-589 (-1087)))))) +(((*1 *2 *1 *1) (-12 (-5 *2 (-108)) (-5 *1 (-466))))) +(((*1 *2 *1) + (-12 (-4 *1 (-627 *2 *3 *4)) (-4 *3 (-349 *2)) (-4 *4 (-349 *2)) + (|has| *2 (-6 (-4250 "*"))) (-4 *2 (-973)))) + ((*1 *2 *3) + (-12 (-4 *4 (-349 *2)) (-4 *5 (-349 *2)) (-4 *2 (-158)) + (-5 *1 (-628 *2 *4 *5 *3)) (-4 *3 (-627 *2 *4 *5)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1037 *3 *2 *4 *5)) (-4 *4 (-216 *3 *2)) + (-4 *5 (-216 *3 *2)) (|has| *2 (-6 (-4250 "*"))) (-4 *2 (-973))))) +(((*1 *1 *2) + (-12 (-5 *2 (-589 *3)) (-4 *3 (-1123)) (-5 *1 (-1059 *3))))) +(((*1 *1 *1 *2 *3 *1) + (-12 (-4 *1 (-302 *2 *3)) (-4 *2 (-973)) (-4 *3 (-731))))) +(((*1 *2 *1) (-12 (-5 *2 (-1020)) (-5 *1 (-1091))))) +(((*1 *1 *2 *2 *3 *1) + (-12 (-5 *2 (-1087)) (-5 *3 (-1020)) (-5 *1 (-268))))) +(((*1 *2 *1) + (-12 (-4 *1 (-1048 *3)) (-4 *3 (-973)) (-5 *2 (-589 (-157)))))) +(((*1 *2 *2) + (-12 (-5 *2 (-589 *6)) (-4 *6 (-987 *3 *4 *5)) (-4 *3 (-515)) + (-4 *4 (-732)) (-4 *5 (-786)) (-5 *1 (-906 *3 *4 *5 *6))))) (((*1 *2 *3) - (-12 (-5 *3 (-2 (|:| -3149 (-383 (-523))) (|:| -3159 (-383 (-523))))) - (-5 *2 (-383 (-523))) (-5 *1 (-947 *4)) (-4 *4 (-1144 (-523)))))) + (-12 (-4 *1 (-851)) (-5 *2 (-2 (|:| -3474 (-589 *1)) (|:| -1621 *1))) + (-5 *3 (-589 *1))))) +(((*1 *2 *3 *1) + (|partial| -12 (-4 *1 (-560 *3 *2)) (-4 *3 (-1016)) (-4 *2 (-1016))))) +(((*1 *2 *3 *1) + (-12 (-5 *3 (-836 *4)) (-4 *4 (-1016)) (-5 *2 (-589 (-710))) + (-5 *1 (-835 *4))))) (((*1 *1 *2 *3) (-12 (-5 *3 (-337 (-110))) (-4 *2 (-973)) (-5 *1 (-654 *2 *4)) (-4 *4 (-591 *2)))) ((*1 *1 *2 *3) (-12 (-5 *3 (-337 (-110))) (-5 *1 (-773 *2)) (-4 *2 (-973))))) +(((*1 *2 *1) + (|partial| -12 (-4 *1 (-880 *3 *4 *2)) (-4 *3 (-973)) (-4 *4 (-732)) + (-4 *2 (-786)))) + ((*1 *2 *3) + (|partial| -12 (-4 *4 (-732)) (-4 *5 (-973)) (-4 *6 (-880 *5 *4 *2)) + (-4 *2 (-786)) (-5 *1 (-881 *4 *2 *5 *6 *3)) + (-4 *3 + (-13 (-339) + (-10 -8 (-15 -1691 ($ *6)) (-15 -3316 (*6 $)) + (-15 -3329 (*6 $))))))) + ((*1 *2 *3) + (|partial| -12 (-5 *3 (-383 (-883 *4))) (-4 *4 (-515)) + (-5 *2 (-1087)) (-5 *1 (-969 *4))))) +(((*1 *2 *1) + (-12 (-4 *1 (-318 *3 *4 *5)) (-4 *3 (-1127)) (-4 *4 (-1145 *3)) + (-4 *5 (-1145 (-383 *4))) (-5 *2 (-108))))) +(((*1 *2 *3 *3 *3 *3 *4 *3) + (-12 (-5 *3 (-523)) (-5 *4 (-629 (-203))) (-5 *2 (-962)) + (-5 *1 (-695))))) +(((*1 *1 *2 *2 *3) (-12 (-5 *2 (-523)) (-5 *3 (-852)) (-4 *1 (-380)))) + ((*1 *1 *2 *2) (-12 (-5 *2 (-523)) (-4 *1 (-380)))) + ((*1 *2 *1) + (-12 (-4 *1 (-1019 *3 *4 *5 *2 *6)) (-4 *3 (-1016)) (-4 *4 (-1016)) + (-4 *5 (-1016)) (-4 *6 (-1016)) (-4 *2 (-1016))))) +(((*1 *2 *3) + (-12 (-5 *3 (-1 (-108) *6)) (-4 *6 (-13 (-1016) (-964 *5))) + (-4 *5 (-817 *4)) (-4 *4 (-1016)) (-5 *2 (-1 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*4 (-13 (-786) - (-10 -8 (-15 -3663 ((-1087) $)) - (-15 -2700 ((-3 $ "failed") (-1087)))))) + (-10 -8 (-15 -1400 ((-1087) $)) + (-15 -2724 ((-3 $ "failed") (-1087)))))) (-4 *5 (-732)) (-4 *7 (-515)) (-5 *2 (-394 *3)) (-5 *1 (-431 *4 *5 *6 *7 *3)) (-4 *6 (-515)) (-4 *3 (-880 *7 *5 *4)))) @@ -13506,9 +9614,9 @@ (-12 (-4 *4 (-284)) (-5 *2 (-394 (-1083 *4))) (-5 *1 (-433 *4)) (-5 *3 (-1083 *4)))) ((*1 *2 *3 *4) - (-12 (-5 *4 (-1 (-394 *6) *6)) (-4 *6 (-1144 *5)) (-4 *5 (-339)) + (-12 (-5 *4 (-1 (-394 *6) *6)) (-4 *6 (-1145 *5)) (-4 *5 (-339)) (-4 *7 (-13 (-339) (-136) (-664 *5 *6))) (-5 *2 (-394 *3)) - (-5 *1 (-465 *5 *6 *7 *3)) (-4 *3 (-1144 *7)))) + (-5 *1 (-465 *5 *6 *7 *3)) (-4 *3 (-1145 *7)))) ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-394 (-1083 *7)) (-1083 *7))) (-4 *7 (-13 (-284) (-136))) (-4 *5 (-786)) (-4 *6 (-732)) @@ -13523,19 +9631,19 @@ ((*1 *2 *3 *4) (-12 (-5 *4 (-1 (-589 *5) *6)) (-4 *5 (-13 (-339) (-136) (-964 (-523)) (-964 (-383 (-523))))) - (-4 *6 (-1144 *5)) (-5 *2 (-589 (-596 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(-1472 'X) (-1472 '-1294) (-638)))) + (-12 (-5 *2 (-1169 (-315 (-1704 'X) (-1704 '-1343) (-638)))) (-5 *1 (-84 *3)) (-14 *3 (-1087)))) ((*1 *1 *2) - (-12 (-5 *2 (-629 (-315 (-1472 'XL 'XR 'ELAM) (-1472) (-638)))) + (-12 (-5 *2 (-629 (-315 (-1704 'XL 'XR 'ELAM) (-1704) (-638)))) (-5 *1 (-85 *3)) (-14 *3 (-1087)))) ((*1 *1 *2) - (-12 (-5 *2 (-315 (-1472 'X) (-1472 '-1294) (-638))) (-5 *1 (-87 *3)) + (-12 (-5 *2 (-315 (-1704 'X) (-1704 '-1343) (-638))) (-5 *1 (-87 *3)) (-14 *3 (-1087)))) ((*1 *2 *1) (-12 (-5 *2 (-932 2)) (-5 *1 (-103)))) ((*1 *2 *1) (-12 (-5 *2 (-383 (-523))) (-5 *1 (-103)))) @@ -15615,14 +13669,14 @@ (-12 (-5 *2 (-218 *4 *5)) (-14 *4 (-710)) (-4 *5 (-158)) (-5 *1 (-128 *3 *4 *5)) (-14 *3 (-523)))) ((*1 *2 *3) - (-12 (-5 *3 (-1168 (-629 *4))) (-4 *4 (-158)) - (-5 *2 (-1168 (-629 (-383 (-883 *4))))) (-5 *1 (-169 *4)))) + (-12 (-5 *3 (-1169 (-629 *4))) (-4 *4 (-158)) + (-5 *2 (-1169 (-629 (-383 (-883 *4))))) (-5 *1 (-169 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-589 *3)) (-4 *3 (-13 (-786) - (-10 -8 (-15 -3223 ((-1070) $ (-1087))) (-15 -3973 ((-1173) $)) - (-15 -2823 ((-1173) $))))) + (-10 -8 (-15 -1937 ((-1070) $ (-1087))) (-15 -1239 ((-1174) $)) + (-15 -4048 ((-1174) $))))) (-5 *1 (-193 *3)))) ((*1 *2 *1) (-12 (-5 *2 (-932 10)) (-5 *1 (-196)))) ((*1 *2 *1) (-12 (-5 *2 (-383 (-523))) (-5 *1 (-196)))) @@ -15635,12 +13689,12 @@ ((*1 *1 *2) (-12 (-4 *1 (-243 *2)) (-4 *2 (-786)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-523))) (-5 *1 (-252)))) ((*1 *2 *1) - (-12 (-4 *2 (-1144 *3)) (-5 *1 (-266 *3 *2 *4 *5 *6 *7)) + (-12 (-4 *2 (-1145 *3)) (-5 *1 (-266 *3 *2 *4 *5 *6 *7)) (-4 *3 (-158)) (-4 *4 (-23)) (-14 *5 (-1 *2 *2 *4)) (-14 *6 (-1 (-3 *4 "failed") *4 *4)) (-14 *7 (-1 (-3 *2 "failed") *2 *2 *4)))) ((*1 *1 *2) - (-12 (-5 *2 (-1153 *4 *5 *6)) (-4 *4 (-13 (-27) (-1108) (-406 *3))) + (-12 (-5 *2 (-1154 *4 *5 *6)) (-4 *4 (-13 (-27) (-1109) (-406 *3))) (-14 *5 (-1087)) (-14 *6 *4) (-4 *3 (-13 (-786) (-964 (-523)) (-585 (-523)) (-427))) (-5 *1 (-289 *3 *4 *5 *6)))) @@ -15656,21 +13710,21 @@ (-4 *3 (-305 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-350 *3 *4)) (-4 *3 (-786)) (-4 *4 (-158)) - (-5 *2 (-1190 *3 *4)))) + (-5 *2 (-1191 *3 *4)))) ((*1 *2 *1) (-12 (-4 *1 (-350 *3 *4)) (-4 *3 (-786)) (-4 *4 (-158)) - (-5 *2 (-1181 *3 *4)))) + (-5 *2 (-1182 *3 *4)))) ((*1 *1 *2) (-12 (-4 *1 (-350 *2 *3)) (-4 *2 (-786)) (-4 *3 (-158)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -3189 (-589 (-306))))) + (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -2108 (-589 (-306))))) (-4 *1 (-359)))) ((*1 *1 *2) (-12 (-5 *2 (-306)) (-4 *1 (-359)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-306))) (-4 *1 (-359)))) ((*1 *1 *2) (-12 (-5 *2 (-629 (-638))) (-4 *1 (-359)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -3189 (-589 (-306))))) + (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -2108 (-589 (-306))))) (-4 *1 (-360)))) ((*1 *1 *2) (-12 (-5 *2 (-306)) (-4 *1 (-360)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-306))) (-4 *1 (-360)))) @@ -15680,71 +13734,71 @@ ((*1 *1 *2) (-12 (-5 *2 (-794)) (-5 *1 (-370)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -3189 (-589 (-306))))) + (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -2108 (-589 (-306))))) (-4 *1 (-372)))) ((*1 *1 *2) (-12 (-5 *2 (-306)) (-4 *1 (-372)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-306))) (-4 *1 (-372)))) ((*1 *1 *2) (-12 (-5 *2 (-271 (-292 (-155 (-355))))) (-5 *1 (-374 *3 *4 *5 *6)) - (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 (-5 *2 (-271 (-292 (-355)))) (-5 *1 (-374 *3 *4 *5 *6)) - (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 (-5 *2 (-271 (-292 (-523)))) (-5 *1 (-374 *3 *4 *5 *6)) - (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *3 (-1087)) 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-3853 "void"))) + (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 (-5 *2 (-292 (-640))) (-5 *1 (-374 *3 *4 *5 *6)) - (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -3189 (-589 (-306))))) + (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -2108 (-589 (-306))))) (-5 *1 (-374 *3 *4 *5 *6)) (-14 *3 (-1087)) - (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-306))) (-5 *1 (-374 *3 *4 *5 *6)) - (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *3 (-1087)) (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 (-5 *2 (-306)) (-5 *1 (-374 *3 *4 *5 *6)) (-14 *3 (-1087)) - (-14 *4 (-3 (|:| |fst| (-410)) (|:| -3853 "void"))) + (-14 *4 (-3 (|:| |fst| (-410)) (|:| -1495 "void"))) (-14 *5 (-589 (-1087))) (-14 *6 (-1091)))) ((*1 *1 *2) (-12 (-5 *2 (-307 *4)) (-4 *4 (-13 (-786) (-21))) @@ -15772,28 +13826,28 @@ ((*1 *2 *1) (-12 (-5 *2 (-794)) (-5 *1 (-413)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -3189 (-589 (-306))))) + (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -2108 (-589 (-306))))) (-4 *1 (-415)))) ((*1 *1 *2) (-12 (-5 *2 (-306)) (-4 *1 (-415)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-306))) (-4 *1 (-415)))) - ((*1 *1 *2) (-12 (-5 *2 (-1168 (-638))) (-4 *1 (-415)))) + ((*1 *1 *2) (-12 (-5 *2 (-1169 (-638))) (-4 *1 (-415)))) ((*1 *1 *2) (-12 - (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -3189 (-589 (-306))))) + (-5 *2 (-2 (|:| |localSymbols| (-1091)) (|:| -2108 (-589 (-306))))) (-4 *1 (-416)))) ((*1 *1 *2) (-12 (-5 *2 (-306)) (-4 *1 (-416)))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-306))) (-4 *1 (-416)))) ((*1 *1 *2) - (-12 (-5 *2 (-1168 (-383 (-883 *3)))) (-4 *3 (-158)) - (-14 *6 (-1168 (-629 *3))) (-5 *1 (-428 *3 *4 *5 *6)) + (-12 (-5 *2 (-1169 (-383 (-883 *3)))) (-4 *3 (-158)) + (-14 *6 (-1169 (-629 *3))) (-5 *1 (-428 *3 *4 *5 *6)) (-14 *4 (-852)) (-14 *5 (-589 (-1087))))) ((*1 *1 *2) (-12 (-5 *2 (-589 (-589 (-874 (-203))))) (-5 *1 (-443)))) ((*1 *2 *1) (-12 (-5 *2 (-794)) (-5 *1 (-443)))) ((*1 *1 *2) - (-12 (-5 *2 (-1153 *3 *4 *5)) (-4 *3 (-973)) (-14 *4 (-1087)) + (-12 (-5 *2 (-1154 *3 *4 *5)) (-4 *3 (-973)) (-14 *4 (-1087)) (-14 *5 *3) (-5 *1 (-449 *3 *4 *5)))) ((*1 *1 *2) - (-12 (-5 *2 (-1164 *4)) (-14 *4 (-1087)) (-5 *1 (-449 *3 *4 *5)) + (-12 (-5 *2 (-1165 *4)) (-14 *4 (-1087)) (-5 *1 (-449 *3 *4 *5)) (-4 *3 (-973)) (-14 *5 *3))) ((*1 *2 *1) (-12 (-5 *2 (-932 16)) (-5 *1 (-460)))) ((*1 *2 *1) (-12 (-5 *2 (-383 (-523))) (-5 *1 (-460)))) @@ -15804,13 +13858,13 @@ (-4 *4 (-732)) (-4 *5 (-786)) (-5 *1 (-475 *3 *4 *5 *6)))) ((*1 *1 *2) (-12 (-4 *3 (-158)) (-5 *1 (-557 *3 *2)) (-4 *2 (-684 *3)))) - ((*1 *2 *1) (-12 (-4 *1 (-563 *2)) (-4 *2 (-1122)))) + ((*1 *2 *1) (-12 (-4 *1 (-563 *2)) (-4 *2 (-1123)))) ((*1 *1 *2) (-12 (-4 *1 (-567 *2)) (-4 *2 (-973)))) ((*1 *2 *1) - (-12 (-5 *2 (-1186 *3 *4)) (-5 *1 (-573 *3 *4 *5)) (-4 *3 (-786)) + (-12 (-5 *2 (-1187 *3 *4)) (-5 *1 (-573 *3 *4 *5)) (-4 *3 (-786)) (-4 *4 (-13 (-158) (-657 (-383 (-523))))) (-14 *5 (-852)))) ((*1 *2 *1) - (-12 (-5 *2 (-1181 *3 *4)) (-5 *1 (-573 *3 *4 *5)) (-4 *3 (-786)) + (-12 (-5 *2 (-1182 *3 *4)) (-5 *1 (-573 *3 *4 *5)) (-4 *3 (-786)) (-4 *4 (-13 (-158) (-657 (-383 (-523))))) (-14 *5 (-852)))) ((*1 *1 *2) (-12 (-4 *3 (-158)) (-5 *1 (-581 *3 *2)) (-4 *2 (-684 *3)))) @@ -15843,20 +13897,20 @@ (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-4 *3 (-973)) (-5 *1 (-652 *3 *2)) (-4 *2 (-1144 *3)))) + (-12 (-4 *3 (-973)) (-5 *1 (-652 *3 *2)) (-4 *2 (-1145 *3)))) ((*1 *2 *1) - (-12 (-5 *2 (-2 (|:| -3878 *3) (|:| -2735 *4))) + (-12 (-5 *2 (-2 (|:| -4013 *3) (|:| -1475 *4))) (-5 *1 (-653 *3 *4 *5)) (-4 *3 (-786)) (-4 *4 (-1016)) (-14 *5 (-1 (-108) *2 *2)))) ((*1 *1 *2) - (-12 (-5 *2 (-2 (|:| -3878 *3) (|:| -2735 *4))) (-4 *3 (-786)) + (-12 (-5 *2 (-2 (|:| -4013 *3) (|:| -1475 *4))) (-4 *3 (-786)) (-4 *4 (-1016)) (-5 *1 (-653 *3 *4 *5)) (-14 *5 (-1 (-108) *2 *2)))) ((*1 *2 *1) (-12 (-4 *2 (-158)) (-5 *1 (-655 *2 *3 *4 *5 *6)) (-4 *3 (-23)) (-14 *4 (-1 *2 *2 *3)) (-14 *5 (-1 (-3 *3 "failed") *3 *3)) (-14 *6 (-1 (-3 *2 "failed") *2 *2 *3)))) ((*1 *1 *2) - (-12 (-5 *2 (-589 (-2 (|:| -2935 *3) (|:| -2302 *4)))) (-4 *3 (-973)) + (-12 (-5 *2 (-589 (-2 (|:| -3474 *3) (|:| -2836 *4)))) (-4 *3 (-973)) (-4 *4 (-666)) (-5 *1 (-675 *3 *4)))) ((*1 *1 *2) (-12 (-5 *2 (-523)) (-4 *1 (-703)))) ((*1 *1 *2) @@ -15865,34 +13919,34 @@ (-3 (|:| |nia| (-2 (|:| |var| (-1087)) (|:| |fn| (-292 (-203))) - (|:| -3499 (-1011 (-779 (-203)))) (|:| |abserr| (-203)) + (|:| -2464 (-1011 (-779 (-203)))) (|:| |abserr| (-203)) (|:| |relerr| (-203)))) (|:| |mdnia| (-2 (|:| |fn| (-292 (-203))) - (|:| -3499 (-589 (-1011 (-779 (-203))))) + (|:| -2464 (-589 (-1011 (-779 (-203))))) (|:| |abserr| (-203)) (|:| |relerr| (-203)))))) (-5 *1 (-708)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |fn| (-292 (-203))) - (|:| -3499 (-589 (-1011 (-779 (-203))))) (|:| |abserr| (-203)) + (|:| -2464 (-589 (-1011 (-779 (-203))))) (|:| |abserr| (-203)) (|:| |relerr| (-203)))) (-5 *1 (-708)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |var| (-1087)) (|:| |fn| (-292 (-203))) - (|:| -3499 (-1011 (-779 (-203)))) (|:| |abserr| (-203)) + (|:| -2464 (-1011 (-779 (-203)))) (|:| |abserr| (-203)) (|:| |relerr| (-203)))) (-5 *1 (-708)))) ((*1 *2 *1) (-12 (-5 *2 (-794)) (-5 *1 (-708)))) - ((*1 *2 *3) (-12 (-5 *2 (-713)) (-5 *1 (-712 *3)) (-4 *3 (-1122)))) + ((*1 *2 *3) (-12 (-5 *2 (-713)) (-5 *1 (-712 *3)) (-4 *3 (-1123)))) ((*1 *1 *2) (-12 (-5 *2 (-2 (|:| |xinit| (-203)) (|:| |xend| (-203)) - (|:| |fn| (-1168 (-292 (-203)))) (|:| |yinit| (-589 (-203))) + (|:| |fn| (-1169 (-292 (-203)))) (|:| |yinit| (-589 (-203))) (|:| |intvals| (-589 (-203))) (|:| |g| (-292 (-203))) (|:| |abserr| (-203)) (|:| |relerr| (-203)))) (-5 *1 (-747)))) @@ -15909,29 +13963,29 @@ (-5 *2 (-3 (|:| |noa| - (-2 (|:| |fn| (-292 (-203))) (|:| -2262 (-589 (-203))) + (-2 (|:| |fn| (-292 (-203))) (|:| -2773 (-589 (-203))) (|:| |lb| (-589 (-779 (-203)))) (|:| |cf| (-589 (-292 (-203)))) (|:| |ub| (-589 (-779 (-203)))))) (|:| |lsa| (-2 (|:| |lfn| (-589 (-292 (-203)))) - (|:| -2262 (-589 (-203))))))) + (|:| -2773 (-589 (-203))))))) (-5 *1 (-777)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |lfn| (-589 (-292 (-203)))) (|:| -2262 (-589 (-203))))) + (-2 (|:| |lfn| (-589 (-292 (-203)))) (|:| -2773 (-589 (-203))))) (-5 *1 (-777)))) ((*1 *1 *2) (-12 (-5 *2 - (-2 (|:| |fn| (-292 (-203))) (|:| -2262 (-589 (-203))) + (-2 (|:| |fn| (-292 (-203))) (|:| -2773 (-589 (-203))) (|:| |lb| (-589 (-779 (-203)))) (|:| |cf| (-589 (-292 (-203)))) (|:| |ub| (-589 (-779 (-203)))))) (-5 *1 (-777)))) 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(-1123)))) + ((*1 *2 *3) (-12 (-5 *3 (-288)) (-5 *1 (-960 *2)) (-4 *2 (-1123)))) ((*1 *1 *2) (-12 (-4 *3 (-339)) (-4 *4 (-732)) (-4 *5 (-786)) (-5 *1 (-961 *3 *4 *5 *2 *6)) (-4 *2 (-880 *3 *4 *5)) (-14 *6 (-589 *2)))) - ((*1 *1 *2) (-12 (-4 *1 (-964 *2)) (-4 *2 (-1122)))) + ((*1 *1 *2) (-12 (-4 *1 (-964 *2)) (-4 *2 (-1123)))) ((*1 *2 *3) (-12 (-5 *2 (-383 (-883 *3))) (-5 *1 (-969 *3)) (-4 *3 (-515)))) ((*1 *1 *2) (-12 (-5 *2 (-523)) (-4 *1 (-973)))) @@ -16006,24 +14060,24 @@ (-4 *4 (-973)))) ((*1 *1 *2) (-12 (-5 *2 (-133)) (-4 *1 (-1056)))) ((*1 *1 *2) - (-12 (-5 *2 (-589 *3)) (-4 *3 (-1122)) (-5 *1 (-1068 *3)))) + (-12 (-5 *2 (-589 *3)) (-4 *3 (-1123)) (-5 *1 (-1068 *3)))) ((*1 *2 *3) (-12 (-5 *2 (-1068 *3)) (-5 *1 (-1072 *3)) (-4 *3 (-973)))) ((*1 *1 *2) - (-12 (-5 *2 (-1164 *4)) (-14 *4 (-1087)) (-5 *1 (-1078 *3 *4 *5)) + (-12 (-5 *2 (-1165 *4)) (-14 *4 (-1087)) (-5 *1 (-1078 *3 *4 *5)) (-4 *3 (-973)) (-14 *5 *3))) ((*1 *1 *2) - (-12 (-5 *2 (-1164 *4)) (-14 *4 (-1087)) (-5 *1 (-1084 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65535) + (-3892 . 65441) (-3893 . 65230) (-3894 . 65199) (-3895 . 65131) + (-3896 . 65034) (-3897 . 64718) (-3898 . 64446) (-3899 . 64393) + (-3900 . 64362) (-3901 . 63545) (-3902 . 63365) (-3903 . 63072) + (-3904 . 62722) (-3905 . 62339) (-3906 . 62290) (-3907 . 62259) + (-3908 . 62132) (-3909 . 62009) (-3910 . 61924) (-3911 . 61832) + (-3912 . 61762) (-3913 . 61604) (-3914 . 61446) (-3915 . 61340) + (-3916 . 61222) (-3917 . 61167) (-3918 . 61090) (-3919 . 60952) + (-3920 . 60658) (-3921 . 60549) (-3922 . 60477) (-3923 . 60211) + (-3924 . 59958) (-3925 . 59811) (-3926 . 59762) (-3927 . 59380) + (-3928 . 59343) (-3929 . 59256) (-3930 . 58924) (-3931 . 58875) + (-3932 . 58715) (-3933 . 58663) (-3934 . 58346) (-3935 . 58234) + (-3936 . 58206) (-3937 . 58093) (-3938 . 57992) (-3939 . 57763) + (-3940 . 57645) (-3941 . 57377) (-3942 . 57170) (-3943 . 56852) + (-3944 . 56685) (-3945 . 56567) (-3946 . 56270) (-3947 . 56128) + (-3948 . 56073) (-3949 . 55955) (-3950 . 55454) (-3951 . 55256) + 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\ No newline at end of file |